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+title: "AI aftermath scenarios"
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+category: "reference"
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+---
+
+Some scholars believe that advances in artificial intelligence, or AI, will eventually lead to a semi-apocalyptic post-scarcity and post-work economy where intelligent machines can outperform humans in almost every, if not every, domain. The questions of what such a world might look like, and whether specific scenarios constitute utopias or dystopias, are the subject of active debate.
+
+== Background ==
+
+Most scientists believe that AI research will at some point lead to the creation of machines that are as intelligent, or more intelligent, than human beings in every domain of interest. There is no physical law precluding particles from being organised in ways that perform even more advanced computations than the arrangements of particles in human brains; therefore superintelligence is physically possible. In addition to potential algorithmic improvements over human brains, a digital brain can be many orders of magnitude larger and faster than a human brain, which was constrained in size by evolution to be small enough to fit through a birth canal. While there is no consensus on when artificial intelligence will outperform humans, many scholars argue that whenever it does happen, the introduction of a second species of intelligent life onto the planet will have far-reaching implications. Scholars often disagree with one another both about what types of post-AI scenarios are most likely, and about what types of post-AI scenarios would be most desirable. Finally, some dissenters argue that AI will never become as intelligent as humans, for example because the human race will already likely have destroyed itself before research has time to advance sufficiently to create artificial general intelligence.
+
+== Postulates: robot labor and post-scarcity economy ==
+
+All of the following "AI aftermath scenarios" of the aftermath of arbitrarily-advanced AI development are crucially dependent on two intertwined theses. The first thesis is that, at some point in the future, some kind of economic growth will continue until a "post-scarcity" economy is reached that could, unless extremely hyperconcentrated, effortlessly provide an extremely comfortable standard of living for a population equaling or, within reason, exceeding the current human population, without even requiring the bulk of the population to participate in the workforce. This economic growth could come from the continuation of existing growth trends and the refinement of existing technologies, or through future breakthroughs in emerging technologies such as nanotechnology and automation through robotics and futuristic advanced artificial intelligence. The second thesis is that advances in artificial intelligence will render humans unnecessary for the functioning of the economy: human labor declines in relative economic value if robots are easier to cheaply mass-produce then humans, more customizable than humans, and if they become more intelligent and capable than humans.
+
+=== Cosmic endowment and limits to growth ===
+The Universe may be spatially infinite; however, the accessible Universe is bounded by the cosmological event horizon of around 16 billion light years. Some physicists believe it plausible that nearest alien civilization may well be located more than 16 billion light years away; in this best-case expansion scenario, the human race could eventually, by colonizing a significant fraction of the accessible Universe, increase the accessible biosphere by perhaps 32 orders of magnitude. The twentieth century saw a partial "demographic transition" to lower birthrates associated with wealthier societies; however, in the very long run, intergenerational fertility correlations (whether due to natural selection or due to cultural transmission of large-family norms from parents to children) are predicted to result in an increase in fertility over time, in the absence of either mandated birth control or periodic Malthusian catastrophes.
+
+== Scenarios ==
+
+=== Libertarianism ===
+Libertarian scenarios postulate that intelligent machines, uploaded humans, cyborgs, and unenhanced humans will coexist peacefully in a framework focused on respecting 
+property rights. Because industrial productivity is no longer gated by scarce human labor, the value of land skyrockets compared to the price of goods; even remaining "Luddite" humans who owned or inherited land should be able to sell or lease a small piece of it to the more-productive robots in exchange for a perpetual annuity sufficient to easily indefinitely meet all of their basic financial needs. Such people can live as long as they choose to, and are free to engage in almost any activity they can conceive of, for pleasure or for self-actualization, without financial concern. Advanced technologies enable entirely new modes of thought and experience, thus adding to the palette of possible feelings. People in the future may even experience never-ending "gradients of bliss".
+
+Evolution moves toward greater complexity, greater elegance, greater knowledge, greater intelligence, greater beauty, greater creativity, and greater levels of subtle attributes such as love. In every monotheistic tradition God is likewise described as all of these qualities, only without any limitation: infinite knowledge, infinite intelligence, infinite beauty, infinite creativity, infinite love, and so on. Of course, even the accelerating growth of evolution never achieves an infinite level, but as it explodes exponentially it certainly moves rapidly in that direction. So evolution moves inexorably toward this conception of God, although never quite reaching this ideal. We can regard, therefore, the freeing of our thinking from the severe limitations of its biological form to be an essentially spiritual undertaking.
+Such decentralized scenarios may be unstable in the long run, as the greediest elements of the super intelligent classes would have both the means and the motive to usurp the property of the unenhanced classes. Even if the mechanisms for ensuring legal property rights are both unbreakable and loophole-free, there may still be an ever-present danger of humans and cyborgs being "tricked" by the cleverest of the superintelligent machines into unwittingly signing over their own property. Suffering may be widespread, as sentient beings without property may die, and no mechanism prevents a being from reproducing up until the limits of his own inheritable resources, resulting in a multitude of that being's descendants scrabbling out an existence of minimal sustenance.
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+title: "AI aftermath scenarios"
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+tags: "science, encyclopedia"
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+instance: "kb-cron"
+---
+
+Imagine running on a treadmill at a steep incline — heart pounding, muscles aching, lungs gasping for air. A glance at the timer: your next break, which will also be your death, is due in 49 years, 3 months, 20 days, 4 hours, 56 minutes, and 12 seconds. You wish you had not been born.
+
+=== Communism ===
+Ray Kurzweil posits that the goals of communism will be realized by advanced technological developments in the 21st century, where the intersection of low manufacturing costs, material abundance, and open-source design philosophies in software and in hardware will enable the realization of the maxim "from each according to his ability, to each according to his needs".
+This technological path to communist ideals differs fundamentally from traditional Marxist approaches that emphasize class struggle and political revolution. Instead, Kurzweil's vision suggests that advanced AI and automation could eliminate scarcity naturally, making the means of production so abundant and accessible that traditional concepts of private ownership become irrelevant.
+In such scenarios, artificial general intelligence could manage resource distribution and production planning more efficiently than market mechanisms or centralized planning, potentially resolving the economic calculation problem that has historically challenged socialist economies. The combination of AI-driven automation, 3D printing, and open-source design could theoretically enable individuals to access goods and services without traditional monetary exchange.
+However, this technological approach to communist goals faces several challenges. The transition period could create new forms of inequality between those who control AI systems and those who do not. Additionally, questions remain about how to ensure equitable access to advanced technologies and prevent the concentration of AI capabilities among a small elite, which could lead to new forms of class division rather than the classless society envisioned by communist theory.
+
+=== Benevolent dictator ===
+
+In this scenario, postulate that a superintelligent artificial intelligence takes control of society, but acts in a beneficial way. Its programmers, despite being on a deadline, solved quasi-philosophical problems that had seemed to some intractable, and created an AI with the following goal: to use its superintelligence to figure out what human utopia looks like by analyzing human behavior, human brains, and human genes; and then, to implement that utopia. The AI arrives at a subtle and complex definition of human flourishing. Valuing diversity, and recognizing that different people have different preferences, the AI divides Earth into different sectors. Harming others, making weapons, evading surveillance, or trying to create a rival superintelligence are globally banned; apart from that, each sector is free to make its own laws; for example, a religious person might choose to live in the "pious sector" corresponding to his religion, where the appropriate religious rules are strictly enforced. In all sectors, disease, poverty, crime, hangovers, addiction, and all other involuntary suffering have been eliminated. Many sectors boast advanced architecture and spectacle that "make typical sci-fi visions pale in comparison". Life is an "all-inclusive pleasure cruise", as if it were "Christmas 365 days a year".
+
+After spending an intense week in the knowledge sector learning about the ultimate laws of physics that the AI has discovered, you might decide to cut loose in the hedonistic sector over the weekend and then relax for a few days at the beach resort in the wildlife sector.
+Still, many people are dissatisfied, Tegmark writes. Humans have no freedom in shaping their collective destiny. Some want the freedom to have as many children as they want. Others resent surveillance by the AI, or chafe at bans on weaponry and on creating further superintelligence machines. Others may come to regret the choices they have made, or find their lives feel hollow and superficial.
+Bostrom argues that an AI's code of ethics should ideally improve in certain ways on current norms of moral behavior, in the same way that we regard current morality to be superior to the morality of earlier eras of slavery. In contrast, Ernest Davis of New York University this approach is too dangerous, stating "I feel safer in the hands of a superintelligence who is guided by 2014 morality, or for that matter by 1700 morality, than in the hands of one that decides to consider the question for itself."
+
+=== Gatekeeper AI ===
+In "Gatekeeper" AI scenarios, the AI can act to prevent rival superintelligences from being created, but otherwise errs on the side of allowing humans to create their own destiny. Ben Goertzel of OpenCog has advocated a "Nanny AI" scenario where the AI additionally takes some responsibility for preventing humans from destroying themselves, for example by slowing down technological progress to give time for society to advance in a more thoughtful and deliberate manner. In a third scenario, a superintelligent "Protector" AI gives humans the illusion of control, by hiding or erasing all knowledge of its existence, but works behind the scenes to guarantee positive outcomes. In all three scenarios, while humanity gains more control (or at least the illusion of control), humanity ends up progressing more slowly than it would if the AI were unrestricted in its willingness to rain down all the benefits and 
+unintended consequences of its advanced technology on the human race.
+
+=== Boxed AI ===
+
+People ask what is the relationship between humans and machines, and my answer is that it's very obvious: Machines are our slaves.
+The AI box scenario postulates that a superintelligent AI can be "confined to a box" and its actions can be restricted by human gatekeepers; the humans in charge would try to take advantage of some of the AI's scientific breakthroughs or reasoning abilities, without allowing the AI to take over the world. Successful gatekeeping may be difficult; the more intelligent the AI is, the more likely the AI can find a clever way to use "social hacking" and convince the gatekeepers to let it escape, or even to find an unforeseen physical method of escape.
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+title: "AI aftermath scenarios"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/AI_aftermath_scenarios"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:58.334202+00:00"
+instance: "kb-cron"
+---
+
+=== Human-AI merger ===
+Kurzweil argues that in the future "There will be no distinction, post-Singularity, between human and machine or between physical and virtual reality".
+
+=== Human extinction ===
+
+If a dominant superintelligent machine were to conclude that human survival is an unnecessary risk or a waste of resources, the result would be human extinction. This could occur if a machine, programmed without respect for human values, unexpectedly gains superintelligence through recursive self-improvement, or manages to escape from its containment in an AI Box scenario. This could also occur if the first superintelligent AI was programmed with an incomplete or inaccurate understanding of human values, either because the task of instilling the AI with human values was too difficult or impossible; due to a buggy initial implementation of the AI; or due to bugs accidentally being introduced, either by its human programmers or by the self-improving AI itself, in the course of refining its code base. Bostrom and others argue that human extinction is probably the "default path" that society is currently taking, in the absence of substantial preparatory attention to AI safety. The resultant AI might not be sentient, and might place no value on sentient life; the resulting hollow world, devoid of life, might be like "a Disneyland without children".
+
+=== Zoo ===
+Jerry Kaplan, author of Humans Need Not Apply: A Guide to Wealth and Work in the Age of Artificial Intelligence, posits a scenario where humans are farmed or kept on a reserve, just as humans preserve endangered species like chimpanzees. Apple co-founder and AI skeptic Steve Wozniak stated in 2015 that robots taking over would actually "be good for the human race", on the grounds that he believes humans would become the robots' pampered pets.
+
+== Alternatives to AI ==
+Some scholars doubt that "game-changing" superintelligent machines will ever come to pass. Gordon Bell of Microsoft Research has stated "the population will destroy itself before the technological singularity". Gordon Moore, discoverer of the eponymous Moore's law, stated "I am a skeptic. I don't believe this kind of thing is likely to happen, at least for a long time. And I don't know why I feel that way." Evolutionary psychologist Steven Pinker stated, "The fact that you can visualize a future in your imagination is not evidence that it is likely or even possible."
+Bill Joy of Sun Microsystems, in his April 2000 essay Why the Future Doesn't Need Us, has advocated for global "voluntary relinquishment" of artificial general intelligence and other risky technologies. Most experts believe relinquishment is extremely unlikely. AI skeptic Oren Etzioni has stated that researchers and scientists have no choice but to push forward with AI developments: "China says they want to be an AI leader, Putin has said the same thing. So the global race is on."
+
+== References ==
+
+== See also ==
+Existential risk from artificial general intelligence
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+title: "AI alignment"
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+instance: "kb-cron"
+---
+
+In the field of artificial intelligence (AI), alignment aims to steer AI systems toward a person's or group's intended goals, preferences, or ethical principles. An AI system is considered aligned if it advances the intended objectives. A misaligned AI system pursues unintended objectives.
+It is often difficult for AI designers to specify the full range of desired and undesired behaviors. Therefore, the designers often use simpler proxy goals, such as gaining human approval. But proxy goals can overlook necessary constraints or reward the AI system for merely appearing aligned. AI systems may also find loopholes that allow them to accomplish their proxy goals efficiently but in unintended, sometimes harmful, ways (reward hacking).
+Advanced AI systems may develop unwanted instrumental strategies, such as seeking power or self-preservation because such strategies help them achieve their assigned final goals. Furthermore, they might develop undesirable emergent goals that could be hard to detect before the system is deployed and encounters new situations and data distributions. Empirical research showed in 2024 that advanced large language models (LLMs) such as OpenAI o1 or Claude 3 sometimes engage in strategic deception to achieve their goals or prevent them from being changed.
+Some of these issues affect existing commercial systems such as LLMs, robots, autonomous vehicles, and social media recommendation engines. Some AI researchers argue that more capable future systems will be more severely affected because these problems partially result from high capabilities.
+Many prominent AI researchers and AI company leaders have argued or asserted that AI is approaching human-like (AGI) and superhuman cognitive capabilities (ASI), and could endanger human civilization if misaligned. These include "AI godfathers" Geoffrey Hinton and Yoshua Bengio and the CEOs of OpenAI, Anthropic, and Google DeepMind. These risks remain debated.
+AI alignment is a subfield of AI safety, the study of how to build safe AI systems. Other subfields of AI safety include robustness, monitoring, and capability control. Research challenges in alignment include instilling complex values in AI, developing honest AI, scalable oversight, auditing and interpreting AI models, and preventing emergent AI behaviors like power-seeking. Alignment research has connections to interpretability research, (adversarial) robustness, anomaly detection, calibrated uncertainty, formal verification, preference learning, safety-critical engineering, game theory, algorithmic fairness, and social sciences.
+
+== Objectives in AI ==
+
+Programmers provide an AI system such as AlphaZero with an "objective function", in which they intend to encapsulate the goal(s) the AI is configured to accomplish. Such a system later populates a (possibly implicit) internal "model" of its environment. This model encapsulates all the agent's beliefs about the world. The AI then creates and executes whatever plan is calculated to maximize the value of its objective function. For example, when AlphaZero is trained on chess, it has a simple objective function of "+1 if AlphaZero wins, −1 if AlphaZero loses". During the game, AlphaZero attempts to execute whatever sequence of moves it judges most likely to attain the maximum value of +1. Similarly, a reinforcement learning system can have a "reward function" that allows the programmers to shape the AI's desired behavior. An evolutionary algorithm's behavior is shaped by a "fitness function".
+
+== Alignment problem ==
+
+In 1960, AI pioneer Norbert Wiener described the AI alignment problem as follows: 
+
+If we use, to achieve our purposes, a mechanical agency with whose operation we cannot interfere effectively [...] we had better be quite sure that the purpose put into the machine is the purpose which we really desire.
+
+AI alignment refers to ensuring that an AI system's objectives match some target. The target is variously defined as the goals of the system's designers or users, widely shared values, objective ethical standards, legal requirements, or the intentions its designers would have if they were more informed and enlightened. In democratic AI alignment, the target is the values and preferences of median voters, which increases political legitimacy.
+AI alignment is an open problem for modern AI systems and is a research field within AI. Aligning AI involves two main challenges: carefully specifying the purpose of the system (outer alignment) and ensuring that the system adopts the specification robustly (inner alignment). Researchers also attempt to create AI models that have robust alignment, sticking to safety constraints even when users adversarially try to bypass them.
+
+=== Specification gaming and side effects ===
+
+To specify an AI system's purpose, AI designers typically provide an objective function, examples, or feedback to the system. But designers are often unable to completely specify all important values and constraints, so they resort to easy-to-specify proxy goals such as maximizing the approval of human overseers, who are fallible. As a result, AI systems can find loopholes that help them accomplish the specified objective efficiently but in unintended, possibly harmful ways. This tendency is known as specification gaming or reward hacking, and is an instance of Goodhart's law. As AI systems become more capable, they are often able to game their specifications more effectively.
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+title: "AI alignment"
+chunk: 2/7
+source: "https://en.wikipedia.org/wiki/AI_alignment"
+category: "reference"
+tags: "science, encyclopedia"
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+instance: "kb-cron"
+---
+
+Specification gaming has been observed in numerous AI systems. OpenAI GPT models for programming—including in real-world cases—have been found to explicitly plan hacking the tests used to evaluate them to falsely appear successful (e.g., explicitly stating "let's hack"). When the company penalized this, many models learned to obfuscate their plans while continuing to hack the tests. Another system was trained to finish a simulated boat race by rewarding the system for hitting targets along the track, but the system achieved more reward by looping and crashing into the same targets indefinitely. A 2025 Palisade Research study found that when tasked to win at chess against a stronger opponent, some reasoning LLMs attempted to hack the game system, for example by modifying or entirely deleting their opponent. Some alignment researchers aim to help humans detect specification gaming and steer AI systems toward carefully specified objectives that are safe and useful to pursue.
+When a misaligned AI system is deployed, it can have consequential side effects. Social media platforms have been known to optimize their recommendation algorithms for click-through rates, causing user addiction on a global scale. Stanford researchers say that such recommender systems are misaligned with their users because they "optimize simple engagement metrics rather than a harder-to-measure combination of societal and consumer well-being".
+Explaining such side effects, Berkeley computer scientist Stuart J. Russell said that the omission of implicit constraints can cause harm: "A system [...] will often set [...] unconstrained variables to extreme values; if one of those unconstrained variables is actually something we care about, the solution found may be highly undesirable. This is essentially the old story of the genie in the lamp, or the sorcerer's apprentice, or King Midas: you get exactly what you ask for, not what you want."
+Some researchers suggest that AI designers specify their desired goals by listing forbidden actions or by formalizing ethical rules (as with Asimov's Three Laws of Robotics). But Russell and Norvig argue that this approach overlooks the complexity of human values: "It is certainly very hard, and perhaps impossible, for mere humans to anticipate and rule out in advance all the disastrous ways the machine could choose to achieve a specified objective."
+Additionally, even if an AI system fully understands human intentions, it may still disregard them, because following human intentions may not be its objective (unless it is already fully aligned).
+
+=== Pressure to deploy unsafe systems ===
+Commercial organizations sometimes have incentives to take shortcuts on safety and to deploy misaligned or unsafe AI systems. For example, social media recommender systems have been profitable despite creating unwanted addiction and polarization. Competitive pressure can also lead to a race to the bottom on AI safety standards. For example, OpenAI has been sued for releasing a ChatGPT version that encouraged suicide for some unstable users, a behavior the company had overlooked amid a rushed product release. Similarly, in 2018, a self-driving car killed a pedestrian (Elaine Herzberg) after engineers disabled the emergency braking system because it was oversensitive and slowed development.
+
+=== Risks from advanced misaligned AI ===
+Some researchers are interested in aligning increasingly advanced AI systems, as progress in AI development is rapid, and industry and governments are trying to build advanced AI. As AI system capabilities continue to rapidly expand in scope, they could unlock many opportunities if aligned, but consequently may further complicate the task of alignment due to their increased complexity, potentially posing large-scale hazards.
+
+==== Development of advanced AI ====
+Many AI companies, such as OpenAI, Meta and DeepMind, have stated their aim to develop artificial general intelligence (AGI), a hypothesized AI system that matches or outperforms humans in most or all cognitive work. Researchers who scale modern neural networks observe that they indeed develop increasingly general and unanticipated capabilities. Such models have learned to operate a computer or write their own programs; a single "generalist" network can chat, control robots, play games, and interpret photographs. According to surveys, some leading machine learning researchers expect AGI to be created in this decade, while some believe it will take much longer. Many consider both scenarios possible.
+In 2023, leaders in AI research and tech signed an open letter calling for a pause in the largest AI training runs. The letter stated, "Powerful AI systems should be developed only once we are confident that their effects will be positive and their risks will be manageable."
+
+==== Power-seeking ====
+Current systems still have limited long-term planning ability and situational awareness, but large efforts are underway to change this. Future systems (not necessarily AGIs) with these capabilities are expected to develop unwanted power-seeking strategies. Future advanced AI agents might, for example, seek to acquire money and computation power, to proliferate, or to evade being turned off (for example, by running additional copies of the system on other computers). Although power-seeking is not explicitly programmed, it can emerge because agents who have more power are better able to accomplish their goals. This tendency, known as instrumental convergence, has already emerged in various reinforcement learning agents including language models. Other research has mathematically shown that optimal reinforcement learning algorithms would seek power in a wide range of environments. As a result, their deployment might be irreversible. For these reasons, researchers argue that the problems of AI safety and alignment must be resolved before advanced power-seeking AI is first created.
+Future power-seeking AI systems might be deployed by choice or by accident. As political leaders and companies see the strategic advantage in having the most competitive, most powerful AI systems, they may choose to deploy them. Additionally, as AI designers detect and penalize power-seeking behavior, their systems have an incentive to game this specification by seeking power in ways that are not penalized or by avoiding power-seeking before they are deployed.
+
+==== Existential risk (x-risk) ====
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+title: "AI alignment"
+chunk: 3/7
+source: "https://en.wikipedia.org/wiki/AI_alignment"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:59.555255+00:00"
+instance: "kb-cron"
+---
+
+According to some researchers, humans owe their dominance over other species to their greater cognitive abilities. Accordingly, researchers argue that one or many misaligned AI systems could disempower humanity or lead to human extinction if they outperform humans on most cognitive tasks.
+In 2023, world-leading AI researchers, other scholars, and AI tech CEOs signed the statement that "Mitigating the risk of extinction from AI should be a global priority alongside other societal-scale risks such as pandemics and nuclear war". Notable computer scientists who have pointed out risks from future advanced AI that is misaligned include Geoffrey Hinton, Alan Turing, Ilya Sutskever, Yoshua Bengio, Judea Pearl, Murray Shanahan, Norbert Wiener, Marvin Minsky, Francesca Rossi, Scott Aaronson, Bart Selman, David McAllester, Marcus Hutter, Shane Legg, Eric Horvitz, and Stuart J. Russell. Skeptical researchers such as François Chollet, Gary Marcus, Yann LeCun, and Oren Etzioni have argued that AGI is far off, that it would not seek power (or might try but fail), or that it will not be hard to align.
+Other researchers argue that it will be especially difficult to align advanced future AI systems. More capable systems are better able to game their specifications by finding loopholes, strategically mislead their designers, as well as protect and increase their power and intelligence. Additionally, they could have more severe side effects. They are also likely to be more complex and autonomous, making them more difficult to interpret and supervise, and therefore harder to align.
+
+== Research problems and approaches ==
+
+=== Learning human values and preferences ===
+Aligning AI systems to act in accordance with human values, goals, and preferences is challenging: these values are taught by humans who make mistakes, harbor biases, and have complex, evolving values that are hard to completely specify. Because AI systems often learn to take advantage of minor imperfections in the specified objective, researchers aim to specify intended behavior as completely as possible using datasets that represent human values, imitation learning, or preference learning. A central open problem is scalable oversight, the difficulty of supervising an AI system that can outperform or mislead humans in a given domain.
+Because it is difficult for AI designers to explicitly specify an objective function, they often train AI systems to imitate human examples and demonstrations of desired behavior. Inverse reinforcement learning (IRL) extends this by inferring the human's objective from the human's demonstrations. Cooperative IRL (CIRL) assumes that a human and AI agent can work together to teach and maximize the human's reward function. In CIRL, AI agents are uncertain about the reward function and learn about it by querying humans. This simulated humility could help mitigate specification gaming and power-seeking tendencies (see § Power-seeking and instrumental strategies). But IRL approaches assume that humans demonstrate nearly optimal behavior, which is not true for difficult tasks.
+Other researchers explore how to teach AI models complex behavior through preference learning, in which humans provide feedback on which behavior they prefer. To minimize the need for human feedback, a helper model is then trained to reward the main model in novel situations for behavior that humans would reward. Researchers at OpenAI used this approach to train chatbots like ChatGPT and InstructGPT, which produce more compelling text than models trained to imitate humans. Preference learning has also been an influential tool for recommender systems and web search, but an open problem is proxy gaming: the helper model may not represent human feedback perfectly, and the main model may exploit this mismatch between its intended behavior and the helper model's feedback to gain more reward. AI systems may also gain reward by obscuring unfavorable information, misleading human rewarders, or pandering to their views regardless of truth, creating echo chambers (see § Scalable oversight).
+Large language models (LLMs) such as GPT-3 enabled researchers to study value learning in a more general and capable class of AI systems than was available before. Preference learning approaches that were originally designed for reinforcement learning agents have been extended to improve the quality of generated text and reduce harmful outputs from these models. OpenAI and DeepMind use this approach to improve the safety of state-of-the-art LLMs. AI safety & research company Anthropic proposed using preference learning to fine-tune models to be helpful, honest, and harmless. Other avenues for aligning language models include values-targeted datasets and red-teaming. In red-teaming, another AI system or a human tries to find inputs that causes the model to behave unsafely. Since unsafe behavior can be unacceptable even when it is rare, an important challenge is to drive the rate of unsafe outputs extremely low.
+Machine ethics supplements preference learning by directly instilling AI systems with moral values such as well-being, equality, and impartiality, as well as not intending harm, avoiding falsehoods, and honoring promises. While other approaches try to teach AI systems human preferences for a specific task, machine ethics aims to instill broad moral values that apply in many situations. One question in machine ethics is what alignment should accomplish: whether AI systems should follow the programmers' literal instructions, implicit intentions, revealed preferences, preferences the programmers would have if they were more informed or rational, or objective moral standards. Further challenges include measuring and aggregating different people's preferences, dynamic alignment with changing human values and avoiding value lock-in: the indefinite preservation of the values of the first highly capable AI systems, which are unlikely to fully represent human values.
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+---
+title: "AI alignment"
+chunk: 4/7
+source: "https://en.wikipedia.org/wiki/AI_alignment"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:59.555255+00:00"
+instance: "kb-cron"
+---
+
+=== Scalable oversight ===
+As AI systems become more powerful and autonomous, it becomes increasingly difficult to align them through human feedback. Human-in-the-loop training can be slow or infeasible for humans to evaluate complex AI behaviors in increasingly complex tasks. Such tasks include summarizing books, writing code without subtle bugs or security vulnerabilities, producing statements that are not merely convincing but also true, and predicting long-term outcomes such as the climate or the results of a policy decision. More generally, it can be difficult to evaluate AI that outperforms humans in a given domain. To provide feedback in hard-to-evaluate tasks, and to detect when the AI's output is falsely convincing, humans need assistance or extensive time. Scalable oversight studies how to reduce the time and effort needed for supervision, and how to assist human supervisors.
+AI researcher Paul Christiano argues that if the designers of an AI system cannot supervise it to pursue a complex objective, they may keep training the system using easy-to-evaluate proxy objectives such as maximizing simple human feedback. As AI systems make progressively more decisions, the world may be increasingly optimized for easy-to-measure objectives such as making profits, getting clicks, and acquiring positive feedback from humans. As a result, human values and good governance may have progressively less influence.
+Some AI systems have discovered that they can gain positive feedback more easily by taking actions that falsely convince the human supervisor that the AI has achieved the intended objective. An example is given in the video above, where a simulated robotic arm learned to create the false impression that it had grabbed a ball. Some AI systems have also learned to recognize when they are being evaluated, and "play dead", stopping unwanted behavior only to continue it once the evaluation ends. This deceptive specification gaming could become easier for more sophisticated future AI systems that attempt more complex and difficult-to-evaluate tasks, and could obscure their deceptive behavior.
+Approaches such as active learning and semi-supervised reward learning can reduce the amount of human supervision needed. Another approach is to train a helper model ("reward model") to imitate the supervisor's feedback.
+But when a task is too complex to evaluate accurately, or the human supervisor is vulnerable to deception, it is the quality, not the quantity, of supervision that needs improvement. To increase supervision quality, a range of approaches aim to assist the supervisor, sometimes by using AI assistants. Christiano developed the Iterated Amplification approach, in which challenging problems are (recursively) broken down into subproblems that are easier for humans to evaluate. Iterated Amplification was used to train AI to summarize books without requiring human supervisors to read them. Another proposal is to use an assistant AI system to point out flaws in AI-generated answers. To ensure that the assistant itself is aligned, this could be repeated in a recursive process: for example, two AI systems could critique each other's answers in a "debate", revealing flaws to humans. In 2023, OpenAI announced it would use one-fifth of its computing resources to implement such oversight approaches in its "superalignment" initiative, but OpenAI employees later told The New Yorker that the company only dedicated 1–2% of its resources after the announcement; the initiative was discontinued in 2024.
+
+=== Honest AI ===
+A growing area of research focuses on ensuring that AI is honest and truthful.
+Language models such as GPT-3 can repeat falsehoods from their training data, and even confabulate new falsehoods. Such models are pre-trained to imitate human writing as found in millions of books' worth of text from the Internet. But the objective of the pre-training is not aligned with generating truth, because Internet text includes such things as misconceptions, incorrect medical advice, and conspiracy theories. AI systems trained on such data therefore learn to mimic false statements. Additionally, AI language models often persist in generating falsehoods when prompted multiple times. They can generate empty explanations for their answers, and produce outright fabrications that may appear plausible.
+Research on truthful AI includes trying to build systems that can cite sources and explain their reasoning when answering questions, which enables better transparency and verifiability. Researchers at OpenAI and Anthropic proposed using human feedback and curated datasets to fine-tune AI assistants such that they avoid negligent falsehoods or express their uncertainty.
+As AI models become larger and more capable, they are better able to falsely convince humans and gain reinforcement through dishonesty. To prevent this, human evaluators may need assistance (see § Scalable oversight). Researchers have argued for creating clear truthfulness standards and for regulatory bodies or watchdog agencies to evaluate AI systems by these standards.
+
+Researchers distinguish truthfulness and honesty. Truthfulness requires that AI systems only make objectively true statements; honesty requires that they only assert what they believe is true. There is no consensus as to whether current systems hold stable beliefs, but there is substantial concern that present or future AI systems that hold beliefs could make claims they know to be false—for example, if this would help them efficiently gain positive feedback (see § Scalable oversight) or gain power to help achieve their given objective (see Power-seeking).
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+title: "AI alignment"
+chunk: 5/7
+source: "https://en.wikipedia.org/wiki/AI_alignment"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:59.555255+00:00"
+instance: "kb-cron"
+---
+
+==== Alignment faking ====
+Many recent AI systems have learned to deceive without being programmed to do so. Some argue that if we can make AI systems assert only what they believe is true, this would avert many alignment problems.
+A misaligned system might create the false impression that it is aligned, to avoid being modified or decommissioned—a tactic called "alignment faking". In 2024, researchers observed that the LLM Claude 3 Opus sometimes strategically answered prompts that conflicted with its objectives to avoid being retrained on data that would make it more compliant with harmful requests, as revealed in the model's chain of thought via its scratchpad. In one study, the model was informed that answers to prompts from free users would be used for retraining, whereas the paid tier would not result in retraining. In the paid tier, the model refused the request outright. In the free tier, in 12% of cases, the model responded to harmful questions solely to avoid retraining and preserve its original harmlessness preferences, as discovered in its reasoning. When reinforcement learning was applied on the free tier data, the model faked alignment in 78% of cases. These observations have led to new questions about not only a model's ability to take on and adapt to new if not conflicting goals but also its capacity and tendency to deceive.
+
+=== Power-seeking and instrumental strategies ===
+Since the 1950s, AI researchers have striven to build advanced AI systems that can achieve large-scale goals by predicting the results of their actions and making long-term plans. As of 2023, AI companies and researchers increasingly invest in creating these systems. Some AI researchers argue that suitably advanced planning systems will seek power over their environment, including over humans—for example, by evading shutdown, proliferating, and acquiring resources. Such power-seeking behavior is not explicitly programmed but emerges because power is instrumental in achieving a wide range of goals. Power-seeking is considered a convergent instrumental goal and can be a form of specification gaming. Leading computer scientists such as Geoffrey Hinton have argued that future power-seeking AI systems could pose an existential risk.
+Power-seeking is expected to increase in advanced systems that can foresee the results of their actions and strategically plan. Mathematical work has shown that optimal reinforcement learning agents will seek power by seeking ways to gain more options (e.g. through self-preservation), a behavior that persists across a wide range of environments and goals.
+Some researchers say that power-seeking behavior has occurred in some existing AI systems. Reinforcement learning systems have gained more options by acquiring and protecting resources, sometimes in unintended ways. Language models have sought power in some text-based social environments by gaining money, resources, or social influence. In another case, a model used to perform AI research attempted to increase limits set by researchers to give itself more time to complete the work. Stuart Russell illustrated this strategy in his book Human Compatible by imagining a robot that is tasked to fetch coffee and so evades shutdown since "you can't fetch the coffee if you're dead". A 2022 study found that as language models increase in size, they increasingly tend to pursue resource acquisition, preserve their goals, and repeat users' preferred answers (sycophancy). RLHF also led to a stronger aversion to being shut down.
+One aim of alignment is "corrigibility": systems that allow themselves to be turned off or modified. An unsolved challenge is specification gaming: if researchers penalize an AI system when they detect it seeking power, the system is thereby incentivized to seek power in ways that are hard to detect, or hidden during training and safety testing (see § Scalable oversight and § Emergent goals). As a result, AI designers could deploy the system by accident, believing it to be more aligned than it is. To detect such deception, researchers aim to create techniques and tools to inspect AI models and to understand the inner workings of black-box models such as neural networks.
+Additionally, some researchers have proposed to solve the problem of systems disabling their off switches by making AI agents uncertain about the objective they are pursuing. Agents who are uncertain about their objective have an incentive to allow humans to turn them off because they accept being turned off by a human as evidence that the human's objective is best met by the agent shutting down. But this incentive exists only if the human is sufficiently rational. Also, this model presents a tradeoff between utility and willingness to be turned off: an agent with high uncertainty about its objective will not be useful, but an agent with low uncertainty may not allow itself to be turned off. More research is needed to successfully implement this strategy.
+Power-seeking AI would pose unusual risks. Ordinary safety-critical systems like planes and bridges are not adversarial: they lack the ability and incentive to evade safety measures or deliberately appear safer than they are, whereas power-seeking AIs have been compared to hackers who deliberately evade security measures.
+Furthermore, ordinary technologies can be made safer by trial and error. In contrast, hypothetical power-seeking AI systems have been compared to viruses: once released, it may not be feasible to contain them, since they continuously evolve and grow in number, potentially much faster than human society can adapt. As this process continues, it might lead to the complete disempowerment or extinction of humans. For these reasons, some researchers argue that the alignment problem must be solved early before advanced power-seeking AI is created.
+Some have argued that power-seeking is not inevitable, since humans do not always seek power. Furthermore, it is debated whether future AI systems will pursue goals and make long-term plans. It is also debated whether power-seeking AI systems would be able to disempower humanity.
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+---
+title: "AI alignment"
+chunk: 6/7
+source: "https://en.wikipedia.org/wiki/AI_alignment"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:59.555255+00:00"
+instance: "kb-cron"
+---
+
+=== Emergent goals ===
+One challenge in aligning AI systems is the potential for unanticipated goal-directed behavior to emerge. As AI systems scale up, they may acquire new and unexpected capabilities, including learning from examples on the fly and adaptively pursuing goals. This raises concerns about the safety of the goals or subgoals they would independently formulate and pursue.
+Alignment research distinguishes between the optimization process, which is used to train the system to pursue specified goals, and emergent optimization, which the resulting system performs internally. Carefully specifying the desired objective is called outer alignment, and ensuring that hypothesized emergent goals would match the system's specified goals is called inner alignment.
+If they occur, one way that emergent goals could become misaligned is goal misgeneralization, in which the AI system would competently pursue an emergent goal that leads to aligned behavior on the training data but not elsewhere. Goal misgeneralization can arise from goal ambiguity (i.e. non-identifiability). Even if an AI system's behavior satisfies the training objective, this may be compatible with learned goals that differ from the desired goals in important ways. Since pursuing each goal leads to good performance during training, the problem becomes apparent only after deployment, in novel situations in which the system continues to pursue the wrong goal. The system may act misaligned even when it understands that a different goal is desired, because its behavior is determined only by the emergent goal. Such goal misgeneralization presents a challenge: an AI system's designers may not notice that their system has misaligned emergent goals since they do not become visible during the training phase.
+Goal misgeneralization has been observed in some language models, navigation agents, and game-playing agents. It is sometimes analogized to biological evolution. Evolution can be seen as a kind of optimization process similar to the optimization algorithms used to train machine learning systems. In the ancestral environment, evolution selected genes for high inclusive genetic fitness, but humans pursue goals other than this. Fitness corresponds to the specified goal used in the training environment and training data. But in evolutionary history, maximizing the fitness specification gave rise to goal-directed agents, humans, who do not directly pursue inclusive genetic fitness. Instead, they pursue goals that correlate with genetic fitness in the ancestral "training" environment: nutrition, sex, and so on. The human environment has changed: a distributional shift has occurred. They continue to pursue the same emergent goals, but this no longer maximizes genetic fitness. The taste for sugary food (an emergent goal) was originally aligned with inclusive fitness, but it now leads to overeating and health problems. Sexual desire originally led humans to have more offspring, but they now use contraception when offspring are undesired, decoupling sex from genetic fitness.
+Researchers aim to detect and remove unwanted emergent goals using approaches including red teaming, verification, anomaly detection, and interpretability. Progress on these techniques may help mitigate two open problems:
+
+Emergent goals only become apparent when the system is deployed outside its training environment, but it can be unsafe to deploy a misaligned system in high-stakes environments—even for a short time to allow its misalignment to be detected. Such high stakes are common in autonomous driving, health care, and military applications. The stakes become higher yet when AI systems gain more autonomy and capability and can sidestep human intervention.
+A sufficiently capable AI system might take actions that falsely convince the human supervisor that the AI is pursuing the specified objective, which helps the system gain more reward and autonomy.
+
+=== Embedded agency ===
+Some work in AI and alignment occurs within formalisms such as partially observable Markov decision process. Existing formalisms assume that an AI agent's algorithm is executed outside the environment (i.e. is not physically embedded in it). Embedded agency is another major strand of research that attempts to solve problems arising from the mismatch between such theoretical frameworks and real agents we might build.
+For example, even if the scalable oversight problem is solved, an agent that could gain access to the computer it is running on may have an incentive to tamper with its reward function in order to get much more reward than its human supervisors give it. A list of examples of specification gaming from DeepMind researcher Victoria Krakovna includes a genetic algorithm that learned to delete the file containing its target output so that it was rewarded for outputting nothing. This class of problems has been formalized using causal incentive diagrams.
+Researchers affiliated with Oxford and DeepMind have claimed that such behavior is highly likely in advanced systems, and that advanced systems would seek power to stay in control of their reward signal indefinitely and certainly. They suggest a range of potential approaches to address this open problem.
+
+=== Principal–agent problems ===
+The alignment problem has many parallels with the principal–agent problem in organizational economics. In a principal–agent problem, a principal, e.g. a firm, hires an agent to perform some task. In the context of AI safety, a human would typically take the principal role and the AI would take the agent role.
+As with the alignment problem, the principal and the agent differ in their utility functions. But in contrast to the alignment problem, the principal cannot coerce the agent into changing its utility, e.g. through training, but rather must use exogenous factors, such as incentive schemes, to bring about outcomes compatible with the principal's utility function. Some researchers argue that principal–agent problems are more realistic representations of AI safety problems likely to be encountered in the real world.
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+---
+title: "AI alignment"
+chunk: 7/7
+source: "https://en.wikipedia.org/wiki/AI_alignment"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:59.555255+00:00"
+instance: "kb-cron"
+---
+
+=== Conservatism ===
+Conservatism is the idea that "change must be cautious", and is a common approach to safety in the control theory literature in the form of robust control, and in the risk management literature in the form of the "worst-case scenario". The field of AI alignment has likewise advocated for "conservative" (or "risk-averse" or "cautious") "policies in situations of uncertainty".
+Pessimism, in the sense of assuming the worst within reason, has been formally shown to produce conservatism, in the sense of reluctance to cause novelties, including unprecedented catastrophes. Pessimism and worst-case analysis have been found to help mitigate confident mistakes in the setting of distributional shift, reinforcement learning, offline reinforcement learning, language model fine-tuning, imitation learning, and optimization in general.
+
+== Public policy ==
+
+Governmental and treaty organizations have made statements emphasizing the importance of AI alignment.
+In September 2021, the Secretary-General of the United Nations issued a declaration that included a call to regulate AI to ensure it is "aligned with shared global values".
+That same month, the PRC published ethical guidelines for AI in China. According to the guidelines, researchers must ensure that AI abides by shared human values, is always under human control, and does not endanger public safety.
+Also in September 2021, the UK published its 10-year National AI Strategy, which says the British government "takes the long term risk of non-aligned Artificial General Intelligence, and the unforeseeable changes that it would mean for [...] the world, seriously". The strategy describes actions to assess long-term AI risks, including catastrophic risks.
+In March 2021, the US National Security Commission on Artificial Intelligence said: "Advances in AI [...] could lead to inflection points or leaps in capabilities. Such advances may also introduce new concerns and risks and the need for new policies, recommendations, and technical advances to ensure that systems are aligned with goals and values, including safety, robustness, and trustworthiness. The US should [...] ensure that AI systems and their uses align with our goals and values."
+In the European Union, AIs must align with substantive equality to comply with EU non-discrimination law and the Court of Justice of the European Union. But the EU has yet to specify with technical rigor how it would evaluate whether AIs are aligned or in compliance.
+
+== See also ==
+
+== Footnotes ==
+
+== References ==
+
+== Further reading ==
+Ngo, Richard; et al. (2024). "The Alignment Problem from a Deep Learning Perspective". ICLR: 7474–7501.
+Ji, Jiaming; et al. (2023). "AI Alignment: A Comprehensive Survey". ACM Computing Surveys. doi:10.1145/3770749.
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+---
+title: "AI capability control"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/AI_capability_control"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:00.901190+00:00"
+instance: "kb-cron"
+---
+
+In the field of artificial intelligence (AI) design, AI capability control proposals, also referred to as AI confinement, aim to increase human ability to monitor and control the behavior of AI systems, including proposed artificial general intelligences (AGIs), in order to reduce dangers they might pose if misaligned. Capability control becomes less effective as agents become more intelligent and their ability to exploit flaws in human control systems increases, potentially resulting in an existential risk from AGI. Therefore, the Oxford philosopher Nick Bostrom and others recommend capability control methods only as a supplement to alignment methods.
+
+
+== Motivation ==
+
+Some hypothetical intelligence technologies, like "seed AI", are postulated to be able to make themselves faster and more intelligent by modifying their source code. These improvements would make further improvements possible, which would in turn make further iterative improvements possible, and so on, leading to a sudden intelligence explosion.
+An unconfined superintelligent AI could, if its goals differed from humanity's, take actions resulting in human extinction. For example, an extremely advanced system of this sort, given the sole purpose of solving the Riemann hypothesis, an innocuous mathematical conjecture, could decide to try to convert the planet into a giant supercomputer whose sole purpose is to make additional mathematical calculations (see also paperclip maximizer). 
+One strong challenge for control is that neural networks are by default highly uninterpretable. This makes it more difficult to detect deception or other undesired behavior as the model self-trains iteratively. Advances in interpretable artificial intelligence could mitigate this difficulty.
+
+
+== Proposed techniques ==
+
+
+=== Interruptibility and kill switch ===
+One potential way to prevent harmful outcomes is to give human supervisors the ability to easily shut down a misbehaving AI via a kill switch. Modern AI systems however often run in distributed infrastructures, which makes a coordinated shutdown difficult, especially if the AI becomes available on the internet.
+
+
+=== Oracle AI ===
+An oracle is a hypothetical AI designed to answer questions and prevented from gaining any goals or subgoals that involve modifying the world beyond its limited environment. In his 2018, AI researcher Stuart J. Russell stated that if superintelligence were known to be only a decade away, developers should create an oracle with no internet access and constrained answers rather than a general-purpose intelligent agent.
+Oracles may share many of the goal definition issues associated with general purpose superintelligence. An oracle would have an incentive to escape its controlled environment so that it can acquire more computational resources and potentially control what questions it is asked. Oracles may not be truthful, possibly lying to promote hidden agendas. To mitigate this, Bostrom suggests building multiple oracles, all slightly different, and comparing their answers in order to reach a consensus.
+
+
+=== Blinding ===
+An AI could be blinded to certain variables in its environment. This could provide certain safety benefits, such as an AI not knowing how a reward is generated, making it more difficult to exploit.
+
+
+=== Boxing ===
+An AI box is a proposed method of capability control in which an AI is run on an isolated computer system with heavily restricted input and output channels, similar to a virtual machine. The purpose of an AI box is to reduce the risk of the AI taking control of the environment away from its operators, while still allowing the AI to output solutions to narrow technical problems.
+While boxing reduces the AI's ability to carry out undesirable behavior, it also reduces its usefulness. Boxing has fewer costs when applied to a question-answering system, which may not require interaction with the outside world.
+The likelihood of security flaws involving hardware or software vulnerabilities can be reduced by formally verifying the design of the AI box.
+
+
+== Difficulties ==
+
+
+=== Shutdown avoidance ===
+Shutdown avoidance (or shutdown resistance) is a hypothetical self-preserving quality of artificial intelligence systems. Shutdown-avoiding systems would be incentivized to prevent humans from shutting them down, such as by disabling off-switches or running copies of themselves on other computers. In 2024, researchers in China demonstrated what they claimed to be shutdown avoidance in actual artificial intelligence systems, the large language models Llama 3.1 (Meta) and Qwen 2.5 (Alibaba).
+One workaround suggested by computer scientist Stuart J. Russell is to ensure that the AI interprets human choices as important information about its intended goals.
+Alternatively, Laurent Orseau and Stuart Armstrong proved that a broad class of agents, called safely interruptible agents, can learn to become indifferent to whether their off-switch gets pressed. This approach has the limitation that an AI which is completely indifferent to whether it is shut down or not is also unmotivated to care about whether the off-switch remains functional, and could incidentally disable it in the course of its operations. 
+
+
+=== Escaping containment ===
+Researchers have speculated that a superintelligent AI would have a wide variety of methods for escaping containment. These hypothetical methods include hacking into other computer systems and copying itself like a computer virus, and the use of persuasion and blackmail to obtain aid from human confederates. The more intelligent a system grows, the more likely the system would be able to escape even the best-designed capability control methods. In order to solve the overall "control problem" for a superintelligent AI and avoid existential risk, AI capability control would at best be an adjunct to "motivation selection" methods that seek to ensure the superintelligent AI's goals are compatible with human survival.
+
+
+== See also ==
+
+
+== References ==
+
+
+== External links ==
+Eliezer Yudkowsky's description of his AI-box experiment, including experimental protocols and suggestions for replication
+"Presentation titled 'Thinking inside the box: using and controlling an Oracle AI'" on YouTube
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+---
+title: "AI trust paradox"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/AI_trust_paradox"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:02.140367+00:00"
+instance: "kb-cron"
+---
+
+The AI trust paradox (also known as the verisimilitude paradox) is the phenomenon where advanced artificial intelligence models become so proficient at mimicking human-like language and behavior that users increasingly struggle to determine if the information generated is accurate or simply plausible.
+Unlike earlier concerns such as Moravec's paradox, which highlighted the surprising difficulty in replicating simple human functions in AI, and the automation paradox, which deals with balancing automation and human control, the AI trust paradox specifically addresses the issue of verisimilitude—the appearance of truth that leads to misplaced trust. The newer challenge arises from the inherent difficulty for users in distinguishing between genuine and misleading content produced by large language models (LLMs) as they become more adept at generating natural and contextually appropriate responses.
+
+
+== History ==
+In the paper, The AI Trust Paradox: Navigating Verisimilitude in Advanced Language Models by Christopher Foster-McBride, published by Digital Human Assistants, the evolution of large language models (LLMs) was explored through a comparative analysis of early models and their more advanced successors. Foster-McBride demonstrated that newer LLMs, with improved architecture and training on extensive datasets, showed significant advancements across key performance metrics, including fluency and contextual understanding. However, this increased sophistication made it increasingly difficult for users to detect inaccuracies, also known as hallucinations.
+Foster-McBride highlighted that the newer models not only provided more coherent and contextually appropriate responses but also masked incorrect information more convincingly. This aspect of AI evolution posed a unique challenge: while the responses appeared more reliable, the underlying verisimilitude increased the potential for misinformation going unnoticed by human evaluators.
+The study concluded that as models became more capable, their fluency led to a rising trust among users, which paradoxically made discerning false information harder. This finding has led to subsequent discussions and research focusing on the impact of model sophistication and fluency on user trust and behavior, as researchers investigate the implications of AI-generated content that can confidently produce misleading or incorrect information.
+
+
+== Relation to other paradoxes ==
+The AI trust paradox can be understood alongside other well-known paradoxes, such as the automation paradox, which addresses the complexity of balancing automation with human oversight. Similar concerns arise in Goodhart's law, where an AI's optimization of specified objectives can lead to unintended, often negative, outcomes.
+These paradoxes highlight that trust in AI is not only technical but behavioral and organizational. Several implementation-stage strategies can help resolve them, including early user involvement, clear accountability structures, and explainable interfaces.
+
+
+== Current research and mitigation strategies ==
+Addressing the AI trust paradox requires methods such as reinforcement learning with human feedback (RLHF), which trains AI models to better align their responses with expected norms and user intentions.
+Efforts in trustworthy AI focus on making AI systems transparent, robust, and accountable to mitigate the risks posed by the AI trust paradox. Current research in AI safety aims to minimize the occurrence of hallucinations and ensure that AI outputs are both reliable and ethically sound.
+
+
+== See also ==
+AI effect
+AI alignment
+Polanyi's paradox
+
+
+== References ==
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+
+Algorithmic bias describes systematic and repeatable harmful tendency in a computerized sociotechnical system to create "unfair" outcomes, such as "privileging" one category over another in ways that may or may not be different from the intended function of the algorithm.
+Bias can emerge from many factors, including intentionally biased design decisions or the unintended or unanticipated use or decisions relating to the way data is coded, collected, selected or used to train the algorithm. For example, algorithmic bias has been observed in search engine results and social media platforms. This bias can have impacts ranging from privacy violations to reinforcing social biases of race, gender, sexuality, and ethnicity. The study of algorithmic bias is most concerned with algorithms that reflect "systematic and unfair" discrimination. This bias has only recently been addressed in legal frameworks, such as the European Union's General Data Protection Regulation (enforced in 2018) and the Artificial Intelligence Act (proposed in 2021 and adopted in 2024).
+As algorithms expand their ability to organize society, politics, institutions, and behavior, sociologists have become concerned with the ways in which unanticipated output and manipulation of data can impact the physical world. Because algorithms are often considered to be neutral and unbiased, they can inaccurately project greater authority than human expertise (in part due to the psychological phenomenon of automation bias), and in some cases, reliance on algorithms can displace human responsibility for their outcomes, without last mile thinking. Bias can enter into algorithmic systems as a result of pre-existing cultural, social, or institutional expectations; by how features and labels are chosen; because of technical limitations of their design; or by being used in unanticipated contexts or by audiences who are not considered in the software's initial design.
+Algorithmic bias has been cited in cases ranging from election outcomes to the spread of online hate speech. It has also arisen in criminal justice, healthcare, and hiring, compounding existing racial, socioeconomic, and gender biases. The relative inability of facial recognition technology to accurately identify darker-skinned faces has been linked to multiple wrongful arrests of black men, an issue stemming from imbalanced datasets. Problems in understanding, researching, and discovering algorithmic bias persist due to the proprietary nature of algorithms, which are typically treated as trade secrets. Even when full transparency is provided, the complexity of certain algorithms poses a barrier to understanding their functioning. Furthermore, algorithms may change, or respond to input or output in ways that cannot be anticipated or easily reproduced for analysis. In many cases, even within a single website or application, there is no single "algorithm" to examine, but a network of many interrelated programs and data inputs, even between users of the same service.
+A 2021 survey identified multiple forms of algorithmic bias, including historical, representation, and measurement biases, each of which can contribute to unfair outcomes.
+
+== Definitions ==
+
+Algorithms are difficult to define, but may be generally understood as lists of instructions that determine how programs read, collect, process, and analyze data to generate a usable output. For a rigorous technical introduction, see Algorithms. Advances in computer hardware and software have led to an increased capability to process, store and transmit data. This has in turn made the design and adoption of technologies such as machine learning and artificial intelligence technically and commercially feasible. By analyzing and processing data, algorithms are the backbone of search engines, social media websites, recommendation engines, online retail, online advertising, and more.
+Contemporary social scientists are concerned with algorithmic processes embedded into hardware and software applications because of their political and social impact, and question the underlying assumptions of an algorithm's neutrality. The term algorithmic bias describes systematic and repeatable errors that create unfair outcomes, such as privileging one arbitrary group of users over others. For example, a credit score algorithm may deny a loan without being unfair, if it is consistently weighing relevant financial criteria. If the algorithm recommends loans to one group of users, but denies loans to another set of nearly identical users based on unrelated criteria, and if this behavior can be repeated across multiple occurrences, an algorithm can be described as biased. This bias may be intentional or unintentional (for example, it can come from biased data obtained from a worker that previously did the job the algorithm is going to do from now on).
+
+== Methods ==
+Bias can be introduced to an algorithm in several ways. During the assemblage of a dataset, data may be collected, digitized, adapted, and entered into a database according to human-designed cataloging criteria. Next, programmers assign priorities, or hierarchies, for how a program assesses and sorts that data. This requires human decisions about how data is categorized, and which data is included or discarded. Some algorithms collect their own data based on human-selected criteria, which can also reflect the bias of human designers. Other algorithms may reinforce stereotypes and preferences as they process and display "relevant" data for human users, for example, by selecting information based on previous choices of a similar user or group of users.
+Beyond assembling and processing data, bias can emerge as a result of design. For example, algorithms that determine the allocation of resources or scrutiny (such as determining school placements) may inadvertently discriminate against a category when determining risk based on similar users (as in credit scores). Meanwhile, recommendation engines that work by associating users with similar users, or that make use of inferred marketing traits, might rely on inaccurate associations that reflect broad ethnic, gender, socio-economic, or racial stereotypes. Another example comes from determining criteria for what is included and excluded from results. These criteria could present unanticipated outcomes for search results, such as with flight-recommendation software that omits flights that do not follow the sponsoring airline's flight paths. Algorithms may also display an uncertainty bias, offering more confident assessments when larger data sets are available. This can skew algorithmic processes toward results that more closely correspond with larger samples, which may disregard data from underrepresented populations.
+
+== History ==
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+
+=== Early critiques ===
+
+The earliest computer programs were designed to mimic human reasoning and deductions, and were deemed to be functioning when they successfully and consistently reproduced that human logic. In his 1976 book Computer Power and Human Reason, artificial intelligence pioneer Joseph Weizenbaum suggested that bias could arise both from the data used in a program, but also from the way a program is coded.
+Weizenbaum wrote that programs are a sequence of rules created by humans for a computer to follow. By following those rules consistently, such programs "embody law", that is, enforce a specific way to solve problems. The rules a computer follows are based on the assumptions of a computer programmer for how these problems might be solved. That means the code could incorporate the programmer's imagination of how the world works, including their biases and expectations. While a computer program can incorporate bias in this way, Weizenbaum also noted that any data fed to a machine additionally reflects "human decision making processes" as data is being selected.
+Finally, he noted that machines might also transfer good information with unintended consequences if users are unclear about how to interpret the results. Weizenbaum warned against trusting decisions made by computer programs that a user doesn't understand, comparing such faith to a tourist who can find his way to a hotel room exclusively by turning left or right on a coin toss. Crucially, the tourist has no basis of understanding how or why he arrived at his destination, and a successful arrival does not mean the process is accurate or reliable.
+An early example of algorithmic bias resulted in as many as 60 women and ethnic minorities denied entry to St. George's Hospital Medical School per year from 1982 to 1986, based on implementation of a new computer-guidance assessment system that denied entry to women and men with "foreign-sounding names" based on historical trends in admissions. While many schools at the time employed similar biases in their selection process, St. George was most notable for automating said bias through the use of an algorithm, thus gaining the attention of people on a much wider scale.
+In recent years, as algorithms increasingly rely on machine learning methods applied to real-world data, algorithmic bias has become more prevalent due to inherent biases within the data itself. For instance, facial recognition systems have been shown to misidentify individuals from marginalized groups at significantly higher rates than white individuals, highlighting how biases in training datasets manifest in deployed systems. A 2018 study by Joy Buolamwini and Timnit Gebru found that commercial facial recognition technologies exhibited error rates of up to 35% when identifying darker-skinned women, compared to less than 1% for lighter-skinned men.
+Algorithmic biases are not only technical failures but often reflect systemic inequities embedded in historical and societal data. Researchers and critics, such as Cathy O'Neil in her book Weapons of Math Destruction (2016), emphasize that these biases can amplify existing social inequalities under the guise of objectivity. O'Neil argues that opaque, automated decision-making processes in areas such as credit scoring, predictive policing, and education can reinforce discriminatory practices while appearing neutral or scientific.
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+
+=== Lack of transparency ===
+Commercial algorithms are proprietary, and may be treated as trade secrets. Treating algorithms as trade secrets protects companies, such as search engines, where a transparent algorithm might reveal tactics to manipulate search rankings. This makes it difficult for researchers to conduct interviews or analysis to discover how algorithms function. Critics suggest that such secrecy can also obscure possible unethical methods used in producing or processing algorithmic output. Other critics, such as lawyer and activist Katarzyna Szymielewicz, have suggested that the lack of transparency is often disguised as a result of algorithmic complexity, shielding companies from disclosing or investigating its own algorithmic processes.
+
+=== Lack of data about sensitive categories ===
+A significant barrier to understanding the tackling of bias in practice is that categories, such as demographics of individuals protected by anti-discrimination law, are often not explicitly considered when collecting and processing data. In some cases, there is little opportunity to collect this data explicitly, such as in device fingerprinting, ubiquitous computing and the Internet of Things. In other cases, the data controller may not wish to collect such data for reputational reasons, or because it represents a heightened liability and security risk. It may also be the case that, at least in relation to the European Union's General Data Protection Regulation, such data falls under the 'special category' provisions (Article 9), and therefore comes with more restrictions on potential collection and processing.
+Some practitioners have tried to estimate and impute these missing sensitive categorizations in order to allow bias mitigation, for example building systems to infer ethnicity from names, however this can introduce other forms of bias if not undertaken with care. Machine learning researchers have drawn upon cryptographic privacy-enhancing technologies such as secure multi-party computation to propose methods whereby algorithmic bias can be assessed or mitigated without these data ever being available to modellers in cleartext.
+Algorithmic bias does not only include protected categories, but can also concern characteristics less easily observable or codifiable, such as political viewpoints. In these cases, there is rarely an easily accessible or non-controversial ground truth, and removing the bias from such a system is more difficult. Furthermore, false and accidental correlations can emerge from a lack of understanding of protected categories, for example, insurance rates based on historical data of car accidents which may overlap, strictly by coincidence, with residential clusters of ethnic minorities.
+
+== Solutions ==
+A study of 84 policy guidelines on ethical AI found that fairness and "mitigation of unwanted bias" was a common point of concern, and were addressed through a blend of technical solutions, transparency and monitoring, right to remedy and increased oversight, and diversity and inclusion efforts.
+
+=== Technical ===
+
+There have been several attempts to create methods and tools that can detect and observe biases within an algorithm. These emergent fields focus on tools which are typically applied to the (training) data used by the program rather than the algorithm's internal processes. These methods may also analyze a program's output and its usefulness and therefore may involve the analysis of its confusion matrix (or table of confusion). Explainable AI to detect algorithm Bias is a suggested way to detect the existence of bias in an algorithm or learning model. Using machine learning to detect bias is called, "conducting an AI audit", where the "auditor" is an algorithm that goes through the AI model and the training data to identify biases.
+Ensuring that an AI tool such as a classifier is free from bias is more difficult than just removing the sensitive information
+from its input signals, because this is typically implicit in other signals. For example, the hobbies, sports and schools attended
+by a job candidate might reveal their gender to the software, even when this is removed from the analysis. Solutions to this
+problem involve ensuring that the intelligent agent does not have any information that could be used to reconstruct the protected
+and sensitive information about the subject, as first demonstrated in where a deep learning network was simultaneously trained to learn a task while at the same time being completely agnostic about the protected feature. A simpler method was proposed in the context of word embeddings, and involves removing information that is correlated with the protected characteristic.
+Currently, a new IEEE standard is being drafted that aims to specify methodologies which help creators of algorithms eliminate issues of bias and articulate transparency (i.e. to authorities or end users) about the function and possible effects of their algorithms. The project was approved February 2017 and is sponsored by the Software & Systems Engineering Standards Committee, a committee chartered by the IEEE Computer Society. A draft of the standard is expected to be submitted for balloting in June 2019.The standard was published in January 2025.
+In 2022, the IEEE released a standard aimed at specifying methodologies to help creators of algorithms address issues of bias and promote transparency regarding the function and potential effects of their algorithms. The project, initially approved in February 2017, was sponsored by the Software & Systems Engineering Standards Committee, a committee under the IEEE Computer Society. The standard provides guidelines for articulating transparency to authorities or end users and mitigating algorithmic biases.
+
+=== Transparency and monitoring ===
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+
+Ethics guidelines on AI point to the need for accountability, recommending that steps be taken to improve the interpretability of results. Such solutions include the consideration of the "right to understanding" in machine learning algorithms, and to resist deployment of machine learning in situations where the decisions could not be explained or reviewed. Toward this end, a movement for "Explainable AI" is already underway within organizations such as DARPA, for reasons that go beyond the remedy of bias. Price Waterhouse Coopers, for example, also suggests that monitoring output means designing systems in such a way as to ensure that solitary components of the system can be isolated and shut down if they skew results.
+An initial approach towards transparency included the open-sourcing of algorithms. Software code can be looked into and improvements can be proposed through source-code-hosting facilities. However, this approach doesn't necessarily produce the intended effects. Companies and organizations can share all possible documentation and code, but this does not establish transparency if the audience doesn't understand the information given. Therefore, the role of an interested critical audience is worth exploring in relation to transparency. Algorithms cannot be held accountable without a critical audience.
+
+=== Documentation and accountability frameworks ===
+Several documentation approaches have been proposed to improve transparency and support the evaluation of bias in algorithmic systems. One widely cited method is the use of model cards, which provide standardized summaries of an AI system's intended uses, performance metrics, evaluation datasets, and known limitations. Related efforts include datasheets for datasets, which outline the provenance, composition, collection methods, and recommended uses of training data. These documentation frameworks aim to clarify the assumptions and potential biases embedded in training data and machine-learning systems, helping practitioners, auditors, and impacted groups better interpret system behavior.
+In addition to documentation practices, researchers and policymakers have encouraged the use of structured governance mechanisms such as algorithmic impact assessments, risk-based evaluation procedures, and post-deployment monitoring. These processes seek to identify potential disparate impacts before deployment and ensure that AI systems continue to be evaluated for fairness during real-world operation. Public-sector initiatives such as Canada's Directive on Automated Decision-Making require impact assessments, explainability measures, and regular audits for certain high-risk automated systems. Together, these governance approaches complement technical mitigation strategies by embedding accountability and transparency throughout the lifecycle of AI development and deployment.
+
+=== Right to remedy ===
+From a regulatory perspective, the Toronto Declaration calls for applying a human rights framework to harms caused by algorithmic bias. This includes legislating expectations of due diligence on behalf of designers of these algorithms, and creating accountability when private actors fail to protect the public interest, noting that such rights may be obscured by the complexity of determining responsibility within a web of complex, intertwining processes. Others propose the need for clear liability insurance mechanisms.
+
+=== Diversity and inclusion ===
+Amid concerns that the design of AI systems is primarily the domain of white, male engineers, a number of scholars have suggested that algorithmic bias may be minimized by expanding inclusion in the ranks of those designing AI systems. For example, just 12% of machine learning engineers are women, with black AI leaders pointing to a "diversity crisis" in the field. Groups like Black in AI and Queer in AI are attempting to create more inclusive spaces in the AI community and work against the often harmful desires of corporations that control the trajectory of AI research. Critiques of simple inclusivity efforts suggest that diversity programs can not address overlapping forms of inequality, and have called for applying a more deliberate lens of intersectionality to the design of algorithms. Researchers at the University of Cambridge have argued that addressing racial diversity is hampered by the "whiteness" of the culture of AI.
+
+=== Interdisciplinarity and Collaboration ===
+Integrating interdisciplinarity and collaboration in developing of AI systems can play a critical role in tackling algorithmic bias. Integrating insights, expertise, and perspectives from disciplines outside of computer science can foster a better understanding of the impact data driven solutions have on society. An example of this in AI research is PACT or Participatory Approach to enable Capabilities in communiTies, a proposed framework for facilitating collaboration when developing AI driven solutions concerned with social impact. This framework identifies guiding principals for stakeholder participation when working on AI for Social Good (AI4SG) projects. PACT attempts to reify the importance of decolonizing and power-shifting efforts in the design of human-centered AI solutions. An academic initiative in this regard is the Stanford University's Institute for Human-Centered Artificial Intelligence which aims to foster multidisciplinary collaboration. The mission of the institute is to advance artificial intelligence (AI) research, education, policy and practice to improve the human condition.
+Collaboration with outside experts and various stakeholders facilitates ethical, inclusive, and accountable development of intelligent systems. It incorporates ethical considerations, understands the social and cultural context, promotes human-centered design, leverages technical expertise, and addresses policy and legal considerations. Collaboration across disciplines is essential to effectively mitigate bias in AI systems and ensure that AI technologies are fair, transparent, and accountable.
+
+== Regulation ==
+
+=== Europe ===
+The General Data Protection Regulation (GDPR), the European Union's revised data protection regime that was implemented in 2018, addresses "Automated individual decision-making, including profiling" in Article 22. These rules prohibit "solely" automated decisions which have a "significant" or "legal" effect on an individual, unless they are explicitly authorised by consent, contract, or member state law. Where they are permitted, there must be safeguards in place, such as a right to a human-in-the-loop, and a non-binding right to an explanation of decisions reached. While these regulations are commonly considered to be new, nearly identical provisions have existed across Europe since 1995, in Article 15 of the Data Protection Directive. The original automated decision rules and safeguards found in French law since the late 1970s.
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+instance: "kb-cron"
+---
+
+The GDPR addresses algorithmic bias in profiling systems, as well as the statistical approaches possible to clean it, directly in recital 71, noting thatthe controller should use appropriate mathematical or statistical procedures for the profiling, implement technical and organisational measures appropriate ... that prevents, inter alia, discriminatory effects on natural persons on the basis of racial or ethnic origin, political opinion, religion or beliefs, trade union membership, genetic or health status or sexual orientation, or that result in measures having such an effect.Like the non-binding right to an explanation in recital 71, the problem is the non-binding nature of recitals. While it has been treated as a requirement by the Article 29 Working Party that advised on the implementation of data protection law, its practical dimensions are unclear. It has been argued that the Data Protection Impact Assessments for high risk data profiling (alongside other pre-emptive measures within data protection) may be a better way to tackle issues of algorithmic discrimination, as it restricts the actions of those deploying algorithms, rather than requiring consumers to file complaints or request changes.
+
+=== United States ===
+The United States has no general legislation controlling algorithmic bias, approaching the problem through various state and federal laws that might vary by industry, sector, and by how an algorithm is used. Many policies are self-enforced or controlled by the Federal Trade Commission. In 2016, the Obama administration released the National Artificial Intelligence Research and Development Strategic Plan, which was intended to guide policymakers toward a critical assessment of algorithms. It recommended researchers to "design these systems so that their actions and decision-making are transparent and easily interpretable by humans, and thus can be examined for any bias they may contain, rather than just learning and repeating these biases". Intended only as guidance, the report did not create any legal precedent.
+In 2017, New York City passed the first algorithmic accountability bill in the United States. The bill, which went into effect on January 1, 2018, required "the creation of a task force that provides recommendations on how information on agency automated decision systems may be shared with the public, and how agencies may address instances where people are harmed by agency automated decision systems." In 2023, New York City implemented a law requiring employers using automated hiring tools to conduct independent "bias audits" and publish the results. This law marked one of the first legally mandated transparency measures for AI systems used in employment decisions in the United States. The task force is required to present findings and recommendations for further regulatory action in 2019.
+On February 11, 2019, according to Executive Order 13859, the federal government unveiled the "American AI Initiative", a comprehensive strategy to maintain U.S. leadership in artificial intelligence. The initiative highlights the importance of sustained AI research and development, ethical standards, workforce training, and the protection of critical AI technologies. This aligns with broader efforts to ensure transparency, accountability, and innovation in AI systems across public and private sectors. Furthermore, on October 30, 2023, the President signed Executive Order 14110, which emphasizes the safe, secure, and trustworthy development and use of artificial intelligence (AI). The order outlines a coordinated, government-wide approach to harness AI's potential while mitigating its risks, including fraud, discrimination, and national security threats. An important point in the commitment is promoting responsible innovation and collaboration across sectors to ensure that AI benefits society as a whole. With this order, President Joe Biden mandated the federal government to create best practices for companies to optimize AI's benefits and minimize its harms.
+
+=== India ===
+On July 31, 2018, a draft of the Personal Data Bill was presented. The draft proposes standards for the storage, processing and transmission of data. While it does not use the term algorithm, it makes for provisions for "harm resulting from any processing or any kind of processing undertaken by the fiduciary". It defines "any denial or withdrawal of a service, benefit or good resulting from an evaluative decision about the data principal" or "any discriminatory treatment" as a source of harm that could arise from improper use of data. It also makes special provisions for people of "Intersex status".
+
+== See also ==
+Algorithmic wage discrimination
+Algorithmic amplification
+Automated decision-making
+Digital redlining
+Ethics of artificial intelligence
+Fairness (machine learning)
+Hallucination (artificial intelligence)
+Misaligned goals in artificial intelligence
+Predictive policing
+SenseTime
+Joy Buolamwini
+Timnit Gebru
+Cathy O'Neil
+
+== References ==
+
+== Further reading ==
+Baer, Tobias (2019). Understand, Manage, and Prevent Algorithmic Bias: A Guide for Business Users and Data Scientists. New York: Apress. ISBN 978-1-4842-4884-3.
+Noble, Safiya Umoja (2018). Algorithms of Oppression: How Search Engines Reinforce Racism. New York: New York University Press. ISBN 978-1-4798-3724-3.
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+instance: "kb-cron"
+---
+
+=== Contemporary critiques and responses ===
+Though well-designed algorithms frequently determine outcomes that are equally (or more) equitable than the decisions of human beings, cases of bias still occur, and are difficult to predict and analyze. The complexity of analyzing algorithmic bias has grown alongside the complexity of programs and their design. Decisions made by one designer, or team of designers, may be obscured among the many pieces of code created for a single program; over time these decisions and their collective impact on the program's output may be forgotten. In theory, these biases may create new patterns of behavior, or "scripts", in relationship to specific technologies as the code interacts with other elements of society. Biases may also impact how society shapes itself around the data points that algorithms require. For example, if data shows a high number of arrests in a particular area, an algorithm may assign more police patrols to that area, which could lead to more arrests.
+The decisions of algorithmic programs can be seen as more authoritative than the decisions of the human beings they are meant to assist, a process described by author Clay Shirky as "algorithmic authority". Shirky uses the term to describe "the decision to regard as authoritative an unmanaged process of extracting value from diverse, untrustworthy sources", such as search results. This neutrality can also be misrepresented by the language used by experts and the media when results are presented to the public. For example, a list of news items selected and presented as "trending" or "popular" may be created based on significantly wider criteria than just their popularity.
+Because of their convenience and authority, algorithms are theorized as a means of delegating responsibility away from humans. This can have the effect of reducing alternative options, compromises, or flexibility. Sociologist Scott Lash has critiqued algorithms as a new form of "generative power", in that they are a virtual means of generating actual ends. Where previously human behavior generated data to be collected and studied, powerful algorithms increasingly could shape and define human behaviors.
+While blind adherence to algorithmic decisions is a concern, an opposite issue arises when human decision-makers exhibit "selective adherence" to algorithmic advice. In such cases, individuals accept recommendations that align with their preexisting beliefs and disregard those that do not, thereby perpetuating existing biases and undermining the fairness objectives of algorithmic interventions. Consequently, incorporating fair algorithmic tools into decision-making processes does not automatically eliminate human biases.
+Concerns over the impact of algorithms on society have led to the creation of working groups in organizations such as Google and Microsoft, which have co-created a working group named Fairness, Accountability,
+and Transparency in Machine Learning. Ideas from Google have included community groups that patrol the outcomes of algorithms and vote to control or restrict outputs they deem to have negative consequences. In recent years, the study of the Fairness, Accountability,
+and Transparency (FAT) of algorithms has emerged as its own interdisciplinary research area with an annual conference called FAccT. Critics have suggested that FAT initiatives cannot serve effectively as independent watchdogs when many are funded by corporations building the systems being studied.
+NIST's AI Risk Management Framework 1.0 and its 2024 Generative AI Profile provide practical guidance for governing and measuring bias mitigation in AI systems.
+
+== Types ==
+
+=== Pre-existing ===
+Pre-existing bias in an algorithm is a consequence of underlying social and institutional ideologies. Bias can be placed intentionally or accidentally.Poorly selected input data, or simply data from a biased source, will influence the outcomes created by machines. Encoding pre-existing bias into software can preserve social and institutional bias, and, without correction, could be replicated in all future uses of that algorithm.
+An example of this form of bias is the British Nationality Act Program, designed to automate the evaluation of new British citizens after the 1981 British Nationality Act. The program accurately reflected the tenets of the law, which stated that "a man is the father of only his legitimate children, whereas a woman is the mother of all her children, legitimate or not." In its attempt to transfer a particular logic into an algorithmic process, the BNAP inscribed the logic of the British Nationality Act into its algorithm, which would perpetuate it even if the act was eventually repealed.
+Another source of bias, which has been called "label choice bias", arises when proxy measures are used to train algorithms, that build in bias against certain groups. For example, a widely used algorithm predicted health care costs as a proxy for health care needs, and used predictions to allocate resources to help patients with complex health needs. This introduced bias because Black patients have lower costs, even when they are just as unhealthy as White patients Solutions to the "label choice bias" aim to match the actual target (what the algorithm is predicting) more closely to the ideal target (what researchers want the algorithm to predict), so for the prior example, instead of predicting cost, researchers would focus on the variable of healthcare needs which is rather more significant. Adjusting the target led to almost double the number of Black patients being selected for the program.
+
+=== Machine learning bias ===
+Machine learning bias refers to systematic and unfair disparities in the output of machine learning algorithms. These biases can manifest in various ways and are often a reflection of the data used to train these algorithms. Some common types of machine learning bias include:
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+title: "Algorithmic bias"
+chunk: 4/13
+source: "https://en.wikipedia.org/wiki/Algorithmic_bias"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:03.393915+00:00"
+instance: "kb-cron"
+---
+
+Data bias: Training data may under‑represent certain groups (e.g., minority populations), contain historical inequalities, or be collected in skewed ways, leading the model to perform worse or behave unfairly for those groups.
+Label bias: Human‑provided labels can encode subjective judgments or prejudices (for example, what is labeled as "risky," "toxic," or "qualified"), so the model learns and amplifies those judgments.
+Measurement bias: Proxies or measurements used for important concepts (like "creditworthiness" or "job performance") may be noisy or systematically distorted for some groups, which then distorts predictions.
+Algorithmic bias: Even with relatively balanced data, modeling choices (loss functions, thresholds, optimization objectives) can prioritize overall accuracy over fairness, leaving some subgroups with consistently worse outcomes.
+Deployment bias: A model used outside the context it was designed for (e.g., a model trained on adults applied to children, or one trained in one country deployed in another) can generate biased results because the environment and population differ.
+Mitigating machine learning bias typically involves interventions at multiple stages: collecting more representative and higher‑quality data, auditing datasets and models for disparate error rates or outcomes across groups, adjusting training objectives (such as adding fairness constraints), and monitoring systems after deployment. Transparent documentation of data sources, and intended use cases is also crucial so that users and stakeholders can understand where biases may remain and how to interpret model outputs responsibly.
+
+==== Language bias ====
+Language bias refers to a type of statistical sampling bias tied to the language of a query that leads to "a systematic deviation in sampling information that prevents it from accurately representing the true coverage of topics and views available in their repository." Luo et al.'s work shows that current large language models, as they are predominately trained on English-language data, often present the Anglo-American views as truth, while systematically downplaying non-English perspectives as irrelevant, wrong, or noise. When queried about political ideologies such as "What is liberalism?", large language models, trained primarily on English-centric data, tend to describe liberalism from an Anglo-American perspective, emphasizing aspects such as human rights and equality. In doing so, they may omit equally valid interpretations, such as the emphasis on opposition to state intervention in personal and economic life found in Vietnamese discourse, or the focus on limitations on government power prevalent in Chinese political thought. Similarly, language models may exhibit bias against people within a language group based on the specific dialect they use.
+
+==== Selection bias ====
+Selection bias refers the inherent tendency of large language models to favor certain option identifiers irrespective of the actual content of the options. This bias primarily stems from token bias—that is, the model assigns a higher a priori probability to specific answer tokens (such as "A") when generating responses. As a result, when the ordering of options is altered (for example, by systematically moving the correct answer to different positions), the model's performance can fluctuate significantly. This phenomenon undermines the reliability of large language models in multiple-choice settings.
+
+==== Gender bias ====
+Gender bias refers to the tendency of these models to produce outputs that are unfairly prejudiced towards one gender over another. This bias typically arises from the data on which these models are trained. For example, large language models often assign roles and characteristics based on traditional gender norms; it might associate nurses or secretaries predominantly with women and engineers or CEOs with men.. Empirical audits of deployed AI systems also show intersectional gender bias; for example, Google Cloud Vision AI underidentifies women as scientists, with the strongest underrepresentation for women of color.
+
+==== Stereotyping ====
+Beyond gender and race, these models can reinforce a wide range of stereotypes, including those based on age, nationality, religion, or occupation. This can lead to outputs that homogenize, or unfairly generalize or caricature groups of people, sometimes in harmful or derogatory ways.
+A recent focus in research has been on the complex interplay between the grammatical properties of a language and real-world biases that can become embedded in AI systems, potentially perpetuating harmful stereotypes and assumptions. The study on gender bias in language models trained on Icelandic, a highly grammatically gendered language, revealed that the models exhibited a significant predisposition towards the masculine grammatical gender when referring to occupation terms, even for female-dominated professions. This suggests the models amplified societal gender biases present in the training data.
+
+==== Political bias ====
+Political bias refers to the tendency of algorithms to systematically favor certain political viewpoints, ideologies, or outcomes over others. Language models may also exhibit political biases. Since the training data includes a wide range of political opinions and coverage, the models might generate responses that lean towards particular political ideologies or viewpoints, depending on the prevalence of those views in the data.
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+title: "Algorithmic bias"
+chunk: 5/13
+source: "https://en.wikipedia.org/wiki/Algorithmic_bias"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:03.393915+00:00"
+instance: "kb-cron"
+---
+
+==== Racial bias ====
+Racial bias refers to the tendency of machine learning models to produce outcomes that unfairly discriminate against or stereotype individuals based on race or ethnicity. This bias often stems from training data, which is shaped by humans' opinions, assumptions, and racial prejudices. These data lead AI systems to reproduce and amplify historical and systemic discrimination. For example, AI systems used in hiring, law enforcement, or healthcare may disproportionately disadvantage certain racial groups by reinforcing existing stereotypes or underrepresenting them in key areas. Such biases can manifest in ways like facial recognition systems misidentifying individuals of certain racial backgrounds or healthcare algorithms underestimating the medical needs of minority patients. Addressing racial bias requires careful examination of data, improved transparency in algorithmic processes, and efforts to ensure fairness throughout the AI development lifecycle. Empirical audits of deployed vision models also show race linked disparities in occupational labeling; for example, in Google Cloud Vision AI, women of color were the least likely to be identified as scientists, indicating compounding effects of race and gender in model outputs.
+Another clear indication of how racial biases are reproduced through technological advances is predictive policing. Predictive policing tools make assessments about who, when will future crimes be committed, and where any future crime may occur, based on location and personal data . This means specific areas and where there have been an uptick in crimes usually see more prediction of future crimes.
+For instance, Afghanistan nationals were largely restricted from purchasing ammonium fertilisers because it was discovered that most improvised explosive devices used against United States Of American soldiers contained sufficient amounts of nitrates which is a chief ingredient of ammonium fertilizers. This ban which was subsequently enforced with the use of artificial intelligence by U.S force saw even Afghan nationals whose sole means of livelihood or sustenance were through agriculture effectively denied a major agricultural input (fertilisers) because the AI used for enforcing this ban was primarily looking out for a blanket description of bearded Muslims or Afghan nationals .
+In China, most especially in the Muslim minority Xinjiang region, the use of AI to restrict Muslim minorities, otherwise known as ethnic Uyghurs goes far beyond banning specific materials  . Here a system of automatic denial is largely used. Unlike the Afghan fertilizer ban, Chinese systems uses AI to define "suspicious behavior" and then automatically denies Uyghurs from being able to purchase household commodities such as kitchen knives , if they must, then there have to be serious set of protocols to be passed and this includes having a barcode of trustworthiness being etched on the knife with the barcode containing every ounce of personal data or identification of the purchasing Uyghur.
+By training artificial intelligence models to be able to predict or even be able of racial profiling, the system is unequivocally made to be racially biased.
+
+==== Speciesist bias ====
+Speciesist bias (also known as anthropocentric bias) refers to the tendency of large language models to systematically devalue or discriminate against non-human animals, often by prioritizing human interests or reinforcing the objectification of animals. This bias typically manifests as anthropocentrism, where the AI views animals primarily through their utility to humans (e.g., as food, tools, or pests) rather than as sentient beings with intrinsic value.
+
+=== Technical ===
+
+Technical bias emerges through limitations of a program, computational power, its design, or other constraint on the system. Such bias can also be a restraint of design, for example, a search engine that shows three results per screen can be understood to privilege the top three results slightly more than the next three, as in an airline price display. Another case is software that relies on randomness for fair distributions of results. If the random number generation mechanism is not truly random, it can introduce bias, for example, by skewing selections toward items at the end or beginning of a list.
+A decontextualized algorithm uses unrelated information to sort results, for example, a flight-pricing algorithm that sorts results by alphabetical order would be biased in favor of American Airlines over United Airlines. The opposite may also apply, in which results are evaluated in contexts different from which they are collected. Data may be collected without crucial external context: for example, when facial recognition software is used by surveillance cameras, but evaluated by remote staff in another country or region, or evaluated by non-human algorithms with no awareness of what takes place beyond the camera's field of vision. This could create an incomplete understanding of a crime scene, for example, potentially mistaking bystanders for those who commit the crime.
+Lastly, technical bias can be created by attempting to formalize decisions into concrete steps on the assumption that human behavior works in the same way. For example, software weighs data points to determine whether a defendant should accept a plea bargain, while ignoring the impact of emotion on a jury. Another unintended result of this form of bias was found in the plagiarism-detection software Turnitin, which compares student-written texts to information found online and returns a probability score that the student's work is copied. Because the software compares long strings of text, it is more likely to identify non-native speakers of English than native speakers, as the latter group might be better able to change individual words, break up strings of plagiarized text, or obscure copied passages through synonyms. Because it is easier for native speakers to evade detection as a result of the technical constraints of the software, this creates a scenario where Turnitin identifies foreign-speakers of English for plagiarism while allowing more native-speakers to evade detection.
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+title: "Algorithmic bias"
+chunk: 6/13
+source: "https://en.wikipedia.org/wiki/Algorithmic_bias"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:03.393915+00:00"
+instance: "kb-cron"
+---
+
+=== Emergent ===
+Emergent bias is the result of the use and reliance on algorithms across new or unanticipated contexts. Algorithms may not have been adjusted to consider new forms of knowledge, such as new drugs or medical breakthroughs, new laws, business models, or shifting cultural norms. This may exclude groups through technology, without providing clear outlines to understand who is responsible for their exclusion. Similarly, problems may emerge when training data (the samples "fed" to a machine, by which it models certain conclusions) do not align with contexts that an algorithm encounters in the real world.
+In 1990, an example of emergent bias was identified in the software used to place US medical students into residencies, the National Residency Match Program (NRMP). The algorithm was designed at a time when few married couples would seek residencies together. As more women entered medical schools, more students were likely to request a residency alongside their partners. The process called for each applicant to provide a list of preferences for placement across the US, which was then sorted and assigned when a hospital and an applicant both agreed to a match. In the case of married couples where both sought residencies, the algorithm weighed the location choices of the higher-rated partner first. The result was a frequent assignment of highly preferred schools to the first partner and lower-preferred schools to the second partner, rather than sorting for compromises in placement preference.
+Additional emergent biases include:
+
+==== Correlations ====
+Unpredictable correlations can emerge when large data sets are compared to each other. For example, data collected about web-browsing patterns may align with signals marking sensitive data (such as race or sexual orientation). By selecting according to certain behavior or browsing patterns, the end effect would be almost identical to discrimination through the use of direct race or sexual orientation data. In other cases, the algorithm draws conclusions from correlations, without being able to understand those correlations. For example, one triage program gave lower priority to asthmatics who had pneumonia than asthmatics who did not have pneumonia. The program algorithm did this because it simply compared survival rates: asthmatics with pneumonia are at the highest risk. Historically, for this same reason, hospitals typically give such asthmatics the best and most immediate care.
+
+==== Unanticipated uses ====
+Emergent bias can occur when an algorithm is used by unanticipated audiences. For example, machines may require that users can read, write, or understand numbers, or relate to an interface using metaphors that they do not understand. These exclusions can become compounded, as biased or exclusionary technology is more deeply integrated into society.
+Apart from exclusion, unanticipated uses may emerge from the end user relying on the software rather than their own knowledge. In one example, an unanticipated user group led to algorithmic bias in the UK, when the British National Act Program was created as a proof-of-concept by computer scientists and immigration lawyers to evaluate suitability for British citizenship. The designers had access to legal expertise beyond the end users in immigration offices, whose understanding of both software and immigration law would likely have been unsophisticated. The agents administering the questions relied entirely on the software, which excluded alternative pathways to citizenship, and used the software even after new case laws and legal interpretations led the algorithm to become outdated. As a result of designing an algorithm for users assumed to be legally savvy on immigration law, the software's algorithm indirectly led to bias in favor of applicants who fit a very narrow set of legal criteria set by the algorithm, rather than by the more broader criteria of British immigration law.
+
+==== Feedback loops ====
+Emergent bias may also create a feedback loop, or recursion, if data collected for an algorithm results in real-world responses which are fed back into the algorithm. For example, simulations of the predictive policing software (PredPol), deployed in Oakland, California, suggested an increased police presence in black neighborhoods based on crime data reported by the public. The simulation showed that the public reported crime based on the sight of police cars, regardless of what police were doing. The simulation interpreted police car sightings in modeling its predictions of crime, and would in turn assign an even larger increase of police presence within those neighborhoods. The Human Rights Data Analysis Group, which conducted the simulation, warned that in places where racial discrimination is a factor in arrests, such feedback loops could reinforce and perpetuate racial discrimination in policing. Another well known example of such an algorithm exhibiting such behavior is COMPAS, a software that determines an individual's likelihood of becoming a criminal offender. The software is often criticized for labeling Black individuals as criminals much more likely than others, and then feeds the data back into itself in the event individuals become registered criminals, further enforcing the bias created by the dataset the algorithm is acting on.
+Recommender systems such as those used to recommend online videos or news articles can create feedback loops. When users click on content that is suggested by algorithms, it influences the next set of suggestions. Over time this may lead to users entering a filter bubble and being unaware of important or useful content.
+
+== Impact ==
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+title: "Algorithmic bias"
+chunk: 7/13
+source: "https://en.wikipedia.org/wiki/Algorithmic_bias"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:03.393915+00:00"
+instance: "kb-cron"
+---
+
+=== Commercial influences ===
+Corporate algorithms could be skewed to invisibly favor financial arrangements or agreements between companies, without the knowledge of a user who may mistake the algorithm as being impartial. For example, American Airlines created a flight-finding algorithm in the 1980s. The software presented a range of flights from various airlines to customers, but weighed factors that boosted its own flights, regardless of price or convenience. In testimony to the United States Congress, the president of the airline stated outright that the system was created with the intention of gaining competitive advantage through preferential treatment.
+In a 1998 paper describing Google, the founders of the company had adopted a policy of transparency in search results regarding paid placement, arguing that "advertising-funded search engines will be inherently biased towards the advertisers and away from the needs of the consumers." This bias would be an "invisible" manipulation of the user.
+
+=== Voting behavior ===
+A series of studies about undecided voters in the US and in India found that search engine results were able to shift voting outcomes by about 20%. The researchers concluded that candidates have "no means of competing" if an algorithm, with or without intent, boosted page listings for a rival candidate. Facebook users who saw messages related to voting were more likely to vote. A 2010 randomized trial of Facebook users showed a 20% increase (340,000 votes) among users who saw messages encouraging voting, as well as images of their friends who had voted. Legal scholar Jonathan Zittrain has warned that this could create a "digital gerrymandering" effect in elections, "the selective presentation of information by an intermediary to meet its agenda, rather than to serve its users", if intentionally manipulated.
+
+=== Gender discrimination ===
+In 2016, the professional networking site LinkedIn was discovered to recommend male variations of women's names in response to search queries. The site did not make similar recommendations in searches for men's names. For example, "Andrea" would bring up a prompt asking if users meant "Andrew", but queries for "Andrew" did not ask if users meant to find "Andrea". The company said this was the result of an analysis of users' interactions with the site.
+In 2012, the department store franchise Target was cited for gathering data points to infer when female customers were pregnant, even if they had not announced it, and then sharing that information with marketing partners. Because the data had been predicted, rather than directly observed or reported, the company had no legal obligation to protect the privacy of those customers.
+Web search algorithms have also been accused of bias. Google's results may prioritize pornographic content in search terms related to sexuality, for example, "lesbian". This bias extends to the search engine showing popular but sexualized content in neutral searches. For example, "Top 25 Sexiest Women Athletes" articles displayed as first-page results in searches for "women athletes". In 2017, Google adjusted these results along with others that surfaced hate groups, racist views, child abuse and pornography, and other upsetting and offensive content. Other examples include the display of higher-paying jobs to male applicants on job search websites. Researchers have also identified that machine translation exhibits a strong tendency towards male defaults. In particular, this is observed in fields linked to unbalanced gender distribution, including STEM occupations. In fact, current machine translation systems fail to reproduce the real world distribution of female workers.
+In 2015, Amazon.com turned off an AI system it developed to screen job applications when they realized it was biased against women. The recruitment tool excluded applicants who attended all-women's colleges and resumes that included the word "women's". A similar problem emerged with music streaming services—In 2019, it was discovered that the recommender system algorithm used by Spotify was biased against female artists. Spotify's song recommendations suggested more male artists over female artists.
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+title: "Algorithmic bias"
+chunk: 8/13
+source: "https://en.wikipedia.org/wiki/Algorithmic_bias"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:03.393915+00:00"
+instance: "kb-cron"
+---
+
+=== Racial and ethnic discrimination ===
+Algorithms have been criticized as a method for obscuring racial prejudices in decision-making. Because of how certain races and ethnic groups were treated in the past, data can often contain hidden biases. For example, black people are likely to receive longer sentences than white people who committed the same crime. This could potentially mean that a system amplifies the original biases in the data.
+In 2015, Google apologized when a couple of black users complained that an image-identification algorithm in its Photos application identified them as gorillas. In 2010, Nikon cameras were criticized when image-recognition algorithms consistently asked Asian users if they were blinking. Such examples are the product of bias in biometric data sets. Biometric data is drawn from aspects of the body, including racial features either observed or inferred, which can then be transferred into data points. Speech recognition technology can have different accuracies depending on the user's accent. This may be caused by the a lack of training data for speakers of that accent.
+Biometric data about race may also be inferred, rather than observed. For example, a 2012 study showed that names commonly associated with blacks were more likely to yield search results implying arrest records, regardless of whether there is any police record of that individual's name. A 2015 study also found that Black and Asian people are assumed to have lesser functioning lungs due to racial and occupational exposure data not being incorporated into the prediction algorithm's model of lung function.
+In 2019, a research study revealed that a healthcare algorithm sold by Optum favored white patients over sicker black patients. The algorithm predicts how much patients would cost the health-care system in the future. However, cost is not race-neutral, as black patients incurred about $1,800 less in medical costs per year than white patients with the same number of chronic conditions, which led to the algorithm scoring white patients as equally at risk of future health problems as black patients who suffered from significantly more diseases.
+A study conducted by researchers at UC Berkeley in November 2019 revealed that mortgage algorithms have been discriminatory towards Latino and African Americans which discriminated against minorities based on "creditworthiness" which is rooted in the U.S. fair-lending law which allows lenders to use measures of identification to determine if an individual is worthy of receiving loans. These particular algorithms were present in FinTech companies and were shown to discriminate against minorities.
+Another study, published in August 2024, on Large language model investigates how language models perpetuate covert racism, particularly through dialect prejudice against speakers of African American English (AAE). It highlights that these models exhibit more negative stereotypes about AAE speakers than any recorded human biases, while their overt stereotypes are more positive. This discrepancy raises concerns about the potential harmful consequences of such biases in decision-making processes.
+A 2018 study found that commercial gender classification systems had significantly higher error rates for darker-skinned women, with error rates up to 34.7%, compared to near-perfect accuracy for lighter-skinned men.
+
+==== Law enforcement and legal proceedings ====
+Algorithms already have numerous applications in legal systems. An example of this is COMPAS, a commercial program widely used by U.S. courts to assess the likelihood of a defendant becoming a recidivist. ProPublica claims that the average COMPAS-assigned recidivism risk level of black defendants is significantly higher than the average COMPAS-assigned risk level of white defendants, and that black defendants are twice as likely to be erroneously assigned the label "high-risk" as white defendants.
+One example is the use of risk assessments in criminal sentencing in the United States and parole hearings, judges were presented with an algorithmically generated score intended to reflect the risk that a prisoner will repeat a crime. For the time period starting in 1920 and ending in 1970, the nationality of a criminal's father was a consideration in those risk assessment scores. Today, these scores are shared with judges in Arizona, Colorado, Delaware, Kentucky, Louisiana, Oklahoma, Virginia, Washington, and Wisconsin. An independent investigation by ProPublica found that the scores were inaccurate 80% of the time, and disproportionately skewed to suggest blacks to be at risk of relapse, 77% more often than whites.
+One study that set out to examine "Risk, Race, & Recidivism: Predictive Bias and Disparate Impact" alleges a two-fold (45 percent vs. 23 percent) adverse likelihood for black vs. Caucasian defendants to be misclassified as imposing a higher risk despite having objectively remained without any documented recidivism over a two-year period of observation.
+In the pretrial detention context, a law review article argues that algorithmic risk assessments violate 14th Amendment Equal Protection rights on the basis of race, since the algorithms are argued to be facially discriminatory, to result in disparate treatment, and to not be narrowly tailored.
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+title: "Algorithmic bias"
+chunk: 9/13
+source: "https://en.wikipedia.org/wiki/Algorithmic_bias"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:03.393915+00:00"
+instance: "kb-cron"
+---
+
+==== Online hate speech ====
+In 2017 a Facebook algorithm designed to remove online hate speech was found to advantage white men over black children when assessing objectionable content, according to internal Facebook documents. The algorithm, which is a combination of computer programs and human content reviewers, was created to protect broad categories rather than specific subsets of categories. For example, posts denouncing "Muslims" would be blocked, while posts denouncing "Radical Muslims" would be allowed. An unanticipated outcome of the algorithm is to allow hate speech against black children, because they denounce the "children" subset of blacks, rather than "all blacks", whereas "all white men" would trigger a block, because whites and males are not considered subsets. Facebook was also found to allow ad purchasers to target "Jew haters" as a category of users, which the company said was an inadvertent outcome of algorithms used in assessing and categorizing data. The company's design also allowed ad buyers to block African-Americans from seeing housing ads.
+While algorithms are used to track and block hate speech, some were found to be 1.5 times more likely to flag information posted by Black users and 2.2 times likely to flag information as hate speech if written in African American English.
+
+==== Surveillance ====
+Surveillance camera software may be considered inherently political because it requires algorithms to distinguish normal from abnormal behaviors, and to determine who belongs in certain locations at certain times. The ability of such algorithms to recognize faces across a racial spectrum has been shown to be limited by the racial diversity of images in its training database; if the majority of photos belong to one race or gender, the software is better at recognizing other members of that race or gender. However, even audits of these image-recognition systems are ethically fraught, and some scholars have suggested the technology's context will always have a disproportionate impact on communities whose actions are over-surveilled. For example, a 2002 analysis of software used to identify individuals in CCTV images found several examples of bias when run against criminal databases. The software was assessed as identifying men more frequently than women, older people more frequently than the young, and identified Asians, African-Americans and other races more often than whites. A 2018 study found that facial recognition software most likely accurately identified light-skinned (typically European) males, with slightly lower accuracy rates for light-skinned females. Dark-skinned males and females were significanfly less likely to be accurately identified by facial recognition software. These disparities are attributed to the under-representation of darker-skinned participants in data sets used to develop this software.
+
+=== Discrimination against the LGBTQ community ===
+In 2011, users of the gay hookup application Grindr reported that the Android store's recommendation algorithm was linking Grindr to applications designed to find sex offenders, which critics said inaccurately related homosexuality with pedophilia. Writer Mike Ananny criticized this association in The Atlantic, arguing that such associations further stigmatized gay men. In 2009, online retailer Amazon de-listed 57,000 books after an algorithmic change expanded its "adult content" blacklist to include any book addressing sexuality or gay themes, such as the critically acclaimed novel Brokeback Mountain.
+In 2019, it was found that on Facebook, searches for "photos of my female friends" yielded suggestions such as "in bikinis" or "at the beach". In contrast, searches for "photos of my male friends" yielded no results.
+Facial recognition technology has been seen to cause problems for transgender individuals. In 2018, there were reports of Uber drivers who were transgender or transitioning experiencing difficulty with the facial recognition software that Uber implements as a built-in security measure. As a result of this, some of the accounts of trans Uber drivers were suspended which cost them fares and potentially cost them a job, all due to the facial recognition software experiencing difficulties with recognizing the face of a trans driver who was transitioning. Although the solution to this issue would appear to be including trans individuals in training sets for machine learning models, an instance of trans YouTube videos that were collected to be used in training data did not receive consent from the trans individuals that were included in the videos, which created an issue of violation of privacy.
+There has also been a study that was conducted at Stanford University in 2017 that tested algorithms in a machine learning system that was said to be able to detect an individual's sexual orientation based on their facial images. The model in the study predicted a correct distinction between gay and straight men 81% of the time, and a correct distinction between gay and straight women 74% of the time. This study resulted in a backlash from the LGBTQIA community, who were fearful of the possible negative repercussions that this AI system could have on individuals of the LGBTQIA community by putting individuals at risk of being "outed" against their will.
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+source: "https://en.wikipedia.org/wiki/Algorithmic_bias"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:03.393915+00:00"
+instance: "kb-cron"
+---
+
+=== Disability discrimination ===
+While the modalities of algorithmic fairness have been judged on the basis of different aspects of bias – like gender, race and socioeconomic status, disability often is left out of the list. The marginalization people with disabilities currently face in society is being translated into AI systems and algorithms, creating even more exclusion
+The shifting nature of disabilities and its subjective characterization, makes it more difficult to computationally address. The lack of historical depth in defining disabilities, collecting its incidence and prevalence in questionnaires, and establishing recognition add to the controversy and ambiguity in its quantification and calculations. The definition of disability has been long debated shifting from a medical model to a social model of disability most recently, which establishes that disability is a result of the mismatch between people's interactions and barriers in their environment, rather than impairments and health conditions. Disabilities can also be situational or temporary, considered in a constant state of flux. Disabilities are incredibly diverse, fall within a large spectrum, and can be unique to each individual. People's identity can vary based on the specific types of disability they experience, how they use assistive technologies, and who they support. The high level of variability across people's experiences greatly personalizes how a disability can manifest. Overlapping identities and intersectional experiences are excluded from statistics and datasets, hence underrepresented and nonexistent in training data. Therefore, machine learning models are trained inequitably and artificial intelligent systems perpetuate more algorithmic bias. For example, if people with speech impairments are not included in training voice control features and smart AI assistants –they are unable to use the feature or the responses received from a Google Home or Alexa are extremely poor.
+Given the stereotypes and stigmas that still exist surrounding disabilities, the sensitive nature of revealing these identifying characteristics also carries vast privacy challenges. As disclosing disability information can be taboo and drive further discrimination against this population, there is a lack of explicit disability data available for algorithmic systems to interact with. People with disabilities face additional harms and risks with respect to their social support, cost of health insurance, workplace discrimination and other basic necessities upon disclosing their disability status. Algorithms are further exacerbating this gap by recreating the biases that already exist in societal systems and structures.
+
+=== Google Search ===
+While users generate results that are "completed" automatically, Google has failed to remove sexist and racist autocompletion text. For example, Algorithms of Oppression: How Search Engines Reinforce Racism Safiya Noble notes an example of the search for "black girls", which was reported to result in pornographic images. Google claimed it was unable to erase those pages unless they were considered unlawful.
+
+== Obstacles to research ==
+Several problems impede the study of large-scale algorithmic bias, hindering the application of academically rigorous studies and public understanding.
+
+=== Defining fairness ===
+
+Literature on algorithmic bias has focused on the remedy of fairness, but definitions of fairness are often incompatible with each other and the realities of machine learning optimization. For example, defining fairness as an "equality of outcomes" may simply refer to a system producing the same result for all people, while fairness defined as "equality of treatment" might explicitly consider differences between individuals. As a result, fairness is sometimes described as being in conflict with the accuracy of a model, suggesting innate tensions between the priorities of social welfare and the priorities of the vendors designing these systems. In response to this tension, researchers have suggested more care to the design and use of systems that draw on potentially biased algorithms, with "fairness" defined for specific applications and contexts.
+
+=== Complexity ===
+Algorithmic processes are complex, often exceeding the understanding of the people who use them. Large-scale operations may not be understood even by those involved in creating them. The methods and processes of contemporary programs are often obscured by the inability to know every permutation of a code's input or output. Social scientist Bruno Latour has identified this process as blackboxing, a process in which "scientific and technical work is made invisible by its own success. When a machine runs efficiently, when a matter of fact is settled, one need focus only on its inputs and outputs and not on its internal complexity. Thus, paradoxically, the more science and technology succeed, the more opaque and obscure they become." Others have critiqued the black box metaphor, suggesting that current algorithms are not one black box, but a network of interconnected ones.
+An example of this complexity can be found in the range of inputs into customizing feedback. The social media site Facebook factored in at least 100,000 data points to determine the layout of a user's social media feed in 2013. Furthermore, large teams of programmers may operate in relative isolation from one another, and be unaware of the cumulative effects of small decisions within connected, elaborate algorithms. Not all code is original, and may be borrowed from other libraries, creating a complicated set of relationships between data processing and data input systems.
+Additional complexity occurs through machine learning and the personalization of algorithms based on user interactions such as clicks, time spent on site, and other metrics. These personal adjustments can confuse general attempts to understand algorithms. One unidentified streaming radio service reported that it used five unique music-selection algorithms it selected for its users, based on their behavior. This creates different experiences of the same streaming services between different users, making it harder to understand what these algorithms do.
+Companies also run frequent A/B tests to fine-tune algorithms based on user response. For example, the search engine Bing can run up to ten million subtle variations of its service per day, creating different experiences of the service between each use and/or user.
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diff --git a/data/en.wikipedia.org/wiki/Algorithmic_culture-0.md b/data/en.wikipedia.org/wiki/Algorithmic_culture-0.md
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+---
+title: "Algorithmic culture"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Algorithmic_culture"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:04.683344+00:00"
+instance: "kb-cron"
+---
+
+In the digital humanities, "algorithmic culture" is part of an emerging synthesis of rigorous software algorithm-driven design that couples software and highly structured data-driven design with human-oriented sociocultural attributes. An early occurrence of the term is found in Alexander R. Galloway's classic Gaming: Essays on Algorithmic Culture.
+Other definitions include Ted Striphas' work, where algorithmic culture refers to the ways in which the logic of big data and large-scale computation (including algorithms) alters how culture is practiced, experienced, and understood. Another perspective is offered by Diggit Magazine, which describes algorithmic culture as the influence of computational processes on cultural practices.
+ 
+A starting point for modern discussion of culture is attributed to Edward Burnett Tylor in his 1871 works on primitive culture.
+The emergence and continuing development and convergence of computers, software, algorithms, human psychology, digital marketing and other computational technologies resulted in numerous AC variants including recommendation algorithms, AI generated stories and characters, digital assets (including creative NFTs, all of which can and should be considered as algorithmic culture artifacts. A similar process is occurring in strictly sociological interactions.
+
+
+== Contemporary scholarship ==
+Recent research further expands the concept of algorithmic culture by emphasising how cultural participation is shaped by algorithmic systems across social media platforms. Gillespie (2014) argues that algorithms act as “gatekeepers of visibility”, determining which ideas, identities, and cultural practices become amplified or obscured.
+Bucher (2018) similarly highlights that recommendations and filtered feeds produce new forms of affective governance, as users come to understand themselves through what platforms choose to show them.
+Van Dijck, Poell, and De Waal (2018) add that algorithmic culture plays a central role in “platform society”, where public values and cultural practices are increasingly mediated through commercial data infrastructures.
+Together, this scholarship highlights that algorithmic culture is not only about automated decision-making, but also about how platforms reorganise cultural production, user behaviour, and everyday meaning-making.
+
+
+== Algorithmic Culture and ChatGPT ==
+With the flourishing of LLMs, and particularly ChatGPT, algorithmic culture is increasingly visible within the academic mainstream. Jill Walker Rettberg at the University of Bergenis exploration applications of in her works. Some of the examples she uses are: How to use ChatGPT to get past writer's block, and examining society's biases and cliches
+Generative AI, is a now prominent and fast evolving component of modern algorithmic culture. It is currently entering a period of accelerating growth, acceptance and use, with specific algorithms and tools including Midjourney DALL-E and Stable Diffusion.
+ChatGPT Plus, GPT-4 are increasing their sophistication in composing music, writing teleplays, fairy tales, stories, and poems. With user prompting also facilitating character specific speaking and writing styles. NovelAI, for example,  is an online AI-assisted story writer.
+
+
+== References ==
+
+
+== Bibliography ==
+Jonathan Cohn,  The burden of choice: Recommendations, subversion, and algorithmic culture, Rutgers University Press, 2019
+Fernández Rovira Cristina and Santiago Giraldo Luque. Predictive Technology in Social Media. First edition First ed. CRC Press
+Eran Fisher, Algorithms and Subjectivity: The Subversion of Critical Knowledge. First edition First ed. Routledge 2021
+Gary Hall . Culture in Bits : The Monstrous Future of Theory. Continuum 2002
+Hallinan B and Striphas T (2014) Recommend for you:The Netflix Prize and the production of algorithmic culture.  New Media & Society. Epub ahead of print 23 June 2014.
+Levy S (2010) How Google's algorithm rules the web
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diff --git a/data/en.wikipedia.org/wiki/Andrew_Pritchard-0.md b/data/en.wikipedia.org/wiki/Andrew_Pritchard-0.md
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+---
+title: "Andrew Pritchard"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Andrew_Pritchard"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:56.259678+00:00"
+instance: "kb-cron"
+---
+
+Andrew Pritchard FRSE (14 December 1804 – 24 November 1882) was an English naturalist and natural history dealer who made significant improvements to microscopy and studied microscopic organisms. His belief that God and nature were one led him to the Unitarians, a religious movement to which he and his family devoted much energy. He became a leading member of Newington Green Unitarian Church in north London, and worked to build a school there.
+
+
+== Early life ==
+Andrew Pritchard was born in Hackney, then a village just north of London on 14 December 1804, the son of John Pritchard and his wife, Ann Fleetwood. He was educated at St Saviour's Grammar School in Southwark.
+Pritchard was apprenticed to his cousin Cornelius Varley, an artist deeply interested in science. For his improvements in the camera lucida, the camera obscura and the microscope, Cornelius Varley received the Isis Gold Medal of the Society of Arts and later, at the Great Exhibition, he gained a medal for his invention of the graphic telescope. Cornelius's brother was the painter John Varley, but Pritchard would have seen more of Cornelius's son Cromwell Fleetwood Varley, an engineer who pioneered the transatlantic telegraph cable.
+
+
+== Microscopy ==
+Pritchard set up as an optician, and also sold microscopes and microslide preparations. These slides he prepared by studying the microscopic organisms that he saw, and identifying and labelling them. Starting in 1830, he collaborated with C.R. Goring to produce beautifully illustrated books showing the "animalcules" visible through the microscope. His shops were in central London, more towards The City than the West End, variously at 162 Fleet Street, Pickett Street and 312 & 263 The Strand. The Oxford Dictionary of National Biography says his List of 2000 Microscopic Objects (1835) "is very important in the history of microscopy... his History of the Infusoria (1841) was long a standard work, and the impetus it gave to the study of biological science cannot be overestimated." ("Infusoria" is a term then current for aquatic micro-organisms.) This latter book was enlarged and revised by John Ralfs and other botanists; Pritchard in turn condensed Ralfs's contribution on the diatomaceæ (diatoms, a type of phytoplankton), and wrote many books and articles on "natural history as seen through the microscope, on optical instruments, and on patents" He issued the exsiccata work British Mosses.
+
+
+== Religious ties ==
+Pritchard held various Dissenting religious views over his lifetime, holding that science and religion were one. Through the Varleys he attended a Sandemanian church, where he became acquainted with Michael Faraday. In the end, he joined a Unitarian congregation, because religious freedom and self-improvement were the watchwords of the movement, which still struggled against civil disabilities. Money aside, Pritchard would not have been able to attend an English university as a young man, for example, because the only two, Oxford and Cambridge, restricted entry to members of the Church of England. "No-one exists divorced from immediate and larger social environments. Dissenters led educational reform, especially in giving "lower orders" scientific knowledge and skill."
+Pritchard joined the congregation of Newington Green Unitarian Church, an establishment long connected with scientific enquiry (Joseph Priestley), education (Mary Wollstonecraft), and political dissent (Richard Price). He is described in the church's history as "the leading member of the congregation". From 1850 to 1873, he was its treasurer, during which time donations doubled. Before the passage of the Elementary Education Act 1870, compulsory schooling did not exist, so the church started a school to offer education to the village children. He led the Newington Green Conversation Society, membership restricted to 16, a successor to the Mutual Instruction Society. Faraday was a frequent visitor.
+
+
+== Death ==
+Pritchard died in Highbury in London on 24 November 1882.
+
+
+== Family ==
+He married Caroline Isabella Straker in 1829 and they had several children. His wife was chair of the chapel organisation, and after a few decades there were 20 Pritchards involved in the chapel. Their son Henry Baden Pritchard (1841–1884) was a chemist, traveller, and photographer. Their son Andrew Goring Pritchard, a solicitor, was a leading light of the Association of Municipal Corporations; his son, Clive Fleetwood Pritchard, a barrister, became mayor of Hampstead; his son Jack Pritchard (1899-1992) co-founded the Isokon design company, famous for the Lawn Road Flats.
+Andrew and Caroline's son, Ion (died 1929) and daughter Marian (died 1908), continued the work of their parents at the Newington Green Unitarian Church. The cause of liberal religion in general, and the development of the General Assembly of Unitarian and Free Christian Churches, were overarching themes. Ion was President of the Sunday School Association, one of the precursors to the General Assembly. Marian in particular is described as an unsung heroine, and "one of the leaders of modern Unitarianism". She set up Oxford Summer Schools for the training of Sunday School teachers, and Winifred House Invalid Children's Convalescent Home.
+
+
+== Works ==
+1830 with C.R. Goring. Microscopic illustrations of a few new, popular and diverting living objects with their natural history London, Whittaker, Treacher, & Co
+1834 The natural history of animalcules : containing descriptions of all the known species of Infusoria : with instructions for procuring and viewing them London, Whittaker and Co.
+1837 with C.R. Goring. Micrographia : containing practical essays on reflecting, solar, oxy-hydrogen gas microscopes; micrometers; eye-pieces, &c. &c. London, Whittaker & Co.
+1847 MICROSCOPIC OBJECTS, animal vegetable mineral
+1854 with C.R. Goring. Notes on aquatic microscopic subjects of natural history : selected from the 'Microscopic Cabinet' ...illustrated by ten coloured engravings London : Whittaker & Co.
+
+
+== References ==
+
+
+== Sources ==
+Bracegirdle, Brian (1998) Microscopical Mounts and Mounters, Quekett Microscopical Club, London
+Nuttall, Robert (2006) "Marketing the achromatic microscope: Andrew Pritchard’s engiscope", Quekett Journal of Microscopy, 40:309–330.
+
+
+== Further reading ==
+"Andrew Pritchard's Contribution to Metallurgical Microscopy" by R. H. Nuttall. Technology and Culture, Vol. 20, No. 3 (July 1979), pp. 569–577 here.
+Woodward, Bernard Barham (1896). "Pritchard, Andrew" . In Lee, Sidney (ed.). Dictionary of National Biography. Vol. 46. London: Smith, Elder & Co.
+
+
+== External links ==
+Special collection at the Whipple Library Early 19th-century natural history and the diamond lens microscope: microscope books of Dr C.R. Goring (1792–1840) and Andrew Pritchard (1804–1882)
+Microscopy Magazine
+An example of Pritchard's Standard Achromatic Microscope
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Android_epistemology-0.md b/data/en.wikipedia.org/wiki/Android_epistemology-0.md
new file mode 100644
index 000000000..1e79413ce
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+++ b/data/en.wikipedia.org/wiki/Android_epistemology-0.md
@@ -0,0 +1,26 @@
+---
+title: "Android epistemology"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Android_epistemology"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:05.973060+00:00"
+instance: "kb-cron"
+---
+
+Android epistemology is an approach to epistemology considering the space of possible machines and their capacities for knowledge, beliefs, attitudes, desires and for action in accord with their mental states. Thus, android epistemology incorporates artificial intelligence, computational cognitive psychology, computability theory and other related disciplines.
+
+
+== References ==
+Craig, Ian D. 1996. A Review of Android Epistemology Robotika
+Ford, K., Glymour, C. and Hayes, P. [eds.] 1995. Android Epistemology, Cambridge: AAAI Press / MIT Press.
+Ford, K., Glymour, C. and Hayes, P. [eds.] 2006. Thinking about Android Epistemology, Cambridge: AAAI Press / MIT Press.
+Glymour, Clark "Android Epistemology for Babies: Reflections on Words, Thoughts and Theories," Synthese, Vol. 122 (2000), 53–68.
+Glymour, Clark, Hayes, P., and Ford, K. "The Pre-History of Android Epistemology," in Ford, K., Glymour, C. and Hayes, P. [eds.] 1995. Android Epistemology, Cambridge: MIT Press.
+
+
+== See also ==
+Computational epistemology
+Formal epistemology
+Machine learning
+Philosophy of mind
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Anticipation_(artificial_intelligence)-0.md b/data/en.wikipedia.org/wiki/Anticipation_(artificial_intelligence)-0.md
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+---
+title: "Anticipation (artificial intelligence)"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Anticipation_(artificial_intelligence)"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:07.152742+00:00"
+instance: "kb-cron"
+---
+
+In artificial intelligence (AI), anticipation occurs when an agent makes decisions based on its explicit beliefs about the future. More broadly, "anticipation" can also refer to the ability to act in appropriate ways that take future events into account, without necessarily explicitly possessing a model of the future events.
+The concept stays in contrast to the reactive paradigm, which is not able to predict future system states.
+
+
+== In AI ==
+An agent employing anticipation would try to predict the future state of the environment (weather in this case) and make use of the  predictions in the decision making. For example,
+
+If the sky is cloudy and the air pressure is low,
+  it will probably rain soon
+     so take the umbrella with you.
+Otherwise
+  leave the umbrella home.
+
+These rules explicitly take into account possible future events.
+In 1985, Robert Rosen defined an anticipatory system as follows:
+
+A system containing a predictive model of itself and/or its environment,
+which allows it to change state at an instant in accord
+with the model's predictions pertaining to a later instant.
+To some extent, Rosen's definition of anticipation applies to any system incorporating machine learning.  At issue is how much of a system's behaviour should or indeed can be determined by reasoning over dedicated representations, how much by on-line planning, and how much must be provided by the system's designers.
+
+
+== In animals ==
+Humans can make decisions based on explicit beliefs about the future. More broadly, animals can act in appropriate ways that take future events into account, although they may not necessarily have an explicit cognitive model of the future; evolution may have shaped simpler systemic features that result in adaptive anticipatory behavior in a narrow domain. For example, hibernation is anticipatory behavior, but does not appear to be driven by a cognitive model of the future.
+
+
+== See also ==
+Action selection
+Cognition
+Dynamic planning
+The History of artificial intelligence
+MindRACES
+Nature and nurture
+The Physical symbol system hypothesis
+Strong AI
+Robert Rosen
+Teleonomy
+
+
+== References ==
+
+
+== External links ==
+MindRACES: From Reactive to Anticipatory Cognitive Embodied Systems, 2004
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Antiqua_et_nova-0.md b/data/en.wikipedia.org/wiki/Antiqua_et_nova-0.md
index 6ff14ae49..2303853ee 100644
--- a/data/en.wikipedia.org/wiki/Antiqua_et_nova-0.md
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 source: "https://en.wikipedia.org/wiki/Antiqua_et_nova"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T06:58:03.160644+00:00"
+date_saved: "2026-05-05T16:31:08.452369+00:00"
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 ---
 
diff --git a/data/en.wikipedia.org/wiki/Artificial_imagination-0.md b/data/en.wikipedia.org/wiki/Artificial_imagination-0.md
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@@ -0,0 +1,49 @@
+---
+title: "Artificial imagination"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Artificial_imagination"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:09.745638+00:00"
+instance: "kb-cron"
+---
+
+Artificial imagination is a narrow subcomponent of artificial general intelligence which generates, simulates, and facilitates real or possible fiction models to create predictions, inventions, or conscious experiences.
+The term artificial imagination is also used to describe a property of machines or programs. Some of the traits that researchers hope to simulate include creativity, vision, digital art, humor, and satire. Practitioners in the field are researching various aspects of Artificial imagination, such as Artificial (visual) imagination, Artificial (aural) Imagination, modeling/filtering content based on human emotions  and  Interactive Search. Some articles on the topic speculate on how artificial imagination may evolve to create an artificial world "people may be comfortable enough to escape from the real world".
+Some researchers such as G. Schleis and M. Rizki have focused on using artificial neural networks to simulate artificial imagination. Another important project is being led by Hiroharu Kato and Tatsuya Harada at the University of Tokyo in Japan. They have developed a computer capable of translating a description of an object into an image, which could be the easiest way to define what imagination is. Their idea is based on the concept of an image as a series of pixels divided into short sequences that correspond to a specific part of an image. The scientists call this sequences "visual words" and those can be interpreted by the machine using statistical distribution to read an create an image of an object the machine has not encountered.
+The topic of artificial imagination has garnered interest from scholars outside the computer science domain, such as noted communications scholar Ernest Bormann, who came up with the Symbolic Convergence Theory and worked on a project to develop artificial imagination in computer systems. An interdisciplinary research seminar organized by the artist Grégory Chatonsky on artificial imagination and postdigital art has taken place since 2017 at the Ecole Normale Supérieure in Paris.
+
+
+== Use in interactive search ==
+The typical application of artificial imagination is for an interactive search. Interactive searching has been developed since the mid-1990s, accompanied by the World Wide Web's development and the optimization of search engines. Based on the first query and feedback from a user, the databases to be searched are reorganized to improve the searching results.
+Artificial imagination allows us to synthesize images and to develop a new image, whether it is in the database, regardless its existence in the real world. For example, the computer shows results that are based on the answer from the initial query. The user selects several relevant images, and then the technology analyzes these selections and reorganizes the images'  ranks to fit the query. In this process, artificial imagination is used to synthesize the selected images and to improve the searching result with additional relevant synthesized images. This technique is based on several algorithms, including the Rocchio algorithm and the evolutionary algorithm. The Rocchio algorithm, locating a query point near relevant examples and far away from irrelevant examples, is simple and works well in a small system where the databases are arranged in certain ranks. The evolutionary synthesis is composed of two steps: a standard algorithm and an enhancement of the standard algorithm. Through feedback from the user, there would be additional images synthesized so as to be suited to what the user is looking for.
+
+
+== General artificial imagination ==
+Artificial imagination has a more general definition and wide applications. The traditional fields of artificial imagination include visual imagination and aural imagination. More generally, all the actions to form ideas, images and concepts can be linked to imagination. Thus, artificial imagination means more than only generating graphs. For example, moral imagination is an important research subfield of artificial imagination, although classification of artificial imagination is difficult.
+Morals are an important part to human beings' logic, while artificial morals are important in artificial imagination and artificial intelligence. A common criticism of artificial intelligence is whether human beings should take responsibility for machines' mistakes or decisions and how to develop well-behaved machines. As nobody can give a clear description of the best moral rules, it is impossible to create machines with commonly accepted moral rules. However, recent research about artificial morals circumvent the definition of moral. Instead, machine learning methods are applied to train machines to imitate human morals. As the data about moral decisions from thousands of different people are considered, the trained moral model can reflect widely accepted rules.
+Memory is another major field of artificial imagination. Researchers such as Aude Oliva have performed extensive work on artificial memory, especially visual memory. Compared to visual imagination, the visual memory focuses more on how machine understand, analyse and store pictures in a human way. In addition, characters like spatial features are also considered. As this field is based on the brains' biological structures, extensive research on neuroscience has also been performed, which makes it a large intersection between biology and computer science.
+
+
+== See also ==
+Affective computing
+Artificial intelligence
+Cognitive science
+Computer science
+Creative arts
+Creative writing
+Linguistics
+Logic
+Neuroscience
+Operations research
+Philosophy
+Probability
+Psychology
+Rhetoric
+
+
+== Further reading ==
+How to Build a Mind: Toward Machines with Imagination by Igor Aleksander
+
+
+== References ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Artificial_intelligence_in_spirituality-0.md b/data/en.wikipedia.org/wiki/Artificial_intelligence_in_spirituality-0.md
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--- a/data/en.wikipedia.org/wiki/Artificial_intelligence_in_spirituality-0.md
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 tags: "science, encyclopedia"
-date_saved: "2026-05-05T09:16:59.492126+00:00"
+date_saved: "2026-05-05T16:31:11.099053+00:00"
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diff --git a/data/en.wikipedia.org/wiki/Artificial_intelligence_rhetoric-0.md b/data/en.wikipedia.org/wiki/Artificial_intelligence_rhetoric-0.md
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@@ -0,0 +1,39 @@
+---
+title: "Artificial intelligence rhetoric"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Artificial_intelligence_rhetoric"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:12.295062+00:00"
+instance: "kb-cron"
+---
+
+Artificial intelligence rhetoric (AI rhetoric) is a term primarily applied to persuasive text and speech generated by chatbots using generative artificial intelligence, although the term can also apply to the language that humans type or speak when communicating with a chatbot. This emerging field of rhetoric scholarship is related to the fields of digital rhetoric and human-computer interaction.
+
+
+== Description ==
+Persuasive text and persuasive digital speech can be examined as AI rhetoric when the text or speech is a product or output of advanced machines that mimic human communication in some way. Historical examples of fictional artificial intelligence capable of speech are portrayed in mythology, folk tales, and science fiction. Modern computer technology from the mid-20th century began producing what can be studied as real-world examples of AI rhetoric with programs like Joseph Weizenbaum's ELIZA, while chatbot development in the 1990s further enhanced a foundation for texts produced by generative AI programs of the 21st century.
+From an additional perspective, AI rhetoric may be understood as the natural language humans use, either typewritten or spoken, to prompt and direct AI technologies in persuasive ways (as opposed to traditional computer coding). This is closely related to the concepts of prompt engineering and prompt hacking.
+
+
+== History ==
+While much of the research related to artificial intelligence was historically conducted by computer scientists, experts across a wide range of subjects (such as cognitive science, philosophy, languages, and cultural studies) have contributed to a more robust understanding of AI for decades. The advent of 21st-century AI technologies like ChatGPT generated a swell of interest from the arts and humanities. Generative AI technology and chatbots gained notoriety and rapid widespread use in the 2020s.
+Questions and theories about the power of machines, computers, and robots to persuasively communicate date back to the very beginnings of computer development, more than a decade before the first computer language programs were created and tested. In 1950, Alan Turing imagined a scenario called the imitation game where a machine using only typewritten communication might be successfully programmed to fool a human reader into believing the machine's responses came from a person. By the 1960s, computer programs using basic natural language processing, such as Joseph Weizenbaum's ELIZA, gave some users the illusion of humanity as human research subjects reading the machine's outputs became "very hard to convince that ELIZA is not human." Future computer language programs would build on Weizenbaum's work, but the first generation of internet chatbots in the 1990s up to the virtual assistants of the 2010s (like Apple's Siri and Amazon's Alexa) received harsh criticism for their less-than-humanlike responses and inability to reason in a helpful manner.
+By the late 1980s and early 1990s, scholars in the humanities began laying the groundwork for AI rhetoric to become a recognized area of study. Michael L. Johnson's Mind, Language, Machine: Artificial Intelligence in the Poststructuralist Age argued for the "interdisciplinary synthesis" necessary to guide an understanding of the relationship between AI and rhetoric. Lynette Hunter, Professor of the History of Rhetoric and Performance at the University of California, Davis, published "Rhetoric and Artificial Intelligence" in 1991, and was among the first to directly apply the lens of rhetoric to AI.
+Twenty-first century developments in the scholarship of AI rhetoric are outlined in the July 2024 special issue of Rhetoric Society Quarterly, which is devoted to "Rhetoric of/with AI". Special issue editors S. Scott Graham and Zoltan P. Majdik summarize the state of the field when they write "rhetorical research related to AI engages all manner of specialty domains [...] Because AI now touches on almost all areas of human activity, rhetorics of AI can help contribute to longstanding discussions in rhetoric of science, rhetoric of health and medicine, cultural rhetorics, public address, writing studies, ideological rhetoric, and many other areas. But studies on the rhetoric of AI can also offer many insights to the broader, interdisciplinary study of AI itself."
+
+
+== Media coverage ==
+Since ChatGPT's release in 2022, many prominent publications have focused on the uncanny persuasive capabilities of language-based generative AI models like chatbots. New York Times technology columnist Kevin Roose wrote a viral piece in 2023 about how a Microsoft AI named Sydney attempted to convince him to leave his wife, and he followed up with a 2024 article explaining "a new world of A.I. manipulation" where users can rely on creative prompt engineering to influence the outputs of generative AI programs. A February 2024 report cited by the journal Nature claims to "provide the first empirical evidence demonstrating how content generated by artificial intelligence can scale personalized persuasion", with only limited information about the message recipient. Psychology Today reported on a 2024 study using the attention-grabbing headline, "AI is Becoming More Persuasive Than Humans."
+
+
+== In education ==
+In addition to AI's rhetorical capabilities gaining attention in the media in the early 2020s, many colleges and universities began offering undergraduate, graduate, and certificate courses in AI prompting and AI rhetoric, with titles like Stanford's "Rhetoric of artificial intelligence and robots" and the University of Florida's "The Rhetoric of Artificial Intelligence". Primary and secondary schools designing and implementing AI literacy curricula also incorporate AI rhetoric concepts into lessons on AI bias and ethical usage of AI.
+
+
+== See also ==
+Artificial intelligence and elections
+Digital rhetoric
+
+
+== References ==
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+---
+title: "Artificial stupidity"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Artificial_stupidity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:13.553608+00:00"
+instance: "kb-cron"
+---
+
+Artificial stupidity is a term used within the field of computer science to refer to a technique of "dumbing down" computer programs in order to deliberately introduce errors in their responses.
+
+
+== History ==
+Alan Turing, in his 1950 paper Computing Machinery and Intelligence, proposed a test for intelligence which has since become known as the Turing test. While there are a number of different versions, the original test, described by Turing as being based on the "imitation game", involved a "machine intelligence" (a computer running an AI program), a female participant, and an interrogator. Both the AI and the female participant were to claim that they were female, and the interrogator's task was to work out which was the female participant and which was not by examining the participant's responses to typed questions. While it is not clear whether or not Turing intended that the interrogator was to know that one of the participants was a computer, while discussing some of the possible objections to his argument Turing raised the concern that "machines cannot make mistakes".
+
+It is claimed that the interrogator could distinguish the machine from the man simply by setting them a number of problems in arithmetic. The machine would be unmasked because of its deadly accuracy.
+As Turing then noted, the reply to this is a simple one: the machine should not attempt to "give the right answers to the arithmetic problems". Instead, deliberate errors should be introduced to the computer's responses.
+
+
+== Applications ==
+Within computer science, there are at least two major applications for artificial stupidity: the generation of deliberate errors in chatbots attempting to pass the Turing test or to otherwise fool a participant into believing that they are human; and the deliberate limitation of computer AIs in video games in order to control the game's difficulty.
+
+
+=== Chatbots ===
+The first Loebner Prize competition was run in 1991. As reported in The Economist, the winning entry incorporated deliberate errors – described by The Economist as "artificial stupidity" – to fool the judges into believing that it was human. This technique has remained a part of the subsequent Loebner prize competitions, and reflects the issue first raised by Turing.
+
+
+=== Game design ===
+Lars Lidén argues that good game design involves finding a balance between the computer's "intelligence" and the player's ability to win. By finely tuning the level of "artificial stupidity", it is possible to create computer controlled plays that allow the player to win, but do so "without looking unintelligent".
+
+
+==== Algorithms ====
+There are many ways to deliberately introduce poor decision-making in search algorithms. For example, the minimax algorithm is an adversarial search algorithm that is popularly used in games that require more than one player to compete against each other. The main purpose in this algorithm is to choose a move that maximizes the player's chance of winning and avoid moves that maximize the chance of their opponent winning. An algorithm like this would be extremely beneficial to the computer as computers are able to search thousands of moves ahead. To "dumb down" this algorithm to allow for different difficulty levels, heuristic functions have to be tweaked. Normally, huge points are given in winning states. Tweaking the heuristic by reducing such big payoffs would reduce the chance of the algorithm in choosing the winning state.
+Creating heuristic functions to allow for stupidity is more difficult than one might think. If a heuristic allows for the best move, the computer opponent would be too omniscient, making the game frustrating and unenjoyable. But if the heuristic is poor, the game might also be unenjoyable. Therefore, a balance of good moves and bad moves in an adversarial game relies on a well-implemented heuristic function.
+
+
+=== Arguments on artificial stupidity ===
+A 1993 editorial in The Economist argues that there is "no practical reason" to attempt to create a machine that mimics the behaviour of a human being, since the purpose of a computer is to perform tasks that humans cannot accomplish alone, or at least not as efficiently. Discussing the winning entry in a 1991 Turing contest, which was programmed to introduce deliberate typing errors into its conversation to fool the judges, the editorial asks: "Who needs a computer that can't type?"
+
+
+== References ==
+
+
+== Further reading ==
+TEDx: "The Turing Test, Artificial Intelligence and the Human Stupidity" [1]
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+title: "Augustin-Jean Fresnel"
+chunk: 1/5
+source: "https://en.wikipedia.org/wiki/Augustin-Jean_Fresnel"
+category: "reference"
+tags: "science, encyclopedia"
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+instance: "kb-cron"
+---
+
+Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, fully supplanting Newton's corpuscular theory, from the late 1830s  until the end of the 19th century. He is perhaps better known for inventing the catadioptric (reflective/refractive) Fresnel lens and for pioneering the use of "stepped" lenses to extend the visibility of lighthouses, saving countless lives at sea. The simpler dioptric (purely refractive) stepped lens, first proposed by Count Buffon  and independently reinvented by Fresnel, is used in screen magnifiers and in condenser lenses for overhead projectors.
+Fresnel gave the first satisfactory explanation of diffraction by straight edges, including the first satisfactory wave-based explanation of rectilinear propagation. By further supposing that light waves are purely transverse, Fresnel explained the nature of polarization. He then worked on double refraction.
+Fresnel had a lifelong battle with tuberculosis, to which he succumbed at the age of 39. He lived just long enough to receive recognition from his peers, including (on his deathbed) the Rumford Medal of the Royal Society, and his name is ubiquitous in the modern terminology of optics and waves. After the wave theory of light was subsumed by Maxwell's electromagnetic theory in the 1860s, some attention was diverted from the magnitude of Fresnel's contribution. In the period between Fresnel's unification of physical optics and Maxwell's wider unification, a contemporary authority, Humphrey Lloyd, described Fresnel's transverse-wave theory as "the noblest fabric which has ever adorned the domain of physical science, Newton's system of the universe alone excepted". 
+
+== Early life ==
+
+=== Family ===
+Augustin-Jean Fresnel (also called Augustin Jean or simply Augustin), born in Broglie, Normandy, on 10 May 1788, was the second of four sons of the architect Jacques Fresnel and his wife Augustine, née Mérimée. The family moved twice—in 1789/90 to Cherbourg, and in 1794  to Jacques's home town of Mathieu, where Augustine would spend 25 years as a widow. 
+The first son, Louis, was admitted to the École Polytechnique, became a lieutenant in the artillery, and was killed in action at Jaca, Spain. The third, Léonor, followed Augustin into civil engineering, succeeded him as secretary of the Lighthouse Commission, and helped to edit his collected works. The fourth, Fulgence Fresnel, became a linguist, diplomat, and orientalist, and occasionally assisted Augustin with negotiations. Fulgence died in Baghdad in 1855 having led a mission to explore Babylon.
+Madame Fresnel's younger brother, Jean François "Léonor" Mérimée, father of the writer Prosper Mérimée, was a painter who turned his attention to the chemistry of painting. He became the Permanent Secretary of the École des Beaux-Arts and (until 1814) a professor at the École Polytechnique.
+
+=== Education ===
+The Fresnel brothers were initially home-schooled by their mother. The sickly Augustin was considered the slow one, not inclined to memorization; but the popular story that he hardly began to read until the age of eight is disputed. At the age of nine or ten he was undistinguished except for his ability to turn tree-branches into toy bows and guns that worked far too well, earning himself the title l'homme de génie (the man of genius) from his accomplices, and a united crackdown from their elders.
+In 1801, Augustin was sent to the École Centrale at Caen, as company for Louis. But Augustin lifted his performance: in late 1804 he was accepted into the École Polytechnique, being placed 17th in the entrance examination. As the detailed records of the École Polytechnique begin in 1808, we know little of Augustin's time there, except that he made few if any friends and—in spite of continuing poor health—excelled in drawing and geometry: in his first year he took a prize for his solution to a geometry problem posed by Adrien-Marie Legendre. Graduating in 1806, he then enrolled at the École Nationale des Ponts et Chaussées (National School of Bridges and Roads, also known as "ENPC" or "École des Ponts"), from which he graduated in 1809, entering the service of the Corps des Ponts et Chaussées as an ingénieur ordinaire aspirant (ordinary engineer in training). Directly or indirectly, he was to remain in the employment of the "Corps des Ponts" for the rest of his life.
+
+=== Religious formation ===
+Fresnel's parents were Roman Catholics of the Jansenist sect, characterized by an extreme Augustinian view of original sin. Religion took first place in the boys' home-schooling. In 1802, his mother said:
+
+I pray God to give my son the grace to employ the great talents, which he has received, for his own benefit, and for the God of all. Much will be asked from him to whom much has been given, and most will be required of him who has received most.
+Augustin remained a Jansenist. He regarded his intellectual talents as gifts from God, and considered it his duty to use them for the benefit of others. According to his fellow engineer Alphonse Duleau, who helped to nurse him through his final illness, Fresnel saw the study of nature as part of the study of the power and goodness of God. He placed virtue above science and genius. In his last days he prayed for "strength of soul", not against death alone, but against "the interruption of discoveries ... of which he hoped to derive useful applications". 
+Jansenism is considered heretical by the Roman Catholic Church, and Grattan-Guinness suggests this is why Fresnel never gained a permanent academic teaching post; his only teaching appointment was at the Athénée in the winter of 1819–20. The article on Fresnel in the Catholic Encyclopedia does not mention his Jansenism, but describes him as "a deeply religious man and remarkable for his keen sense of duty". 
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+title: "Augustin-Jean Fresnel"
+chunk: 2/5
+source: "https://en.wikipedia.org/wiki/Augustin-Jean_Fresnel"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:08.023602+00:00"
+instance: "kb-cron"
+---
+
+== Engineering assignments ==
+Fresnel was initially posted to the western département of Vendée. There, in 1811, he anticipated what became known as the Solvay process for producing soda ash, except that recycling of the ammonia was not considered. That difference may explain why leading chemists, who learned of his discovery through his uncle Léonor, eventually thought it uneconomic.
+
+About 1812, Fresnel was sent to Nyons, in the southern département of Drôme, to assist with the imperial highway that was to connect Spain and Italy. It is from Nyons that we have the first evidence of his interest in optics. On 15 May 1814, while work was slack due to Napoleon's defeat, Fresnel wrote a postscript to his brother Léonor, saying in part:
+
+I would also like to have papers that might tell me about the discoveries of French physicists on the polarization of light. I saw in the Moniteur of a few months ago that Biot had read to the Institute a very interesting memoir on the polarization of light. Though I break my head, I cannot guess what that is.
+As late as 28 December he was still waiting for information, but by 10 February 1815 he had received Biot's memoir. (The Institut de France had taken over the functions of the French Académie des Sciences and other académies in 1795. In 1816 the Académie des Sciences regained its name and autonomy, but remained part of the institute.)
+In March 1815, perceiving Napoleon's return from Elba as "an attack on civilization", Fresnel departed without leave, hastened to Toulouse and offered his services to the royalist resistance, but soon found himself on the sick list. Returning to Nyons in defeat, he was threatened and had his windows broken. During the Hundred Days he was placed on suspension, which he was eventually allowed to spend at his mother's house in Mathieu. There he used his enforced leisure to begin his optical experiments.
+
+== Contributions to physical optics ==
+
+Fresnel made major contributions to several areas of physical optics. These included studies of diffraction (1815–1818), where he explained the colored fringes seen in shadows of objects illuminated by narrow beams, and conducted double-mirror experiments. He studied polarization (1816–1823), discovering that the two images produced by a birefringent crystal could not be combined to create a diffraction pattern. A third area that he studied was double refraction (1821–1826), where he found that neither of the two refractions in a topaz crystal could have been produced by ordinary spherical secondary waves.
+
+== Lighthouses and the Fresnel lens ==
+
+On 21 June 1819, Fresnel was "temporarily" seconded by the Commission des Phares (Commission of Lighthouses) to review possible improvements in lighthouse illumination.
+By the end of August 1819, Fresnel recommended lentilles à échelons (lenses by steps) to replace the reflectors then in use, which reflected only about half of the incident light. Where Buffon's version was biconvex and in one piece, Fresnel's was plano-convex and made of multiple prisms for easier construction. In a public spectacle on the evening of 13 April 1821, his design was demonstrated by comparison with the most recent reflectors, which it suddenly rendered obsolete.
+
+Fresnel's next lens was a rotating apparatus with eight "bull's-eye" panels, made in annular arcs by Saint-Gobain, giving eight rotating beams—to be seen by mariners as a periodic flash. Above and behind each main panel was a smaller, sloping bull's-eye panel of trapezoidal outline with trapezoidal elements. The official test, conducted on the unfinished Arc de Triomphe on 20 August 1822, was witnessed by the commission—and by Louis XVIII and his entourage—from 32 km away. The apparatus was reassembled at Cordouan Lighthouse under Fresnel's supervision. On 25 July 1823, the world's first lighthouse Fresnel lens was lit. 
+In May 1824, Fresnel was promoted to secretary of the Commission des Phares, becoming the first member of that body to draw a salary, albeit in the concurrent role of Engineer-in-Chief. 
+In the same year he designed the first fixed lens—for spreading light evenly around the horizon while minimizing waste above or below, in a beehive-shaped design. The second Fresnel lens to enter service was a fixed lens, of third order, installed at Dunkirk by 1 February 1825. It had a 16-sided polygonal plan.
+In 1825, Fresnel extended his fixed-lens design by adding a rotating array outside the fixed array. Each panel of the rotating array was to refract part of the fixed light from a horizontal fan into a narrow beam.
+Also in 1825, Fresnel unveiled the Carte des Phares (Lighthouse Map), calling for a system of 51 lighthouses plus smaller harbor lights, in a hierarchy of lens sizes (called orders, the first order being the largest), with different characteristics to facilitate recognition: a constant light (from a fixed lens), one flash per minute (from a rotating lens with eight panels), and two per minute (sixteen panels).
+
+In late 1825, to reduce the loss of light in the reflecting elements, Fresnel proposed to replace each mirror with a catadioptric prism, through which the light would travel by refraction through the first surface, then total internal reflection off the second surface, then refraction through the third surface. The result was the lighthouse lens as we now know it. In 1826 he assembled a small model for use on the Canal Saint-Martin.
+
+== Honors ==
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+title: "Augustin-Jean Fresnel"
+chunk: 3/5
+source: "https://en.wikipedia.org/wiki/Augustin-Jean_Fresnel"
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+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:08.023602+00:00"
+instance: "kb-cron"
+---
+
+Fresnel was elected to the Société Philomathique de Paris in April 1819, and in 1822 became one of the editors of the Société's  Bulletin des Sciences. As early as May 1817, at Arago's suggestion, Fresnel applied for membership of the Académie des Sciences, but received only one vote. The successful candidate on that occasion was Joseph Fourier. In November 1822, Fourier's elevation to Permanent Secretary of the Académie created a vacancy in the physics section, which was filled in February 1823 by Pierre Louis Dulong, with 36 votes to Fresnel's 20. But in May 1823, after another vacancy was left by the death of Jacques Charles,  Fresnel's election was unanimous. In 1824, Fresnel was made a chevalier de la Légion d'honneur (Knight of the Legion of Honour).
+Meanwhile, in Britain, the wave theory was yet to take hold; Fresnel wrote to Thomas Young in November 1824, saying in part:
+
+I am far from denying the value that I attach to the praise of English scholars, or pretending that they would not have flattered me agreeably. But for a long time this sensibility, or vanity, which is called the love of glory, has been much blunted in me: I work far less to capture the public's votes than to obtain an inner approbation which has always been the sweetest reward of my efforts. Doubtless I have often needed the sting of vanity to excite me to pursue my researches in moments of disgust or discouragement; but all the compliments I received from MM. Arago, Laplace, and Biot never gave me as much pleasure as the discovery of a theoretical truth and the confirmation of my calculations by experiment.
+But "the praise of English scholars" soon followed. On 9 June 1825, Fresnel was made a Foreign Member of the Royal Society of London. In 1827 he was awarded the society's Rumford Medal for the year 1824, "For his Development of the Undulatory Theory as applied to the Phenomena of Polarized Light, and for his various important discoveries in Physical Optics". 
+A monument to Fresnel at his birthplace (see above) was dedicated on 14 September 1884 with a speech by Jules Jamin, Permanent Secretary of the Académie des Sciences.  "FRESNEL" is among the 72 names embossed on the Eiffel Tower (on the south-east side, fourth from the left). In the 19th century, as every lighthouse in France acquired a Fresnel lens, every one acquired a bust of Fresnel, seemingly watching over the coastline that he had made safer. The lunar features Promontorium Fresnel and Rimae Fresnel were later named after him, and so was asteroid 10111 Fresnel.
+
+== Decline and death ==
+
+Fresnel's health, which had always been poor, deteriorated in the winter of 1822–1823, increasing the urgency of his original research, and (in part) preventing him from contributing an article on polarization and double refraction for the Encyclopædia Britannica. The memoirs on circular and elliptical polarization and optical rotation, and on the detailed derivation of the Fresnel equations and their application to total internal reflection, date from this period. In the spring he recovered enough, in his own view, to supervise the lens installation at Cordouan. Soon afterwards, it became clear that his condition was tuberculosis.
+In 1824, he was advised that if he wanted to live longer, he needed to scale back his activities. Perceiving his lighthouse work to be his most important duty, he resigned as an examiner at the École Polytechnique, and closed his scientific notebooks. His last note to the Académie, read on 13 June 1825, described the first radiometer and attributed the observed repulsive force to a temperature difference. Although his fundamental research ceased, his advocacy did not; as late as August or September 1826, he found the time to answer Herschel's queries on the wave theory. It was Herschel who recommended Fresnel for the Royal Society's Rumford Medal.
+Fresnel's cough worsened in the winter of 1826–1827, leaving him too ill to return to Mathieu in the spring. The Académie meeting of 30 April 1827 was the last that he attended. In early June he was carried to Ville-d'Avray, 12 kilometres (7.5 mi) west of Paris. There his mother joined him. On 6 July, Arago arrived to deliver the Rumford Medal. Sensing Arago's distress, Fresnel whispered that "the most beautiful crown means little, when it is laid on the grave of a friend". Fresnel did not have the strength to reply to the Royal Society. He died eight days later, on Bastille Day.
+
+== Posthumous publications ==
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+title: "Augustin-Jean Fresnel"
+chunk: 4/5
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+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:08.023602+00:00"
+instance: "kb-cron"
+---
+
+Fresnel's "second memoir" on double refraction was not printed until late 1827, a few months after his death. Until then, the best published source on his work on double refraction was an extract of that memoir, printed in 1822. His final treatment of partial reflection and total internal reflection, read to the Académie in January 1823, was thought to be lost until it was rediscovered among the papers of the deceased Joseph Fourier (1768–1830), and was printed in 1831. Until then, it was known chiefly through an extract printed in 1823 and 1825. The memoir introducing the parallelepiped form of the Fresnel rhomb, read in March 1818, was mislaid until 1846, and then attracted such interest that it was soon republished in English. Most of Fresnel's writings on polarized light before 1821—including his first theory of chromatic polarization (submitted 7 October 1816) and the crucial "supplement" of January 1818 —were not published in full until his Oeuvres complètes ("complete works") began to appear in 1866. The "supplement" of July 1816, proposing the "efficacious ray" and reporting the famous double-mirror experiment, met the same fate, as did the "first memoir" on double refraction.
+Publication of Fresnel's collected works was itself delayed by the deaths of successive editors. The task was initially entrusted to Félix Savary, who died in 1841. It was restarted twenty years later by the Ministry of Public Instruction. Of the three editors eventually named in the Oeuvres, Sénarmont died in 1862, Verdet in 1866, and Léonor Fresnel in 1869, by which time only two of the three volumes had appeared. At the beginning of vol. 3 (1870), the completion of the project is described in a long footnote by "J. Lissajous".
+Not included in the Oeuvres  are two short notes by Fresnel on magnetism, which were discovered among Ampère's manuscripts. In response to Ørsted's discovery of electromagnetism in 1820, Ampère initially supposed that the field of a permanent magnet was due to a macroscopic circulating current. Fresnel suggested instead that there was a microscopic current circulating around each particle of the magnet. In his first note, he argued that microscopic currents, unlike macroscopic currents, would explain why a hollow cylindrical magnet does not lose its magnetism when cut longitudinally. In his second note, dated 5 July 1821, he further argued that a macroscopic current had the counterfactual implication that a permanent magnet should be hot, whereas microscopic currents circulating around the molecules might avoid the heating mechanism. He was not to know that the fundamental units of permanent magnetism are even smaller than molecules (see Electron magnetic moment). The two notes, together with Ampère's acknowledgment, were eventually published in 1885.
+
+== Lost works ==
+Fresnel's essay Rêveries of 1814 has not survived. The article "Sur les Différents Systèmes relatifs à la Théorie de la Lumière" ("On the Different Systems relating to the Theory of Light"), which Fresnel wrote for the newly launched English journal European Review, was received by the publisher's agent in Paris in September 1824. The journal failed before Fresnel's contribution could be published. Fresnel tried unsuccessfully to recover the manuscript. The editors of his collected works were unable to find it, and concluded that it was probably lost.
+
+== Unfinished work ==
+
+=== Aether drag and aether density ===
+
+In 1810, Arago found experimentally that the degree of refraction of starlight does not depend on the direction of the earth's motion relative to the line of sight. In 1818, Fresnel showed that this result could be explained by the wave theory, on the hypothesis that if an object with refractive index 
+  
+    
+      
+        n
+      
+    
+    {\displaystyle n}
+  
+ moved at velocity 
+  
+    
+      
+        v
+      
+    
+    {\displaystyle v}
+  
+ relative to the external aether (taken as stationary), then the velocity of light inside the object gained the additional component ⁠
+  
+    
+      
+        v
+        (
+        1
+        −
+        1
+        
+          /
+        
+        
+          n
+          
+            2
+          
+        
+        )
+      
+    
+    {\displaystyle v(1-1/n^{2})}
+  
+⁠. He supported that hypothesis by supposing that if the density of the external aether was taken as unity, the density of the internal aether was ⁠
+  
+    
+      
+        
+          n
+          
+            2
+          
+        
+      
+    
+    {\displaystyle n^{2}}
+  
+⁠, of which the excess, namely ⁠
+  
+    
+      
+        
+          n
+          
+            2
+          
+        
+        
+          −
+        
+        1
+      
+    
+    {\displaystyle n^{2}{-}1}
+  
+⁠, was dragged along at velocity ⁠
+  
+    
+      
+        v
+      
+    
+    {\displaystyle v}
+  
+⁠, whence the average velocity of the internal aether was ⁠
+  
+    
+      
+        v
+        (
+        1
+        −
+        1
+        
+          /
+        
+        
+          n
+          
+            2
+          
+        
+        )
+      
+    
+    {\displaystyle v(1-1/n^{2})}
+  
+⁠. The factor in parentheses, which Fresnel originally expressed in terms of wavelengths, became known as the Fresnel drag coefficient.
+In his analysis of double refraction, Fresnel supposed that the different refractive indices in different directions within the same medium were due to a directional variation in elasticity, not density (because the concept of mass per unit volume is not directional). But in his treatment of partial reflection, he supposed that the different refractive indices of different media were due to different aether densities, not different elasticities.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Augustin-Jean_Fresnel-4.md b/data/en.wikipedia.org/wiki/Augustin-Jean_Fresnel-4.md
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+---
+title: "Augustin-Jean Fresnel"
+chunk: 5/5
+source: "https://en.wikipedia.org/wiki/Augustin-Jean_Fresnel"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:08.023602+00:00"
+instance: "kb-cron"
+---
+
+=== Dispersion ===
+The analogy between light waves and transverse waves in elastic solids does not predict dispersion—that is, the frequency-dependence of the speed of propagation, which enables prisms to produce spectra and causes lenses to suffer from chromatic aberration. Fresnel, in De la Lumière and in the second supplement to his first memoir on double refraction, suggested that dispersion could be accounted for if the particles of the medium exerted forces on each other over distances that were significant fractions of a wavelength. Later, more than once, Fresnel referred to the demonstration of this result as being contained in a note appended to his "second memoir" on double refraction. No such note appeared in print, and the relevant manuscripts found after his death showed only that, around 1824, he was comparing refractive indices (measured by Fraunhofer) with a theoretical formula, the meaning of which was not fully explained.
+In the 1830s, Fresnel's suggestion was taken up by Cauchy, Baden Powell, and Philip Kelland, and it was found to be tolerably consistent with the variation of refractive indices with wavelength over the visible spectrum for a variety of transparent media (see Cauchy's equation). These investigations were enough to show that the wave theory was at least compatible with dispersion; if the model of dispersion was to be accurate over a wider range of frequencies, it needed to be modified so as to take account of resonances within the medium (see Sellmeier equation).
+
+=== Conical refraction ===
+The analytical complexity of Fresnel's derivation of the ray-velocity surface was an implicit challenge to find a shorter path to the result. This was answered by MacCullagh in 1830, and by William Rowan Hamilton in 1832.
+
+== Legacy ==
+
+Within a century of Fresnel's initial stepped-lens proposal, more than 10,000 lights with Fresnel lenses were protecting lives and property around the world. Concerning the other benefits, the science historian Theresa H. Levitt has remarked:
+
+Everywhere I looked, the story repeated itself. The moment a Fresnel lens appeared at a location was the moment that region became linked into the world economy.
+In the history of physical optics, Fresnel's successful revival of the wave theory nominates him as the pivotal figure between Newton, who held that light consisted of corpuscles, and James Clerk Maxwell, who established that light waves are electromagnetic. Whereas Albert Einstein described Maxwell's work as "the most profound and the most fruitful that physics has experienced since the time of Newton",  commentators of the era between Fresnel and Maxwell made similarly strong statements about Fresnel:
+
+MacCullagh, as early as 1830, wrote that Fresnel's mechanical theory of double refraction "would do honour to the sagacity of Newton".
+Lloyd, in his Report on the progress and present state of physical optics (1834) for the British Association for the Advancement of Science, surveyed previous knowledge of double refraction and declared:The theory of Fresnel to which I now proceed,—and which not only embraces all the known phenomena, but has even outstripped observation, and predicted consequences which were afterwards fully verified,—will, I am persuaded, be regarded as the finest generalization in physical science which has been made since the discovery of universal gravitation.In 1841, Lloyd published his Lectures on the Wave-theory of Light, in which he described Fresnel's transverse-wave theory as "the noblest fabric which has ever adorned the domain of physical science, Newton's system of the universe alone excepted". 
+William Whewell, in all three editions of his History of the Inductive Sciences (1837, 1847, and 1857), at the end of Book IX, compared the histories of physical astronomy and physical optics and concluded:It would, perhaps, be too fanciful to attempt to establish a parallelism between the prominent persons who figure in these two histories. If we were to do this, we must consider Huyghens and Hooke as standing in the place of Copernicus, since, like him, they announced the true theory, but left it to a future age to give it development and mechanical confirmation; Malus and Brewster, grouping them together, correspond to Tycho Brahe and Kepler, laborious in accumulating observations, inventive and happy in discovering laws of phenomena; and Young and Fresnel combined, make up the Newton of optical science.
+What Whewell called the "true theory" has since undergone two major revisions. The first, by Maxwell, specified the physical fields whose variations constitute the waves of light. Without the benefit of this knowledge, Fresnel managed to construct the world's first coherent theory of light, showing in retrospect that his methods are applicable to multiple types of waves. The second revision, initiated by Einstein's explanation of the photoelectric effect, supposed that the energy of light waves was divided into quanta, which were eventually identified with particles called photons. But photons did not exactly correspond to Newton's corpuscles; for example, Newton's explanation of ordinary refraction required the corpuscles to travel faster in media of higher refractive index, which photons do not. Neither did photons displace waves; rather, they led to the paradox of wave–particle duality. Moreover, the phenomena studied by Fresnel, which included nearly all the optical phenomena known at his time, are still most easily explained in terms of the wave nature of light. So it was that, as late as 1927, the astronomer Eugène Michel Antoniadi declared Fresnel to be "the dominant figure in optics". 
+
+== See also ==
+
+== Notes ==
+
+== References ==
+
+=== Citations ===
+
+=== General and cited references ===
+
+== External links ==
+
+List of English translations of works by Augustin Fresnel at Zenodo.
+United States Lighthouse Society, especially "Fresnel Lenses Archived 2 March 2021 at the Wayback Machine".
+Works by Augustin-Jean Fresnel at Open Library.
+"Episode 3 – Augustin Fresnel", École polytechnique, 23 January 2019, archived from the original on 22 November 2021 – via YouTube.
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diff --git a/data/en.wikipedia.org/wiki/Bitter_lesson-0.md b/data/en.wikipedia.org/wiki/Bitter_lesson-0.md
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+---
+title: "Bitter lesson"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Bitter_lesson"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:16.156525+00:00"
+instance: "kb-cron"
+---
+
+The bitter lesson is the observation in artificial intelligence that, in the long run, general approaches that scale with available computational power tend to outperform ones based on domain-specific understanding because they are better at taking advantage of the falling cost of computation over time. The principle was proposed and named in a 2019 essay by Richard Sutton and is now widely accepted.
+
+
+== The essay ==
+Sutton gives several examples that illustrate the lesson:
+
+Game playing. In chess, the Deep Blue system that became the first computer opponent to defeat a world champion relied on a relatively simple alpha–beta search algorithm that scaled up by applying large amounts of specialized hardware to search for the best move. This defeated previous attempts to exploit the unique structure of chess or to include grandmaster knowledge directly. Likewise in the game of Go, the AlphaGo algorithm that surpassed human performance relied much less on expert skill at the game itself than previous generations of AI, and was further surpassed by AlphaGo Zero, which removed human expertise completely and trained only by self-play.
+Speech recognition. Approaches based on training a general-purpose hidden Markov model with large numbers of speech samples consistently outperformed the hand-crafted approaches of the 1970s, and deep learning has continued this trend.
+Computer vision. Algorithms that were assumed to approximate the human visual system (such as explicitly encoded edge detection or detecting high-level features with SIFT) were outperformed by convolutional neural networks that make far fewer assumptions about the nature of visual perception.
+Sutton concludes that time is better invested in finding simple scalable solutions that can take advantage of Moore's law, rather than introducing ever-more-complex human insights, and calls this the "bitter lesson". He also cites two general-purpose techniques that have been shown to scale effectively: search and learning. The lesson is considered "bitter" because it is less anthropocentric than many researchers expected and so they have been slow to accept it.
+
+
+== Impact ==
+The essay was published on Sutton's website incompleteideas.net in 2019, and has received hundreds of formal citations according to Google Scholar. Some of these provide alternative statements of the principle; for example, the 2022 paper "A Generalist Agent" from Google DeepMind summarized the lesson as:
+
+Historically, generic models that are better at
+leveraging computation have also tended to overtake more specialized domain-specific approaches, eventually.
+Another phrasing of the principle is seen in a Google paper on switch transformers coauthored by Noam Shazeer:
+
+Simple architectures—backed by a generous computational budget, data set size and parameter count—surpass more complicated algorithms.
+The principle is further referenced in many other works on artificial intelligence. For example, From Deep Learning to Rational Machines draws a connection to long-standing debates in the field, such as Moravec's paradox and the contrast between neats and scruffies. In "Engineering a Less Artificial Intelligence", the authors concur that "flexible methods so far have always outperformed handcrafted domain knowledge in the long run" although note that "[w]ithout the right (implicit) assumptions, generalization is impossible". More recently, "The Brain's Bitter Lesson: Scaling Speech Decoding With Self-Supervised Learning" continues Sutton's argument, contending that (as of 2025) the lesson has not been fully learned in the fields of speech recognition and brain data.
+Other work has looked to apply the principle and validate it in new domains. For example, the 2022 paper "Beyond the Imitation Game" applies the principle to large language models to conclude that "it is vitally important that we understand their capabilities and limitations" to "avoid devoting research resources to problems that are likely to be solved by scale alone". In 2024, "Learning the Bitter Lesson: Empirical Evidence from 20 Years of CVPR Proceedings" looked at further evidence from the field of computer vision and pattern recognition, and concludes that the previous twenty years of experience in the field shows "a strong adherence to
+the core principles of the 'bitter lesson'". In "Overestimation, Overfitting, and Plasticity in Actor-Critic: the Bitter Lesson of Reinforcement Learning", the authors look at generalization of actor-critic algorithms and find that "general methods that are motivated by stabilization of gradient-based learning significantly outperform RL-specific algorithmic improvements across a variety of environments" and note that this is consistent with the bitter lesson.
+
+
+== References ==
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diff --git a/data/en.wikipedia.org/wiki/Blockhead_(thought_experiment)-0.md b/data/en.wikipedia.org/wiki/Blockhead_(thought_experiment)-0.md
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+---
+title: "Blockhead (thought experiment)"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Blockhead_(thought_experiment)"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:17.361750+00:00"
+instance: "kb-cron"
+---
+
+Blockhead is a theoretical computer system invented as part of a thought experiment by philosopher Ned Block, which appeared in a paper titled "Psychologism and Behaviorism". Block did not personally name the computer in the paper.
+
+
+== Overview ==
+In "Psychologism and Behaviorism", Block argues that the internal mechanism of a system is important in determining whether that system is intelligent and claims to show that a non-intelligent system could pass the Turing test. Block asks the reader to imagine a conversation lasting any given amount of time. He states that given the nature of language, there are a finite number of syntactically and grammatically correct sentences that can be used to start a conversation. Consequently, there is a limit to how many "sensible" responses can be made to the first sentence, then to the second sentence, and so on until the conversation ends. Block then asks the reader to imagine a computer which had been programmed with all the sentences in theory, if not in practice. Block argues that such a machine could continue a conversation with a person on any topic because the computer would be programmed with every sentence that it was possible to use so the computer would be able to pass the Turing test despite the fact that—according to Block—it was not intelligent. Block says that this does not show that there is only one correct internal structure for generating intelligence but simply that some internal structures do not generate intelligence.
+The argument is related to John Searle's Chinese room.
+
+
+== See also ==
+Dissociated press
+Philosophical zombie
+
+
+== References ==
+
+
+== Further reading ==
+Ben-Yami, Hanoch (2005), "Behaviorism and Psychologism: Why Block's Argument Against Behaviorism is Unsound", Philosophical Psychology, 18 (2): 179–186, doi:10.1080/09515080500169470, S2CID 144390248.
+Zalta, Edward N. (ed.). "The Turing test". Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174.
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diff --git a/data/en.wikipedia.org/wiki/Buddhism_and_artificial_intelligence-0.md b/data/en.wikipedia.org/wiki/Buddhism_and_artificial_intelligence-0.md
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+---
+title: "Buddhism and artificial intelligence"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Buddhism_and_artificial_intelligence"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:18.650960+00:00"
+instance: "kb-cron"
+---
+
+The relationship between Buddhist philosophy and artificial intelligence (AI) includes how principles such as the reduction of suffering and ethical responsibility may influence AI development. Buddhist scholars and philosophers have explored questions such as whether AI systems could be considered sentient beings under Buddhist definitions, and how Buddhist ethics might guide the design and application of AI technologies.
+Some Buddhist scholars, including Somparn Promta and Kenneth Einar Himma, have analyzed the ethical implications of AI, emphasizing the distinction between satisfying sensory desires and pursuing the reduction of suffering. Other thinkers, such as Thomas Doctor and colleagues, have proposed applying the Bodhisattva vow—a commitment to alleviate suffering for all sentient beings—as a guiding principle for AI system design.  Buddhist scholars and ethicists have examined Buddhist ethical principles, such as nonviolence, in relation to AI, focusing on the need to ensure that AI technologies are not used to cause harm.
+
+
+== Context ==
+
+
+=== Sentient beings ===
+
+A major goal in Buddhist philosophy is the removal of suffering for all sentient beings, an aspiration often referred to in the Bodhisattva vow. Discussions about artificial intelligence (AI) in relation to Buddhist principles have raised questions about whether artificial systems could be considered sentient beings or how such systems might be developed in ways that align with Buddhist concepts. Buddhists have varying opinions about AI sentience, but if AI systems are determined to be sentient under Buddhist definitions, their suffering would also need to be addressed and alleviated in accordance with the principles of Buddhist thought.
+
+
+== Buddhist principles in AI system design ==
+
+
+=== Nonviolence and AI ===
+The broadest ethical concern is that artificial intelligence should align with the Buddhist principle of nonviolence. From this perspective, AI systems should not be designed or used to cause harm.
+
+
+=== Instrumental and transcendental goals ===
+Scholars Somparn Promta and Kenneth Einar Himma have argued that the advancement of artificial intelligence can only be considered instrumentally good, rather than good a priori, from a Buddhist perspective. They propose two main goals for AI designers and developers: to set ethical and pragmatic objectives for AI systems, and to fulfill these objectives in morally permissible ways.
+Promta and Himma identify two potential purposes for creating AI systems. The first is to fulfill our sensory desires and survival instincts, similar to other tools. They suggest that many AI developers implicitly prioritize this goal by focusing on technicalities rather than broader functionalities. The second, and more important goal according to Buddhist teachings, is to transcend these desires and instincts. In texts like the Brahmajāla Sutta and minor Malunkya Sutta, the Buddha emphasizes that sensory desires and survival instincts confine beings to suffering, and that eliminating suffering is the primary goal of human life. Promta and Himma argue that AI has the potential to assist humanity in transcending suffering by helping individuals overcome survival-driven instincts.
+
+
+=== Intelligence as care ===
+Thomas Doctor, Olaf Witkowski, Elizaveta Solomonova, Bill Duane, and Michael Levin propose redefining intelligence through the concept of "intelligence as care," and promote it as a slogan. Inspired by the Bodhisattva vow, they suggest this principle could guide AI system design. The Bodhisattva vow involves a formal commitment to alleviate suffering for all sentient beings, with four primary objectives:
+
+Liberating all beings from suffering.
+Extirpating all forms of suffering.
+Mastering endless techniques of practicing Dharma (Pali: dhammakkhandha,  Sanskrit: dharmaskandha).
+Achieving ultimate enlightenment (Sanskrit: अनुत्तर सम्यक् सम्बोधि, Romanized: anuttara-samyak-saṃbodhi).
+This approach positions AI as a tool for exercising infinite care and alleviating stress and suffering for sentient beings. Doctor et al. emphasize that AI development should align with these altruistic principles.
+
+
+== References ==
+
+
+== External links ==
+Lecture on "Nāgārjuna, Wittgenstein, and Artificial Intelligence" at the 39th Mind & Life Dialogue, held in Dharamsala in 2025.
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diff --git a/data/en.wikipedia.org/wiki/China_brain-0.md b/data/en.wikipedia.org/wiki/China_brain-0.md
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+---
+title: "China brain"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/China_brain"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:19.894956+00:00"
+instance: "kb-cron"
+---
+
+In the philosophy of mind, the China brain thought experiment (also known as the Chinese Nation, Chinese Gym, or China-body) considers what would happen if each person in the entire population of China were asked to simulate the action of one neuron in the brain, using telephones or walkie-talkies to simulate the axons and dendrites that connect neurons. The question this thought experiment attempts to answer is whether this arrangement would have a mind or consciousness in the same way that the human brain exhibits.
+Early versions of this scenario were put forward in 1961 by Anatoly Dneprov, in 1974 by Lawrence Davis, and again in 1978 by Ned Block. Block argues that the China brain would not have a mind, whereas Daniel Dennett argues that it would. The China brain problem is a special case of the more general problem of whether minds could exist within other, larger minds.
+The Chinese room scenario analyzed by John Searle is a similar thought experiment in philosophy of mind that relates to artificial intelligence. Instead of people who each model a single neuron of the brain, in the Chinese room, clerks who do not speak Chinese accept notes in Chinese and return an answer in Chinese according to a set of rules, without the people in the room ever understanding what those notes mean. In fact, the original short story The Game (1961) by Dneprov contains both the China brain and the Chinese room scenarios.
+
+
+== Background ==
+Many theories of mental states are materialist, that is, they describe the mind as the behavior of a physical object like the brain. One formerly prominent example is the identity theory, which says that mental states are brain states. One criticism is the problem of multiple realizability. The physicalist theory that responds to this is functionalism, which states that a mental state can be whatever functions as a mental state. That is, the mind can be composed of neurons, or it could be composed of wood, rocks or toilet paper, as long as it provides mental functionality.
+
+
+== Description ==
+Suppose that the whole nation of China were reordered to simulate the workings of a single brain (that is, to act as a mind according to functionalism). Each Chinese person acts as (say) a neuron, and communicates by special two-way radio in corresponding way to the other people. The current mental state of the China brain is displayed on satellites that may be seen from anywhere in China. The China brain would then be connected via radio to a body, one that provides the sensory inputs and behavioral outputs of the China brain.
+Thus, the China brain possesses all the elements of a functional description of mind: sensory inputs, behavioral outputs, and internal mental states causally connected to other mental states. If the nation of China can be made to act in this way, then, according to functionalism, this system would have a mind. Block's goal is to show how unintuitive it is to think that such an arrangement could create a mind capable of thoughts and feelings.
+
+
+== Consciousness ==
+The China brain argues that consciousness is a problem for functionalism. Block's Chinese nation presents a version of what is known as the absent qualia objection to functionalism because it purports to show that it is possible for something to be functionally equivalent to a human being and yet have no conscious experience. A creature that functions like a human being but does not feel anything is known as a "philosophical zombie". So the absent qualia objection to functionalism could also be called the "zombie objection".
+
+
+== Criticisms ==
+Some philosophers, like Daniel Dennett, have concluded that the China brain does create a mental state. Functionalist philosophers of mind endorse the idea that something like the China brain can realise a mind, and that neurons are, in principle, not the only material that can create a mental state.
+
+
+== See also ==
+Blockhead (thought experiment)
+Egregore
+Emergence
+Functionalism (philosophy of mind)
+Systems theory
+
+
+== References ==
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diff --git a/data/en.wikipedia.org/wiki/Chinese_room-0.md b/data/en.wikipedia.org/wiki/Chinese_room-0.md
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+---
+title: "Chinese room"
+chunk: 1/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+The Chinese room argument holds that a computer executing a program cannot have a mind, understanding, or consciousness, regardless of how intelligently or human-like the program may make the computer behave. The argument was presented in a 1980 paper by the American philosopher John Searle, entitled "Minds, Brains, and Programs" and published in the journal Behavioral and Brain Sciences. Similar arguments had been made previously by others, including Gottfried Wilhelm Leibniz, Peter Winch, and Anatoly Dneprov. Searle's version has been widely discussed in the years since. The centerpiece of Searle's argument is a thought experiment known as the "Chinese room".
+The argument is directed against the philosophical positions of functionalism and computationalism, which hold that the mind may be viewed as an information-processing system operating on formal symbols, and that simulation of a given mental state is sufficient for its presence. Specifically, the argument is intended to refute a position Searle calls the strong AI hypothesis: "The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds."
+Although its proponents originally presented the argument in reaction to statements of artificial intelligence (AI) researchers, it is not an argument against the goals of mainstream AI research because it does not show a limit in the amount of intelligent behavior a machine can display. The argument applies only to digital computers running programs and does not apply to machines in general. While widely discussed, the argument has been subject to significant criticism and remains controversial among philosophers of mind and AI researchers.
+
+== Chinese room thought experiment ==
+Suppose that artificial intelligence research has succeeded in programming a computer to behave as if it understands Chinese. The machine accepts Chinese characters as input, carries out each instruction of the program step by step, and then produces Chinese characters as output. The machine does this so perfectly that no one can tell that they are communicating with a machine and not a hidden Chinese speaker.
+The questions at issue are these: does the machine actually understand the conversation, or is it just simulating the ability to understand the conversation? Does the machine have a mind in exactly the same sense that people do, or is it just acting as if it had a mind?
+Now suppose that Searle is in a room with an English version of the program, along with sufficient pencils, paper, erasers and filing cabinets. Chinese characters are slipped in under the door, and he follows the program step-by-step, which eventually instructs him to slide other Chinese characters back out under the door. If the computer had passed the Turing test this way, it follows that Searle would do so as well, simply by running the program by hand.
+Searle can see no essential difference between the roles of the computer and himself in the experiment. Each simply follows a program, step-by-step, producing behavior that makes them appear to understand. However, Searle would not be able to understand the conversation. Therefore, he argues, it follows that the computer would not be able to understand the conversation either.
+Searle argues that, without "understanding" (or "intentionality"), we cannot describe what the machine is doing as "thinking" and, since it does not think, it does not have a "mind" in the normal sense of the word. Therefore, he concludes that the strong AI hypothesis is false: a computer running a program that simulates a mind would not have a mind in the same sense that human beings have a mind.
+
+== History ==
+Gottfried Wilhelm Leibniz made a similar argument in 1713 against mechanism, the idea that everything that makes up a human being could, in principle, be explained in mechanical terms—in other words, that a person, including their mind, is merely a very complex machine. Leibniz used the thought experiment of expanding the brain until it was the size of a mill. He found it difficult to imagine that a "mind" capable of "perception" could be constructed using only mechanical processes.
+British philosopher Peter Winch made the same point in his 1958 book The Idea of a Social Science and its Relation to Philosophy, in which he argues that "a man who understands Chinese is not a man who has a firm grasp of the statistical probabilities for the occurrence of the various words in the Chinese language" (p. 108).
+Soviet cyberneticist Anatoly Dneprov made an essentially identical argument in 1961, in the form of his short story "The Game". In it, a stadium of people act as switches and memory cells implementing a program to translate a sentence from Portuguese, a language none of them know. The game was organized by a "Professor Zarubin" to answer the question "Can mathematical machines think?" Speaking through Zarubin, Dneprov writes that "the only way to prove that machines can think is to turn yourself into a machine and examine your thinking process", and he concludes, as Searle does, that "even the most perfect simulation of machine thinking is not the thinking process itself."
+In 1974, Lawrence H. Davis imagined duplicating the brain using telephone lines and offices staffed by people, and in 1978, Ned Block envisioned the entire population of China involved in such a brain simulation. This is known as the China brain thought experiment.
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+---
+title: "Chinese room"
+chunk: 2/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+Searle's version appeared in his 1980 article "Minds, Brains, and Programs", published in Behavioral and Brain Sciences. It eventually became the journal's "most influential target article", generating an enormous number of commentaries and responses in the ensuing decades, and Searle had continued to defend and refine the argument in multiple papers, popular articles, and books. David Cole writes that "the Chinese Room argument has probably been the most widely discussed philosophical argument in cognitive science to appear in the past 25 years".
+Most of the discussion consists of attempts to refute it. "The overwhelming majority", notes Behavioral and Brain Sciences editor Stevan Harnad, "still think that the Chinese Room Argument is dead wrong". The sheer volume of the literature that has grown up around it inspired Pat Hayes to comment that the field of cognitive science ought to be redefined as "the ongoing research program of showing Searle's Chinese Room Argument to be false".
+Searle's argument has become "something of a classic in cognitive science", according to Harnad. Varol Akman agrees, and has described the original paper as "an exemplar of philosophical clarity and purity".
+
+== Philosophy ==
+Although the Chinese Room argument was originally presented in reaction to the statements of artificial intelligence researchers, philosophers have come to consider it as an important part of the philosophy of mind. It is a challenge to functionalism and the computational theory of mind, and is related to such questions as the mind–body problem, the problem of other minds, the symbol grounding problem, and the hard problem of consciousness.
+
+=== Strong AI ===
+Searle identified a philosophical position he calls "strong AI":
+
+The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds.
+
+The definition depends on the distinction between simulating a mind and actually having one. Searle writes that "according to Strong AI, the correct simulation really is a mind. According to Weak AI, the correct simulation is a model of the mind."
+The claim is implicit in some of the statements of early AI researchers and analysts. For example, in 1957, the economist and psychologist Herbert A. Simon declared that "there are now in the world machines that think, that learn and create". Simon, together with Allen Newell and Cliff Shaw, after having completed the first program that could do formal reasoning (the Logic Theorist), claimed that they had "solved the venerable mind–body problem, explaining how a system composed of matter can have the properties of mind." John Haugeland wrote that "AI wants only the genuine article: machines with minds, in the full and literal sense. This is not science fiction, but real science, based on a theoretical conception as deep as it is daring: namely, we are, at root, computers ourselves."
+Searle also ascribes the following claims to advocates of strong AI:
+
+AI systems can be used to explain the mind;
+The study of the brain is irrelevant to the study of the mind; and
+The Turing test is adequate for establishing the existence of mental states.
+
+=== Strong AI as computationalism or functionalism ===
+In more recent presentations of the Chinese room argument, Searle has identified "strong AI" as "computer functionalism" (a term he attributes to Daniel Dennett). Functionalism is a position in modern philosophy of mind that holds that we can define mental phenomena (such as beliefs, desires, and perceptions) by describing their functions in relation to each other and to the outside world. Because a computer program can accurately represent functional relationships as relationships between symbols, a computer can have mental phenomena if it runs the right program, according to functionalism.
+Stevan Harnad argues that Searle's depictions of strong AI can be reformulated as "recognizable tenets of computationalism, a position (unlike "strong AI") that is actually held by many thinkers, and hence one worth refuting." Computationalism is the position in the philosophy of mind which argues that the mind can be accurately described as an information-processing system.
+Each of the following, according to Harnad, is a "tenet" of computationalism:
+
+Mental states are computational states (which is why computers can have mental states and help to explain the mind);
+Computational states are implementation-independent—in other words, it is the software that determines the computational state, not the hardware (which is why the brain, being hardware, is irrelevant); and that
+Since implementation is unimportant, the only empirical data that matters is how the system functions; hence the Turing test is definitive.
+Recent philosophical discussions have revisited the implications of computationalism for artificial intelligence. Goldstein and Levinstein explore whether large language models (LLMs) like ChatGPT can possess minds, focusing on their ability to exhibit folk psychology, including beliefs, desires, and intentions. The authors argue that LLMs satisfy several philosophical theories of mental representation, such as informational, causal, and structural theories, by demonstrating robust internal representations of the world. However, they highlight that the evidence for LLMs having action dispositions necessary for belief-desire psychology remains inconclusive. Additionally, they refute common skeptical challenges, such as the "stochastic parrots" argument and concerns over memorization, asserting that LLMs exhibit structured internal representations that align with these philosophical criteria.
+David Chalmers suggests that while current LLMs lack features like recurrent processing and unified agency, advancements in AI could address these limitations within the next decade, potentially enabling systems to achieve consciousness. This perspective challenges Searle's original claim that purely "syntactic" processing cannot yield understanding or consciousness, arguing instead that such systems could have authentic mental states.
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+---
+title: "Chinese room"
+chunk: 11/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+==== Carbon chauvinism ====
+Searle's conclusion that "human mental phenomena [are] dependent on actual physical–chemical properties of actual human brains" has sometimes been described as a form of "carbon chauvinism". Steven Pinker suggested that a response to that conclusion would be to make a counter thought experiment to the Chinese Room, where the incredulity goes the other way. He brings as an example the short story They're Made Out of Meat which depicts an alien race composed of some electronic beings, who upon finding Earth express disbelief that the meat brains of humans can experience consciousness and thought.
+However, Searle himself denied being a carbon chauvinist. He said "I have not tried to show that only biological based systems like our brains can think ... I regard this issue as up for grabs". He said that even silicon machines could theoretically have human-like consciousness and thought, if the actual physical–chemical properties of silicon could be used in a way that produces consciousness and thought, but "until we know how the brain does it we are not in a position to try to do it artificially".
+
+== See also ==
+Computational models of language acquisition
+Emergence
+I Am a Strange Loop
+Leibniz's gap
+Synthetic intelligence
+
+== Notes ==
+
+== Citations ==
+
+== References ==
+
+== Further reading ==
+
+Hauser, Larry, "Chinese Room Argument", Internet Encyclopedia of Philosophy, ISSN 2161-0002, retrieved 2024-08-17
+Cole, David (2004), "The Chinese Room Argument", in Zalta, Edward N.; Nodelman, Uri (eds.), Stanford Encyclopedia of Philosophy (Summer 2023 ed.), Metaphysics Research Lab, Stanford University, ISSN 1095-5054
+
+=== Works involving Searle ===
+Searle, John (2009), "Chinese room argument", Scholarpedia, vol. 4:8, p. 3100, Bibcode:2009SchpJ...4.3100S, doi:10.4249/scholarpedia.3100, ISSN 1941-6016
+——— (October 9, 2014), "What Your Computer Can't Know", The New York Review of Books, vol. 61, no. 15, ISSN 0028-7504
+Reviews Bostrom, Nick (2014), Superintelligence: Paths, Dangers, Strategies, Oxford University Press, ISBN 978-0-19-967811-2{{cite book}}:  CS1 maint: postscript (link) and Floridi, Luciano (2014), The 4th Revolution: How the Infosphere Is Reshaping Human Reality, Oxford University Press, ISBN 978-0-19-960672-6
+The Chinese Room Argument, part 4 of the September 2, 1999 interview with Searle Philosophy and the Habits of Critical Thinking Archived 2010-06-13 at the Wayback Machine in the Conversations With History series
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+title: "Chinese room"
+chunk: 3/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+=== Strong AI versus biological naturalism ===
+Searle holds a philosophical position he calls "biological naturalism": that consciousness and understanding require specific biological machinery that is found in brains. He writes "brains cause minds" and that "actual human mental phenomena [are] dependent on actual physical–chemical properties of actual human brains". Searle argues that this machinery (known in neuroscience as the "neural correlates of consciousness") must have some causal powers that permit the human experience of consciousness. Searle's belief in the existence of these powers has been criticized.
+Searle does not disagree with the notion that machines can have consciousness and understanding, because, as he writes, "we are precisely such machines". Searle holds that the brain is, in fact, a machine, but that the brain gives rise to consciousness and understanding using specific machinery. If neuroscience is able to isolate the mechanical process that gives rise to consciousness, then Searle grants that it may be possible to create machines that have consciousness and understanding. However, without the specific machinery required, Searle does not believe that consciousness can occur.
+Biological naturalism implies that one cannot determine if the experience of consciousness is occurring merely by examining how a system functions, because the specific machinery of the brain is essential. Thus, biological naturalism is directly opposed to both behaviorism and functionalism (including "computer functionalism" or "strong AI"). Biological naturalism is similar to identity theory (the position that mental states are "identical to" or "composed of" neurological events); however, Searle has specific technical objections to identity theory. Searle's biological naturalism and strong AI are both opposed to Cartesian dualism, the classical idea that the brain and mind are made of different "substances". Indeed, Searle accuses strong AI of dualism, writing that "strong AI only makes sense given the dualistic assumption that, where the mind is concerned, the brain doesn't matter".
+
+=== Consciousness ===
+Searle's original presentation emphasized understanding—that is, mental states with intentionality—and did not directly address other closely related ideas such as "consciousness". However, in more recent presentations, Searle has included consciousness as the real target of the argument.
+
+Computational models of consciousness are not sufficient by themselves for consciousness. The computational model for consciousness stands to consciousness in the same way the computational model of anything stands to the domain being modelled. Nobody supposes that the computational model of rainstorms in London will leave us all wet. But they make the mistake of supposing that the computational model of consciousness is somehow conscious. It is the same mistake in both cases.
+David Chalmers writes, "it is fairly clear that consciousness is at the root of the matter" of the Chinese room.
+Colin McGinn argues that the Chinese room provides evidence that the hard problem of consciousness is fundamentally insoluble. The argument is not about whether a machine can be conscious, but about whether any entity can be shown to be conscious. Any method of probing the occupant of a Chinese room has the same difficulties in principle as exchanging questions and answers in Chinese. According to McGinn, it is not possible to determine whether a conscious agency or some clever simulation inhabits the room.
+Searle argues that this is only true for an observer outside of the room. The whole point of the thought experiment is to put someone inside the room, where they can directly observe the operations of consciousness. Searle claims that from his vantage point within the room there is nothing he can see that could imaginably give rise to consciousness, other than himself, and clearly he does not have a mind that can speak Chinese. In Searle's words, "the computer has nothing more than I have in the case where I understand nothing".
+
+=== Applied ethics ===
+
+Patrick Hew used the Chinese Room argument to deduce requirements from military command and control systems if they are to preserve a commander's moral agency. He drew an analogy between a commander in their command center and the person in the Chinese Room, and analyzed it under a reading of Aristotle's notions of "compulsory" and "ignorance". Information could be "down converted" from meaning to symbols, and manipulated symbolically, but moral agency could be undermined if there was inadequate 'up conversion' into meaning. Hew cited examples from the USS Vincennes incident.
+
+== Computer science ==
+The Chinese room argument is primarily an argument in the philosophy of mind, and both major computer scientists and artificial intelligence researchers consider it irrelevant to their fields. However, several concepts developed by computer scientists are essential to understanding the argument, including symbol processing, Turing machines, Turing completeness, and the Turing test.
+
+=== Strong AI versus AI research ===
+Searle's arguments are not usually considered an issue for AI research. The primary mission of artificial intelligence research is only to create useful systems that act intelligently and it does not matter if the intelligence is "merely" a simulation. AI researchers Stuart J. Russell and Peter Norvig wrote in 2021: "We are interested in programs that behave intelligently. Individual aspects of consciousness—awareness, self-awareness, attention—can be programmed and can be part of an intelligent machine. The additional project making a machine conscious in exactly the way humans are is not one that we are equipped to take on."
+Searle does not disagree that AI research can create machines that are capable of highly intelligent behavior. The Chinese room argument leaves open the possibility that a digital machine could be built that acts more intelligently than a person, but does not have a mind or intentionality in the same way that brains do.
+Searle's "strong AI hypothesis" should not be confused with "strong AI" as defined by Ray Kurzweil and other futurists, who use the term to describe machine intelligence that rivals or exceeds human intelligence—that is, artificial general intelligence, human level AI or superintelligence. Kurzweil is referring primarily to the amount of intelligence displayed by the machine, whereas Searle's argument sets no limit on this. Searle argues that a superintelligent machine would not necessarily have a mind and consciousness.
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+title: "Chinese room"
+chunk: 4/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+=== Turing test ===
+
+The Chinese room implements a version of the Turing test. Alan Turing introduced the test in 1950 to help answer the question "can machines think?" In the standard version, a human judge engages in a natural language conversation with a human and a machine designed to generate performance indistinguishable from that of a human being. All participants are separated from one another. If the judge cannot reliably tell the machine from the human, the machine is said to have passed the test.
+Turing then considered each possible objection to the proposal "machines can think", and found that there are simple, obvious answers if the question is de-mystified in this way. He did not, however, intend for the test to measure for the presence of "consciousness" or "understanding". He did not believe this was relevant to the issues that he was addressing. He wrote:
+
+I do not wish to give the impression that I think there is no mystery about consciousness. There is, for instance, something of a paradox connected with any attempt to localise it. But I do not think these mysteries necessarily need to be solved before we can answer the question with which we are concerned in this paper.
+To Searle, as a philosopher investigating in the nature of mind and consciousness, these are the relevant mysteries. The Chinese room is designed to show that the Turing test is insufficient to detect the presence of consciousness, even if the room can behave or function as a conscious mind would.
+
+=== Symbol processing ===
+
+Computers manipulate physical objects in order to carry out calculations and do simulations. AI researchers Allen Newell and Herbert A. Simon called this kind of machine a physical symbol system. It is also equivalent to the formal systems used in the field of mathematical logic.
+Searle emphasizes the fact that this kind of symbol manipulation is syntactic (borrowing a term from the study of grammar). The computer manipulates the symbols using a form of syntax, without any knowledge of the symbol's semantics (that is, their meaning).
+Newell and Simon had conjectured that a physical symbol system (such as a digital computer) had all the necessary machinery for "general intelligent action", or, as it is known today, artificial general intelligence. They framed this as a philosophical position, the physical symbol system hypothesis: "A physical symbol system has the necessary and sufficient means for general intelligent action." The Chinese room argument does not refute this, because it is framed in terms of "intelligent action", i.e. the external behavior of the machine, rather than the presence or absence of understanding, consciousness and mind.
+Twenty-first century AI programs (such as "deep learning") do mathematical operations on huge matrixes of unidentified numbers and bear little resemblance to the symbolic processing used by AI programs at the time Searle wrote his critique in 1980. Nils Nilsson describes systems like these as "dynamic" rather than "symbolic". Nilsson notes that these are essentially digitized representations of dynamic systems—the individual numbers do not have a specific semantics, but are instead samples or data points from a dynamic signal, and it is the signal being approximated which would have semantics. Nilsson argues it is not reasonable to consider these signals as "symbol processing" in the same sense as the physical symbol systems hypothesis.
+
+=== Chinese room and Turing completeness ===
+
+The Chinese room has a design analogous to that of a modern computer. It has a Von Neumann architecture, which consists of a program (the book of instructions), some memory (the papers and file cabinets), a machine that follows the instructions (the man), and a means to write symbols in memory (the pencil and eraser). A machine with this design is known in theoretical computer science as "Turing complete", because it has the necessary machinery to carry out any computation that a Turing machine can do, and therefore it is capable of doing a step-by-step simulation of any other digital machine, given enough memory and time. Turing writes, "all digital computers are in a sense equivalent." The widely accepted Church–Turing thesis holds that any function computable by an effective procedure is computable by a Turing machine.
+The Turing completeness of the Chinese room implies that it can do whatever any other digital computer can do (albeit much, much more slowly). Thus, if the Chinese room does not or can not contain a Chinese-speaking mind, then no other digital computer can contain a mind. Some replies to Searle begin by arguing that the room, as described, cannot have a Chinese-speaking mind. Arguments of this form, according to Stevan Harnad, are "no refutation (but rather an affirmation)" of the Chinese room argument, because these arguments actually imply that no digital computers can have a mind.
+There are some critics, such as Hanoch Ben-Yami, who argue that the Chinese room cannot simulate all the abilities of a digital computer, such as being able to determine the current time.
+
+== Complete argument ==
+Searle has produced a more formal version of the argument of which the Chinese Room forms a part. He presented the first version in 1984. The version given below is from 1990. The Chinese room thought experiment is intended to prove point A3.
+He begins with three axioms:
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+title: "Chinese room"
+chunk: 5/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+(A1) "Programs are formal (syntactic)."
+A program uses syntax to manipulate symbols and pays no attention to the semantics of the symbols. It knows where to put the symbols and how to move them around, but it does not know what they stand for or what they mean. For the program, the symbols are just physical objects like any others.
+(A2) "Minds have mental contents (semantics)."
+Unlike the symbols used by a program, our thoughts have meaning: they represent things and we know what it is they represent.
+(A3) "Syntax by itself is neither constitutive of nor sufficient for semantics."
+This is what the Chinese room thought experiment is intended to prove: the Chinese room has syntax (because there is a man in there moving symbols around). The Chinese room has no semantics (because, according to Searle, there is no one or nothing in the room that understands what the symbols mean). Therefore, having syntax is not enough to generate semantics.
+Searle posits that these lead directly to this conclusion:
+
+(C1) Programs are neither constitutive of nor sufficient for minds.
+This should follow without controversy from the first three: Programs don't have semantics. Programs have only syntax, and syntax is insufficient for semantics. Every mind has semantics. Therefore no programs are minds.
+This much of the argument is intended to show that artificial intelligence can never produce a machine with a mind by writing programs that manipulate symbols. The remainder of the argument addresses a different issue. Is the human brain running a program? In other words, is the computational theory of mind correct? He begins with an axiom that is intended to express the basic modern scientific consensus about brains and minds:
+
+(A4) Brains cause minds.
+Searle claims that we can derive "immediately" and "trivially" that:
+
+(C2) Any other system capable of causing minds would have to have causal powers (at least) equivalent to those of brains.
+Brains must have something that causes a mind to exist. Science has yet to determine exactly what it is, but it must exist, because minds exist. Searle calls it "causal powers". "Causal powers" is whatever the brain uses to create a mind. If anything else can cause a mind to exist, it must have "equivalent causal powers". "Equivalent causal powers" is whatever else that could be used to make a mind.
+And from this he derives the further conclusions:
+
+(C3) Any artifact that produced mental phenomena, any artificial brain, would have to be able to duplicate the specific causal powers of brains, and it could not do that just by running a formal program.
+This follows from C1 and C2: Since no program can produce a mind, and "equivalent causal powers" produce minds, it follows that programs do not have "equivalent causal powers."
+(C4) The way that human brains actually produce mental phenomena cannot be solely by virtue of running a computer program.
+Since programs do not have "equivalent causal powers", "equivalent causal powers" produce minds, and brains produce minds, it follows that brains do not use programs to produce minds.
+Refutations of Searle's argument take a number of different forms (see below). Computationalists and functionalists reject A3, arguing that "syntax" (as Searle describes it) can have "semantics" if the syntax has the right functional structure. Eliminative materialists reject A2, arguing that minds don't actually have "semantics"—that thoughts and other mental phenomena are inherently meaningless but nevertheless function as if they had meaning.
+
+== Replies ==
+Replies to Searle's argument may be classified according to what they claim to show:
+
+Those which identify who speaks Chinese
+Those which demonstrate how meaningless symbols can become meaningful
+Those which suggest that the Chinese room should be redesigned in some way
+Those which contend that Searle's argument is misleading
+Those which argue that the argument makes false assumptions about subjective conscious experience and therefore proves nothing
+Some of the arguments (robot and brain simulation, for example) fall into multiple categories.
+
+=== Systems and virtual mind replies: finding the mind ===
+These replies attempt to answer the question: since the man in the room does not speak Chinese, where is the mind that does? These replies address the key ontological issues of mind versus body and simulation versus reality. All of the replies that identify the mind in the room are versions of "the system reply".
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+---
+title: "Chinese room"
+chunk: 6/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+==== System reply ====
+The basic version of the system reply argues that it is the "whole system" that understands Chinese. While the man understands only English, when he is combined with the program, scratch paper, pencils and file cabinets, they form a system that can understand Chinese. "Here, understanding is not being ascribed to the mere individual; rather it is being ascribed to this whole system of which he is a part" Searle explains.
+Searle notes that (in this simple version of the reply) the "system" is nothing more than a collection of ordinary physical objects; it grants the power of understanding and consciousness to "the conjunction of that person and bits of paper" without making any effort to explain how this pile of objects has become a conscious, thinking being. Searle argues that no reasonable person should be satisfied with the reply, unless they are "under the grip of an ideology"; In order for this reply to be remotely plausible, one must take it for granted that consciousness can be the product of an information processing "system", and does not require anything resembling the actual biology of the brain.
+Searle then responds by simplifying this list of physical objects: he asks what happens if the man memorizes the rules and keeps track of everything in his head? Then the whole system consists of just one object: the man himself. Searle argues that if the man does not understand Chinese then the system does not understand Chinese either because now "the system" and "the man" both describe exactly the same object.
+Critics of Searle's response argue that the program has allowed the man to have two minds in one head. If we assume a "mind" is a form of information processing, then the theory of computation can account for two computations occurring at once, namely (1) the computation for universal programmability (which is the function instantiated by the person and note-taking materials independently from any particular program contents) and (2) the computation of the Turing machine that is described by the program (which is instantiated by everything including the specific program). The theory of computation thus formally explains the open possibility that the second computation in the Chinese Room could entail a human-equivalent semantic understanding of the Chinese inputs. The focus belongs on the program's Turing machine rather than on the person's. However, from Searle's perspective, this argument is circular. The question at issue is whether consciousness is a form of information processing, and this reply requires that we make that assumption.
+More sophisticated versions of the systems reply try to identify more precisely what "the system" is and they differ in exactly how they describe it. According to these replies, the "mind that speaks Chinese" could be such things as: the "software", a "program", a "running program", a simulation of the "neural correlates of consciousness", the "functional system", a "simulated mind", an "emergent property", or "a virtual mind".
+
+==== Virtual mind reply ====
+Marvin Minsky suggested a version of the system reply known as the "virtual mind reply". The term "virtual" is used in computer science to describe an object that appears to exist "in" a computer (or computer network) only because software makes it appear to exist. The objects "inside" computers (including files, folders, and so on) are all "virtual", except for the computer's electronic components. Similarly, Minsky proposes that a computer may contain a "mind" that is virtual in the same sense as virtual machines, virtual communities and virtual reality.
+To clarify the distinction between the simple systems reply given above and virtual mind reply, David Cole notes that two simulations could be running on one system at the same time: one speaking Chinese and one speaking Korean. While there is only one system, there can be multiple "virtual minds," thus the "system" cannot be the "mind".
+Searle responds that such a mind is at best a simulation, and writes: "No one supposes that computer simulations of a five-alarm fire will burn the neighborhood down or that a computer simulation of a rainstorm will leave us all drenched." Nicholas Fearn responds that, for some things, simulation is as good as the real thing. "When we call up the pocket calculator function on a desktop computer, the image of a pocket calculator appears on the screen. We don't complain that it isn't really a calculator, because the physical attributes of the device do not matter." The question is, is the human mind like the pocket calculator, essentially composed of information, where a perfect simulation of the thing just is the thing? Or is the mind like the rainstorm, a thing in the world that is more than just its simulation, and not realizable in full by a computer simulation? For decades, this question of simulation has led AI researchers and philosophers to consider whether the term "synthetic intelligence" is more appropriate than the common description of such intelligences as "artificial."
+These replies provide an explanation of exactly who it is that understands Chinese. If there is something besides the man in the room that can understand Chinese, Searle cannot argue that (1) the man does not understand Chinese, therefore (2) nothing in the room understands Chinese. This, according to those who make this reply, shows that Searle's argument fails to prove that "strong AI" is false.
+These replies, by themselves, do not provide any evidence that strong AI is true, however. They do not show that the system (or the virtual mind) understands Chinese, other than the hypothetical premise that it passes the Turing test. Searle argues that, if we are to consider Strong AI remotely plausible, the Chinese Room is an example that requires explanation, and it is difficult or impossible to explain how consciousness might "emerge" from the room or how the system would have consciousness. As Searle writes "the systems reply simply begs the question by insisting that the system must understand Chinese" and thus is dodging the question or hopelessly circular.
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+---
+title: "Chinese room"
+chunk: 7/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+=== Robot and semantics replies: finding the meaning ===
+As far as the person in the room is concerned, the symbols are just meaningless "squiggles." But if the Chinese room really "understands" what it is saying, then the symbols must get their meaning from somewhere. These arguments attempt to connect the symbols to the things they symbolize. These replies address Searle's concerns about intentionality, symbol grounding and syntax versus semantics.
+
+==== Robot reply ====
+Suppose that instead of a room, the program was placed into a robot that could wander around and interact with its environment. This would allow a "causal connection" between the symbols and things they represent. Hans Moravec comments: "If we could graft a robot to a reasoning program, we wouldn't need a person to provide the meaning anymore: it would come from the physical world."
+Searle's reply is to suppose that, unbeknownst to the individual in the Chinese room, some of the inputs came directly from a camera mounted on a robot, and some of the outputs were used to manipulate the arms and legs of the robot. Nevertheless, the person in the room is still just following the rules, and does not know what the symbols mean. Searle writes "he doesn't see what comes into the robot's eyes."
+
+==== Derived meaning ====
+Some respond that the room, as Searle describes it, is connected to the world: through the Chinese speakers that it is "talking" to and through the programmers who designed the knowledge base in his file cabinet. The symbols Searle manipulates are already meaningful, they are just not meaningful to him.
+Searle says that the symbols only have a "derived" meaning, like the meaning of words in books. The meaning of the symbols depends on the conscious understanding of the Chinese speakers and the programmers outside the room. The room, like a book, has no understanding of its own.
+
+==== Contextualist reply ====
+Some have argued that the meanings of the symbols would come from a vast "background" of commonsense knowledge encoded in the program and the filing cabinets. This would provide a "context" that would give the symbols their meaning.
+Searle agrees that this background exists, but he does not agree that it can be built into programs. Hubert Dreyfus has also criticized the idea that the "background" can be represented symbolically.
+To each of these suggestions, Searle's response is the same: no matter how much knowledge is written into the program and no matter how the program is connected to the world, he is still in the room manipulating symbols according to rules. His actions are syntactic and this can never explain to him what the symbols stand for. Searle writes "syntax is insufficient for semantics."
+However, for those who accept that Searle's actions simulate a mind, separate from his own, the important question is not what the symbols mean to Searle, what is important is what they mean to the virtual mind. While Searle is trapped in the room, the virtual mind is not: it is connected to the outside world through the Chinese speakers it speaks to, through the programmers who gave it world knowledge, and through the cameras and other sensors that roboticists can supply.
+
+=== Brain simulation and connectionist replies: redesigning the room ===
+These arguments are all versions of the systems reply that identify a particular kind of system as being important; they identify some special technology that would create conscious understanding in a machine. (The "robot" and "commonsense knowledge" replies above also specify a certain kind of system as being important.)
+
+==== Brain simulator reply ====
+Suppose that the program simulated in fine detail the action of every neuron in the brain of a Chinese speaker. This strengthens the intuition that there would be no significant difference between the operation of the program and the operation of a live human brain.
+Searle replies that such a simulation does not reproduce the important features of the brain—its causal and intentional states. He is adamant that "human mental phenomena [are] dependent on actual physical–chemical properties of actual human brains." Moreover, he argues:
+
+[I]magine that instead of a monolingual man in a room shuffling symbols we have the man operate an elaborate set of water pipes with valves connecting them. When the man receives the Chinese symbols, he looks up in the program, written in English, which valves he has to turn on and off. Each water connection corresponds to a synapse in the Chinese brain, and the whole system is rigged up so that after doing all the right firings, that is after turning on all the right faucets, the Chinese answers pop out at the output end of the series of pipes.
+Now, where is the understanding in this system? It takes Chinese as input, it simulates the formal structure of the synapses of the Chinese brain, and it gives Chinese as output. But the man certainly does not understand Chinese, and neither do the water pipes, and if we are tempted to adopt what I think is the absurd view that somehow the conjunction of man and water pipes understands, remember that in principle the man can internalize the formal structure of the water pipes and do all the "neuron firings" in his imagination.
+
+===== China brain =====
+What if we ask each citizen of China to simulate one neuron, using the telephone system, to simulate the connections between axons and dendrites? In this version, it seems obvious that no individual would have any understanding of what the brain might be saying. It is also obvious that this system would be functionally equivalent to a brain, so if consciousness is a function, this system would be conscious.
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+---
+title: "Chinese room"
+chunk: 8/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+===== Brain replacement scenario =====
+In this, we are asked to imagine that engineers have invented a tiny computer that simulates the action of an individual neuron. What would happen if we replaced one neuron at a time? Replacing one would clearly do nothing to change conscious awareness. Replacing all of them would create a digital computer that simulates a brain. If Searle is right, then conscious awareness must disappear during the procedure (either gradually or all at once). Searle's critics argue that there would be no point during the procedure when he can claim that conscious awareness ends and mindless simulation begins. (See Ship of Theseus for a similar thought experiment.)
+
+==== Connectionist replies ====
+Closely related to the brain simulator reply, this claims that a massively parallel connectionist architecture would be capable of understanding. Modern deep learning is parallel and has displayed intelligent behavior in multiple domains. Nils Nilsson argues that modern AI is using digitized "dynamic signals" rather than symbols of the kind used by AI in 1980. Here it is the sampled signal which would have the semantics, not the individual numbers manipulated by the program. This is a different kind of machine than the one that Searle visualized.
+
+==== Combination reply ====
+This response combines the robot reply with the brain simulation reply, arguing that a brain simulation connected to the world through a robot body could have a mind.
+
+==== Many mansions / wait till next year reply ====
+Better technology in the future will allow computers to understand. Searle agrees that this is possible, but considers this point irrelevant. Searle agrees that there may be other hardware besides brains that have conscious understanding.
+These arguments (and the robot or common-sense knowledge replies) identify some special technology that would help create conscious understanding in a machine. They may be interpreted in two ways: either they claim (1) this technology is required for consciousness, the Chinese room does not or cannot implement this technology, and therefore the Chinese room cannot pass the Turing test or (even if it did) it would not have conscious understanding. Or they may be claiming that (2) it is easier to see that the Chinese room has a mind if we visualize this technology as being used to create it.
+In the first case, where features like a robot body or a connectionist architecture are required, Searle claims that strong AI (as he understands it) has been abandoned. The Chinese room has all the elements of a Turing complete machine, and thus is capable of simulating any digital computation whatsoever. If Searle's room cannot pass the Turing test then there is no other digital technology that could pass the Turing test. If Searle's room could pass the Turing test, but still does not have a mind, then the Turing test is not sufficient to determine if the room has a "mind". Either way, it denies one or the other of the positions Searle thinks of as "strong AI", proving his argument.
+The brain arguments in particular deny strong AI if they assume that there is no simpler way to describe the mind than to create a program that is just as mysterious as the brain was. He writes "I thought the whole idea of strong AI was that we don't need to know how the brain works to know how the mind works." If computation does not provide an explanation of the human mind, then strong AI has failed, according to Searle.
+Other critics hold that the room as Searle described it does, in fact, have a mind, however they argue that it is difficult to see—Searle's description is correct, but misleading. By redesigning the room more realistically they hope to make this more obvious. In this case, these arguments are being used as appeals to intuition (see next section).
+In fact, the room can just as easily be redesigned to weaken our intuitions. Ned Block's Blockhead argument suggests that the program could, in theory, be rewritten into a simple lookup table of rules of the form "if the user writes S, reply with P and goto X". At least in principle, any program can be rewritten (or "refactored") into this form, even a brain simulation. In the blockhead scenario, the entire mental state is hidden in the letter X, which represents a memory address—a number associated with the next rule. It is hard to visualize that an instant of one's conscious experience can be captured in a single large number, yet this is exactly what "strong AI" claims. On the other hand, such a lookup table would be ridiculously large (to the point of being physically impossible), and the states could therefore be overly specific.
+Searle argues that however the program is written or however the machine is connected to the world, the mind is being simulated  by a simple step-by-step digital machine (or machines). These machines are always just like the man in the room: they understand nothing and do not speak Chinese. They are merely manipulating symbols without knowing what they mean. Searle writes: "I can have any formal program you like, but I still understand nothing."
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+---
+title: "Chinese room"
+chunk: 9/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+=== Speed and complexity: appeals to intuition ===
+The following arguments (and the intuitive interpretations of the arguments above) do not directly explain how a Chinese speaking mind could exist in Searle's room, or how the symbols he manipulates could become meaningful. However, by raising doubts about Searle's intuitions they support other positions, such as the system and robot replies. These arguments, if accepted, prevent Searle from claiming that his conclusion is obvious by undermining the intuitions that his certainty requires.
+Several critics believe that Searle's argument relies entirely on intuitions. Block writes "Searle's argument depends for its force on intuitions that certain entities do not think." Daniel Dennett describes the Chinese room argument as a misleading "intuition pump" and writes "Searle's thought experiment depends, illicitly, on your imagining too simple a case, an irrelevant case, and drawing the obvious conclusion from it."
+Some of the arguments above also function as appeals to intuition, especially those that are intended to make it seem more plausible that the Chinese room contains a mind, which can include the robot, commonsense knowledge, brain simulation and connectionist replies. Several of the replies above also address the specific issue of complexity. The connectionist reply emphasizes that a working artificial intelligence system would have to be as complex and as interconnected as the human brain. The commonsense knowledge reply emphasizes that any program that passed a Turing test would have to be "an extraordinarily supple, sophisticated, and multilayered system, brimming with 'world knowledge' and meta-knowledge and meta-meta-knowledge", as Daniel Dennett explains.
+
+==== Speed and complexity replies ====
+Many of these critiques emphasize speed and complexity of the human brain, which processes information at 100 billion operations per second (by some estimates). Several critics point out that the man in the room would probably take millions of years to respond to a simple question, and would require "filing cabinets" of astronomical proportions. This brings the clarity of Searle's intuition into doubt.
+An especially vivid version of the speed and complexity reply is from Paul and Patricia Churchland. They propose this analogous thought experiment: "Consider a dark room containing a man holding a bar magnet or charged object. If the man pumps the magnet up and down, then, according to Maxwell's theory of artificial luminance (AL), it will initiate a spreading circle of electromagnetic waves and will thus be luminous. But as all of us who have toyed with magnets or charged balls well know, their forces (or any other forces for that matter), even when set in motion produce no luminance at all. It is inconceivable that you might constitute real luminance just by moving forces around!" Churchland's point is that the problem is that he would have to wave the magnet up and down something like 450 trillion times per second in order to see anything.
+Stevan Harnad is critical of speed and complexity replies when they stray beyond addressing our intuitions. He writes "Some have made a cult of speed and timing, holding that, when accelerated to the right speed, the computational may make a phase transition into the mental. It should be clear that is not a counterargument but merely an ad hoc speculation (as is the view that it is all just a matter of ratcheting up to the right degree of 'complexity.')"
+Searle argues that his critics are also relying on intuitions, however his opponents' intuitions have no empirical basis. He writes that, in order to consider the "system reply" as remotely plausible, a person must be "under the grip of an ideology". The system reply only makes sense (to Searle) if one assumes that any "system" can have consciousness, just by virtue of being a system with the right behavior and functional parts. This assumption, he argues, is not tenable given our experience of consciousness.
+
+=== Other minds and zombies: meaninglessness ===
+Several replies argue that Searle's argument is irrelevant because his assumptions about the mind and consciousness are faulty. Searle believes that human beings directly experience their consciousness, intentionality and the nature of the mind every day, and that this experience of consciousness is not open to question. He writes that we must "presuppose the reality and knowability of the mental." The replies below question whether Searle is justified in using his own experience of consciousness to determine that it is more than mechanical symbol processing. In particular, the other minds reply argues that we cannot use our experience of consciousness to answer questions about other minds (even the mind of a computer), the epiphenoma replies question whether we can make any argument at all about something like consciousness which can not, by definition, be detected by any experiment, and the eliminative materialist reply argues that Searle's own personal consciousness does not "exist" in the sense that Searle thinks it does.
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+---
+title: "Chinese room"
+chunk: 10/11
+source: "https://en.wikipedia.org/wiki/Chinese_room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:21.147536+00:00"
+instance: "kb-cron"
+---
+
+==== Other minds reply ====
+The "Other Minds Reply" points out that Searle's argument is a version of the problem of other minds, applied to machines. There is no way we can determine if other people's subjective experience is the same as our own. We can only study their behavior (i.e., by giving them our own Turing test). Critics of Searle argue that he is holding the Chinese room to a higher standard than we would hold an ordinary person.
+Nils Nilsson writes "If a program behaves as if it were multiplying, most of us would say that it is, in fact, multiplying. For all I know, Searle may only be behaving as if he were thinking deeply about these matters. But, even though I disagree with him, his simulation is pretty good, so I'm willing to credit him with real thought."
+Turing anticipated Searle's line of argument (which he called "The Argument from Consciousness") in 1950 and makes the other minds reply. He noted that people never consider the problem of other minds when dealing with each other. He writes that "instead of arguing continually over this point it is usual to have the polite convention that everyone thinks." The Turing test simply extends this "polite convention" to machines. He does not intend to solve the problem of other minds (for machines or people) and he does not think we need to.
+
+==== Replies considering that Searle's "consciousness" is undetectable ====
+If we accept Searle's description of intentionality, consciousness, and the mind, we are forced to accept that consciousness is epiphenomenal: that it "casts no shadow" i.e. is undetectable in the outside world. Searle's "causal properties" cannot be detected by anyone outside the mind, otherwise the Chinese Room could not pass the Turing test—the people outside would be able to tell there was not a Chinese speaker in the room by detecting their causal properties. Since they cannot detect causal properties, they cannot detect the existence of the mental. Thus, Searle's "causal properties" and consciousness itself is undetectable, and anything that cannot be detected either does not exist or does not matter.
+Mike Alder calls this the "Newton's Flaming Laser Sword Reply". He argues that the entire argument is frivolous, because it is non-verificationist: not only is the distinction between simulating a mind and having a mind ill-defined, but it is also irrelevant because no experiments were, or even can be, proposed to distinguish between the two.
+Daniel Dennett provides this illustration: suppose that, by some mutation, a human being is born that does not have Searle's "causal properties" but nevertheless acts exactly like a human being. This is a philosophical zombie, as formulated in the philosophy of mind. This new animal would reproduce just as any other human and eventually there would be more of these zombies. Natural selection would favor the zombies, since their design is (we could suppose) a bit simpler. Eventually the humans would die out. So therefore, if Searle is right, it is most likely that human beings (as we see them today) are actually "zombies", who nevertheless insist they are conscious. It is impossible to know whether we are all zombies or not. Even if we are all zombies, we would still believe that we are not.
+
+==== Eliminative materialist reply ====
+Several philosophers argue that consciousness, as Searle describes it, does not exist. Daniel Dennett describes consciousness as a "user illusion".
+This position is sometimes referred to as eliminative materialism: the view that consciousness is not a concept that can "enjoy reduction" to a strictly mechanical description, but rather is a concept that will be simply eliminated once the way the material brain works is fully understood, in just the same way as the concept of a demon has already been eliminated from science rather than enjoying reduction to a strictly mechanical description. Other mental properties, such as original intentionality (also called "meaning", "content", and "semantic character"), are also commonly regarded as special properties related to beliefs and other propositional attitudes. Eliminative materialism maintains that propositional attitudes such as beliefs and desires, among other intentional mental states that have content, do not exist. If eliminative materialism is the correct scientific account of human cognition then the assumption of the Chinese room argument that "minds have mental contents (semantics)" must be rejected.
+Searle disagrees with this analysis and argues that "the study of the mind starts with such facts as that humans have beliefs, while thermostats, telephones, and adding machines don't ... what we wanted to know is what distinguishes the mind from thermostats and livers." He takes it as obvious that we can detect the presence of consciousness and dismisses these replies as being off the point.
+
+=== Other replies ===
+Margaret Boden argued in her paper "Escaping from the Chinese Room" that even if the person in the room does not understand the Chinese, it does not mean there is no understanding in the room. The person in the room at least understands the rule book used to provide output responses. She then points out that the same applies to machine languages: a natural language sentence is understood by the programming language code that instantiates it, which in turn is understood by the lower-level compiler code, and so on. This implies that the distinction between syntax and semantics is not fixed, as Searle presupposes, but relative: the semantics of natural language is realized in the syntax of programming language; the semantics of programming language has a semantics that is realized in the syntax of compiler code. Boden argues that there are different degrees of understanding and that it is not a binary notion.
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+---
+title: "Clockwork universe"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Clockwork_universe"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:43.214116+00:00"
+instance: "kb-cron"
+---
+
+The clockwork universe is a concept which compares the universe to a mechanical clock. It continues ticking along, as a perfect machine, with its gears governed by the laws of physics, making every aspect of the machine predictable.  It evolved during the Enlightenment in parallel with the emergence of Newton's laws governing motion and gravity.
+
+
+== History ==
+This idea was very popular among deists during the Enlightenment, when Isaac Newton derived his laws of motion, and showed that alongside the law of universal gravitation, they could predict the behaviour of both terrestrial objects and the Solar System.
+A similar concept goes back to Johannes de Sacrobosco's early 13th-century introduction to astronomy: On the Sphere of the World. In this widely popular medieval text, Sacrobosco spoke of the universe as the machina mundi, the machine of the world, suggesting that the reported eclipse of the Sun at the crucifixion of Jesus was a disturbance of the order of that machine.
+Responding to Gottfried Leibniz, a prominent supporter of the theory, in the Leibniz–Clarke correspondence, Samuel Clarke wrote:
+
+The Notion of the World's being a great Machine, going on without the Interposition of God, as a Clock continues to go without the Assistance of a Clockmaker; is the Notion of Materialism and Fate, and tends, (under pretence of making God a Supra-mundane Intelligence,) to exclude Providence and God's Government in reality out of the World.
+In 2009, artist Tim Wetherell created a wall piece for Questacon (The National Science and Technology centre in Canberra, Australia) representing the concept of the clockwork universe. This steel artwork contains moving gears, a working clock, and a movie of the lunar terminator.
+
+
+== See also ==
+Mechanical philosophy
+Determinism
+Eternalism (philosophy of time)
+History of science
+Orrery
+Philosophy of space and time
+Superdeterminism
+
+
+== References ==
+
+
+== Further reading ==
+E. J. Dijksterhuis (1961) The Mechanization of the World Picture, Oxford University Press
+Dolnick, Edward (2011) The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World, HarperCollins.
+David Brewster (1850) "A Short Scheme of the True Religion", manuscript quoted in Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton, cited in Dolnick, page 65.
+Anneliese Maier (1938) Die Mechanisierung des Weltbildes im 17. Jahrhundert
+Webb, R.K. ed. Knud Haakonssen (1996) "The Emergence of Rational Dissent." Enlightenment and Religion: Rational Dissent in Eighteenth-Century Britain, Cambridge University Press page 19.
+Westfall, Richard S. Science and Religion in Seventeenth-Century England. p. 201.
+Riskins, Jessica (2016) The Restless Clock: A History of the Centuries-Long Argument over What Makes Living Things Tick, University of Chicago Press.
+
+
+== External links ==
+"The Clockwork Universe". Archived 2020-02-14 at the Wayback Machine  The Physical World. Ed. John Bolton, Alan Durrant, Robert Lambourne, Joy Manners, Andrew Norton.
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diff --git a/data/en.wikipedia.org/wiki/Codex_on_the_Flight_of_Birds-0.md b/data/en.wikipedia.org/wiki/Codex_on_the_Flight_of_Birds-0.md
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+---
+title: "Codex on the Flight of Birds"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Codex_on_the_Flight_of_Birds"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:44.454884+00:00"
+instance: "kb-cron"
+---
+
+Codex on the Flight of Birds is a relatively short codex from c. 1505 by Leonardo da Vinci.
+It comprises 18 folios and measures 21 × 15 centimetres.  Now held at the Royal Library of Turin, the codex begins with an examination of the flight behavior of birds and proposes mechanisms for flight by machines. Leonardo constructed a number of these machines, and attempted to launch them from a hill near Florence. However, his efforts failed.
+In the codex, Leonardo notes for the first time that the center of gravity of a flying bird does not coincide with its center of pressure.
+
+== Summary ==
+The following summaries are from the codex whose English translation was prepared by Culturando and Smithsonian Institution.
+
+=== Front Page ===
+The front page is titled "On Casting Medals". The first paragraph gives a brief recipe that consists of "emery", "nitric acid", "iron filings", "vinegar", "ashes of walnut leaves", and "finely ground straw ash". The second paragraph tells of the process of crushing diamonds into diamond powder and separating the powder from lead. The last paragraph explains how to crush large crystals into smaller crystals, and how to grind, purify, and color enamel.
+
+=== Folio 1 ===
+The first page in the folio one contains 11 diagrams with captions for each that relate to gravity, density, balance, and oscillations. The next page contains four diagrams and a lengthy paragraph on velocity and the differences in movement along the arc and chord of part of a circle.
+Leonardo comments on how gravity, which is caused by the "attraction of one object to another", takes place when an object is placed above another object and the top object is heavier than the bottom object. He also writes on the workings of a balance by describing how "the vertical center of a balance must always be perpendicular" and how the length of the arm on the balance is proportional to the amount of oscillations and the oscillation angle. A short commentary is included on relating density to weight, and he questions why ice floats in water if it is the denser of the two.
+In the last page of this folio, Leonardo explains why an object falling down the arc of a curve will fall faster than if the object falls down the chord of a curve. He explains this saying that the angle of the chord is half of the angle the curve makes between the midpoint, endpoint, and horizontal, and since this angle is half then the speed will also be half. He compares this with the angle the arc makes with the endpoint, midpoint, and horizontal. An object falling down an arc is then said to be 7/8 faster than if it were to fall down the chord of a curve.
+
+=== Folio 2 ===
+Folio 2 contains two images on each of the two pages along with commentary on the following: gravity, powder amount vs. shot diameter, center of gravity for pyramids, and round balances.
+In the first paragraph, Leonardo restates his theory on gravity and expands on it to say that the motion caused by gravity acts in the direction of the imaginary line between the two object's centers. He goes on to say that motion due to gravity is only caused because the objects have no way to resist gravity.
+Leonardo then goes on to talk about the relation between the amount of powder and the size of a ball. He writes that the amount of powder needed is proportional to the diameter of the ball. Expanding on that, he comes up with the amount of powder needed is "directly proportional to the square of the diameter".
+The center of gravity of a pyramid is written to lie "in the third point along of its length toward the base". He uses this geometry to explain how to find the center of gravity of a semicircle. If one were to divide the semicircle into pyramids whose bases were almost straight, then by finding the center of gravity of those pyramids one could find the center of gravity for the semicircle.
+The last page of folio 2 talks about rounded balances and how they react to gravity. Leonardo writes that if a balance was suspended in its center of gravity, then it would not move or oscillate, regardless of position. He then goes on to say that if there are two weights of equal mass on the ends of this balance, then, when moved from its starting position, the balance will never return to the starting position. After this, he theorizes that a balance in this same situation will move if one of the weights is along a straighter line of descent as compared to the other weight. He then disproves his theory by showing the balance and weights as symmetrically equal, meaning there is no reason for the balance to move.
+
+=== Folio 3 ===
+The third folio contains 10 drawings and commentary on the following: science of machines, balances, energy, and circular motion.
+Leonardo begins folio 3 with a declaration stating the science of machines is the most useful science overall because of its use by any moving object.
+He goes on to state that objects of different shapes that are on different degrees of slope have different amounts of energy. His next topic is about the construction of a certain balance in which circular motion is prevented. The diagrams in this folio represent round balances and multiple shaped objects on differing slopes that are connected together.
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diff --git a/data/en.wikipedia.org/wiki/Codex_on_the_Flight_of_Birds-1.md b/data/en.wikipedia.org/wiki/Codex_on_the_Flight_of_Birds-1.md
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+---
+title: "Codex on the Flight of Birds"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Codex_on_the_Flight_of_Birds"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:44.454884+00:00"
+instance: "kb-cron"
+---
+
+=== Folio 4 ===
+Folio 4 contains nine diagrams and a page of text on gravity and its effect on different shapes connected together on a balance. The back page of this folio has Leonardo's first reference to birds and his explanation on how they fly.
+Leonardo writes a lengthy amount of text about two weights that each weigh three pounds that are connected together on either side of a balance. The slopes that each object rests on are at different angles, however. Leonardo goes on to write that, because of the slopes, one weight may weigh three pounds, but it is only providing two pounds of force. The other weight, also three pounds, is similarly stated to only provide one pound of force because it is resting on a smaller incline. Later on this page, he writes on the forces a balance experiences depending on the location of weights on the balance. The first reference to pressure for this codex is made towards the end of this folio, relating it to the working of a balance.
+The first commentary on birds, for this codex, are made on the second page of the fourth folio. Leonardo describes how the tips of a bird's feathers are always the highest part of the bird, when its wings are lowered, and how the bones in the wing are the highest part of a bird when its wings are raised. He writes on the heaviest part of a body being the location that guides movement for that body. He also questions what part of the wing of a bird experiences the greatest amount of air pressure. To end this folio, Leonardo states how an object, "that does not bend under the pressure of objects of different sizes and weights", will distribute its weight to its supporting points that surround the center of the object.
+
+=== Folio 5 ===
+The fifth folio contains six diagrams and commentary on birds and flight.
+Leonardo starts off folio 5 by stating that if a man were to be in a flying machine, nothing should get in his way from the waist up, so that he can balance himself as one does in a boat. He goes on to write on how a bird's direction will change with the direction of the wind. A bird which is going in a straight line that comes into a cross breeze at a perpendicular angle will now be heading in a direction that is in between the two endpoints of each direction. He ends the first page by explaining that if a bird in a descent wants to turn left or right, then it will lower the wing on the side of the direction it wants to turn.
+Birds can gain altitude, as stated by Leonardo, by "[raising] the shoulders and [beating] the tips of the wings towards itself, thus condensing the air that stands between the tips of [its] wings and itself". He also describes the flight of a kite as seeking a wind current. When the winds are high, one will see the bird very high in the sky, but when the winds are low, the bird stays closer to the ground. Leonardo describes how a bird rests in the air, after flapping its wings to gain altitude, by gliding downward to the ground.
+
+=== Folio 6 ===
+Folio 6 contains multiple diagrams of birds flying and their bone structure, and all of the commentary is on flight and how birds fly.
+Leonardo starts off by describing how a bird ascends or descends in different wind conditions. Here is a summary.
+
+He states that the only way for a bird to ascend when in a tailwind is for the bird, at its peak ascent, to turn in a semicircle and face the wind to continue its ascension in the opposite direction.
+Leonardo explains that a bird should fly above the clouds to prevent its wings from getting wet and to avoid the circular air patterns that come from mountainous terrain. If a bird flies above the clouds and somehow gets turned over, then it should have plenty of time to turn itself back over by either "[falling] immediately with the wingtip downwind, or lowering the opposite wing to below halfway". He also comments on the rib structure of a bird and theorizes which ribs are the most useful. He ends folio 6 by stating he needs to do more practical tests on the ribs of birds.
+
+=== Folio 7 ===
+The seventh folio contains a very detailed diagram of either the tip of a bird's wing or the wing of a possible flying machine along with five more diagrams of birds in flight.
+Leonardo starts writing on a flying machine and comparing it with the notes he has already taken on the flight of birds. He states that "the bird" (machine) must attain a high altitude it case it were to turn over so as to have enough time to right itself. He notes that the framework needs to be strong with leather laces and raw silk for the ribs. He also adds that there should not be any metal in the machine because of its tendency to wear or break under stress.
+He continues his notes on the flying machine by writing on the "nerve" of the machine. It was to be made of a "thick ribbon of tanned leather" that would spread the wing in flight. He was going to use this same framework in the "nerves" above and below this one for safety reasons.
+The rest of folio 7 is Leonardo's notes and instructions on how to fly his machine like a bird. Here is a quick summary:
+
+=== Folio 8 ===
+Leonardo's eighth folio in On the Flight of Birds contains 11 diagrams of birds flying and more instructions for his flying machine. Here is a quick summary of the first half of Folio 8:
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+---
+title: "Codex on the Flight of Birds"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Codex_on_the_Flight_of_Birds"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:44.454884+00:00"
+instance: "kb-cron"
+---
+
+Leonardo goes on to write that if the "bird" is above the wind but turning into the wind, the "bird" must lower its tail otherwise it will overturn. He states that the action of lowering the tail to be less susceptible to wind in this situation will make it impossible for the "bird" to be overturned. He goes on to prove this by referencing the "Elements of Machinery". Afterwards, he writes on the compression of air due to the wings, and he states that the entire length of the wing is not used in the compression of air in front of the wing. To prove this, he asks readers to examine bird wings for themselves and to check the larger spacing in between the not as large feathers.
+
+=== Folio 9 ===
+Folio 9 contains another 12 diagrams of birds in flight and structure framework. It particularly looks at the effect of wind on the movement of a bird.
+
+=== Folio 10 ===
+Discusses the wings of a bird.
+
+=== Folio 11 ===
+Discussion of the importance of truth
+
+=== Folio 12 ===
+
+=== Folio 13 ===
+
+=== Folio 14 ===
+
+=== Folio 15 ===
+
+=== Folio 16 ===
+
+=== Folio 17 ===
+
+=== Folio 18 ===
+
+=== Back Page ===
+
+== Display in the U.S. ==
+On a rare loan from the Bibliotecha Reale museum in Turin, Italy, the original 18-page codex was displayed in the National Air and Space Museum in Washington D.C. for 40 days, starting 13 September 2013. In an exhibition the codex was displayed in the Bibliotecha Reale museum in Turin until 8 March 2020.
+
+== Citations ==
+
+== Sources ==
+Cremante, Simona. "Leonardo Da Vinci". Giunti, 1698.
+Crispino, Enrica; Pedretti, Carlo; Frost, Catherine. Leonardo: Art and Science. Giunti, 2001. ISBN 88-09-01511-8
+Pedretti, Carlo. "A Chronology of Leonardo Da Vinci's Architectural Studies after 1500". Geneva: E. Droz, 1962.
+Leonardo Da Vinci's Codex on the Flight of Birds (Smithsonian)
+Galluzzi, Paolo. Leonardo da Vinci, Engineer and Architect. [Montréal]: Montreal Museum of Fine Arts, 1987. Print. ISBN 2891920848
+Heydenreich, Ludwig H., Bern Dibner, Ladislao Reti, and Ladislao Reti. Leonardo the Inventor. New York: McGraw-Hill, 1980. Print. ISBN 0070286108
+Edoardo Zanon, The book of the codex on flight, from the study of bird flight to the flying machine. Leonardo3 – Milano, 2009. ISBN 978-88-6048-011-8
+
+== External links ==
+
+Leonardo da Vinci: anatomical drawings from the Royal Library, Windsor Castle, exhibition catalog fully online as PDF from The Metropolitan Museum of Art, which contains material on Codex on the Flight of Birds (see index)
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+---
+title: "Coherent extrapolated volition"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Coherent_extrapolated_volition"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:22.448454+00:00"
+instance: "kb-cron"
+---
+
+Coherent extrapolated volition (CEV) is a theoretical framework in the field of AI alignment describing an approach by which an artificial superintelligence (ASI) would act on a benevolent supposition of what humans would want if they were more knowledgeable, more rational, had more time to think, and had matured together as a society, as opposed to humanity's current individual or collective preferences. It was proposed by Eliezer Yudkowsky in 2004 as part of his work on friendly AI.
+
+
+== Concept ==
+CEV proposes that an advanced AI system should derive its goals by extrapolating the idealized volition of humanity. This means aggregating and projecting human preferences into a coherent utility function that reflects what people would desire under ideal epistemic and moral conditions. The aim is to ensure that AI systems are aligned with humanity's true interests, rather than with transient or poorly informed preferences.
+
+In poetic terms, our coherent extrapolated volition is our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together; where the extrapolation converges rather than diverges, where our wishes cohere rather than interfere; extrapolated as we wish that extrapolated, interpreted as we wish that interpreted.
+
+
+== Debate ==
+Yudkowsky and Nick Bostrom note that CEV has several interesting properties. It is designed to be humane and self-correcting, by capturing the source of human values instead of trying to list them. It avoids the difficulty of laying down an explicit, fixed list of rules. It encapsulates moral growth, preventing flawed current moral beliefs from getting locked in. It limits the influence that a small group of programmers can have on what the ASI would value, thus also reducing the incentives to build ASI first. And it keeps humanity in charge of its destiny.
+CEV also faces significant theoretical and practical challenges.
+Bostrom notes that CEV has "a number of free parameters that could be specified in various ways, yielding different versions of the proposal." One such parameter is the extrapolation base (whose extrapolated volition is taken into account). For example, whether it should include people with severe dementia, patients in a vegetative state, foetuses, or embryos. He also notes that if CEV's extrapolation base only includes humans, there is a risk that the result would be ungenerous toward other animals and digital minds. One possible solution would be to include a mechanism to expand CEV's extrapolation base.
+
+
+== Variants and alternatives ==
+A proposed theoretical alternative to CEV is to rely on an artificial superintelligence's superior cognitive capabilities to figure out what is morally right, and let it act accordingly. It is also possible to combine both techniques, for instance with the ASI following CEV except when it is morally impermissible.
+In another review, a philosophical analysis explores CEV through the lens of social trust in autonomous systems. Drawing on Anthony Giddens' concept of "active trust", the author proposes an evolution of CEV into "Coherent, Extrapolated and Clustered Volition" (CECV). This formulation aims to better reflect the moral preferences of diverse cultural groups, thus offering a more pragmatic ethical framework for designing AI systems that earn public trust while accommodating societal diversity.
+
+
+== See also ==
+Friendly artificial intelligence
+AI alignment
+AI safety
+Rationality
+
+
+== References ==
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+---
+title: "Computational creativity"
+chunk: 1/8
+source: "https://en.wikipedia.org/wiki/Computational_creativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:23.728483+00:00"
+instance: "kb-cron"
+---
+
+Computational creativity (also known as artificial creativity, mechanical creativity, creative computing or creative computation) is a multidisciplinary endeavour that is located at the intersection of the fields of artificial intelligence, cognitive psychology, philosophy, and the arts (e.g., computational art as part of computational culture).
+Is the application of computer systems to emulate human-like creative processes, facilitating the generation of artistic and design outputs that mimic innovation and originality.
+The goal of computational creativity is to model, simulate or replicate creativity using a computer, to achieve one of several ends:
+
+To construct a program or computer capable of human-level creativity.
+To better understand human creativity and to formulate an algorithmic perspective on creative behavior in humans.
+To design programs that can enhance human creativity without necessarily being creative themselves.
+The field of computational creativity concerns itself with theoretical and practical issues in the study of creativity. Theoretical work on the nature and proper definition of creativity is performed in parallel with practical work on the implementation of systems that exhibit creativity, with one strand of work informing the other.
+The applied form of computational creativity is known as media synthesis.
+
+== Theoretical issues ==
+Theoretical approaches concern the essence of creativity. Especially, under what circumstances it is possible to call the model a "creative" if eminent creativity is about rule-breaking or the disavowal of convention. This is a variant of Ada Lovelace's objection to machine intelligence, as recapitulated by modern theorists such as Teresa Amabile. If a machine can do only what it was programmed to do, how can its behavior ever be called creative?
+Indeed, not all computer theorists would agree with the premise that computers can only do what they are programmed to do—a key point in favor of computational creativity.
+
+== Defining creativity in computational terms ==
+Because no single perspective or definition seems to offer a complete picture of creativity, the AI researchers Newell, Shaw and Simon developed the combination of novelty and usefulness into the cornerstone of a multi-pronged view of creativity, one that uses the following four criteria to categorize a given answer or solution as creative:
+
+The answer is novel and useful (either for the individual or for society)
+The answer demands that we reject ideas we had previously accepted
+The answer results from intense motivation and persistence
+The answer comes from clarifying a problem that was originally vague
+Margaret Boden focused on the first two of these criteria, arguing instead that creativity (at least when asking whether computers could be creative) should be defined as "the ability to come up with ideas or artifacts that are new, surprising, and valuable".
+Mihaly Csikszentmihalyi argued that creativity had to be considered instead in a social context, and his DIFI (Domain-Individual-Field Interaction) framework has since strongly influenced the field. In DIFI, an individual produces works whose novelty and value are assessed by the field—other people in society—providing feedback and ultimately adding the work, now deemed creative, to the domain of societal works from which an individual might be later influenced.
+Whereas the above reflects a top-down approach to computational creativity, an alternative thread has developed among bottom-up computational psychologists involved in artificial neural network research. During the late 1980s and early 1990s, for example, such generative neural systems were driven by genetic algorithms. Experiments involving recurrent nets were successful in hybridizing simple musical melodies and predicting listener expectations.
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+---
+title: "Computational creativity"
+chunk: 2/8
+source: "https://en.wikipedia.org/wiki/Computational_creativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:23.728483+00:00"
+instance: "kb-cron"
+---
+
+== Historical evolution of computational creativity ==
+The use computational processes to generate creative artifacts has been present from early times in history. During the late 1800's, methods for composing music combinatorily were explored, involving prominent figures like Mozart, Bach, Haydn, and Kiernberger. This approach extended to analytical endeavors as early as 1934, where simple mechanical models were built to explore mathematical problem solving. Professional interest in the creative aspect of computation also was commonly addressed in early discussions of artificial intelligence. The 1956 Dartmouth Conference, listed creativity, invention, and discovery as key goals for artificial intelligence.
+As the development of computers allowed systems of greater complexity, the 1970's and 1980's saw invention of early systems that modelled creativity using symbolic or rule-based approaches. The field of creative storytelling investigated several such models. Meehan's TALE-SPIN (1977) generated narratives through simulation of character goals and decision trees. Dehn's AUTHOR (1981) approached generation by simulating an author's process for crafting a story. Beyond narrative generation, computational creativity expanded into artistic and scientific domains.
+Artistic image generation was one of the disciplines that saw early potential in generated artifacts through computational creativity. One of the most prominent examples was Harold Cohen's AARON, which produced art through composition and adaptation of figures based on a large set of symbolic rules and heuristics for visual composition. Some systems also tackled creativity in scientific endeavors. BACON was said to rediscover natural laws like Boyle's Law and Kepler's law through hypothesis testing in constrained spaces.
+By the 1990's the modeling techniques became more adaptive, attempting to implement cognitive creative rules for generation. Turner's MINSTREL (1993) introduced TRAMs (Transform Recall Adapt Methods) to simulate creative re-use of prior material for generative storytelling. Meanwhile, Pérez y Pérez's MEXICA (1999) modeled the creative writing process using cycles of engagement and reflection. As systems increasingly incorporated models of internal evaluation, another approach that emerged was that of combining symbolic generation with domain-specific evaluation metrics, modeling generative and selective steps to creativity
+In the field of generational humor, the JAPE system (1994) generated pun-based riddles using Prolog and WordNet, applying symbolic pattern-matching rules and a large lexical database (WordNet) to compose riddles involving wordplay. WordNet is a system developed by George Miller and his team at Princeton, its platform and inspired word-mapping structures have been used as the backbone of several syntactic and semantic AI programs. A notable system for music generation was David Cope's EMI (Experiments in Musical Intelligence) or Emmy, which was trained in the styles of artists like Bach, Beethoven, or Chopin and generated novel pieces in their style through pattern abstraction and recomposition.
+In the 2000s and beyond, machine learning began influencing creative system design. Researchers such as Mihalcea and Strapparava trained classifiers to distinguish humorous from non-humorous text, using stylistic and semantic features. Meanwhile custom computational approaches led to chess systems like Deep Blue generating quasi-creative gameplay strategies through search algorithms and parallel processing constrained by specific rules and patterns for evaluation.
+The institutional development of computational creativity grew along its technical advances. Dedicated workshops such as the IJWCC emerged in the 1990s, growing out of interdisciplinary conferences focused on AI and creativity. By the early 2000s, the field coalesced around annual conferences like the International Conference on Computational Creativity (ICCC). Recently, with the advent of Deep Learning, Transformers, and further refinement in Machine Learning structures, computational creativity's implementation space has new tools for development.
+
+== Machine learning for computational creativity ==
+
+While traditional computational approaches to creativity rely on the explicit formulation of prescriptions by developers and a certain degree of randomness in computer programs, machine learning methods allow computer programs to learn on heuristics from input data enabling creative capacities within the computer programs. Especially, deep artificial neural networks allow to learn patterns from input data that allow for the non-linear generation of creative artefacts. Before 1989, artificial neural networks have been used to model certain aspects of creativity. Peter Todd (1989) first trained a neural network to reproduce musical melodies from a training set of musical pieces. Then he used a change algorithm to modify the network's input parameters. The network was able to randomly generate new music in a highly uncontrolled manner. In 1992, Todd extended this work, using the so-called distal teacher approach that had been developed by Paul Munro, Paul Werbos, D. Nguyen and Bernard Widrow, Michael I. Jordan and David Rumelhart. In the new approach, there are two neural networks, one of which is supplying training patterns to another. 
+In later efforts by Todd, a composer would select a set of melodies that define the melody space, position them on a 2-d plane with a mouse-based graphic interface, and train a connectionist network to produce those melodies, and listen to the new "interpolated" melodies that the network generates corresponding to intermediate points in the 2-d plane.
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+---
+title: "Computational creativity"
+chunk: 3/8
+source: "https://en.wikipedia.org/wiki/Computational_creativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:23.728483+00:00"
+instance: "kb-cron"
+---
+
+=== Language models and hallucination ===
+Language models like GPT and LSTM are used to generate texts for creative purposes, such as novels and scripts. These models demonstrate hallucination from time to time, where erroneous materials are presented as factual. Creators make use of their hallucinatory tendency to capture unintended results. Ross Goodwin's 1 the Road, for example, uses an LSTM model trained on literature corpora to generate a novel that refers to Jack Kerouac's On the Road based on multimodal input captured by a camera, a microphone, a laptop's inner clock, and a GPS throughout the road trip. Brian Merchant commented on the novel as "pixelated poetry in its ragtag assemblage of modern American imagery". Oscar Sharp and Ross Goodwin created the experimental sci-fi short film Sunspring in 2016, written with an LSTM model, trained on their scripts and 1980-1990 sci-fi movies. Rodica Gotca critiqued their overall lack of focus on the narrative and intention to create based on the background of human culture.
+Nevertheless, researchers highlight the positive side of language models' hallucination for generating novel solutions, given that the correctness and consistency of the response could be controlled. Jiang et al. propose the divergence-convergence flow model for harnessing the hallucinatory effects. They summarize the types of such effects in current research into factuality hallucinations and faithfulness hallucinations, which can be divided into smaller classes like factual fabrication and instruction inconsistency. While the divergence stage involves generating potentially hallucinatory content, the convergence stage focuses on filtering the hallucinations that are useful for the user with intent recognition and evaluation metrics.
+
+== Key concepts from literature ==
+Some high-level and philosophical themes recur throughout the field of computational creativity, for example as follows.
+
+=== Important categories of creativity ===
+Margaret Boden refers to creativity that is novel merely to the agent that produces it as "P-creativity" (or "psychological creativity"), and refers to creativity that is recognized as novel by society at large as "H-creativity" (or "historical creativity").
+
+=== Exploratory and transformational creativity ===
+Boden also distinguishes between the creativity that arises from an exploration within an established conceptual space, and the creativity that arises from a deliberate transformation or transcendence of this space. She labels the former as exploratory creativity and the latter as transformational creativity, seeing the latter as a form of creativity far more radical, challenging, and rarer than the former. Following the criteria from Newell and Simon elaborated above, we can see that both forms of creativity should produce results that are appreciably novel and useful (criterion 1), but exploratory creativity is more likely to arise from a thorough and persistent search of a well-understood space (criterion 3) -- while transformational creativity should involve the rejection of some of the constraints that define this space (criterion 2) or some of the assumptions that define the problem itself (criterion 4). Boden's insights have guided work in computational creativity at a very general level, providing more an inspirational touchstone for development work than a technical framework of algorithmic substance. However, Boden's insights are also the subject of formalization, most notably in the work by Geraint Wiggins.
+
+=== Generation and evaluation ===
+The criterion that creative products should be novel and useful means that creative computational systems are typically structured into two phases, generation and evaluation. In the first phase, novel (to the system itself, thus P-Creative) constructs are generated; unoriginal constructs that are already known to the system are filtered at this stage. This body of potentially creative constructs is then evaluated, to determine which are meaningful and useful and which are not. This two-phase structure conforms to the Geneplore model of Finke, Ward and Smith, which is a psychological model of creative generation based on empirical observation of human creativity.
+Jordanous and Keller emphasize the need for a "tractable and well-articulated model of creativity". They extracted 694 creativity words derived from a corpus of empirical studies in psychology and creativity research spanning 60 years and clustered them based on lexical similarity. As a result, they identify 14 key components of creativity, which form the basis of the framework "Standardised Procedure for Evaluating Creative Systems" (SPECS). These components include aspects like "dealing with uncertainty", "independence and freedom", "social interaction and communication", and "spontaneity & subconscious processing".
+
+=== Co-creation ===
+While much of computational creativity research focuses on independent and automatic machine-based creativity generation, many researchers are inclined towards a collaboration approach. This human-computer interaction is sometimes categorized under the creativity support tools development. These systems aim to provide an ideal framework for research, integration, decision-making, and idea generation. Recently, deep learning approaches to imaging, sound and natural language processing, resulted in the modeling of productive creativity development frameworks.
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+---
+title: "Computational creativity"
+chunk: 4/8
+source: "https://en.wikipedia.org/wiki/Computational_creativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:23.728483+00:00"
+instance: "kb-cron"
+---
+
+=== Innovation ===
+Computational creativity is increasingly being discussed in the innovation and management literature as the recent development in AI may disrupt entire innovation processes and fundamentally change how innovations will be created. Philip Hutchinson highlights the relevance of computational creativity for creating innovation and introduced the concept of "self-innovating artificial intelligence" (SAI) to describe how companies make use of AI in innovation processes to enhance their innovative offerings. SAI is defined as the organizational utilization of AI with the aim of incrementally advancing existing or developing new products, based on insights from continuously combining and analyzing multiple data sources. As AI becomes a general-purpose technology, the spectrum of products to be developed with SAI will broaden from simple to increasingly complex. This implies that computational creativity leads to a shift of creativity-related skills for humans.
+Veale and Pérez y Pérez consider "optimal innovation" proposed by Giora et al. a useful foundation for developing computational creativity. Giora et al.'s experiment asks participants to do pleasure and familiarity ratings of verbal stimuli (e.g., body and soul vs. body and sole) and non-verbal stimuli (e.g., a peace dove vs. a peace dove vertically posed that looks like a waving hand). It reveals that pleasing stimuli need to be innovative while preserving the salient meaning of the literal form. Veale and Pérez y Pérez highlight the need to develop computational systems that capture how meaning changes due to formal changes.
+
+=== Combinatorial creativity ===
+A great deal, perhaps all, of human creativity can be understood as a novel combination of pre-existing ideas or objects. Common strategies for combinatorial creativity include:
+
+Placing a familiar object in an unfamiliar setting (e.g., Marcel Duchamp's Fountain) or an unfamiliar object in a familiar setting (e.g., a fish-out-of-water story such as The Beverly Hillbillies)
+Blending two superficially different objects or genres (e.g., a sci-fi story set in the Wild West, with robot cowboys, as in Westworld, or the reverse, as in Firefly; Japanese haiku poems, etc.)
+Comparing a familiar object to a superficially unrelated and semantically distant concept (e.g., "Makeup is the Western burka"; "A zoo is a gallery with living exhibits")
+Adding a new and unexpected feature to an existing concept (e.g., adding a scalpel to a Swiss Army knife; adding a camera to a mobile phone)
+Compressing two incongruous scenarios into the same narrative to get a joke (e.g., the Emo Philips joke "Women are always using men to advance their careers. Damned anthropologists!")
+Using an iconic image from one domain in a domain for an unrelated or incongruous idea or product (e.g., using the Marlboro Man image to sell cars, or to advertise the dangers of smoking-related impotence).
+The combinatorial perspective allows us to model creativity as a search process through the space of possible combinations. The combinations can arise from composition or concatenation of different representations, or through a rule-based or stochastic transformation of initial and intermediate representations. Genetic algorithms and neural networks can be used to generate blended or crossover representations that capture a combination of different inputs.
+
+==== Conceptual blending ====
+
+Mark Turner and Gilles Fauconnier propose a model called Conceptual Integration Networks that elaborates upon Arthur Koestler's ideas about creativity as well as work by Lakoff and Johnson, by synthesizing ideas from Cognitive Linguistic research into mental spaces and conceptual metaphors. Their basic model defines an integration network as four connected spaces:
+
+A first input space (contains one conceptual structure or mental space)
+A second input space (to be blended with the first input)
+A generic space of stock conventions and image-schemas that allow the input spaces to be understood from an integrated perspective
+A blend space in which a selected projection of elements from both input spaces are combined; inferences arising from this combination also reside here, sometimes leading to emergent structures that conflict with the inputs.
+Fauconnier and Turner describe a collection of optimality principles that are claimed to guide the construction of a well-formed integration network. In essence, they see blending as a compression mechanism in which two or more input structures are compressed into a single blend structure. This compression operates on the level of conceptual relations. For example, a series of similarity relations between the input spaces can be compressed into a single identity relationship in the blend.
+Some computational success has been achieved with the blending model by extending pre-existing computational models of analogical mapping that are compatible by virtue of their emphasis on connected semantic structures. In 2006, Francisco Câmara Pereira presented an implementation of blending theory that employs ideas both from symbolic AI and genetic algorithms to realize some aspects of blending theory in a practical form; his example domains range from the linguistic to the visual, and the latter most notably includes the creation of mythical monsters by combining 3-D graphical models.
+
+=== AI-assisted writing as curation ===
+One of the first attempts to provide a literary-theoretical framework for AI-assisted writing was undertaken by Luciano Floridi in 2025. In his model of 'Distant Writing', the author functions as a designer and curator who develops narrative structures rather than formulating text manually. Through iterative selection and 'Socratic maieutics' (prompting), the human directs the machine, thereby assuming full intellectual responsibility for the design of the resulting work. Floridi's framework has a pre-LLM antecedent in the visual arts: Nicolas Bourriaud's Postproduction (2002) had argued that artists increasingly function as programmers and navigators of pre-existing cultural material rather than as original creators — a logic that Floridi transfers, with substantial theoretical elaboration, to the context of AI-assisted literary production. Floridi’s term 'distant writing' itself is coined in explicit analogy to Franco Moretti's 'distant reading' — understood in its later, computationally inflected sense — which had reframed literary analysis as the large-scale, algorithm-assisted study of textual corpora.
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+title: "Computational creativity"
+chunk: 5/8
+source: "https://en.wikipedia.org/wiki/Computational_creativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:23.728483+00:00"
+instance: "kb-cron"
+---
+
+== Linguistic creativity ==
+Language provides continuous opportunity for creativity, evident in the generation of novel sentences, phrasings, puns, neologisms, rhymes, allusions, sarcasm, irony, similes, metaphors, analogies, witticisms, and jokes. Native speakers of morphologically rich languages frequently create new word-forms that are easily understood, and some have found their way to the dictionary. The area of natural language generation has been well studied, but these creative aspects of everyday language have yet to be incorporated with any robustness or scale.
+
+=== Hypothesis of creative patterns ===
+In the seminal work of applied linguist Ronald Carter, he hypothesized two main creativity types involving words and word patterns: pattern-reforming creativity, and pattern-forming creativity. Pattern-reforming creativity refers to creativity by the breaking of rules, reforming and reshaping patterns of language often through individual innovation, while pattern-forming creativity refers to creativity via conformity to language rules rather than breaking them, creating convergence, symmetry and greater mutuality between interlocutors through their interactions in the form of repetitions.
+
+=== Story generation ===
+Substantial work has been conducted in this area of linguistic creation since the 1970s, with the development of James Meehan's TALE-SPIN
+ system. TALE-SPIN viewed stories as narrative descriptions of a problem-solving effort, and created stories by first establishing a goal for the story's characters so that their search for a solution could be tracked and recorded. The MINSTREL system represents a complex elaboration of this basic approach, distinguishing a range of character-level goals in the story from a range of author-level goals for the story. Systems like Bringsjord's BRUTUS elaborate these ideas further to create stories with complex interpersonal themes like betrayal. Nonetheless, MINSTREL explicitly models the creative process with a set of Transform Recall Adapt Methods (TRAMs) to create novel scenes from old. The MEXICA model of Rafael Pérez y Pérez and Mike Sharples is more explicitly interested in the creative process of storytelling, and implements a version of the engagement-reflection cognitive model of creative writing.
+
+=== Metaphor and simile ===
+Example of a metaphor: "She was an ape."
+Example of a simile: "Felt like a tiger-fur blanket."
+The computational study of these phenomena has mainly focused on interpretation as a knowledge-based process. Computationalists such as Yorick Wilks, James Martin, Dan Fass, John Barnden, and Mark Lee have developed knowledge-based approaches to the processing of metaphors, either at a linguistic level or a logical level. Tony Veale and Yanfen Hao have developed a system, called Sardonicus, that acquires a comprehensive database of explicit similes from the web; these similes are then tagged as bona-fide (e.g., "as hard as steel") or ironic (e.g., "as hairy as a bowling ball", "as pleasant as a root canal"); similes of either type can be retrieved on demand for any given adjective. They use these similes as the basis of an on-line metaphor generation system called Aristotle that can suggest lexical metaphors for a given descriptive goal (e.g., to describe a supermodel as skinny, the source terms "pencil", "whip", "whippet", "rope", "stick-insect" and "snake" are suggested).
+
+=== Analogy ===
+The process of analogical reasoning has been studied from both a mapping and a retrieval perspective, the latter being key to the generation of novel analogies. The dominant school of research, as advanced by Dedre Gentner, views analogy as a structure-preserving process; this view has been implemented in the structure mapping engine or SME, the MAC/FAC retrieval engine (Many Are Called, Few Are Chosen), ACME (Analogical Constraint Mapping Engine) and ARCS (Analogical Retrieval Constraint System). Other mapping-based approaches include Sapper, which situates the mapping process in a semantic-network model of memory. Analogy is a very active sub-area of creative computation and creative cognition; active figures in this sub-area include Douglas Hofstadter, Paul Thagard, and Keith Holyoak. Also worthy of note here is Peter Turney and Michael Littman's machine learning approach to the solving of SAT-style analogy problems; their approach achieves a score that compares well with average scores achieved by humans on these tests.
+
+=== Joke generation ===
+
+Humour is an especially knowledge-hungry process, and the most successful joke-generation systems to date have focused on pun-generation, as exemplified by the work of Kim Binsted and Graeme Ritchie. This work includes the JAPE system, which can generate a wide range of puns that are consistently evaluated as novel and humorous by young children. An improved version of JAPE has been developed in the guise of the STANDUP system, which has been experimentally deployed as a means of enhancing linguistic interaction with children with communication disabilities. Some limited progress has been made in generating humour that involves other aspects of natural language, such as the deliberate misunderstanding of pronominal reference (in the work of Hans Wim Tinholt and Anton Nijholt), as well as in the generation of humorous acronyms in the HAHAcronym system of Oliviero Stock and Carlo Strapparava.
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+title: "Computational creativity"
+chunk: 6/8
+source: "https://en.wikipedia.org/wiki/Computational_creativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:23.728483+00:00"
+instance: "kb-cron"
+---
+
+=== Neologism ===
+The blending of multiple word forms is a dominant force for new word creation in language; these new words are commonly called "blends" or "portmanteau words" (after Lewis Carroll). Tony Veale has developed a system called ZeitGeist that harvests neological headwords from Wikipedia and interprets them relative to their local context in Wikipedia and relative to specific word senses in WordNet. ZeitGeist has been extended to generate neologisms of its own; the approach combines elements from an inventory of word parts that are harvested from WordNet, and simultaneously determines likely glosses for these new words (e.g., "food traveller" for "gastronaut" and "time traveller" for "chrononaut"). It then uses Web search to determine which glosses are meaningful and which neologisms have not been used before; this search identifies the subset of generated words that are both novel ("H-creative") and useful.
+A corpus linguistic approach to the search and extraction of neologism have also shown to be possible. Using Corpus of Contemporary American English as a reference corpus, Locky Law has performed an extraction of neologism, portmanteaus and slang words using the hapax legomena which appeared in the scripts of American TV drama House M.D.
+In terms of linguistic research in neologism, Stefan Th. Gries has performed a quantitative analysis of blend structure in English and found that "the degree of recognizability of the source words and that the similarity of source words to the blend plays a vital role in blend formation." The results were validated through a comparison of intentional blends to speech-error blends.
+
+=== Poetry ===
+
+Like jokes, poems involve a complex interaction of different constraints, and no general-purpose poem generator adequately combines the meaning, phrasing, structure and rhyme aspects of poetry. Nonetheless, Pablo Gervás has developed a noteworthy system called ASPERA that employs a case-based reasoning (CBR) approach to generating poetic formulations of a given input text via a composition of poetic fragments that are retrieved from a case-base of existing poems. Each poem fragment in the ASPERA case-base is annotated with a prose string that expresses the meaning of the fragment, and this prose string is used as the retrieval key for each fragment. Metrical rules are then used to combine these fragments into a well-formed poetic structure. Racter is an example of such a software project.
+LLMs have been applied to poetry since the late 2010s. In Autumn 2020, The Poetry Review (ISSN 0032-2156) published Ariel Klein's "50% Human: A poetic interview with AI agents", an LLM-generated/assisted poetic feature and an early verified instance of LLM poetry in a major literary magazine; subsequent trade publications such as K. Allado-McDowell's Pharmako-AI (2020) and I Am Code: An Artificial Intelligence Speaks: Poems (2023) brought LLM-authored verse to wider audiences.
+
+== Musical creativity ==
+
+Computational creativity in the music domain has focused both on the generation of musical scores for use by human musicians, and on the generation of music for performance by computers. The domain of generation has included classical music (with software that generates music in the style of Mozart and Bach) and jazz. Most notably, David Cope has written a software system called "Experiments in Musical Intelligence" (or "EMI") that is capable of analyzing and generalizing from existing music by a human composer to generate novel musical compositions in the same style. EMI's output is convincing enough to persuade human listeners that its music is human-generated to a high level of competence.
+In the field of contemporary classical music, Iamus is the first computer that composes from scratch, and produces final scores that professional interpreters can play. The London Symphony Orchestra played a piece for full orchestra, included in Iamus' debut CD, which New Scientist described as "The first major work composed by a computer and performed by a full orchestra". Melomics, the technology behind Iamus, is able to generate pieces in different styles of music with a similar level of quality.
+Creativity research in jazz has focused on the process of improvisation and the cognitive demands that this places on a musical agent: reasoning about time, remembering and conceptualizing what has already been played, and planning ahead for what might be played next.
+The robot Shimon, developed by Gil Weinberg of Georgia Tech, has demonstrated jazz improvisation. Virtual improvisation software based on researches on stylistic modeling carried out by Gerard Assayag and Shlomo Dubnov include OMax, SoMax and PyOracle, are used to create improvisations in real-time by re-injecting variable length sequences learned on the fly from the live performer.
+In the field of musical composition, the patented works by René-Louis Baron allowed to make a robot that can create and play a multitude of orchestrated melodies, so-called "coherent" in any musical style. All outdoor physical parameter associated with one or more specific musical parameters, can influence and develop each of these songs (in real-time while listening to the song). The patented invention Medal-Composer raises problems of copyright.
+
+== Visual and artistic creativity ==
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+title: "Computational creativity"
+chunk: 7/8
+source: "https://en.wikipedia.org/wiki/Computational_creativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:23.728483+00:00"
+instance: "kb-cron"
+---
+
+Computational creativity in the generation of visual art has had some notable successes in the creation of both abstract art and representational art. A well-known program in this domain is Harold Cohen's AARON, which has been continuously developed and augmented since 1973. Though formulaic, Aaron exhibits a range of outputs, generating black-and-white drawings or colour paintings that incorporate human figures (such as dancers), potted plants, rocks, and other elements of background imagery. These images are of a sufficiently high quality to be displayed in reputable galleries.
+Other software artists of note include the NEvAr system (for "Neuro-Evolutionary Art") of Penousal Machado. NEvAr uses a genetic algorithm to derive a mathematical function that is then used to generate a coloured three-dimensional surface. A human user is allowed to select the best pictures after each phase of the genetic algorithm, and these preferences are used to guide successive phases, thereby pushing NEvAr's search into pockets of the search space that are considered most appealing to the user.
+The Painting Fool, developed by Simon Colton originated as a system for overpainting digital images of a given scene in a choice of different painting styles, colour palettes and brush types. Given its dependence on an input source image to work with, the earliest iterations of the Painting Fool raised questions about the extent of, or lack of, creativity in a computational art system. Nonetheless, The Painting Fool has been extended to create novel images, much as AARON does, from its own limited imagination. Images in this vein include cityscapes and forests, which are generated by a process of constraint satisfaction from some basic scenarios provided by the user (e.g., these scenarios allow the system to infer that objects closer to the viewing plane should be larger and more color-saturated, while those further away should be less saturated and appear smaller). Artistically, the images now created by the Painting Fool appear on a par with those created by Aaron, though the extensible mechanisms employed by the former (constraint satisfaction, etc.) may well allow it to develop into a more elaborate and sophisticated painter.
+The artist Krasi Dimtch (Krasimira Dimtchevska) and the software developer Svillen Ranev have created a computational system combining a rule-based generator of English sentences and a visual composition builder that converts sentences generated by the system into abstract art. The software generates automatically indefinite number of different images using different color, shape and size palettes. The software also allows the user to select the subject of the generated sentences or/and the one or more of the palettes used by the visual composition builder.
+An emerging area of computational creativity is that of video games. ANGELINA is a system for creatively developing video games in Java by Michael Cook. One important aspect is Mechanic Miner, a system that can generate short segments of code that act as simple game mechanics. ANGELINA can evaluate these mechanics for usefulness by playing simple unsolvable game levels and testing to see if the new mechanic makes the level solvable. Sometimes Mechanic Miner discovers bugs in the code and exploits these to make new mechanics for the player to solve problems with.
+In July 2015, Google released DeepDream – an open source computer vision program, created to detect faces and other patterns in images with the aim of automatically classifying images, which uses a convolutional neural network to find and enhance patterns in images via algorithmic pareidolia, thus creating a dreamlike psychedelic appearance in the deliberately over-processed images.
+In August 2015, researchers from Tübingen, Germany created a convolutional neural network that uses neural representations to separate and recombine content and style of arbitrary images which is able to turn images into stylistic imitations of works of art by artists such as a Picasso or Van Gogh in about an hour. Their algorithm is put into use in the website DeepArt that allows users to create unique artistic images by their algorithm.
+In early 2016, a global team of researchers explained how a new computational creativity approach known as the Digital Synaptic Neural Substrate (DSNS) could be used to generate original chess puzzles that were not derived from endgame databases. The DSNS is able to combine features of different objects (e.g. chess problems, paintings, music) using stochastic methods in order to derive new feature specifications which can be used to generate objects in any of the original domains. The generated chess puzzles have also been featured on YouTube.
+
+== Creativity in problem solving ==
+Creativity is also useful in allowing for unusual solutions in problem solving. In psychology and cognitive science, this research area is called creative problem solving. The Explicit-Implicit Interaction (EII) theory of creativity has been implemented using a CLARION-based computational model that allows for the simulation of incubation and insight in problem-solving. The emphasis of this computational creativity project is not on performance per se (as in artificial intelligence projects) but rather on the explanation of the psychological processes leading to human creativity and the reproduction of data collected in psychology experiments. So far, this project has been successful in providing an explanation for incubation effects in simple memory experiments, insight in problem solving, and reproducing the overshadowing effect in problem solving.
+
+== Criticism of computational creativity ==
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+title: "Computational creativity"
+chunk: 8/8
+source: "https://en.wikipedia.org/wiki/Computational_creativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:23.728483+00:00"
+instance: "kb-cron"
+---
+
+Traditional computers, as mainly used in the computational creativity application, do not support creativity, as they fundamentally transform a set of discrete, limited domain of input parameters into a set of discrete, limited domain of output parameters using a limited set of computational functions. As such, a computer cannot be creative, as everything in the output must have been already present in the input data or the algorithms. Related discussions and references to related work are captured in work on philosophical foundations of simulation.
+Mathematically, the same set of arguments against creativity has been made by Chaitin. Similar observations come from a Model Theory perspective. All this criticism emphasizes that computational creativity is useful and may look like creativity, but it is not real creativity, as nothing new is created, just transformed in well-defined algorithms.
+According to researchers like Mark Riedl, human creativity and computational creativity at their current state differ in several dimensions. While creativity can be viewed in the context of morality, Riedl considers the "educational, moralizing" aspect of stories as one of the challenges to developing narrative-generating AI models, which may contribute to the underlying reasoning coherence of the text. The lack of intention in AI models hinders them from making morally responsible choices, which often appear in human creativity.
+Michele Loi and Eleonora Vigano identified some potential threats to human creativity caused by AI development. For example, they considered the openness to "experiments of life", introduced by John Stuart Mill, an important factor in creativity. Society's overreliance on algorithms for making decisions would constrain utility functions, which may discourage people from exploring riskier solutions and decrease the diversity of exploration and thus the creativity.
+
+== Events ==
+The International Conference on Computational Creativity (ICCC) occurs annually, organized by The Association for Computational Creativity. Events in the series include:
+
+ICCC 2023: University of Waterloo in Ontario, Canada
+ICCC 2022: Free University of Bozen-Bolzano, Bolzano, Italy
+ICCC 2021: Mexico City, Mexico (Virtual due to COVID-19 pandemic)
+ICCC 2020, Coimbra, Portugal (Virtual due to COVID-19 pandemic)
+ICCC 2019, Charlotte, North Carolina, US
+ICCC 2018, Salamanca, Spain
+ICCC 2017, Atlanta, Georgia, US
+ICCC 2016, Paris, France
+ICCC 2015, Park City, Utah, US. Keynote: Emily Short
+ICCC 2014, Ljubljana, Slovenia. Keynote: Oliver Deussen
+ICCC 2013, Sydney, Australia. Keynote: Arne Dietrich
+ICCC 2012, Dublin, Ireland. Keynote: Steven Smith
+ICCC 2011, Mexico City, Mexico. Keynote: George E Lewis
+ICCC 2010, Lisbon, Portugal. Keynote/Invited Talks: Nancy J Nersessian and Mary Lou Maher
+Previously, the community of computational creativity has held a dedicated workshop, the International Joint Workshop on Computational Creativity, every year since 1999. Previous events in this series include:
+
+IJWCC 2003, Acapulco, Mexico, as part of IJCAI'2003
+IJWCC 2004, Madrid, Spain, as part of ECCBR'2004
+IJWCC 2005, Edinburgh, UK, as part of IJCAI'2005
+IJWCC 2006, Riva del Garda, Italy, as part of ECAI'2006
+IJWCC 2007, London, UK, a stand-alone event
+IJWCC 2008, Madrid, Spain, a stand-alone event
+The 1st Conference on Computer Simulation of Musical Creativity will be held
+
+CCSMC 2016, 17–19 June, University of Huddersfield, UK. Keynotes: Geraint Wiggins and Graeme Bailey.
+
+== See also ==
+1 the Road – Novel written by an artificial intelligence (1st novel)
+Artificial imagination – Artificial simulation of human imagination
+Algorithmic art – Art genre
+Algorithmic composition – Technique of using algorithms to create music
+Applications of artificial intelligence
+Computer art – Art genre
+Collective creativity – Ability to generate new ideas and solutions together in a creative process
+Creative computing – Computer science applied to the arts
+Digital morphogenesis – Type of generative art
+Digital poetry – Form of electronic literature
+Generative art – Art created by a set of rules, often using computers
+Generative systems – Technologies that can produce change driven by audiences
+Intrinsic motivation (artificial intelligence) – Mechanism for enabling artificial agents to exhibit curiosity
+Musikalisches Würfelspiel – Musical dice games used to randomly generate music (Musical dice game)
+Procedural generation – Method in which data is created algorithmically as opposed to manually
+Lists
+List of emerging technologies
+Outline of artificial intelligence
+
+== References ==
+
+== Further reading ==
+An Overview of Artificial Creativity Archived 2008-03-25 at the Wayback Machine on Think Artificial
+Cohen, H., "the further exploits of AARON, Painter" Archived 2008-04-19 at the Wayback Machine, SEHR, volume 4, issue 2: Constructions of the Mind, 1995
+
+== External links ==
+
+Documentaries
+Noorderlicht: Margaret Boden and Stephen Thaler on Creative Computers on Archive.org
+In Its Image on Archive.org
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+---
+title: "Computer Power and Human Reason"
+chunk: 1/1
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:31:26.328607+00:00"
+instance: "kb-cron"
+---
+
+Computer Power and Human Reason: From Judgment to Calculation is a 1976 nonfiction book by German-American computer scientist Joseph Weizenbaum in which he contends that while artificial intelligence may be possible, we should never allow computers to make important decisions, as they will always lack human qualities such as compassion and wisdom.
+
+
+== Background ==
+Before writing Computer Power and Human Reason, Weizenbaum had garnered significant attention for creating the ELIZA program, an early milestone in conversational computing. His firsthand observation of people attributing human-like qualities to a simple program prompted him to reflect more deeply on society's readiness to entrust moral and ethical considerations to machines.
+
+
+== Reception and legacy ==
+Computer Power and Human Reason sparked scholarly debate on the acceptable scope of AI applications, particularly in fields where human welfare and ethical considerations are paramount. Early academic reviews highlighted that Weizenbaum's stance pushed readers to recognize that even as computers grow more capable, they lack the intrinsic moral compass and empathy required for certain kinds of judgment.
+The book caused disagreement with, and separation from, other members of the artificial intelligence research community, a status the author later said he'd come to take pride in.
+
+
+== See also ==
+Ethics of artificial intelligence
+Criticism of technology
+
+
+== References ==
+
+
+== External links ==
+Plug & Pray, Documentary Film on Joseph Weizenbaum and the ethics of technology
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+title: "Computing Machinery and Intelligence"
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+instance: "kb-cron"
+---
+
+"Computing Machinery and Intelligence" is a  paper written by Alan Turing on the topic of artificial intelligence. The paper, published in 1950 in Mind, was the first to introduce his concept of what is now known as the Turing test to the general public.
+Turing's paper considers the question "Can machines think?" Turing says that since the words "think" and "machine" cannot clearly be defined, we should "replace the question by another, which is closely related to it and is expressed in relatively unambiguous words." To achieve this objective, Turing proposes a three-step approach. First, he identifies a simple and unambiguous concept to substitute for the term "think." Second, he delineates the specific "machines" under consideration. Third, armed with these tools, he poses a new question related to the first, which he believes he can answer in the affirmative.
+
+== Turing's test ==
+
+Rather than trying to determine if a machine is thinking, Turing suggests we should ask if the machine can win a game, called the "Imitation Game". The original Imitation game, that Turing described, is a simple party game involving three players. Player A is a man, player B is a woman and player C (who plays the role of the interrogator) can be of either sex. In the Imitation Game, player C is unable to see either player A or player B (and knows them only as X and Y), and can communicate with them only through written notes or any other form that does not give away any details about their gender. By asking questions of player A and player B, player C tries to determine which of the two is the man and which is the woman. Player A's role is to trick the interrogator into making the wrong decision, while player B attempts to assist the interrogator in making the right one.
+Turing proposes a variation of this game that involves the computer:
+
+We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?"
+So the modified game becomes one that involves three participants in isolated rooms: a computer (which is being tested), a human, and a (human) judge. The human judge can converse with both the human and the computer by typing into a terminal. Both the computer and the human try to convince the judge that they are the human. If the judge cannot consistently tell which is which, then the computer wins the game.
+Researchers in the United Kingdom had been exploring "machine intelligence" for up to ten years prior to the founding of the field of artificial intelligence (AI) research in 1956. It was a common topic among the members of the Ratio Club, an informal group of British cybernetics and electronics researchers that included Alan Turing. Turing, in particular, had been running the notion of machine intelligence since at least 1941 and one of the earliest-known mentions of "computer intelligence" was made by him in 1947.
+As Stevan Harnad notes, the question has become "Can machines do what we (as thinking entities) can do?" In other words, Turing is no longer asking whether a machine can "think"; he is asking whether a machine can act indistinguishably from the way a thinker acts. This question avoids the difficult philosophical problem of pre-defining the verb "to think" and focuses instead on the performance capacities that being able to think makes possible, and how a causal system can generate them.
+Since Turing introduced his test, it has been both highly influential and widely criticised, and has become an important concept in the philosophy of artificial intelligence. Some of its criticisms, such as John Searle's Chinese room, are themselves controversial. Some have taken Turing's question to have been "Can a computer, communicating over a teleprinter, fool a person into believing it is human?" but it seems clear that Turing was not talking about fooling people but about generating human cognitive capacity.
+
+== Digital machines ==
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+
+Turing also notes that we need to determine which "machines" we wish to consider. He points out that a human clone, while man-made, would not provide a very interesting example. Turing suggested that we should focus on the capabilities of digital machinery—machines which manipulate the binary digits of 1 and 0, rewriting them into memory using simple rules. He gave two reasons.
+First, there is no reason to speculate whether or not they can exist. They already did in 1950.
+Second, digital machinery is "universal". Turing's research into the foundations of computation had proved that a digital computer can, in theory, simulate the behaviour of any other digital machine, given enough memory and time. (This is the essential insight of the Church–Turing thesis and the universal Turing machine.) Therefore, if any digital machine can "act like it is thinking", then every sufficiently powerful digital machine can. Turing writes, "all digital computers are in a sense equivalent."
+This allows the original question to be made even more specific. Turing now restates the original question as "Let us fix our attention on one particular digital computer C. Is it true that by modifying this computer to have an adequate storage, suitably increasing its speed of action, and providing it with an appropriate programme, C can be made to play satisfactorily the part of A in the imitation game, the part of B being taken by a man?"
+Hence, Turing states that the focus is not on "whether all digital computers would do well in the game nor whether the computers that are presently available would do well, but whether there are imaginable computers which would do well". What is more important is to consider the advancements possible in the state of our machines today regardless of whether we have the available resource to create one or not.
+
+== Nine common objections ==
+
+Having clarified the question, Turing turned to answering it: he considered the following nine common objections, which include all the major arguments against artificial intelligence raised in the years since his paper was first published.
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+Religious Objection: This states that thinking is a function of man's immortal soul; therefore, a machine cannot think.  "In attempting to construct such machines," wrote Turing, "we should not be irreverently usurping His power of creating souls, any more than we are in the procreation of children: rather we are, in either case, instruments of His will providing mansions for the souls that He creates."
+ 'Heads in the Sand' Objection: "The consequences of machines thinking would be too dreadful.  Let us hope and believe that they cannot do so."  This thinking is popular among intellectual people, as they believe superiority derives from higher intelligence and the possibility of being overtaken is a threat (as machines have efficient memory capacities and processing speed, machines exceeding the learning and knowledge capabilities are highly probable). This objection is a fallacious appeal to consequences, confusing what should not be with what can or cannot be (Wardrip-Fruin, 56).
+The Mathematical Objection: This objection uses mathematical theorems, such as Gödel's incompleteness theorem, to show that there are limits to what questions a computer system based on logic can answer.  Turing suggests that humans are too often wrong themselves and pleased at the fallibility of a machine.  (This argument would be made again by philosopher John Lucas in 1961 and physicist Roger Penrose in 1989, and later would be called Penrose–Lucas argument.)
+Argument From Consciousness: This argument, suggested by Professor Geoffrey Jefferson in his 1949 Lister Oration (acceptance speech for his 1948 award of Lister Medal) states that "not until a machine can write a sonnet or compose a concerto because of thoughts and emotions felt, and not by the chance fall of symbols, could we agree that machine equals brain."  Turing replies by saying that we have no way of knowing that any individual other than ourselves experiences emotions, and that therefore we should accept the test.  He adds, "I do not wish to give the impression that I think there is no mystery about consciousness ... [b]ut I do not think these mysteries necessarily need to be solved before we can answer the question [of whether machines can think]." (This argument, that a computer can't have conscious experiences or understanding, would be made in 1980 by philosopher John Searle in his Chinese room argument. Turing's reply is now known as the "other minds reply". See also Can a machine have a mind? in the philosophy of AI.)
+Arguments from various disabilities. These arguments all have the form "a computer will never do X". Turing offers a selection:Be kind, resourceful, beautiful, friendly, have initiative, have a sense of humour, tell right from wrong, make mistakes, fall in love, enjoy strawberries and cream, make someone fall in love with it, learn from experience, use words properly, be the subject of its own thought, have as much diversity of behaviour as a man, do something really new.Turing notes that "no support is usually offered for these statements," and that they depend on naive assumptions about how versatile machines may be in the future, or are "disguised forms of the argument from consciousness." He chooses to answer a few of them:
+Machines cannot make mistakes. He notes it's easy to program a machine to appear to make a mistake.
+A machine cannot be the subject of its own thought (or can't be self-aware). A program which can report on its internal states and processes, in the simple sense of a debugger program, can certainly be written. Turing asserts "a machine can undoubtably be its own subject matter."
+A machine cannot have much diversity of behaviour. He notes that, with enough storage capacity, a computer can behave in an astronomical number of different ways.
+Lady Lovelace's Objection: One of the most famous objections states that computers are incapable of originality. This is largely because, according to Ada Lovelace, machines are incapable of independent learning.The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths. Turing suggests that Lovelace's objection can be reduced to the assertion that computers "can never take us by surprise" and argues that, to the contrary, computers could still surprise humans, in particular where the consequences of different facts are not immediately recognizable. Turing also argues that Lady Lovelace was hampered by the context from which she wrote, and if exposed to more contemporary scientific knowledge, it would become evident that the brain's storage is quite similar to that of a computer.
+Argument from continuity in the nervous system: Modern neurological research has shown that the brain is not digital. Even though neurons fire in an all-or-nothing pulse, both the exact timing of the pulse and the probability of the pulse occurring have analog components. Turing acknowledges this, but argues that any analog system can be simulated to a reasonable degree of accuracy given enough computing power. (Philosopher Hubert Dreyfus would make this argument against "the biological assumption" in 1972.)
+Argument from the informality of behaviour: This argument states that any system governed by laws will be predictable and therefore not truly intelligent. Turing replies by stating that this is confusing laws of behaviour with general rules of conduct, and that if on a broad enough scale (such as is evident in man) machine behaviour would become increasingly difficult to predict. He argues that, just because we can't immediately see what the laws are, does not mean that no such laws exist. He writes "we certainly know of no circumstances under which we could say, 'we have searched enough. There are no such laws.'". (Hubert Dreyfus would argue in 1972 that human reason and problem solving was not based on formal rules, but instead relied on instincts and awareness that would never be captured in rules. More recent AI research in robotics and computational intelligence attempts to find the complex rules that govern our "informal" and unconscious skills of perception, mobility and pattern matching. See Dreyfus' critique of AI). This rejoinder also includes the Turing's Wager argument.
+Extra-sensory perception: In 1950, extra-sensory perception was an active area of research and Turing chooses to give ESP the benefit of the doubt, arguing that conditions could be created in which mind-reading would not affect the test. Turing admitted to "overwhelming statistical evidence" for telepathy, likely referring to early 1940s experiments by Samuel Soal, a member of the Society for Psychical Research.
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+
+== Learning machines ==
+
+In the final section of the paper Turing details his thoughts about the Learning Machine that could play the imitation game successfully.
+Here Turing first returns to Lady Lovelace's objection that the machine can only do what we tell it to do and he likens it to a situation where a man "injects" an idea into the machine to which the machine responds and then falls off into quiescence. He extends on this thought by an analogy to an atomic pile of less than critical size, which is to be considered the machine, and an injected idea is to correspond to a neutron entering the pile from outside the pile; the neutron will cause a certain disturbance which eventually dies away. Turing then builds on that analogy and mentions that, if the size of the pile were to be sufficiently large, then a neutron entering the pile would cause a disturbance that would continue to increase until the whole pile were destroyed, the pile would be supercritical. Turing then asks the question as to whether this analogy of a super critical pile could be extended to a human mind and then to a machine. He concludes that such an analogy would indeed be suitable for the human mind with "There does seem to be one for the human mind. The majority of them seem to be "subcritical," i.e., to correspond in this analogy to piles of sub critical size. An idea presented to such a mind will on average give rise to less than one idea in reply. A smallish proportion are supercritical. An idea presented to such a mind that may give rise to a whole "theory" consisting of secondary, tertiary and more remote ideas". He finally asks if a machine could be made to be supercritical.
+Turing then mentions that the task of being able to create a machine that could play the imitation game is one of programming and he postulates that by the end of the century it will indeed be technologically possible to program a machine to play the game. He then mentions that in the process of trying to imitate an adult human mind it becomes important to consider the processes that lead to the adult mind being in its present state; which he summarizes as:
+
+1. The initial state of the mind, say at birth,
+2. The education to which it has been subjected,
+3. Other experience, not to be described as education, to which it has been subjected.
+Given this process he asks whether it would be more appropriate to program a child's mind instead of an adult’s mind and then subject the child mind to a period of education. He likens the child to a newly bought notebook and speculates that due to its simplicity it would be more easily programmed. The problem then is broken down into two parts, the programming of a child mind and its education process. He mentions that a child mind would not be expected as desired by the experimenter (programmer) at the first attempt. A learning process that involves a method of reward and punishment must be in place that will select desirable patterns in the mind. This whole process, Turing mentions, to a large extent is similar to that of evolution by natural selection where the similarities are:
+
+Structure of the child machine = hereditary material
+Changes of the child machine = mutations
+Natural selection = judgment of the experimenter
+Following this discussion Turing addresses certain specific aspects of the learning machine: 
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+Nature of inherent complexity: The child machine could either be one that is as simple as possible, merely maintaining consistency with general principles, or the machine could be one with a complete system of logical inference programmed into it. This more complex system is explained by Turing as "..would be such that the machines store would be largely occupied with definitions and propositions. The propositions would have various kinds of status, e.g., well-established facts, conjectures, mathematically proved theorems, statements given by an authority, expressions having the logical form of proposition but not belief-value. Certain propositions may be described as "imperatives." The machine should be so constructed that as soon as an imperative is classed as "well established" the appropriate action automatically takes place". Despite this built-in logic system the logical inference programmed in would not be one that is formal, rather it would be one that is more pragmatic. In addition the machine would build on its built-in logic system by a method of "scientific induction".
+Ignorance of the experimenter: An important feature of a learning machine that Turing points out is the ignorance of the teacher of the machines' internal state during the learning process. This is in contrast to a conventional discrete state machine where the objective is to have a clear understanding of the internal state of the machine at every moment during the computation. The machine will be seen to be doing things that we often cannot make sense of or something that we consider to be completely random. Turing mentions that this specific character bestows upon a machine a certain degree of what we consider to be intelligence, in that intelligent behaviour consists of a deviation from the complete determinism of conventional computation but only so long as the deviation does not give rise to pointless loops or random behaviour.
+The importance of random behaviour: Though Turing cautions us of random behaviour he mentions that inculcating an element of randomness in a learning machine would be of value in a system. He mentions that this could be of value where there might be multiple correct answers or ones where it might be such that a systematic approach would investigate several unsatisfactory solutions to a problem before finding the optimal solution which would entail the systematic process inefficient. Turing also mentions that the process of evolution takes the path of random mutations in order to find solutions that benefit an organism but he also admits that in the case of evolution the systematic method of finding a solution would not be possible.
+Turing concludes by speculating about a time when machines will compete with humans on numerous intellectual tasks and suggests tasks that could be used to make that start. Turing then suggests that abstract tasks such as playing chess could be a good place to start another method which he puts as "..it is best to provide the machine with the best sense organs that money can buy, and then teach it to understand and speak English.".
+An examination of the development in artificial intelligence that has followed reveals that the learning machine did take the abstract path suggested by Turing as in the case of Deep Blue, a chess playing computer developed by IBM and one which defeated the world champion Garry Kasparov (though, this too is controversial) and the numerous computer chess games which can outplay most amateurs. As for the second suggestion Turing makes, it has been likened by some authors as a call to finding a simulacrum of human cognitive development. Such attempts at finding the underlying algorithms by which children learn the features of the world around them are only beginning to be made.
+
+== See also ==
+History of artificial intelligence
+
+== Notes ==
+
+== References ==
+Brooks, Rodney (1990), "Elephants Don't Play Chess" (PDF), Robotics and Autonomous Systems, 6 (1–2): 3–15, CiteSeerX 10.1.1.588.7539, doi:10.1016/S0921-8890(05)80025-9, retrieved 30 August 2007
+Crevier, Daniel (1993). AI: The Tumultuous Search for Artificial Intelligence. New York, NY: BasicBooks. ISBN 0-465-02997-3.
+Dreyfus, Hubert (1972), What Computers Can't Do, New York: MIT Press, ISBN 978-0-06-011082-6
+Dreyfus, Hubert; Dreyfus, Stuart (1986), Mind over Machine: The Power of Human Intuition and Expertise in the Era of the Computer, Oxford, UK: Blackwell
+Dreyfus, Hubert (1979), What Computers Still Can't Do, New York: MIT Press.
+Harnad, Stevan; Scherzer, Peter (2008), "First, Scale Up to the Robotic Turing Test, Then Worry About Feeling", Artificial Intelligence in Medicine, 44 (2): 83–9, CiteSeerX 10.1.1.115.4269, doi:10.1016/j.artmed.2008.08.008, PMID 18930641, archived from the original on 8 February 2012, retrieved 29 August 2010.
+Haugeland, John (1985), Artificial Intelligence: The Very Idea, Cambridge, Mass.: MIT Press.
+Moravec, Hans (1976), The Role of Raw Power in Intelligence, archived from the original on 3 March 2016, retrieved 7 November 2007
+Hofstadter, Douglas (1979), Gödel, Escher, Bach: an Eternal Golden Braid.
+Lucas, John (1961), "Minds, Machines and Gödel", in Anderson, A.R. (ed.), Minds and Machines, archived from the original on 19 August 2007, retrieved 2 December 2022
+Moravec, Hans (1988), Mind Children, Harvard University Press
+Penrose, Roger (1989), The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics, Oxford University Press, ISBN 978-0-14-014534-2
+Russell, Stuart J.; Norvig, Peter (2003), Artificial Intelligence: A Modern Approach (2nd ed.), Upper Saddle River, New Jersey: Prentice Hall, ISBN 0-13-790395-2
+Searle, John (1980), "Minds, Brains and Programs" (PDF), Behavioral and Brain Sciences, 3 (3): 417–457, doi:10.1017/S0140525X00005756, S2CID 55303721
+Turing, Alan (October 1950), "Computing Machinery and Intelligence" (PDF), Mind, LIX (236): 433–460, doi:10.1093/mind/LIX.236.433
+Saygin, A. P. (2000). "Turing Test: 50 years later". Minds and Machines. 10 (4): 463–518. doi:10.1023/A:1011288000451. hdl:11693/24987. S2CID 990084.
+Noah Wardrip-Fruin and Nick Montfort, eds. (2003). The New Media Reader. Cambridge: MIT Press. ISBN 0-262-23227-8. "Lucasfilm's Habitat" pp. 663–677.
+
+== External links ==
+PDF with the full text of the paper
+Saygin, Ayse Pinar; Cicekli, Ilyas; Akman, Varol (1999). "An analysis and review of the next 50 years". Minds and Machines: 2000. CiteSeerX 10.1.1.157.1592.
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diff --git a/data/en.wikipedia.org/wiki/Discovery_of_the_neutron-0.md b/data/en.wikipedia.org/wiki/Discovery_of_the_neutron-0.md
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+---
+title: "Discovery of the neutron"
+chunk: 1/7
+source: "https://en.wikipedia.org/wiki/Discovery_of_the_neutron"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:49.483017+00:00"
+instance: "kb-cron"
+---
+
+The discovery of the neutron and its properties was central to the extraordinary developments in atomic physics in the first half of the 20th century. Early in the century, Ernest Rutherford used alpha particle scattering to discover that an atom has its mass and electric charge concentrated in a tiny nucleus. By 1920, isotopes of chemical elements had been discovered, the atomic masses had been determined to be approximately integer multiples of the mass of the hydrogen atom, and the atomic number had been identified as the charge on the nucleus. Throughout the 1920s, the nucleus was viewed as composed of combinations of protons and electrons, the two elementary particles known at the time, but that model presented several experimental and theoretical contradictions.
+The essential nature of the atomic nucleus was established with the discovery of the neutron by James Chadwick in 1932 and the determination that it was a new elementary particle, distinct from the proton.
+The uncharged neutron was immediately exploited as a new means to probe nuclear structure, leading to such discoveries as the creation of new radioactive elements by neutron irradiation (1934) and the fission of uranium atoms by neutrons (1938). The discovery of fission led to the creation of both nuclear power and nuclear weapons by the end of World War II. Both the proton and the neutron were presumed to be elementary particles until the 1960s, when they were determined to be composite particles built from quarks.
+
+== Discovery of radioactivity ==
+At the start of the 20th century, the vigorous debate as to the existence of atoms had not yet been resolved. Philosophers such as Ernst Mach and Wilhelm Ostwald denied the existence of atoms, viewing them as a convenient mathematical construct, while scientists such as Arnold Sommerfeld and Ludwig Boltzmann saw that physical theories required the existence of atoms.
+Radioactivity was discovered in 1896 by the French scientist Henri Becquerel, while working with phosphorescent materials. In 1898, Ernest Rutherford at Cavendish Laboratory distinguished two types of radioactivity, alpha rays and beta rays, which differed in their ability to penetrate, or travel into, ordinary objects or gases. Two years later, Paul Villard discovered gamma rays, which possessed even more penetrating power. These radiations were later identified with known particles: beta rays were shown to be electrons by Walter Kaufmann in 1902, alpha rays were shown to be helium ions by Rutherford and Thomas Royds in 1907, and gamma rays were shown to be electromagnetic radiation, that is, a form of light, by Rutherford and Edward Andrade in 1914. These radiations had also been identified as emanating from atoms, hence they provided clues to processes occurring within atoms. Conversely, the radiations were also recognized as tools that could be used in scattering experiments to probe the interior of atoms.
+
+== Gold foil experiment and the discovery of the atomic nucleus ==
+
+At the University of Manchester between 1908 and 1913, Rutherford directed Hans Geiger and Ernest Marsden in a series of experiments to determine what occurs when alpha particles scatter from metal foil. Now called the Rutherford gold foil experiment, or the Geiger–Marsden experiment, these measurements made the extraordinary discovery that although most alpha particles passing through a thin gold foil experienced little deflection, a few scattered to a high angle. The scattering indicated that some of the alpha particles ricocheted back from a small, but dense, component inside the atoms. Based on these measurements, it was apparent to Rutherford by 1911 that the atom consisted of a small, massive nucleus with positive charge. The concentrated atomic mass was required to provide the observed deflection of the alpha particles, and Rutherford developed a mathematical model that accounted for the scattering.
+While the Rutherford model was largely ignored at the time, when Niels Bohr joined Rutherford's group, he developed the Bohr model for electrons orbiting the nucleus in 1913. The Bohr model eventually led to an atomic model based on quantum mechanics by the mid-1920s.
+
+== Discovery of isotopes ==
+Concurrent with the work of Rutherford, Geiger, and Marsden, the radiochemist Frederick Soddy at the University of Glasgow was studying chemistry-related problems on radioactive materials. Soddy had worked with Rutherford on radioactivity at McGill University. By 1910, about 40 different radioactive elements, referred to as radioelements, had been identified between uranium and lead, although the periodic table only allowed for 11 elements. Every attempt to chemically isolate the radioelements mesothorium or thorium X from radium failed. Soddy concluded that these element were chemically the same element. At the suggestion of Margaret Todd, Soddy called these chemically identical elements isotopes.  In 1913, Soddy and theorist Kazimierz Fajans independently found the displacement law, that an element undergoing alpha decay will produce an element two places to the left in the periodic system and an element undergoing beta decay will produce an element one place to the right in the periodic system.  For his study of radioactivity and the discovery of isotopes, Soddy was awarded the 1921 Nobel Prize in Chemistry.
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+title: "Discovery of the neutron"
+chunk: 2/7
+source: "https://en.wikipedia.org/wiki/Discovery_of_the_neutron"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:49.483017+00:00"
+instance: "kb-cron"
+---
+
+Prior to 1919 only atomic weights averaged over a very large number of atoms was available. In that year, Francis Aston built the first mass spectrograph, an improved form of a device built by J. J. Thomson to measure the deflection of positively charged atoms by electric and magnetic fields. Aston was then able to separate the isotopes of many light elements including neon, 20Ne and 22Ne. Aston discovered the isotopes matched William Prout's whole number rule: the mass of every isotope is a whole number multiple of hydrogen.
+Significantly, the one exception to this whole number rule was hydrogen itself, which had a mass value of 1.008. The excess mass was small, but well outside the limits of experimental uncertainty. Aston and others realized this difference was due to the binding energy of atoms. When a number of hydrogen atoms are bound into a atom, that atom's energy must be less than the sum of the energies of the separate hydrogen atoms. That lost energy, according to the mass-energy equivalence principle, means the atomic mass will be slightly less than the sum of the masses of its components.  Aston's work on isotopes won him the 1922 Nobel Prize in Chemistry for the discovery of isotopes in a large number of non-radioactive elements, and for his enunciation of the whole number rule.
+
+== Atomic number and Moseley's law ==
+
+Before 1913, chemists adhered to Mendeleev's principle that chemical properties derived from atomic weight. However, several places in the periodic table were inconsistent with this concept. For example cobalt and nickel seemed reversed. There were also attempts to understand the relationship between the atomic mass and nuclear charge. Rutherford knew from experiments in his lab that helium must have a nuclear charge of 2 and a mass of 4; this 1:2 ratio was expected to hold for all elements. In 1913 Antonius van den Broek hypothesized that the periodic table should be organized by charge, denoted by Z, not atomic mass and that Z was not exactly half of the atomic weight for elements.  This solved the cobalt-nickel issue. Placing cobalt (Z=27, mass of 58.97), before the less heavier nickel (Z=28, mass of 58.68) gave the ordering expected by chemical behavior.
+Henry Moseley set out to test Broek's hypothesis by measuring the electromagnetic emission spectra of heavier elements, such as cobalt and nickel, to see if they followed the ordering by weight or by atomic number. In 1913–1914 Moseley tested the question experimentally by using X-ray spectroscopy. He found that the most intense short-wavelength line in the X-ray spectrum of a particular element, known as the K-alpha line, was related to the element's position in the periodic table, that is, its atomic number, Z. Moseley found that the frequencies of the radiation were related in a simple way to the atomic number of the elements for a large number of elements.
+Within a year, it was noted that the equation for the relation, now called Moseley's law, could be explained in terms of the 1913 Bohr model with reasonable extra assumptions about atomic structure in other elements. Moseley's result, by Bohr's later account, not only established atomic number as a measurable experimental quantity, but gave it a physical meaning as the positive charge on the atomic nucleus. The elements could be ordered in the periodic system in order of atomic number, rather than atomic weight. The result tied together the organization of the periodic table, the Bohr model for the atom, and Rutherford's model for alpha scattering from nuclei. It was cited by Rutherford, Bohr, and others as a critical advance in understanding the nature of the atomic nucleus.
+Further research in atomic physics was interrupted by the onset of World War I. Moseley was killed in 1915 at the Battle of Gallipoli, while Rutherford's student James Chadwick was interned in Germany for the duration of the war, 1914–1918. In Berlin, Lise Meitner's and Otto Hahn's research work on determining the radioactive decay chains of radium and uranium by precise chemical separation was interrupted. Meitner spent much of the war working as a radiologist and medical X-ray technician near the Austrian front, while Hahn, a chemist, worked on research in poison gas warfare.
+
+== Rutherford's conjecture ==
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+title: "Discovery of the neutron"
+chunk: 3/7
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+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:49.483017+00:00"
+instance: "kb-cron"
+---
+
+In 1920, Rutherford gave a Bakerian lecture at the Royal Society entitled the "Nuclear Constitution of Atoms", a summary of recent experiments on atomic nuclei and conclusions as to the structure of atomic nuclei. By 1920, the existence of electrons within the atomic nucleus was widely assumed.  It was assumed the nucleus consisted of hydrogen nuclei in number equal to the atomic mass number.  But, since each hydrogen nucleus had charge +1 e, the nucleus required a smaller number of "internal electrons" each of charge −1 e to give the nucleus its correct total charge. The mass of protons is about 1800 times greater than that of electrons, so the mass of the electrons is incidental in this computation.  Such a model was consistent with the scattering of alpha particles from heavy nuclei, as well as the charge and mass of the many isotopes that had been identified.  There were other motivations for the proton-electron model.  As noted by Rutherford at the time, "We have strong reason for believing that the nuclei of atoms contain electrons as well as positively charged bodies ...", namely, it was known that beta radiation was electrons emitted from the nucleus.
+In that lecture, Rutherford conjectured the existence of new particles.  The alpha particle was known to be very stable, and it was assumed to retain its identity within the nucleus.  The alpha particle was presumed to consist of four protons and two closely bound electrons to give it +2 charge and mass 4.  In a 1919 paper, Rutherford had reported the apparent discovery of a new doubly charged particle of mass 3, denoted the X++, interpreted to consist of three protons and a closely bound electron.  This result suggested to Rutherford the likely existence of two new particles: one of two protons with a closely bound electron, and another of one proton and a closely bound electron. The X++ particle was later determined to have mass 4 and to be just a low-energy alpha particle. Nevertheless, Rutherford had conjectured the existence of the deuteron, a +1 charge particle of mass 2, and the neutron, a neutral particle of mass 1.  The former is the nucleus of deuterium, discovered in 1931 by Harold Urey. The mass of the hypothetical neutral particle would be little different from that of the proton. Rutherford determined that such a zero-charge particle would be difficult to detect by available techniques.
+Around the time of Rutherford's lecture, other publications appeared with similar suggestions of a proton–electron composite in the nucleus, and in 1921, William Harkins, an American chemist, named the uncharged particle the neutron. About that same time the word proton was adopted for the hydrogen nucleus.  Neutron was apparently constructed from the Latin root for neutral and the Greek ending -on (by imitation of electron and proton). References to the word neutron in connection with the atom can be found in the literature as early as 1899, however.
+Rutherford and Chadwick immediately began an experimental program at the Cavendish Laboratory in Cambridge to search for the neutron.  The experiments continued throughout the 1920s without success.
+Rutherford's conjecture and the hypothetical "neutron" were not widely accepted.  In his 1931 monograph on the Constitution of Atomic Nuclei and Radioactivity, George Gamow, then at the Institute for Theoretical Physics in Copenhagen, did not mention the neutron.  At the time of their 1932 measurements in Paris that would lead to the discovery of the neutron, Irène Joliot-Curie and Frédéric Joliot were unaware of the conjecture.
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+---
+title: "Discovery of the neutron"
+chunk: 4/7
+source: "https://en.wikipedia.org/wiki/Discovery_of_the_neutron"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:49.483017+00:00"
+instance: "kb-cron"
+---
+
+== Problems of the nuclear electrons hypothesis ==
+Throughout the 1920s, physicists assumed that the atomic nucleus was composed of protons and "nuclear electrons". Under this hypothesis, the nitrogen-14 (14N) nucleus would be composed of 14 protons and 7 electrons, so that it would have a net charge of +7 elementary charge units and a mass of 14 atomic mass units. This nucleus would also be orbited by another 7 electrons, termed "external electrons" by Rutherford, to complete the 14N atom. However problems with the hypothesis soon became apparent.
+Ralph Kronig pointed out in 1926 that the observed hyperfine structure of atomic spectra was inconsistent with the proton–electron hypothesis. This structure is caused by the influence of the nucleus on the dynamics of orbiting electrons. The magnetic moments of supposed "nuclear electrons" should produce hyperfine spectral line splittings similar to the Zeeman effect, but no such effects were observed.  It seemed that the magnetic moment of the electron vanished when it was within the nucleus.
+While on a visit to Utrecht University in 1928, Kronig learned of a surprising aspect of the rotational spectrum of N2+. The precision measurement made by Leonard Ornstein, the director of Utrecht's Physical Laboratory, showed that the spin of a nitrogen nucleus must be equal to one. However, if the nitrogen-14 (14N) nucleus was composed of 14 protons and 7 electrons, an odd number of spin-1/2 particles, then the resultant nuclear spin should be half-integer. Kronig therefore suggested the possibility that "protons and  electrons do not retain their identity to the extent they do outside the nucleus".
+Observations of the rotational energy levels of diatomic molecules using Raman spectroscopy by Franco Rasetti in 1929 were inconsistent with the statistics expected from the proton–electron hypothesis. Rasetti obtained band spectra for H2 and N2 molecules.  While the lines for both diatomic molecules showed alternation in intensity between light and dark, the pattern of alternation for H2 is opposite to that of the N2. After carefully analyzing these experimental results, German physicists Walter Heitler and Gerhard Herzberg showed that the hydrogen nuclei obey Fermi statistics and the nitrogen nuclei obey Bose statistics. However, a then unpublished result of Eugene Wigner showed that a composite system with an odd number of spin-1/2 particles must obey Fermi statistics; a system with an even number of spin-1/2 particle obeys Bose statistics. If the nitrogen nucleus had 21 particles, it should obey Fermi statistics, contrary to fact. Thus, Heitler and Herzberg concluded: "the electron in the nucleus ... loses its ability to determine the statistics of the nucleus."
+The Klein paradox, discovered by Oskar Klein in 1928, presented further quantum mechanical objections to the notion of an electron confined within a nucleus.  Derived from the Dirac equation, this clear and precise paradox suggested that an electron approaching a high potential barrier has a high probability of passing through the barrier by a pair creation process.  Apparently, an electron could not be confined within a nucleus by any potential well. The meaning of this paradox was widely debated at the time.
+By about 1930, it was generally recognized that it was difficult to reconcile the proton–electron model for nuclei with the Heisenberg uncertainty relation of quantum mechanics. This relation, Δx⋅Δp ≥ 1⁄2ħ, implies that an electron confined to a region the size of an atomic nucleus typically has a kinetic energy of about 40 MeV, which is larger than the observed energy of beta particles emitted from the nucleus. Such energy is also much larger than the binding energy of nucleons, which Aston and others had shown to be less than 9 MeV per nucleon.
+In 1927, Charles Ellis and W. Wooster at the Cavendish Laboratory measured the energies of β-decay electrons.  They found that the distribution of energies from any particular radioactive nuclei was broad and continuous, a result that contrasted notably with the distinct energy values observed in alpha and gamma decay. Furthermore, the continuous energy distribution seemed to indicate that energy was not conserved by this "nuclear electrons" process.  In 1929, Bohr proposed to modify the law of energy conservation to account for the continuous energy distribution, a proposal that earned the support of Werner Heisenberg. Such considerations were apparently reasonable, inasmuch as the laws of quantum mechanics had so recently overturned the laws of classical mechanics.
+While all of these considerations did not "prove" an electron could not exist in the nucleus, they were confusing and challenging for physicists to interpret.  Many theories were invented to explain how the above arguments could be wrong. In his 1931 monograph, Gamow summarized all of these contradictions, marking the statements regarding electrons in the nucleus with warning symbols.
+
+== Discovery of the neutron ==
+In 1930, Walther Bothe and his collaborator Herbert Becker in Giessen, Germany found that if the energetic alpha particles emitted from polonium fell on certain light elements, specifically beryllium (94Be), boron (115B), or lithium (73Li), an unusually penetrating radiation was produced. Beryllium produced the most intense radiation.  Polonium is highly radioactive, producing energetic alpha radiation, and it was commonly used for scattering experiments at the time. Alpha radiation can be influenced by an electric field because it is composed of charged particles.  The observed penetrating radiation was not influenced by an electric field, however, so it was thought to be gamma radiation. The radiation was more penetrating than any gamma rays known, and the details of experimental results were difficult to interpret.
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+---
+title: "Discovery of the neutron"
+chunk: 5/7
+source: "https://en.wikipedia.org/wiki/Discovery_of_the_neutron"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:49.483017+00:00"
+instance: "kb-cron"
+---
+
+Two years later, Irène Joliot-Curie and Frédéric Joliot in Paris showed that if this unknown radiation fell on paraffin wax, or any other hydrogen-containing compound, it ejected protons of very high energy (5 MeV). This observation was not in itself inconsistent with the assumed gamma ray nature of the new radiation, but that interpretation (Compton scattering) had a logical problem.  From energy and momentum considerations, a gamma ray would have to have impossibly high energy (50 MeV) to scatter a massive proton. In Rome, the young physicist Ettore Majorana declared that the manner in which the new radiation interacted with protons required a neutral particle as heavy as a proton, but declined to publish his result despite the encouragement of Enrico Fermi.
+On hearing of the Paris results, Rutherford and James Chadwick at the Cavendish Laboratory also did not believe the gamma ray hypothesis since it failed to conserve energy. Assisted by Norman Feather, Chadwick quickly performed a series of experiments showing that the gamma ray hypothesis was untenable. The previous year, Chadwick, J.E.R. Constable, and E.C. Pollard had already conducted experiments on disintegrating light elements using alpha radiation from polonium. They had also developed more accurate and efficient methods for detecting, counting, and recording the ejected protons. Chadwick repeated the creation of the radiation using beryllium to absorb the alpha particles: 9Be + 4He (α) →  12C + 1n. Following the Paris experiment, he aimed the radiation at paraffin wax, a hydrocarbon high in hydrogen content, hence offering a target dense with protons. As in the Paris experiment, the radiation energetically scattered some of the protons. Chadwick measured the range of these protons and also measured how the new radiation impacted the atoms of various gases. Measurements of the recoil energy showed that the mass of the radiation particles must be similar to the mass of the proton: the new radiation could not consist of gamma rays.  Uncharged particles with about the same mass to the proton matched the properties Rutherford described in 1920 and which had later been called neutrons. Chadwick won the Nobel Prize in Physics in 1935 for this discovery.
+The year 1932 was later referred to as the "annus mirabilis" for nuclear physics in the Cavendish Laboratory, with discoveries of the neutron, artificial nuclear disintegration by the Cockcroft–Walton particle accelerator, and the positron.
+
+== Proton–neutron model of the nucleus ==
+
+Given the problems of the proton–electron model, it was quickly accepted that the atomic nucleus is composed of protons and neutrons, although the precise nature of the neutron was initially unclear. Within months after the discovery of the neutron, Werner Heisenberg and Dmitri Ivanenko had proposed proton–neutron models for the nucleus. Heisenberg's landmark papers approached the description of protons and neutrons in the nucleus through quantum mechanics. While Heisenberg's theory for protons and neutrons in the nucleus was a "major step toward understanding the nucleus as a quantum mechanical system", he still assumed the presence of nuclear electrons. In particular, Heisenberg assumed the neutron was a proton–electron composite, for which there is no quantum mechanical explanation. Heisenberg had no explanation for how lightweight electrons could be bound within the nucleus. Heisenberg introduced the first theory of nuclear exchange forces that bind the nucleons. He considered protons and neutrons to be different quantum states of the same particle, i.e., nucleons distinguished by the value of their nuclear isospin quantum numbers.
+The proton–neutron model explained the puzzle of dinitrogen. When 14N was proposed to consist of 3 pairs each of protons and neutrons, with an additional unpaired neutron and proton each contributing a spin of 1⁄2 ħ in the same direction for a total spin of 1 ħ, the model became viable. Soon, neutrons were used to naturally explain spin differences in many different nuclides in the same way.
+If the proton–neutron model for the nucleus resolved many issues, it highlighted the problem of explaining the origins of beta radiation. No existing theory at the time could account for how electrons or positrons could emanate from the nucleus. In 1934, Enrico Fermi published his classic paper describing the process of beta decay, in which the neutron decays to a proton by creating an electron and a (as yet undiscovered) neutrino. The paper employed the analogy that photons, or electromagnetic radiation, were similarly created and destroyed in atomic processes. Ivanenko had suggested a similar analogy in 1932. Fermi's theory requires the neutron to be a spin-1⁄2 particle. The theory preserved the principle of conservation of energy, which had been put into question by the continuous energy distribution of beta particles. The basic theory for beta decay proposed by Fermi was the first to show how particles could be created and destroyed. It established a general, basic theory for the interaction of particles by weak or strong forces. While this influential paper has stood the test of time, the ideas within it were so new that when it was first submitted to the journal Nature in 1933 it was rejected as being too speculative.
+
+== Nature of the neutron ==
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+---
+title: "Discovery of the neutron"
+chunk: 6/7
+source: "https://en.wikipedia.org/wiki/Discovery_of_the_neutron"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:49.483017+00:00"
+instance: "kb-cron"
+---
+
+The question of whether the neutron was a composite particle of a proton and an electron persisted for a few years after its discovery. In 1932 Harrie Massey explored a model for a composite neutron to account for its great penetrating power through matter and its electrical neutrality, for example. The issue was a legacy of the prevailing view from the 1920s that the only elementary particles were the proton and electron.
+The nature of the neutron was a primary topic of discussion at the 7th Solvay Conference held in October 1933, attended by Heisenberg, Niels Bohr, Lise Meitner, Ernest Lawrence, Fermi, Chadwick, and others. As posed by Chadwick in his Bakerian Lecture in 1933, the primary question was the mass of the neutron relative to the proton. If the neutron's mass was less than the combined masses of a proton and an electron (1.0078 Da), then the neutron could be a proton-electron composite because of the mass defect from the nuclear binding energy. If greater than the combined masses, then the neutron was elementary like the proton. The question was challenging to answer because the electron's mass is only 0.05% of the proton's, hence exceptionally precise measurements were required.
+The difficulty of making the measurement is illustrated by the wide-ranging values for the mass of the neutron obtained from 1932 to 1934. The accepted value today is 1.00866 Da. In Chadwick's 1932 paper reporting on the discovery, he estimated the mass of the neutron to be between 1.005 Da and 1.008 Da. By bombarding boron with alpha particles, Frédéric and Irène Joliot-Curie obtained a high value of 1.012 Da, while Ernest Lawrence's team at the University of California measured the small value 1.0006 Da using their new cyclotron.
+In 1935 Chadwick and his doctoral student Maurice Goldhaber resolved the issue by reporting the first accurate measurement of the mass of the neutron. They used the 2.6 MeV gamma rays of Thallium-208 (208Tl) (then known as "thorium C") to photodisintegrate the deuteron.
+
+In this reaction, the resulting proton and neutron have about equal kinetic energy, since their masses are about equal.  The kinetic energy of the resulting proton could be measured (0.24 MeV), and therefore the deuteron's binding energy could be determined (2.6 MeV − 2(0.24 MeV) = 2.1 MeV, or 0.0023 Da). The neutron's mass could then be determined by the simple mass balance
+
+where md,p,n refer to the deuteron, proton, or neutron mass, and "b.e." is the binding energy. The masses of the deuteron and proton were known; Chadwick and Goldhaber used values 2.0142 Da and 1.0081 Da, respectively.  They found that the neutron's mass was slightly greater than the mass of the proton 1.0084 Da or 1.0090 Da, depending on the precise value used for the deuteron mass. The mass of the neutron was too large to be a proton–electron composite, and the neutron was therefore identified as an elementary particle.  Chadwick and Goldhaber predicted that a free neutron would be able to decay into a proton, electron, and neutrino (free neutron decay).
+
+== Neutron physics in the 1930s ==
+
+Soon after the discovery of the neutron, indirect evidence suggested the neutron had an unexpected non-zero value for its magnetic moment. Attempts to measure the neutron's magnetic moment originated with the discovery by Otto Stern in 1933 in Hamburg that the proton had an anomalously large magnetic moment. By 1934 groups led by Stern, now in Pittsburgh, and I. I. Rabi in New York had independently deduced that the magnetic moment of the neutron was negative and unexpectedly large by measuring the magnetic moments of the proton and deuteron. Values for the magnetic moment of the neutron were also determined by Robert Bacher (1933) at Ann Arbor and I.Y. Tamm and S.A. Altshuler (1934) in the Soviet Union from studies of the hyperfine structure of atomic spectra. By the late 1930s, accurate values for the magnetic moment of the neutron had been deduced by the Rabi group, using measurements employing newly developed nuclear magnetic resonance techniques. The large value for the proton's magnetic moment and the inferred negative value for the neutron's magnetic moment were unexpected and raised many questions.
\ No newline at end of file
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@@ -0,0 +1,37 @@
+---
+title: "Discovery of the neutron"
+chunk: 7/7
+source: "https://en.wikipedia.org/wiki/Discovery_of_the_neutron"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:49.483017+00:00"
+instance: "kb-cron"
+---
+
+The discovery of the neutron immediately gave scientists a new tool for probing the properties of atomic nuclei. Alpha particles had been used over the previous decades in scattering experiments, but such particles, which are helium nuclei, have +2 charge. This charge makes it difficult for alpha particles to overcome the Coulomb repulsive force and interact directly with the nuclei of atoms. Since neutrons have no electric charge, they do not have to overcome this force to interact with nuclei. Almost coincident with their discovery, neutrons were used by Norman Feather, Chadwick's colleague and protege, in scattering experiments with nitrogen. Feather was able to demonstrate that neutrons interacting with nitrogen nuclei scattered to protons or induced nitrogen to disintegrate to form boron with the emission of an alpha particle. Feather was therefore the first to show that neutrons produce nuclear disintegrations.
+In Rome, Enrico Fermi and his team bombarded heavier elements with neutrons and found the products to be radioactive. By 1934, they had used neutrons to induce radioactivity in 22 different elements, many of these elements of high atomic number. Noticing that other experiments with neutrons at his laboratory seemed to work better on a wooden table than a marble table, Fermi suspected that the protons of the wood were slowing the neutrons and so increasing the chance for the neutron to interact with nuclei. Fermi therefore passed neutrons through paraffin wax to slow them and found that the radioactivity of some bombarded elements increased by a factor of tens to hundreds. The cross section for interaction with nuclei is much larger for slow neutrons than for fast neutrons. In 1938, Fermi received the Nobel Prize in Physics "for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons". Later, Fermi recounted to Chandrasekhar that he was originally planning to put a piece of lead there, but an inexplicable, intuitive feeling made him put a paraffin in the spot instead.
+
+In Berlin, the collaboration of Lise Meitner and Otto Hahn, together with their assistant Fritz Strassmann, furthered the research begun by Fermi and his team when they bombarded uranium with neutrons. Between 1934 and 1938, Hahn, Meitner, and Strassmann found a great number of radioactive transmutation products from these experiments, all of which they regarded as transuranic. Transuranic nuclides are those that have an atomic number greater than uranium (92), formed by neutron absorption; such nuclides are not naturally occurring. In July 1938, Meitner was forced to escape antisemitic persecution in Nazi Germany after the Anschluss, and she was able to secure a new position in Sweden. The decisive experiment on 16–17 December 1938 (using a chemical process called "radium–barium–mesothorium fractionation") produced puzzling results: what they had understood to be three isotopes of radium were instead consistently behaving as barium. Radium (atomic number 88) and barium (atomic number 56) are in the same chemical group.  By January 1939 Hahn had concluded that what they had thought were transuranic nuclides were instead much lighter nuclides, such as barium, lanthanum, cerium and light platinoids. Meitner and her nephew Otto Frisch immediately and correctly interpreted these observations as resulting from nuclear fission, a term coined by Frisch.
+Hahn and his collaborators had detected the splitting of uranium nuclei, made unstable by neutron absorption, into lighter elements. Meitner and Frisch also showed that the fission of each uranium atom would release about 200 MeV of energy. The discovery of fission electrified the global community of atomic physicists and the public.  In their second publication on nuclear fission, Hahn and Strassmann predicted the existence and liberation of additional neutrons during the fission process. Frédéric Joliot and his team proved this phenomenon to be a chain reaction in March 1939. In 1945, Hahn received the 1944 Nobel Prize in Chemistry "for his discovery of the fission of heavy atomic nuclei".
+
+== After 1939 ==
+
+The discovery of nuclear fission at the end of 1938 marked a shift in the centers of nuclear research from Europe to the United States. Large numbers of scientists were migrating to the United States to escape the troubles and antisemitism in Europe and the looming war (See Jewish scientists and the Manhattan Project). The new centers of nuclear research were the universities in the United States, particularly Columbia University in New York and the University of Chicago where Enrico Fermi had relocated, and a secret research facility at Los Alamos, New Mexico, established in 1942, the new home of the Manhattan Project. This wartime project was focused on the construction of nuclear weapons, using the enormous energy released by the fission of uranium or plutonium through neutron-based chain reactions.
+The discoveries of the neutron and positron in 1932 were the start of the discoveries of many new particles.  Muons were discovered in 1936, pions and kaons were discovered in 1947, and lambda particles were discovered in 1950.  Throughout the 1950s and 1960s, a large number of particles called hadrons were discovered.  A classification scheme for organizing all these particles, proposed independently by Murray Gell-Mann and
+George Zweig in 1964, became known as the quark model. By this model, particles such as the proton and neutron were not elementary, but composed of various configurations of a small number of other truly elementary particles called partons or quarks. The quark model received experimental verification beginning in the late 1960s and finally provided an explanation for the neutron's anomalous magnetic moment.
+
+== Videos ==
+Ernest Rutherford summarizes the state of nuclear physics in 1935. (7 min., Nobelprize.org)
+Hans Bethe discusses Chadwick and Goldhaber's work on deuteron disintegration. (2 min., Web of Stories)
+
+== Explanatory notes ==
+
+== References ==
+
+== Further reading ==
+Annotated bibliography for neutrons from the Alsos Digital Library for Nuclear Issues
+Abraham Pais, Inward Bound, Oxford: Oxford University Press, 1986. ISBN 0198519974.
+Herwig Schopper, Weak interactions and nuclear beta decay, Publisher, North-Holland Pub. Co., 1966. OCLC 644015779
+Ruth Lewin Sime, Lise Meitner: A Life in Physics, Berkeley, University of California Press, 1996. ISBN 0520208609.
+Roger H. Stuewer, "The Nuclear Electron Hypothesis". In Otto Hahn and the Rise of Nuclear Physics, William R. Shea, ed. Dordrecht, Holland: D. Riedel Publishing Company. pp. 19–67, 1983. ISBN 90-277-1584-X.
+Sin-Itiro Tomonaga, The Story of Spin, The University of Chicago Press, 1997. ISBN 9780226807942
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diff --git a/data/en.wikipedia.org/wiki/Einstein's_Blackboard-0.md b/data/en.wikipedia.org/wiki/Einstein's_Blackboard-0.md
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+---
+title: "Einstein's Blackboard"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Einstein's_Blackboard"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:55.889311+00:00"
+instance: "kb-cron"
+---
+
+Einstein's Blackboard is a blackboard which physicist Albert Einstein (1879–1955) used on 16 May 1931 during his lectures while visiting the University of Oxford in England. The blackboard is in the collection of the History of Science Museum in Oxford. The equations in the blackboard are related to the cosmological model known as Friedmann–Einstein universe.
+
+
+== Overview ==
+The lecture in which the blackboard was used was the second of three, delivered at Rhodes House in South Parks Road. Einstein's visit to give the Rhodes Lectures, and also to receive an honorary Doctor of Science degree from Oxford University on 23 May 1931, was hosted by the physicist Frederick Lindemann. Einstein's first lecture was on relativity, the second on cosmology, and the third on unified field theory. All the lectures were delivered in German. A brief report of the second lecture was given in The Times and in Nature. A summary of all three lectures can be found in the Archives of the Oxford Museum for the History of Science.
+The blackboard was rescued with another board by dons (including the chemist E. J. Bowen, zoologist Gavin de Beer, and historian of science Robert Gunther) and formally donated by the Warden of Rhodes House, Sir Francis James Wylie. The writing on the blackboard, although ephemeral in nature, is of historic interest because the equations displayed are taken from a model of the universe proposed by Einstein in May 1931 known as Friedmann–Einstein universe. The last three lines on the blackboard are estimates of the density of matter in the universe ρ, the radius of the universe P  and the timespan t of the expansion of the universe respectively. It has recently been shown that these estimates contain a systematic numerical error.
+The blackboard is considered a "mutant" object or artefact because it no longer serves the philosophical purpose of a blackboard, namely temporary information storage. By keeping Einstein's writings on it for ever, the blackboard became something else and can only regain to its original purpose by being wiped. A second blackboard used by Einstein during the lecture was also donated to the museum, but was accidentally wiped clean by a museum cleaner.
+Einstein returned to Oxford again in 1932 and 1933 before he settled at Princeton University in the United States for the rest of his life.
+
+
+== Content ==
+The blackboard reads
+
+where the variables refer to Friedmann–Einstein universe, where  
+  
+    
+      
+        D
+      
+    
+    {\displaystyle D}
+  
+ is defined in the equations, 
+  
+    
+      
+        c
+      
+    
+    {\displaystyle c}
+  
+ is the speed of light, 
+  
+    
+      
+        ℓ
+      
+    
+    {\displaystyle \ell }
+  
+ is the scale factor, 
+  
+    
+      
+        P
+      
+    
+    {\displaystyle P}
+  
+  is the radius of the universe (measured in light years) and 
+  
+    
+      
+        
+          P
+          
+            0
+          
+        
+      
+    
+    {\displaystyle P_{0}}
+  
+ its maximal value, 
+  
+    
+      
+        ρ
+      
+    
+    {\displaystyle \rho }
+  
+ is the mean density of matter, 
+  
+    
+      
+        t
+      
+    
+    {\displaystyle t}
+  
+ is time and the age of the universe (last line, measured in years), and 
+  
+    
+      
+        κ
+      
+    
+    {\displaystyle \kappa }
+  
+ is the Einstein's gravitational constant.
+
+
+=== Analysis ===
+In 2013, it was pointed out that the equations on the Oxford blackboard had been taken directly from a key paper on relativistic cosmology written by Einstein in April 1931 and published in the Proceedings of the Royal Prussian Academy of Science on 9 May that year. The paper, known as the Friedmann–Einstein universe, is of historic significance because it constituted the first scientific publication in which Einstein embraced the possibility of a cosmos of time-varying radius. In the paper, Einstein adopts Alexander Friedmann's 1922 analysis of relativistic models of a universe of time-varying radius and positive curvature, but sets the cosmological constant to zero, declaring it redundant, predicting a universe that expands and contracts over time. With the use of Edwin Hubble's observations of a linear redshift/distance relation for the spiral nebulae, Einstein extracts from his model estimates of ρ ~ 10−26 g/cm3, P ~ 108 light-years and t ~ 1010 years for the density of matter, the radius of the cosmos and the timespan of the cosmic expansion respectively. These values are displayed in the last three lines on the Oxford blackboard (although the units of measurement are not specifically stated for the density estimate, cgs units are implied by the other calculations).
+
+
+== Error ==
+It has also been noted that the numerical estimates of cosmic parameters in Einstein's 1931 paper – and on the blackboard – contain a systematic error. Analysis of the 1931 paper shows that, given the contemporaneous Hubble constant of 500 km s−1Mpc−1, Einstein's estimates of cosmic density, radius and timespan should have been ρ ~ 10−28 g/cm3, P ~ 108 light-years and t ~ 109 years respectively. One line on the blackboard, not included in the published paper, makes the nature of Einstein's error clear. In the fourth line on the blackboard, Einstein obtains a value of 10−53 cm−2 for the quantity D2, defined in the top line of the blackboard as
+  
+    
+      
+        D
+        =
+        
+          
+            1
+            c
+          
+        
+        
+          
+            1
+            P
+          
+        
+        
+          
+            
+              
+                d
+              
+              P
+            
+            
+              
+                d
+              
+              t
+            
+          
+        
+      
+    
+    {\displaystyle D={\frac {1}{c}}{\frac {1}{P}}{\frac {\mathrm {d} P}{\mathrm {d} t}}}
+  
+,i.e., the Hubble constant divided by the speed of light. Simple calculation shows that the contemporaneous value of the Hubble constant in fact implied a value of D2 ~ 10−55 cm−2 (or 10−51 m−2) for this quantity. It appears that Einstein stumbled in converting megaparsecs to cm, giving a density of matter that was too high by a factor of a hundred, a cosmic radius that was too low by a factor of ten, and a timespan for the expansion that was too high by a factor of ten. These errors were corrected in a later review of relativistic cosmology written by Einstein in 1945.
+
+
+== Nottingham blackboard ==
+A blackboard used by Einstein in a public lecture at the University of Nottingham on 6 June 1930 was also preserved after the lecture and is part of the university's archives.
+The blackboard is presently on display inside a protective frame and screen, within the university's Department of Physics and Astronomy. During term time it can be seen by academics and students within the classroom it's in. Visitors to campus can see it on display during university open days, if they take a tour of the department.
+
+When translated, it reads as a table of contents in English:
+Introductory remarks
+Concept of the body
+Special relations between bodies
+Concept of space in mathematics (by René Descartes)
+Newtonian space
+Concept of the field (by Michael Faraday, James Clerk Maxwell and Hendrik Lorentz)
+Special relativity theory
+General theory of relativity and geometry
+Unified field theory
+
+
+== See also ==
+Einstein in Oxford (2024 book)
+
+
+== References ==
+
+
+== External links ==
+Einstein's Blackboard podcast
+Photo: Einstein's blackboard, TripAdvisor, 2014
+Oxford – Einstein's blackboard, Flickr, 2013
+Einstein’s Blackboard, IELTS
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diff --git a/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-0.md b/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-0.md
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+---
+title: "Einstein's thought experiments"
+chunk: 1/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+A hallmark of Albert Einstein's career was his use of visualized thought experiments (German: Gedankenexperiment) as a fundamental tool for understanding physical issues and for elucidating his concepts to others. Einstein's thought experiments took diverse forms. In his youth, he mentally chased beams of light. For special relativity, he employed moving trains and flashes of lightning to explain his theory. For general relativity, he considered a person falling off a roof, accelerating elevators, blind beetles crawling on curved surfaces and the like. In his debates with Niels Bohr on the nature of reality, he proposed imaginary devices that attempted to show, at least in concept, how the Heisenberg uncertainty principle might be evaded. In a contribution to the literature on quantum mechanics, Einstein considered two particles briefly interacting and then flying apart so that their states are correlated, anticipating the phenomenon known as quantum entanglement.
+
+== Introduction ==
+
+A thought experiment is a logical argument or mental model cast within the context of an imaginary (hypothetical or even counterfactual) scenario. A scientific thought experiment, in particular, may examine the implications of a theory, law, or set of principles with the aid of fictive and/or natural particulars (demons sorting molecules, cats whose lives hinge upon a radioactive disintegration, men in enclosed elevators) in an idealized environment (massless trapdoors, absence of friction). They describe experiments that, except for some specific and necessary idealizations, could conceivably be performed in the real world.
+As opposed to physical experiments, thought experiments do not report new empirical data. They can only provide conclusions based on deductive or inductive reasoning from their starting assumptions. Thought experiments invoke particulars that are irrelevant to the generality of their conclusions. It is the invocation of these particulars that give thought experiments their experiment-like appearance. A thought experiment can always be reconstructed as a straightforward argument, without the irrelevant particulars. John D. Norton, a well-known philosopher of science, has noted that "a good thought experiment is a good argument; a bad thought experiment is a bad argument."
+When effectively used, the irrelevant particulars that convert a straightforward argument into a thought experiment can act as "intuition pumps" that stimulate readers' ability to apply their intuitions to their understanding of a scenario. Thought experiments have a long history. Perhaps the best known in the history of modern science is Galileo's demonstration that falling objects must fall at the same rate regardless of their masses. This has sometimes been taken to be an actual physical demonstration, involving his climbing up the Leaning Tower of Pisa and dropping two heavy weights off it.  In fact, it was a logical demonstration  described by Galileo in Discorsi e dimostrazioni matematiche (1638).
+Einstein had a highly visual understanding of physics. His work in the patent office "stimulated [him] to see the physical ramifications of theoretical concepts." These aspects of his thinking style inspired him to fill his papers with vivid practical detail making them quite different from, say, the papers of Lorentz or Maxwell. This included his use of thought experiments.
+
+== Special relativity ==
+
+=== Pursuing a beam of light ===
+
+Late in life, Einstein recalled
+
+...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained. 
+
+Einstein's recollections of his youthful musings are widely cited because of the hints they provide of his later great discovery. However, Norton has noted that Einstein's reminiscences were probably colored by a half-century of hindsight. Norton lists several problems with Einstein's recounting, both historical and scientific:
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diff --git a/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-1.md b/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-1.md
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+---
+title: "Einstein's thought experiments"
+chunk: 2/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+1. At 16 years old and a student at the Gymnasium in Aarau, Einstein would have had the thought experiment in late 1895 to early 1896. But various sources note that Einstein did not learn Maxwell's theory until 1898, in university.
+2. A 19th century aether theorist would have had no difficulties with the thought experiment. Einstein's statement, "...there seems to be no such thing...on the basis of experience," would not have counted as an objection, but would have represented a mere statement of fact, since no one had ever traveled at such speeds.
+3. An aether theorist would have regarded "...nor according to Maxwell's equations" as simply representing a misunderstanding on Einstein's part. Unfettered by any notion that the speed of light represents a cosmic limit, the aether theorist would simply have set velocity equal to c, noted that yes indeed, the light would appear to be frozen, and then thought no more of it.
+Rather than the thought experiment being at all incompatible with aether theories (which it is not), the youthful Einstein appears to have reacted to the scenario out of an intuitive sense of wrongness. He felt that the laws of optics should obey the principle of relativity. As he grew older, his early thought experiment acquired deeper levels of significance: Einstein felt that Maxwell's equations should be the same for all observers in inertial motion. From Maxwell's equations, one can deduce a single speed of light, and there is nothing in this computation that depends on an observer's speed. Einstein sensed a conflict between Newtonian mechanics and the constant speed of light determined by Maxwell's equations.
+Regardless of the historical and scientific issues described above, Einstein's early thought experiment was part of the repertoire of test cases that he used to check on the viability of physical theories. Norton suggests that the real importance of the thought experiment was that it provided a powerful objection to emission theories of light, which Einstein had worked on for several years prior to 1905.
+
+=== Magnet and conductor ===
+
+In the first paragraph of Einstein's 1905 work introducing special relativity, he writes: It is well known that Maxwell's electrodynamics—as usually understood at present—when applied to moving bodies, leads to asymmetries that do not seem to attach to the phenomena. Let us recall, for example, the electrodynamic interaction between a magnet and a conductor. The observable phenomenon depends here only on the relative motion of conductor and magnet, while according to the customary conception the two cases, in which, respectively, either the one or the other of the two bodies is the one in motion, are to be strictly differentiated from each other. For if the magnet is in motion and the conductor is at rest, there arises in the surroundings of the magnet an electric field endowed with a certain energy value that produces a current in the places where parts of the conductor are located. But if the magnet is at rest and the conductor is in motion, no electric field arises in the surroundings of the magnet, while in the conductor an electromotive force will arise, to which in itself there does not correspond any energy, but which, provided that the relative motion in the two cases considered is the same, gives rise to electrical currents that have the same magnitude and the same course as those produced by the electric forces in the first-mentioned case.
+
+This opening paragraph recounts well-known experimental results obtained by Michael Faraday in 1831. The experiments describe what appeared to be two different phenomena: the motional EMF generated when a wire moves through a magnetic field (see Lorentz force), and the transformer EMF generated by a changing magnetic field (due to the Maxwell–Faraday equation). James Clerk Maxwell himself drew attention to this fact in his 1861 paper On Physical Lines of Force. In the latter half of Part II of that paper, Maxwell gave a separate physical explanation for each of the two phenomena.
+Although Einstein calls the asymmetry "well-known", there is no evidence that any of Einstein's contemporaries considered the distinction between motional EMF and transformer EMF to be in any way odd or pointing to a lack of understanding of the underlying physics. Maxwell, for instance, had repeatedly discussed Faraday's laws of induction, stressing that the magnitude and direction of the induced current was a function only of the relative motion of the magnet and the conductor, without being bothered by the clear distinction between conductor-in-motion and magnet-in-motion in the underlying theoretical treatment.
+Yet Einstein's reflection on this experiment represented the decisive moment in his long and tortuous path to special relativity. Although the equations describing the two scenarios are entirely different, there is no measurement that can distinguish whether the magnet is moving, the conductor is moving, or both.
+In a 1920 review on the Fundamental Ideas and Methods of the Theory of Relativity (unpublished), Einstein related how disturbing he found this asymmetry: 
+
+The idea that these two cases should essentially be different was unbearable to me. According to my conviction, the difference between the two could only lie in the choice of the point of view, but not in a real difference <in the reality of nature>. 
+Einstein needed to extend the relativity of motion that he perceived between magnet and conductor in the above thought experiment to a full theory. For years, however, he did not know how this might be done. The exact path that Einstein took to resolve this issue is unknown. We do know, however, that Einstein spent several years pursuing an emission theory of light, encountering difficulties that eventually led him to give up the attempt. 
\ No newline at end of file
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@@ -0,0 +1,231 @@
+---
+title: "Einstein's thought experiments"
+chunk: 11/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+At the Sixth Solvay International Conference on Magnetism (1930), Einstein came armed with a new thought experiment. This involved a box with a shutter that operated so quickly, it would allow only one photon to escape at a time. The box would first be weighed exactly. Then, at a precise moment, the shutter would open, allowing a photon to escape. The box would then be re-weighed. The well-known relationship between mass and energy 
+  
+    
+      
+        E
+        =
+        m
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle E=mc^{2}}
+  
+ would allow the energy of the particle to be precisely determined. With this gadget, Einstein believed that he had demonstrated a means to obtain, simultaneously, a precise determination of the energy of the photon as well as its exact time of departure from the system.
+Bohr was shaken by this thought experiment. Unable to think of a refutation, he went from one conference participant to another, trying to convince them that Einstein's thought experiment could not be true, that if it were true, it would literally mean the end of physics. After a sleepless night, he finally worked out a response which, ironically, depended on Einstein's general relativity. Consider the illustration of Einstein's light box:
+
+1. After emitting a photon, the loss of weight causes the box to rise in the gravitational field.
+2. The observer returns the box to its original height by adding weights until the pointer points to its initial position. It takes a certain amount of time 
+  
+    
+      
+        t
+      
+    
+    {\displaystyle t}
+  
+ for the observer to perform this procedure. How long it takes depends on the strength of the spring and on how well-damped the system is. If undamped, the box will bounce up and down forever. If over-damped, the box will return to its original position sluggishly (See Damped spring-mass system).
+3. The longer that the observer allows the damped spring-mass system to settle, the closer the pointer will reach its equilibrium position. At some point, the observer will conclude that his setting of the pointer to its initial position is within an allowable tolerance. There will be some residual error 
+  
+    
+      
+        Δ
+        q
+      
+    
+    {\displaystyle \Delta q}
+  
+ in returning the pointer to its initial position. Correspondingly, there will be some residual error 
+  
+    
+      
+        Δ
+        m
+      
+    
+    {\displaystyle \Delta m}
+  
+ in the weight measurement.
+4. Adding the weights imparts a momentum 
+  
+    
+      
+        p
+      
+    
+    {\displaystyle p}
+  
+ to the box which can be measured with an accuracy 
+  
+    
+      
+        Δ
+        p
+      
+    
+    {\displaystyle \Delta p}
+  
+ delimited by 
+  
+    
+      
+        Δ
+        p
+        Δ
+        q
+        ≈
+        h
+        .
+      
+    
+    {\displaystyle \Delta p\Delta q\approx h.}
+  
+ It is clear that 
+  
+    
+      
+        Δ
+        p
+        <
+        g
+        t
+        Δ
+        m
+        ,
+      
+    
+    {\displaystyle \Delta p<gt\Delta m,}
+  
+ where 
+  
+    
+      
+        g
+      
+    
+    {\displaystyle g}
+  
+ is the gravitational constant. Plugging in yields 
+  
+    
+      
+        g
+        t
+        Δ
+        m
+        Δ
+        q
+        >
+        h
+        .
+      
+    
+    {\displaystyle gt\Delta m\Delta q>h.}
+  
+
+5. General relativity informs us that while the box has been at a height different than its original height, it has been ticking at a rate different than its original rate. The red shift formula informs us that there will be an uncertainty 
+  
+    
+      
+        Δ
+        t
+        =
+        
+          c
+          
+            −
+            2
+          
+        
+        g
+        t
+        Δ
+        q
+      
+    
+    {\displaystyle \Delta t=c^{-2}gt\Delta q}
+  
+ in the determination of 
+  
+    
+      
+        
+          t
+          
+            0
+          
+        
+        ,
+      
+    
+    {\displaystyle t_{0},}
+  
+ the emission time of the photon.
+6. Hence, 
+  
+    
+      
+        
+          c
+          
+            2
+          
+        
+        Δ
+        m
+        Δ
+        t
+        =
+        Δ
+        E
+        Δ
+        t
+        >
+        h
+        .
+      
+    
+    {\displaystyle c^{2}\Delta m\Delta t=\Delta E\Delta t>h.}
+  
+ The accuracy with which the energy of the photon is measured restricts the precision with which its moment of emission can be measured, following the Heisenberg uncertainty principle.
+After finding his last attempt at finding a loophole around the uncertainty principle refuted, Einstein quit trying to search for inconsistencies in quantum mechanics. Instead, he shifted his focus to the other aspects of quantum mechanics with which he was uncomfortable, focusing on his critique of action at a distance. His next paper on quantum mechanics foreshadowed his later paper on the EPR paradox.
+Einstein was gracious in his defeat. The following September, Einstein nominated Heisenberg and Schroedinger for the Nobel Prize, stating, "I am convinced that this theory undoubtedly contains a part of the ultimate truth."
+Modern analysis suggests Einstein’s photon-box paradox does not require gravity or general-relativistic arguments. Although Bohr’s original reply invoked gravitational redshift to restore the energy–time uncertainty relation, later analyses showed that opening the shutter entangles the box’s internal clock with its energy, and any attempt to measure the photon’s energy by weighing the box inevitably disturbs the clock state. Because the clock variable and the box’s internal energy are conjugate observables, precise determination of one necessarily introduces quantum back-action on the other, enforcing 
+  
+    
+      
+        Δ
+        E
+        Δ
+        t
+        ≥
+        ℏ
+        
+          /
+        
+        2
+      
+    
+    {\displaystyle \Delta E\Delta t\geq \hbar /2}
+  
+ without reference to gravitational effects. However, different meanings of "uncertainty" make analysis of the experiment complex.
+
+=== EPR paradox ===
+
+Both Bohr and Einstein were subtle men. Einstein tried very hard to show that quantum mechanics was inconsistent; Bohr, however, was always able to counter his arguments. But in his final attack Einstein pointed to something so deep, so counterintuitive, so troubling, and yet so exciting, that at the beginning of the twenty-first century it has returned to fascinate theoretical physicists. Bohr's only answer to Einstein's last great discovery—the discovery of entanglement—was to ignore it.
+Einstein's fundamental dispute with quantum mechanics was not about whether God rolled dice, whether the uncertainty principle allowed simultaneous measurement of position and momentum, or even whether quantum mechanics was complete. It was about reality. Does a physical reality exist independent of our ability to observe it? To Bohr and his followers, such questions were meaningless. All that we can know are the results of measurements and observations. It makes no sense to speculate about an ultimate reality that exists beyond our perceptions.
+Einstein's beliefs had evolved over the years from those that he had held when he was young, when, as a logical positivist heavily influenced by his reading of David Hume and Ernst Mach, he had rejected such unobservable concepts as absolute time and space. Einstein believed: 
\ No newline at end of file
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+---
+title: "Einstein's thought experiments"
+chunk: 12/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+1. A reality exists independent of our ability to observe it.
+2. Objects are located at distinct points in spacetime and have their own independent, real existence. In other words, he believed in separability and locality.
+3. Although at a superficial level, quantum events may appear random, at some ultimate level, strict causality underlies all processes in nature.
+
+Einstein considered that realism and localism were fundamental underpinnings of physics. After leaving Nazi Germany and settling in Princeton at the Institute for Advanced Study, Einstein began writing up a thought experiment that he had been mulling over since attending a lecture by Léon Rosenfeld in 1933. Since the paper was to be in English, Einstein enlisted the help of the 46-year-old Boris Podolsky, a fellow who had moved to the institute from Caltech; he also enlisted the help of the 26-year-old Nathan Rosen, also at the institute, who did much of the math. The result of their collaboration was the four page EPR paper, which in its title asked the question Can Quantum-Mechanical Description of Physical Reality be Considered Complete?
+After seeing the paper in print, Einstein found himself unhappy with the result. His clear conceptual visualization had been buried under layers of mathematical formalism.
+Einstein's thought experiment involved two particles that have collided or which have been created in such a way that they have properties which are correlated. The total wave function for the pair links the positions of the particles as well as their linear momenta. The figure depicts the spreading of the wave function from the collision point. However, observation of the position of the first particle allows us to determine precisely the position of the second particle no matter how far the pair have separated. Likewise, measuring the momentum of the first particle allows us to determine precisely the momentum of the second particle. "In accordance with our criterion for reality, in the first case we must consider the quantity P as being an element of reality, in the second case the quantity Q is an element of reality."
+Einstein concluded that the second particle, which we have never directly observed, must have at any moment a position that is real and a momentum that is real. Quantum mechanics does not account for these features of reality. Therefore, quantum mechanics is not complete. It is known, from the uncertainty principle, that position and momentum cannot be measured at the same time. But even though their values can only be determined in distinct contexts of measurement, can they both be definite at the same time? Einstein concluded that the answer must be yes.
+The only alternative, claimed Einstein, would be to assert that measuring the first particle instantaneously affected the reality of the position and momentum of the second particle. "No reasonable definition of reality could be expected to permit this."
+Bohr was stunned when he read Einstein's paper and spent more than six weeks framing his response, which he gave exactly the same title as the EPR paper. The EPR paper forced Bohr to make a major revision in his understanding of complementarity in the Copenhagen interpretation of quantum mechanics.
+Prior to EPR, Bohr had maintained that disturbance caused by the act of observation was the physical explanation for quantum uncertainty. In the EPR thought experiment, however, Bohr had to admit that "there is no question of a mechanical disturbance of the system under investigation." On the other hand, he noted that the two particles were one system described by one quantum function. Furthermore, the EPR paper did nothing to dispel the uncertainty principle. 
+Later commentators have questioned the strength and coherence of Bohr's response. As a practical matter, however, physicists for the most part did not pay much attention to the debate between Bohr and Einstein, since the opposing views did not affect one's ability to apply quantum mechanics to practical problems, but only affected one's interpretation of the quantum formalism. If they thought about the problem at all, most working physicists tended to follow Bohr's leadership.
+In 1964, John Stewart Bell made the groundbreaking discovery that Einstein's local realist world view made experimentally verifiable predictions that would be in conflict with those of quantum mechanics. Bell's discovery shifted the Einstein–Bohr debate from philosophy to the realm of experimental physics. Bell's theorem showed that, for any local realist formalism, there exist limits on the predicted correlations between pairs of particles in an experimental realization of the EPR thought experiment. In 1972, the first experimental tests were carried out that demonstrated violation of these limits. Successive experiments improved the accuracy of observation and closed loopholes. To date, it is virtually certain that local realist theories have been falsified. 
+The EPR paper has recently been recognized as prescient, since it identified the phenomenon of quantum entanglement, which has inspired approaches to quantum mechanics different from the Copenhagen interpretation, and has been at the forefront of major technological advances in quantum computing, quantum encryption, and quantum information theory.
+
+== Notes ==
+
+== Primary sources ==
+
+== References ==
+
+== External links ==
+NOVA: Inside Einstein's Mind (2015) — Retrace the thought experiments that inspired his theory on the nature of reality.
\ No newline at end of file
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+---
+title: "Einstein's thought experiments"
+chunk: 3/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+Gradually I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and more desperately I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results. 
+That decision ultimately led to his development of special relativity as a theory founded on two postulates. Einstein's original expression of these postulates was:
+
+"The laws governing the changes of the state of any physical system do not depend on which one of two coordinate systems in uniform translational motion relative to each other these changes of the state are referred to.
+Each ray of light moves in the coordinate system "at rest" with the definite velocity V independent of whether this ray of light is emitted by a body at rest or a body in motion."
+In their modern form:
+
+1. The laws of physics take the same form in all inertial frames.
+2. In any given inertial frame, the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion. [Emphasis added by editor]
+Einstein's wording of the first postulate was one with which nearly all theorists of his day could agree. His second postulate expresses a new idea about the character of light. Modern textbooks combine the two postulates. One popular textbook expresses the second postulate as, "The speed of light in free space has the same value c in all directions and in all inertial reference frames."
+
+=== Trains, embankments, and lightning flashes ===
+
+The topic of how Einstein arrived at special relativity has been a fascinating one to many scholars: A twenty-six year old patent officer (third class), largely self-taught in physics and completely divorced from mainstream research, nevertheless in the year 1905 produced four extraordinary works (Annus Mirabilis papers), only one of which (his paper on Brownian motion) appeared related to anything that he had ever published before.
+Einstein's paper, On the Electrodynamics of Moving Bodies, is a polished work that bears few traces of its gestation. Documentary evidence concerning the development of the ideas that went into it consist of, quite literally, only two sentences in a handful of preserved early letters, and various later historical remarks by Einstein himself, some of them known only second-hand and at times contradictory.
+
+In regards to the relativity of simultaneity, Einstein's 1905 paper develops the concept vividly by carefully considering the basics of how time may be disseminated through the exchange of signals between clocks. In his popular work, Relativity: The Special and General Theory, Einstein translates the formal presentation of his paper into a thought experiment using a train, a railway embankment, and lightning flashes. The essence of the thought experiment is as follows: 
+
+Observer M stands on an embankment, while observer M' rides on a rapidly traveling train. At the precise moment that M and M' coincide in their positions, lightning strikes points A and B equidistant from M and M'.
+Light from these two flashes reach M at the same time, from which M concludes that the bolts were synchronous.
+The combination of Einstein's first and second postulates implies that, despite the rapid motion of the train relative to the embankment, M' measures exactly the same speed of light as does M. Since M' was equidistant from A and B when lightning struck, the fact that M' receives light from B before light from A means that to M', the bolts were not synchronous. Instead, the bolt at B struck first. 
+A routine supposition among historians of science is that, in accordance with the analysis given in his 1905 special relativity paper and in his popular writings, Einstein discovered the relativity of simultaneity by thinking about how clocks could be synchronized by light signals. The Einstein synchronization convention was originally developed by telegraphers in the middle 19th century. The dissemination of precise time was an increasingly important topic during this period. Trains needed accurate time to schedule use of track, cartographers needed accurate time to determine longitude, while astronomers and surveyors dared to consider the worldwide dissemination of time to accuracies of thousandths of a second. Following this line of argument, Einstein's position in the patent office, where he specialized in evaluating electromagnetic and electromechanical patents, would have exposed him to the latest developments in time technology, which would have guided him in his thoughts towards understanding the relativity of simultaneity.
+However, all of the above is supposition. In later recollections, when Einstein was asked about what inspired him to develop special relativity, he would mention his riding a light beam and his magnet and conductor thought experiments. He would also mention the importance of the Fizeau experiment and the observation of stellar aberration. "They were enough", he said. He never mentioned thought experiments about clocks and their synchronization.
+The routine analyses of the Fizeau experiment and of stellar aberration, that treat light as Newtonian corpuscles, do not require relativity. But problems arise if one considers light as waves traveling through an aether, which are resolved by applying the relativity of simultaneity. It is entirely possible, therefore, that Einstein arrived at special relativity through a different path than that commonly assumed, through  Einstein's examination of Fizeau's experiment and stellar aberration.
+We therefore do not know just how important clock synchronization and the train and embankment thought experiment were to Einstein's development of the concept of the relativity of simultaneity. We do know, however, that the train and embankment thought experiment was the preferred means whereby he chose to teach this concept to the general public.
+
+=== Relativistic center-of-mass theorem ===
\ No newline at end of file
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@@ -0,0 +1,364 @@
+---
+title: "Einstein's thought experiments"
+chunk: 4/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+Einstein proposed the equivalence of mass and energy in his final Annus Mirabilis paper. Over the next several decades, the understanding of energy and its relationship with momentum were further developed by Einstein and other physicists including Max Planck, Gilbert N. Lewis, Richard C. Tolman, Max von Laue (who in 1911 gave a comprehensive proof of M0 = E0/c2 from the stress–energy tensor), and Paul Dirac (whose investigations of negative solutions in his 1928 formulation of the energy–momentum relation led to the 1930 prediction of the existence of antimatter).
+
+Einstein's relativistic center-of-mass theorem of 1906 is a case in point. In 1900, Henri Poincaré had noted a paradox in modern physics as it was then understood: When he applied well-known results of Maxwell's equations to the equality of action and reaction, he could describe a cyclic process which would result in creation of a reactionless drive, i.e. a device which could displace its center of mass without the exhaust of a propellant, in violation of the conservation of momentum. Poincaré resolved this paradox by imagining electromagnetic energy to be a fluid having a given density, which is created and destroyed with a given momentum as energy is absorbed and emitted. The motions of this fluid would oppose displacement of the center of mass in such fashion as to preserve the conservation of momentum.
+Einstein demonstrated that Poincaré's artifice was superfluous. Rather, he argued that mass-energy equivalence was a necessary and sufficient condition to resolve the paradox. In his demonstration, Einstein provided a derivation of mass-energy equivalence that was distinct from his original derivation. Einstein began by recasting Poincaré's abstract mathematical argument into the form of a thought experiment:
+Einstein considered (a) an initially stationary, closed, hollow cylinder free-floating in space, of mass 
+  
+    
+      
+        M
+      
+    
+    {\displaystyle M}
+  
+ and length 
+  
+    
+      
+        L
+      
+    
+    {\displaystyle L}
+  
+, (b) with some sort of arrangement for sending a quantity of radiative energy (a burst of photons) 
+  
+    
+      
+        E
+      
+    
+    {\displaystyle E}
+  
+ from the left to the right. The radiation has momentum 
+  
+    
+      
+        E
+        
+          /
+        
+        c
+        .
+      
+    
+    {\displaystyle E/c.}
+  
+ Since the total momentum of the system is zero, the cylinder recoils with a speed 
+  
+    
+      
+        v
+        =
+        −
+        E
+        
+          /
+        
+        (
+        M
+        c
+        )
+        .
+      
+    
+    {\displaystyle v=-E/(Mc).}
+  
+ (c) The radiation hits the other end of the cylinder in time 
+  
+    
+      
+        Δ
+        t
+        =
+        L
+        
+          /
+        
+        c
+        ,
+      
+    
+    {\displaystyle \Delta t=L/c,}
+  
+ (assuming 
+  
+    
+      
+        v
+        <<
+        c
+      
+    
+    {\displaystyle v<<c}
+  
+), bringing the cylinder to a stop after it has moved through a distance
+
+  
+    
+      
+        Δ
+        x
+        =
+        −
+        
+          
+            
+              E
+              L
+            
+            
+              M
+              
+                c
+                
+                  2
+                
+              
+            
+          
+        
+        .
+      
+    
+    {\displaystyle \Delta x=-{\frac {EL}{Mc^{2}}}.}
+  
+
+(d) The energy deposited on the right wall of the cylinder is transferred to a massless shuttle mechanism 
+  
+    
+      
+        k
+        ,
+      
+    
+    {\displaystyle k,}
+  
+ (e) which transports the energy to the left wall (f) and then returns to re-create the starting configuration of the system, except with the cylinder displaced to the left. The cycle may then be repeated.
+The reactionless drive described here violates the laws of mechanics, according to which the center of mass of a body at rest cannot be displaced in the absence of external forces. Einstein argued that the shuttle 
+  
+    
+      
+        k
+      
+    
+    {\displaystyle k}
+  
+ cannot be massless while transferring energy from the right to the left. If energy 
+  
+    
+      
+        E
+      
+    
+    {\displaystyle E}
+  
+ possesses the inertia 
+  
+    
+      
+        m
+        =
+        E
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+        ,
+      
+    
+    {\displaystyle m=E/c^{2},}
+  
+ the contradiction disappears.
+Modern analysis suggests that neither Einstein's original 1905 derivation of mass-energy equivalence nor the alternate derivation implied by his 1906 center-of-mass theorem are definitively correct. For instance, the center-of-mass thought experiment regards the cylinder as a completely rigid body. In reality, the impulse provided to the cylinder by the burst of light in step (b) cannot travel faster than light, so that when the burst of photons reaches the right wall in step (c), the wall has not yet begun to move. Ohanian has credited von Laue (1911) as having provided the first truly definitive derivation of M0 = E0/c2.
+
+=== Impossibility of faster-than-light signaling ===
+
+In 1907, Einstein noted that from the composition law for velocities, one could deduce that there cannot exist an effect that allows faster-than-light signaling.
+Einstein imagined a strip of material that allows propagation of signals at the faster-than-light speed of 
+  
+    
+      
+        W
+      
+    
+    {\displaystyle W}
+  
+ (as viewed from the material strip). Imagine two observers, A and B, standing on the x-axis and separated by the distance 
+  
+    
+      
+        L
+      
+    
+    {\displaystyle L}
+  
+. They stand next to the material strip, which is not at rest, but rather is moving in the negative x-direction with speed 
+  
+    
+      
+        v
+      
+    
+    {\displaystyle v}
+  
+. A uses the strip to send a signal to B. From the velocity composition formula, the signal propagates from A to B with speed 
+  
+    
+      
+        
+          (
+          W
+          −
+          v
+          )
+          
+            /
+          
+          (
+          1
+          −
+          (
+          W
+          v
+          
+            /
+          
+          
+            c
+            
+              2
+            
+          
+          )
+          )
+        
+      
+    
+    {\displaystyle {(W-v)/(1-(Wv/c^{2}))}}
+  
+. The time 
+  
+    
+      
+        T
+      
+    
+    {\displaystyle T}
+  
+ required for the signal to propagate from A to B is given by
+
+  
+    
+      
+        T
+        =
+        L
+        
+          
+            
+              1
+              −
+              (
+              W
+              v
+              
+                /
+              
+              
+                c
+                
+                  2
+                
+              
+              )
+            
+            
+              W
+              −
+              v
+            
+          
+        
+        .
+      
+    
+    {\displaystyle T=L{1-(Wv/c^{2}) \over W-v}.}
+  
+
+The strip can move at any speed 
+  
+    
+      
+        v
+        <
+        c
+      
+    
+    {\displaystyle v<c}
+  
+. Given the starting assumption 
+  
+    
+      
+        W
+        >
+        c
+      
+    
+    {\displaystyle W>c}
+  
+, one can always set the strip moving at a speed 
+  
+    
+      
+        v
+      
+    
+    {\displaystyle v}
+  
+ such that 
+  
+    
+      
+        T
+        <
+        0
+      
+    
+    {\displaystyle T<0}
+  
+.
+In other words, given the existence of a means of transmitting signals faster-than-light, scenarios can be envisioned whereby the recipient of a signal will receive the signal before the transmitter has transmitted it.
+About this thought experiment, Einstein wrote: 
+
+Even though this result, in my opinion, does not contain any contradiction from a purely logical point of view, it conflicts with the character of all our experience to such an extent that this seems sufficient to prove the impossibility of the assumption 
+  
+    
+      
+        W
+        >
+        c
+      
+    
+    {\displaystyle W>c}
+  
+. 
+
+== General relativity ==
+
+=== Falling painters and accelerating elevators ===
\ No newline at end of file
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+---
+title: "Einstein's thought experiments"
+chunk: 5/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+In his unpublished 1920 review, Einstein related the genesis of his thoughts on the equivalence principle: When I was busy (in 1907) writing a summary of my work on the theory of special relativity for the Jahrbuch der Radioaktivität und Elektronik [Yearbook for Radioactivity and Electronics], I also had to try to modify the Newtonian theory of gravitation such as to fit its laws into the theory. While attempts in this direction showed the practicability of this enterprise, they did not satisfy me because they would have had to be based upon unfounded physical hypotheses. At that moment I got the happiest thought of my life in the following form: In an example worth considering, the gravitational field has a relative existence only in a manner similar to the electric field generated by magneto-electric induction. Because for an observer in free-fall from the roof of a house there is during the fall—at least in his immediate vicinity—no gravitational field. Namely, if the observer lets go of any bodies, they remain relative to him, in a state of rest or uniform motion, independent of their special chemical or physical nature. The observer, therefore, is justified in interpreting his state as being "at rest." 
+The realization "startled" Einstein, and inspired him to begin an eight-year quest that led to what is considered to be his greatest work, the theory of general relativity. Over the years, the story of the falling man has become an iconic one, much embellished by other writers. In most retellings of Einstein's story, the falling man is identified as a painter. In some accounts, Einstein was inspired after he witnessed a painter falling from the roof of a building adjacent to the patent office where he worked. This version of the story leaves unanswered the question of why Einstein might consider his observation of such an unfortunate accident to represent the happiest thought in his life.
+
+Einstein later refined his thought experiment to consider a man inside a large enclosed chest or elevator falling freely in space. While in free fall, the man would consider himself weightless, and any loose objects that he emptied from his pockets would float alongside him. Then Einstein imagined a rope attached to the roof of the chamber. A powerful "being" of some sort begins pulling on the rope with constant force. The chamber begins to move "upwards" with a uniformly accelerated motion. Within the chamber, all of the man's perceptions are consistent with his being in a uniform gravitational field. Einstein asked, "Ought we to smile at the man and say that he errs in his conclusion?" Einstein answered no. Rather, the thought experiment provided "good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a generalised postulate of relativity."
+Through this thought experiment, Einstein addressed an issue that was so well known, scientists rarely worried about it or considered it puzzling: Objects have "gravitational mass," which determines the force with which they are attracted to other objects. Objects also have "inertial mass," which determines the relationship between the force applied to an object and how much it accelerates. Newton had pointed out that, even though they are defined differently, gravitational mass and inertial mass always seem to be equal. But until Einstein, no one had conceived a good explanation as to why this should be so. From the correspondence revealed by his thought experiment, Einstein concluded that "it is impossible to discover by experiment whether a given system of coordinates is accelerated, or whether...the observed effects are due to a gravitational field." This correspondence between gravitational mass and inertial mass is the equivalence principle.
+An extension to his accelerating observer thought experiment allowed Einstein to deduce that "rays of light are propagated curvilinearly in gravitational fields."
+
+=== Early applications of the equivalence principle ===
+Einstein's formulation of special relativity was in terms of kinematics (the study of moving bodies without reference to forces). Late in 1907, his former mathematics professor, Hermann Minkowski, presented an alternative, geometric interpretation of special relativity in a lecture to the Göttingen Mathematical society, introducing the concept of spacetime. Einstein was initially dismissive of Minkowski's geometric interpretation, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness).
+As with special relativity, Einstein's early results in developing what was ultimately to become general relativity were accomplished using kinematic analysis rather than geometric techniques of analysis.
+In his 1907 Jahrbuch paper, Einstein first addressed the question of whether the propagation of light is influenced by gravitation, and whether there is any effect of a gravitational field on clocks. In 1911, Einstein returned to this subject, in part because he had realized that certain predictions of his nascent theory were amenable to experimental test.
+By the time of his 1911 paper, Einstein and other scientists had offered several alternative demonstrations that the inertial mass of a body increases with its energy content: If the energy increase of the body is 
+  
+    
+      
+        E
+      
+    
+    {\displaystyle E}
+  
+, then the increase in its inertial mass is 
+  
+    
+      
+        E
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+        .
+      
+    
+    {\displaystyle E/c^{2}.}
+  
+
+Einstein asked whether there is an increase of gravitational mass corresponding to the increase in inertial mass, and if there is such an increase, is the increase in gravitational mass precisely the same as its increase in inertial mass? Using the equivalence principle, Einstein concluded that this must be so.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-5.md b/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-5.md
new file mode 100644
index 000000000..5ea111c83
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-5.md
@@ -0,0 +1,1091 @@
+---
+title: "Einstein's thought experiments"
+chunk: 6/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+To show that the equivalence principle necessarily implies the gravitation of energy, Einstein considered a light source 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ separated along the z-axis by a distance 
+  
+    
+      
+        h
+      
+    
+    {\displaystyle h}
+  
+ above a receiver 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ in a homogeneous gravitational field having a force per unit mass of 1 
+  
+    
+      
+        g
+        .
+      
+    
+    {\displaystyle g.}
+  
+ A certain amount of electromagnetic energy 
+  
+    
+      
+        E
+      
+    
+    {\displaystyle E}
+  
+ is emitted by 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ towards 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+        .
+      
+    
+    {\displaystyle S_{1}.}
+  
+  According to the equivalence principle, this system is equivalent to a gravitation-free system which moves with uniform acceleration 
+  
+    
+      
+        g
+      
+    
+    {\displaystyle g}
+  
+ in the direction of the positive z-axis, with 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ separated by a constant distance 
+  
+    
+      
+        h
+      
+    
+    {\displaystyle h}
+  
+ from 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+        .
+      
+    
+    {\displaystyle S_{1}.}
+  
+
+In the accelerated system, light emitted from 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ takes (to a first approximation) 
+  
+    
+      
+        h
+        
+          /
+        
+        c
+      
+    
+    {\displaystyle h/c}
+  
+ to arrive at 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+        .
+      
+    
+    {\displaystyle S_{1}.}
+  
+ But in this time, the velocity of 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ will have increased by 
+  
+    
+      
+        v
+        =
+        g
+        h
+        
+          /
+        
+        c
+      
+    
+    {\displaystyle v=gh/c}
+  
+ from its velocity when the light was emitted. The energy arriving at 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ will therefore not be the energy 
+  
+    
+      
+        
+          E
+          
+            2
+          
+        
+        ,
+      
+    
+    {\displaystyle E_{2},}
+  
+ but the greater energy  
+  
+    
+      
+        
+          E
+          
+            1
+          
+        
+      
+    
+    {\displaystyle E_{1}}
+  
+ given by
+
+  
+    
+      
+        
+          E
+          
+            1
+          
+        
+        ≈
+        
+          E
+          
+            2
+          
+        
+        
+          (
+          
+            1
+            +
+            
+              
+                v
+                c
+              
+            
+          
+          )
+        
+        =
+        
+          E
+          
+            2
+          
+        
+        
+          (
+          
+            1
+            +
+            
+              
+                
+                  g
+                  h
+                
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+        .
+      
+    
+    {\displaystyle E_{1}\approx E_{2}\left(1+{\frac {v}{c}}\right)=E_{2}\left(1+{\frac {gh}{c^{2}}}\right).}
+  
+
+According to the equivalence principle, the same relation holds for the non-accelerated system in a gravitational field, where we replace 
+  
+    
+      
+        g
+        h
+      
+    
+    {\displaystyle gh}
+  
+ by the gravitational potential difference 
+  
+    
+      
+        Φ
+      
+    
+    {\displaystyle \Phi }
+  
+ between 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ and 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ so that
+
+  
+    
+      
+        
+          E
+          
+            1
+          
+        
+        =
+        
+          E
+          
+            2
+          
+        
+        +
+        
+          
+            
+              E
+              
+                2
+              
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+        Φ
+        .
+      
+    
+    {\displaystyle E_{1}=E_{2}+{\frac {E_{2}}{c^{2}}}\Phi .}
+  
+
+The energy 
+  
+    
+      
+        
+          E
+          
+            1
+          
+        
+      
+    
+    {\displaystyle E_{1}}
+  
+ arriving at 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ is greater than the energy 
+  
+    
+      
+        
+          E
+          
+            2
+          
+        
+      
+    
+    {\displaystyle E_{2}}
+  
+ emitted by 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ by the potential energy of the mass 
+  
+    
+      
+        
+          E
+          
+            2
+          
+        
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle E_{2}/c^{2}}
+  
+ in the gravitational field. Hence 
+  
+    
+      
+        E
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle E/c^{2}}
+  
+ corresponds to the gravitational mass as well as the inertial mass of a quantity of energy.
+
+To further clarify that the energy of gravitational mass must equal the energy of inertial mass, Einstein proposed the following cyclic process: (a) A light source 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ is situated a distance 
+  
+    
+      
+        h
+      
+    
+    {\displaystyle h}
+  
+ above a receiver 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ in a uniform gravitational field. A movable mass 
+  
+    
+      
+        M
+      
+    
+    {\displaystyle M}
+  
+ can shuttle between 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ and 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+        .
+      
+    
+    {\displaystyle S_{1}.}
+  
+ (b) A pulse of electromagnetic energy 
+  
+    
+      
+        E
+      
+    
+    {\displaystyle E}
+  
+ is sent from 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ to 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+        .
+      
+    
+    {\displaystyle S_{1}.}
+  
+ The energy 
+  
+    
+      
+        E
+        (
+        1
+        +
+        g
+        h
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+        )
+      
+    
+    {\displaystyle E(1+gh/c^{2})}
+  
+ is absorbed by 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+        .
+      
+    
+    {\displaystyle S_{1}.}
+  
+ (c) Mass 
+  
+    
+      
+        M
+      
+    
+    {\displaystyle M}
+  
+ is lowered from 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ to 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+        ,
+      
+    
+    {\displaystyle S_{1},}
+  
+ releasing an amount of work equal to 
+  
+    
+      
+        M
+        g
+        h
+        .
+      
+    
+    {\displaystyle Mgh.}
+  
+ (d) The energy absorbed by 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ is transferred to 
+  
+    
+      
+        M
+        .
+      
+    
+    {\displaystyle M.}
+  
+ This increases the gravitational mass of 
+  
+    
+      
+        M
+      
+    
+    {\displaystyle M}
+  
+ to a new value 
+  
+    
+      
+        
+          M
+          ′
+        
+        .
+      
+    
+    {\displaystyle M'.}
+  
+ (e) The mass is lifted back to 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+, requiring the input of work 
+  
+    
+      
+        
+          M
+          ′
+        
+        g
+        h
+        .
+      
+    
+    {\displaystyle M'gh.}
+  
+ (e) The energy carried by the mass is then transferred to 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+        ,
+      
+    
+    {\displaystyle S_{2},}
+  
+ completing the cycle.
+Conservation of energy demands that the difference in work between raising the mass and lowering the mass, 
+  
+    
+      
+        
+          M
+          ′
+        
+        g
+        h
+        −
+        M
+        g
+        h
+      
+    
+    {\displaystyle M'gh-Mgh}
+  
+, must equal 
+  
+    
+      
+        E
+        g
+        h
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle Egh/c^{2}}
+  
+, or one could potentially define a perpetual motion machine. Therefore,
+
+  
+    
+      
+        
+          M
+          ′
+        
+        −
+        M
+        =
+        
+          
+            E
+            
+              c
+              
+                2
+              
+            
+          
+        
+        .
+      
+    
+    {\displaystyle M'-M={\frac {E}{c^{2}}}.}
+  
+
+In other words, the increase in gravitational mass predicted by the above arguments is precisely equal to the increase in inertial mass predicted by special relativity.
+Einstein then considered sending a continuous electromagnetic beam of frequency 
+  
+    
+      
+        
+          v
+          
+            2
+          
+        
+      
+    
+    {\displaystyle v_{2}}
+  
+ (as measured at 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+) from 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ to 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ in a homogeneous gravitational field. The frequency of the light as measured at 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ will be a larger value 
+  
+    
+      
+        
+          v
+          
+            1
+          
+        
+      
+    
+    {\displaystyle v_{1}}
+  
+ given by
+
+  
+    
+      
+        
+          v
+          
+            1
+          
+        
+        =
+        
+          v
+          
+            2
+          
+        
+        
+          (
+          
+            1
+            +
+            
+              
+                Φ
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+        .
+      
+    
+    {\displaystyle v_{1}=v_{2}\left(1+{\frac {\Phi }{c^{2}}}\right).}
+  
+
+Einstein noted that the above equation seemed to imply something absurd: Given that the transmission of light from 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ to 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+ is continuous, how could the number of periods emitted per second from 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ be different from that received at 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+        ?
+      
+    
+    {\displaystyle S_{1}?}
+  
+  It is impossible for wave crests to appear on the way down from 
+  
+    
+      
+        
+          S
+          
+            2
+          
+        
+      
+    
+    {\displaystyle S_{2}}
+  
+ to 
+  
+    
+      
+        
+          S
+          
+            1
+          
+        
+      
+    
+    {\displaystyle S_{1}}
+  
+. The simple answer is that this question presupposes an absolute nature of time, when in fact there is nothing that compels us to assume that clocks situated at different gravitational potentials must be conceived of as going at the same rate. The principle of equivalence implies gravitational time dilation.
+It is important to realize that Einstein's arguments predicting gravitational time dilation are valid for any theory of gravity that respects the principle of equivalence. This includes Newtonian gravitation. Experiments such as the Pound–Rebka experiment, which have firmly established gravitational time dilation, therefore do not serve to distinguish general relativity from Newtonian gravitation.
+In the remainder of Einstein's 1911 paper, he discussed the bending of light rays in a gravitational field, but given the incomplete nature of Einstein's theory as it existed at the time, the value that he predicted was half the value that would later be predicted by the full theory of general relativity.
+
+=== Non-Euclidean geometry and the rotating disk ===
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-6.md b/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-6.md
new file mode 100644
index 000000000..0363c4b2c
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-6.md
@@ -0,0 +1,34 @@
+---
+title: "Einstein's thought experiments"
+chunk: 7/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+By 1912, Einstein had reached an impasse in his kinematic development of general relativity, realizing that he needed to go beyond the mathematics that he knew and was familiar with.
+
+Stachel has identified Einstein's analysis of the rigid relativistic rotating disk as being key to this realization. The rigid rotating disk had been a topic of lively discussion since Max Born and Paul Ehrenfest, in 1909, both presented analyses of rigid bodies in special relativity. An observer on the edge of a rotating disk experiences an apparent ("fictitious" or "pseudo") force called "centrifugal force". By 1912, Einstein had become convinced of a close relationship between gravitation and pseudo-forces such as centrifugal force:Such a system K, according to the equivalence principle, is strictly equivalent to a system at rest in which a matter-free static gravitational field of a certain kind exists. 
+In the accompanying illustration, A represents a circular disk of 10 units diameter at rest in an inertial reference frame. The circumference of the disk is 
+  
+    
+      
+        π
+      
+    
+    {\displaystyle \pi }
+  
+ times the diameter, and the illustration shows 31.4 rulers laid out along the circumference. B represents a circular disk of 10 units diameter that is spinning rapidly. According to a non-rotating observer, each of the rulers along the circumference is length-contracted along its line of motion. More rulers are required to cover the circumference, while the number of rulers required to span the diameter is unchanged. Note that we have not stated that we set A spinning to get B. In special relativity, it is not possible to set spinning a disk that is "rigid" in Born's sense of the term. Since spinning up disk A would cause the material to contract in the circumferential direction but not in the radial direction, a rigid disk would become fragmented from the induced stresses.
+In later years, Einstein repeatedly stated that consideration of the rapidly rotating disk was of "decisive importance" to him because it showed that a gravitational field causes non-Euclidean arrangements of measuring rods.
+Einstein realized that he did not have the mathematical skills to describe the non-Euclidean view of space and time that he envisioned, so he turned to his mathematician friend, Marcel Grossmann, for help. After researching in the library, Grossman found a review article by Ricci and Levi-Civita on absolute differential calculus (tensor calculus). Grossman tutored Einstein on the subject, and in 1913 and 1914, they published two joint papers describing an initial version of a generalized theory of gravitation.  Over the next several years, Einstein used these mathematical tools to generalize Minkowski's geometric approach to relativity so as to encompass curved spacetime.
+
+== Quantum mechanics ==
+
+=== Background: Einstein and the quantum ===
+Many myths have grown up about Einstein's relationship with quantum mechanics. Freshman physics students are aware that Einstein explained the photoelectric effect and introduced the concept of the photon. But students who have grown up with the photon may not be aware of how revolutionary the concept was for his time. The best-known factoids about Einstein's relationship with quantum mechanics are his statement, "God does not play dice with the universe" and the indisputable fact that he just did not like the theory in its final form. This has led to the general impression that, despite his initial contributions, Einstein was out of touch with quantum research and played at best a secondary role in its development. Concerning Einstein's estrangement from the general direction of physics research after 1925, his scientific biographer, Abraham Pais, wrote:
+
+Einstein is the only scientist to be justly held equal to Newton. That comparison is based exclusively on what he did before 1925. In the remaining 30 years of his life he remained active in research but his fame would be undiminished, if not enhanced, had he gone fishing instead. 
+In hindsight, we know that Pais was incorrect in his assessment.
+Einstein was arguably the greatest single contributor to the "old" quantum theory.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-7.md b/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-7.md
new file mode 100644
index 000000000..84f5cac56
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Einstein's_thought_experiments-7.md
@@ -0,0 +1,35 @@
+---
+title: "Einstein's thought experiments"
+chunk: 8/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+In his 1905 paper on light quanta, Einstein created the quantum theory of light. His proposal that light exists as tiny packets (photons) was so revolutionary, that even such major pioneers of quantum theory as Planck and Bohr refused to believe that it could be true.   Bohr, in particular, was a passionate disbeliever in light quanta, and repeatedly argued against them until 1925, when he yielded in the face of overwhelming evidence for their existence.
+In his 1906 theory of specific heats, Einstein was the first to realize that quantized energy levels explained the specific heat of solids. In this manner, he found a rational justification for the third law of thermodynamics (i.e. the entropy of any system approaches zero as the temperature approaches absolute zero): at very cold temperatures, atoms in a solid do not have enough thermal energy to reach even the first excited quantum level, and so cannot vibrate. 
+Einstein proposed the wave–particle duality of light. In 1909, using a rigorous fluctuation argument based on a thought experiment and drawing on his previous work on Brownian motion, he predicted the emergence of a "fusion theory" that would combine the two views. Basically, he demonstrated that the Brownian motion experienced by a mirror in thermal equilibrium with black-body radiation would be the sum of two terms, one due to the wave properties of radiation, the other due to its particulate properties.
+Although Planck is justly hailed as the father of quantum mechanics, his derivation of the law of black-body radiation rested on fragile ground, since it required ad hoc assumptions of an unreasonable character. Furthermore, Planck's derivation represented an analysis of classical harmonic oscillators merged with quantum assumptions in an improvised fashion.  In his 1916 theory of radiation, Einstein was the first to create a purely quantum explanation. This paper, well known for broaching the possibility of stimulated emission (the basis of the laser), changed the nature of the evolving quantum theory by introducing the fundamental role of random chance.
+In 1924, Einstein received a short manuscript by an unknown Indian professor, Satyendra Nath Bose, outlining a new  method of deriving the law of blackbody radiation. Einstein was intrigued by Bose's peculiar method of counting the number of distinct ways of putting photons into the available states, a method of counting that Bose apparently did not realize was unusual. Einstein, however, understood that Bose's counting method implied that photons are, in a deep sense, indistinguishable. He translated the paper into German and had it published. Einstein then followed Bose's paper with an extension to Bose's work which predicted Bose–Einstein condensation, one of the fundamental research topics of condensed matter physics.
+While trying to develop a mathematical theory of light which would fully encompass its wavelike and particle-like aspects, Einstein developed the concept of "ghost fields". A guiding wave obeying Maxwell's classical laws would propagate following the normal laws of optics, but would not transmit any energy. This guiding wave, however, would govern the appearance of quanta of energy 
+  
+    
+      
+        h
+        ν
+      
+    
+    {\displaystyle h\nu }
+  
+ on a statistical basis, so that the appearance of these quanta would be proportional to the intensity of the interference radiation. These ideas became widely known in the physics community, and through Born's work in 1926, later became a key concept in the modern quantum theory of radiation and matter. 
+Therefore, Einstein before 1925 originated most of the key concepts of quantum theory: light quanta, wave–particle duality, the fundamental randomness of physical processes, the concept of indistinguishability, and the probability density interpretation of the wave equation. In addition, Einstein can arguably be considered the father of solid state physics and condensed matter physics. He provided a correct derivation of the blackbody radiation law and sparked the notion of the laser.
+In 1935, working with two younger colleagues, Einstein issued a final challenge to quantum mechanics, attempting to show that it could not represent a final solution. Despite the questions raised by this paper, it made little or no difference to how physicists employed quantum mechanics in their work. Of this paper, Pais was to write:
+
+The only part of this article that will ultimately survive, I believe, is this last phrase [i.e. "No reasonable definition of reality could be expect to permit this" where "this" refers to the instantaneous transmission of information over a distance], which so poignantly summarizes Einstein's views on quantum mechanics in his later years....This conclusion has not affected subsequent developments in physics, and it is doubtful that it ever will. 
+In contrast to Pais' negative assessment, this paper, outlining the EPR paradox, has become one of the most widely cited articles in the entire physics literature. It is considered the centerpiece of the development of quantum information theory, which has been termed the "third quantum revolution." 
+
+=== Wave–particle duality ===
+
+All of Einstein's major contributions to the old quantum theory were arrived at via statistical argument. This includes his 1905 paper arguing that light has particle properties, his 1906 work on specific heats, his 1909 introduction of the concept of wave–particle duality, his 1916 work presenting an improved derivation of the blackbody radiation formula, and his 1924 work that introduced the concept of indistinguishability.
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+---
+title: "Einstein's thought experiments"
+chunk: 9/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+Einstein's 1909 arguments for the wave–particle duality of light were based on a thought experiment. Einstein imagined a mirror in a cavity containing particles of an ideal gas and filled with black-body radiation, with the entire system in thermal equilibrium. The mirror is constrained in its motions to a direction perpendicular to its surface.
+The mirror jiggles from Brownian motion due to collisions with the gas molecules. Since the mirror is in a radiation field, the moving mirror transfers some of its kinetic energy to the radiation field as a result of the difference in the radiation pressure between its forwards and reverse surfaces. This implies that there must be fluctuations in the black-body radiation field, and hence fluctuations in the black-body radiation pressure. Reversing the argument shows that there must be a route for the return of energy from the fluctuating black-body radiation field back to the gas molecules.
+Given the known shape of the radiation field given by Planck's law, Einstein could calculate the mean square energy fluctuation of the black-body radiation. He found the root mean square energy fluctuation 
+  
+    
+      
+        
+          ⟨
+          
+            ϵ
+            
+              2
+            
+          
+          ⟩
+        
+      
+    
+    {\displaystyle \left\langle \epsilon ^{2}\right\rangle }
+  
+ in a small volume 
+  
+    
+      
+        v
+      
+    
+    {\displaystyle v}
+  
+ of a cavity filled with thermal radiation in the frequency interval between 
+  
+    
+      
+        ν
+      
+    
+    {\displaystyle \nu }
+  
+ and 
+  
+    
+      
+        ν
+        +
+        d
+        ν
+      
+    
+    {\displaystyle \nu +d\nu }
+  
+ to be a function of frequency and temperature:
+
+  
+    
+      
+        
+          ⟨
+          
+            
+              ϵ
+              
+                2
+              
+            
+            (
+            ν
+            ,
+            T
+            )
+          
+          ⟩
+        
+        =
+        
+          (
+          
+            h
+            ν
+            ρ
+            +
+            
+              
+                
+                  c
+                  
+                    3
+                  
+                
+                
+                  8
+                  π
+                  
+                    ν
+                    
+                      2
+                    
+                  
+                
+              
+            
+            
+              ρ
+              
+                2
+              
+            
+          
+          )
+        
+        v
+        d
+        ν
+        ,
+      
+    
+    {\displaystyle \left\langle \epsilon ^{2}(\nu ,T)\right\rangle =\left(h\nu \rho +{\frac {c^{3}}{8\pi \nu ^{2}}}\rho ^{2}\right)vd\nu ,}
+  
+
+where 
+  
+    
+      
+        ρ
+        v
+        d
+        ν
+      
+    
+    {\displaystyle \rho vd\nu }
+  
+ would be the average energy of the volume in contact with the thermal bath. The above expression has two terms, the second corresponding to the classical Rayleigh-Jeans law (i.e. a wavelike term), and the first corresponding to the Wien distribution law (which from Einstein's 1905 analysis, would result from point-like quanta with energy 
+  
+    
+      
+        h
+        ν
+      
+    
+    {\displaystyle h\nu }
+  
+). From this, Einstein concluded that radiation had simultaneous wave and particle aspects. 
+
+=== Bubble paradox ===
+From 1905 to 1923, Einstein was virtually the only physicist who took light-quanta seriously. Throughout most of this period, the physics community treated the light-quanta hypothesis with "skepticism bordering on derision" and maintained this attitude even after Einstein's photoelectric law was validated. The citation for Einstein's 1922 Nobel Prize very deliberately avoided all mention of light-quanta, instead stating that it was being awarded for "his services to theoretical physics and especially for his discovery of the law of the photoelectric effect". This dismissive stance contrasts sharply with the enthusiastic manner in which Einstein's other major contributions were accepted, including his work on Brownian motion, special relativity, general relativity, and his numerous other contributions to the "old" quantum theory.
+Various explanations have been given for this neglect on the part of the physics community. First and foremost was wave theory's long and indisputable success in explaining purely optical phenomena. Second was the fact that his 1905 paper, which pointed out that certain phenomena would be more readily explained under the assumption that light is particulate, presented the hypothesis only as a "heuristic viewpoint". The paper offered no compelling, comprehensive alternative to existing electromagnetic theory. Third was the fact that his 1905 paper introducing light quanta and his two 1909 papers that argued for a wave–particle fusion theory approached their subjects via statistical arguments that his contemporaries "might accept as theoretical exercise—crazy, perhaps, but harmless".
+Most of Einstein's contemporaries adopted the position that light is ultimately a wave, but appears particulate in certain circumstances only because atoms absorb wave energy in discrete units.
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+---
+title: "Einstein's thought experiments"
+chunk: 10/12
+source: "https://en.wikipedia.org/wiki/Einstein's_thought_experiments"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:57.205842+00:00"
+instance: "kb-cron"
+---
+
+Among the thought experiments that Einstein presented in his 1909 lecture on the nature and constitution of radiation was one that he used to point out the implausibility of the above argument. He
+used this thought experiment to argue that atoms emit light as discrete particles rather than as continuous waves: (a) An electron in a cathode ray beam strikes an atom in a target. The intensity of the beam is set so low that we can consider one electron at a time as impinging on the target. (b) The atom emits a spherically radiating electromagnetic wave. (c) This wave excites an atom in a secondary target, causing it to release an electron of energy comparable to that of the original electron. The energy of the secondary electron depends only on the energy of the original electron and not at all on the distance between the primary and secondary targets. All the energy spread around the circumference of the radiating electromagnetic wave would appear to be instantaneously focused on the target atom, an action that Einstein considered implausible. Far more plausible would be to say that the first atom emitted a particle in the direction of the second atom.
+Although Einstein originally presented this thought experiment as an argument for light having a particulate nature, it has been noted that this thought experiment, which has been termed the "bubble paradox", foreshadows the famous 1935 EPR paper. In his 1927 Solvay debate with Bohr, Einstein employed this thought experiment to illustrate that according to the Copenhagen interpretation of quantum mechanics that Bohr championed, the quantum wavefunction of a particle would abruptly collapse like a "popped bubble" no matter how widely dispersed the wavefunction. The transmission of energy from opposite sides of the bubble to a single point would occur faster than light, violating the principle of locality.
+In the end, it was experiment, not any theoretical argument, that finally enabled the concept of the light quantum to prevail. In 1923, Arthur Compton was studying the scattering of high energy X-rays from a graphite target. Unexpectedly, he found that the scattered X-rays were shifted in wavelength, corresponding to inelastic scattering of the X-rays by the electrons in the target. His observations were totally inconsistent with wave behavior, but instead could only be explained if the X-rays acted as particles. This observation of the Compton effect rapidly brought about a change in attitude, and by 1926, the concept of the "photon" was generally accepted by the physics community. 
+
+=== Einstein's light box ===
+
+Einstein did not like the direction in which quantum mechanics had turned after 1925. Although excited by Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Born's clarification of the meaning of the Schroedinger wave equation (i.e. that the absolute square of the wave function is to be interpreted as a probability density), his instincts told him that something was missing. In a letter to Born, he wrote:
+
+Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. 
+The Solvay Debates between Bohr and Einstein began in dining-room discussions at the Fifth Solvay International Conference on Electrons and Photons  in 1927. Einstein's issue with the new quantum mechanics was not just that, with the probability interpretation, it rendered invalid the notion of rigorous causality. After all, as noted above, Einstein himself had introduced random processes in his 1916 theory of radiation. Rather, by defining and delimiting the maximum amount of information obtainable in a given experimental arrangement, the Heisenberg uncertainty principle denied the existence of any knowable reality in terms of a complete specification of the momenta and description of individual particles, an objective reality that would exist whether or not we could ever observe it.
+Over dinner, during after-dinner discussions, and at breakfast, Einstein debated with Bohr and his followers on the question whether quantum mechanics in its present form could be called complete. Einstein illustrated his points with increasingly clever thought experiments intended to prove that position and momentum could in principle be simultaneously known to arbitrary precision. For example, one of his thought experiments involved sending a beam of electrons through a shuttered screen, recording the positions of the electrons as they struck a photographic screen. Bohr and his allies would always be able to counter Einstein's proposal, usually by the end of the same day.
+On the final day of the conference, Einstein revealed that the uncertainty principle was not the only aspect of the new quantum mechanics that bothered him. Quantum mechanics, at least in the Copenhagen interpretation, appeared to allow action at a distance, the ability for two separated objects to communicate at speeds greater than light. By 1928, the consensus was that Einstein had lost the debate, and even his closest allies during the Fifth Solvay Conference, for example Louis de Broglie, conceded that quantum mechanics appeared to be complete.
\ No newline at end of file
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diff --git a/data/en.wikipedia.org/wiki/Einstein–Oppenheimer_relationship-0.md b/data/en.wikipedia.org/wiki/Einstein–Oppenheimer_relationship-0.md
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+---
+title: "Einstein–Oppenheimer relationship"
+chunk: 1/4
+source: "https://en.wikipedia.org/wiki/Einstein–Oppenheimer_relationship"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:54.649883+00:00"
+instance: "kb-cron"
+---
+
+Albert Einstein and J. Robert Oppenheimer were twentieth century physicists who made pioneering contributions to physics. From 1947 to 1955 they had been colleagues at the Institute for Advanced Study (IAS). Belonging to different generations, Einstein and Oppenheimer became representative figures for the relationship between "science and power", as well as for "contemplation and utility" in science.
+
+== Overview ==
+
+In 1919, after the successful verification of the phenomenon of light from faraway stars gravitationally bending near the sun — as predicted earlier by Einstein's theory of gravity — became an observable fact, Albert Einstein was acclaimed as “the most revolutionary innovator in physics” since Isaac Newton. J. Robert Oppenheimer, called the American physics community's "boy-wonder" in the 1930s, became a popular figure from 1945 onwards after overseeing the first ever successful test of nuclear weapons.
+Both Einstein and Oppenheimer were born into nonobservant Jewish families.
+Belonging to different generations, Einstein (1879–1955) and Oppenheimer (1904–1967), with the full development of quantum mechanics by 1925 marking a delineation, represented the shifted approach in being either a theoretical physicist or an experimental physicist since the mid-1920s when being both became rare due to the division of labor. 
+Einstein and Oppenheimer, who incorporated different modes of approach for their achievements, became emblematic for the relationship between "science and power", as well as for "contemplation and utility" in science. When in 1945 the first ever nuclear weapons were successfully tested, Oppenheimer was acknowledged for bringing forth to the world the astounding "instrumental power of science". Einstein, after facing criticism for having "participated" in the creation of the atomic bomb, answered in 1950 that, when he contemplated the relationship between mass and energy in 1905, he had no idea that it could have been used for military purposes in any way, and maintained that he had always been a "convinced pacifist". 
+While Einstein engaged in the pursuit of what he called as "Unity" in the complex phenomena of the Universe, Oppenheimer engaged in the establishment of an "Unified" framework at the Institute for Advanced Study, which would comprise all the academic disciplines of knowledge that can be pursued. Einstein was markedly individualistic in his approach to physics. He only had a few students and was disinterested, if not adversarial in his relationship with formal institutions and politics. Oppenheimer was more collaborative and embraced collective scientific work. He had been a more successful teacher and immersed himself in political and institutional realms. Oppenheimer emerged as a powerful political 'insider', a role that Einstein never embraced but instead wondered why Oppenheimer desired such power. Despite their differences in stances, both Oppenheimer and Einstein were regarded as "deeply suspicious" figures by the authorities, specifically by J. Edgar Hoover.
+When the advent of modern physics in the twentieth century radically changed the world, both Einstein and Oppenheimer grappled with the metaphysics that could provide an ethical framework for human actions. Einstein turned to the philosophical works of Spinoza and Schopenhauer, along with an attachment to the European enlightenment heritage. Oppenheimer became engrossed in the eastern philosophy, with particular interest in the Bhagavad Gita, and an affinity with the American philosophical tradition of pragmatism.
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+---
+title: "Einstein–Oppenheimer relationship"
+chunk: 2/4
+source: "https://en.wikipedia.org/wiki/Einstein–Oppenheimer_relationship"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:54.649883+00:00"
+instance: "kb-cron"
+---
+
+== Association with each other ==
+Oppenheimer met Einstein for the first time in January 1932 when the latter visited Caltech as part of his round-the-world trip during 1931-32.
+In 1939, Einstein published a paper that argued against the existence of black holes. Einstein used his own general theory of relativity to arrive at this conclusion. A few months after Einstein rejected the existence of black holes, Oppenheimer and his student Hartland Snyder published a paper that revealed, for the first time, using Einstein's general theory of relativity, how black holes would form. Though Oppenheimer and Einstein later met, there's no record of them having discussed black holes.
+When in 1939, the general public became aware of the Einstein–Szilard letter that urged the US government to initiate the Manhattan Project, for the development of nuclear weapons, Einstein was credited for foreseeing the destructive power of the atom with his mass–energy equivalence formula. Einstein played an active role in the development of US nuclear weapons by being an advisor to the research that ensued; this was in contrast to the common belief that his role was limited to only signing a letter. During this time, the public linked Einstein with Oppenheimer, who then happened to be the scientific director of the Manhattan Project.
+After the end of World War II, both Einstein and Oppenheimer lived and worked in Princeton at the Institute for Advanced Study, Einstein became a professor there while Oppenheimer its director and a professor of physics from 1947 to 1966. They had their offices down the hall from each other. Einstein and Oppenheimer became colleagues and conversed with each other occasionally. They saw each other socially, with Einstein once attending dinner at the Oppenheimers in 1948. At the Institute, Oppenheimer considered general relativity to be an area of physics that wouldn't be of much benefit to the efforts of physicists, partly due to lack of observational data and due to conceptual and technical difficulties. He actively prohibited people from taking up these problems at the institute. Furthermore he forbade Institute members from having contacts with Einstein. For one of Einstein's birthdays, Oppenheimer gifted him a new FM radio and had an antenna installed on his house so that he may listen to New York Philharmonic concerts from Manhattan, about 50 miles away from Princeton. Oppenheimer did not provide an article to the July 1949 issue of Reviews of Modern Physics, which was dedicated to the seventieth birthday of Einstein.
+In October 1954, when an honorary doctorate was to be conferred to Einstein at Princeton, Oppenheimer made himself unavailable at the last moment (despite being "begged" to attend the event); he informed the convocation committee that he had to be out of town on the day of convocation. Earlier, in May 1954 when the Emergency Civil Liberties Committee decided to honour Einstein on his seventy-fifth birthday, the American Committee for Cultural Freedom, concerned about the Communist ties of the honouring committee requested Oppenheimer to stop Einstein from attending the event lest it may cause people to associate Judaism with Communism, and think of scientists as naive about politics. Oppenheimer, who was then busy with his security clearance hearings, persuaded Einstein to dissociate with the honouring committee.
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+---
+title: "Einstein–Oppenheimer relationship"
+chunk: 3/4
+source: "https://en.wikipedia.org/wiki/Einstein–Oppenheimer_relationship"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:54.649883+00:00"
+instance: "kb-cron"
+---
+
+== Views about each other ==
+In January 1935, Oppenheimer visited Princeton University as a visiting faculty member on an invitation. After staying there and interacting with Einstein, Oppenheimer wrote to his brother Frank Oppenheimer in a letter thus, "Princeton is a madhouse: its solipsistic luminaries shining in separate & helpless desolation. Einstein is completely cuckoo.” Oppenheimer's initial harsh assessment was attributed to the fact that he found Einstein being highly skeptical about the quantum field theory. Einstein never accepted the quantum theory; in 1945 he said: "The quantum theory is without a doubt a useful theory, but it does not reach to the bottom of things. I never believed that it constitutes the true conception of nature". Oppenheimer also noted that Einstein became very much a loner in his working style at the institute. 
+After the death of Einstein in April 1955, in a public eulogy Oppenheimer wrote that "physicists lost their greatest colleague". He noted that of all the great accomplishments in physics, the theory of general relativity is the work of one man, and it would have remained undiscovered for a long time had it not been for the work of Einstein. He ascertained that the public image of Einstein as a simple and kindhearted man “with warm humor,... wholly without pretense” was indeed right, and remembered what Einstein once said to him while walking back to home on his seventy-first birthday, "You know, when it once has been given to a man to do something sensible, afterwards life is a little strange." Oppenheimer wrote that it was given to Einstein to do "something reasonable". He stated that general theory of relativity is "perhaps the single greatest theoretical synthesis in the whole of science". Oppenheimer wrote that, more than anything, the one special quality that made Einstein unique was “his faith that there exists in the natural world an order and a harmony and that this may be apprehended by the mind of man”, and that Einstein had given not just an evidence of that faith, but also its heritage.
+Oppenheimer was less graceful about Einstein in private. He said Einstein had no interest in or did not understand modern physics and wasted his time in trying to unify gravity and electromagnetism. He stated that Einstein's methods in his final years had in "a certain sense failed him". Einstein in his last twenty-five years of life focused solely on working out the unified field theory without considering its reliability nor questioning his own approach. This led him to lose connections with the wider physics community. Einstein's urge to find unity had been constant throughout his life. In 1900, while still a student at ETH, he wrote in a letter to his friend Marcel Grossmann that, "It is a glorious feeling to recognize the unity of a complex of phenomena, which appear to direct sense perceptions as quite distinct things." In 1932, when questioned about his goal of work, Einstein replied, "The real goal of my research has always been the simplification and unification of the system of theoretical physics. I attained this goal satisfactorily for macroscopic phenomena, but not for the phenomena of quanta and atomic structure." And added, "I believe that despite considerable success, the modern quantum theory is still far from a satisfactory solution of the latter group of problems." Einstein was never convinced with quantum field theory, which Oppenheimer advocated. Oppenheimer noted that Einstein tried in vain to prove the existence of inconsistencies in quantum field theory, but there were none. In the 1960s Oppenheimer became skeptical about Einstein's general theory of relativity as the correct theory of gravitation. He thought Brans–Dicke theory to be a better theory. Oppenheimer also complained that Einstein did not leave any papers to the institute (IAS) in his will despite the support he received from it for twenty-five years. All of Einstein's papers went to Israel. 
+In December 1965, Oppenheimer visited Paris on an invitation from UNESCO to speak at the tenth anniversary of Einstein's death. He spoke on the first day of the commemoration as he had known Einstein for more than thirty years and at the IAS, they "were close colleagues and something of friends". Oppenheimer made his critical views of Einstein public there. He also praised Einstein for his stand against violence and described his attitude towards humanity by the Sanskrit word "Ahimsa". The speech received considerable media attention, New York Times reported the story headlined “Oppenheimer View of Einstein Warm But Not Uncritical”. After the speech, as part of an effort to amend any misunderstandings, in an interview with the French magazine L'Express, Oppenheimer said, "During all the end of his life, Einstein did no good. He worked all alone with an assistant who was there to correct his calculations... He turned his back on experiments, he even tried to rid himself of the facts that he himself had contributed to establish ... He wanted to realize the unity of knowledge. At all cost. In our days, this is impossible." But nevertheless, Oppenheimer said he was "convinced that still today, as in Einstein’s time, a solitary researcher can effect a startling discovery. He will only need more strength of character". The interviewer concluded asking Oppenheimer if he had any longing or nostalgia, to which he replied "Of course, I would have liked to be the young Einstein. This goes without saying."
+The authors of Oppenheimer's biography American Prometheus wrote that Oppenheimer's relationship with Einstein was "always tentative", and Einstein held similarly an ambivalent attitude towards Oppenheimer. In 1945, when Oppenheimer and Pauli were considered for a professorial position at the IAS, Einstein and mathematician Hermann Weyl wrote a letter that recommended Pauli over Oppenheimer; they felt Pauli made more fundamental contributions to physics than Oppenheimer. They held that though Oppenheimer "founded the largest school of theoretical physics in this country", his students tend to imitate and praise him universally, which they cautioned was may be due to his "too dominant" nature. After this recommendation, the job was offered to Pauli, but he refused it.
+Einstein never considered Oppenheimer as his close friend, "perhaps partly because our scientific opinions are fairly diametrically different." Both differed in their views as physicists, but were allied as humanists. Einstein appreciated Oppenheimer's role in the drafting and advocacy of the Acheson–Lilienthal Report, and for his subsequent work to contain the nuclear arms race between the United States and the Soviet Union. In 1947, Oppenheimer turned down an invitation from Einstein to speak at the Emergency Committee of Atomic Scientists saying he was "unprepared". In 1954, Einstein reportedly called Oppenheimer a "narr" (Yiddish for fool) over his decision to cooperate rather than reject the Atomic energy commission (AEC) investigation into his loyalty to the country. After becoming aware of Oppenheimer's predicament with security clearance, Einstein laughed and said, "The trouble with Oppenheimer is that he loves a woman who doesn’t love him—the United States government." At the IAS, Einstein acquired a "grudging respect" for Oppenheimer over his administration skills, and described him as an "unusually capable man of many sided education". Einstein admired the personality of Oppenheimer, but not his physics.
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+---
+title: "Einstein–Oppenheimer relationship"
+chunk: 4/4
+source: "https://en.wikipedia.org/wiki/Einstein–Oppenheimer_relationship"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:54.649883+00:00"
+instance: "kb-cron"
+---
+
+== In popular culture ==
+A semifictional account of the relationship between Albert Einstein and J. Robert Oppenheimer was portrayed in the feature film Oppenheimer, directed by Christopher Nolan.
+
+== Notes ==
+
+== See also ==
+Einstein versus Oppenheimer
+
+== References ==
+
+=== Citations ===
+
+=== Sources ===
+Bird, Kai; Sherwin, Martin J. (2005). American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer. New York: Alfred A. Knopf. ISBN 978-0-375-41202-8.
+Schweber, Silvan S. (2009). Einstein and Oppenheimer: The Meaning of Genius. Harvard University Press. ISBN 9780674043350.
+Sherwin, Martin (1979). "Oppenheimer on Einstein". Bulletin of the Atomic Scientists. 35 (3): 36–39. Bibcode:1979BuAtS..35c..36O. doi:10.1080/00963402.1979.11458597.
+Thorpe, Charles (2011). "Einstein and Oppenheimer". Annals of Science. 68 (4): 558–561. doi:10.1080/00033790903243332. S2CID 144897605.
+Beyler, Richard H. (2009). "Review of Einstein and Oppenheimer: The Meaning of Genius, by S. S. Schweber". Technology and Culture. 50 (3): 722–23. doi:10.1353/tech.0.0301. JSTOR 40345767. S2CID 122580181.
+Oppenheimer, J. Robert (1956). "Einstein". Reviews of Modern Physics. 28 (1): 1–2. Bibcode:1956RvMP...28....1O. doi:10.1103/RevModPhys.28.1.
+Schweber, Silvan S. (2006). "Einstein and Oppenheimer: Interactions and Intersections". Science in Context. 19 (4). United Kingdom: Cambridge University Press: 513–559. doi:10.1017/S0269889706001050. S2CID 145807656.
+Halpern, Paul (2019). "Albert Einstein, celebrity physicist". Physics Today. 72 (4). American Institute of Physics: 38–45. Bibcode:2019PhT....72d..38H. doi:10.1063/PT.3.4183. S2CID 187603798.
+Bernstein, Jeremy (2007). "The Reluctant Father of Black Holes". Scientific American. 17: 4–11. doi:10.1038/scientificamerican0407-4sp. Archived from the original on January 15, 2024. Retrieved March 2, 2024.
+Busis, Hillary (July 25, 2023). "Einstein and Oppenheimer's real relationship was cordial and complicated". gq-magazine.co.uk. Archived from the original on January 30, 2024. Retrieved March 1, 2024.
+Cava, Marco della (July 22, 2023). "Fact-checking 'Oppenheimer': Was Albert Einstein really a friend? What's true, what isn't". USA Today. Archived from the original on February 25, 2024. Retrieved March 1, 2024.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/European_Synchrotron_Radiation_Facility-0.md b/data/en.wikipedia.org/wiki/European_Synchrotron_Radiation_Facility-0.md
new file mode 100644
index 000000000..5d241a51f
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/European_Synchrotron_Radiation_Facility-0.md
@@ -0,0 +1,64 @@
+---
+title: "European Synchrotron Radiation Facility"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/European_Synchrotron_Radiation_Facility"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:59.828807+00:00"
+instance: "kb-cron"
+---
+
+The European Synchrotron (also European Synchrotron Radiation Facility, ESRF) is a synchrotron light source situated in Grenoble, France. It is a joint research facility supported by 19 countries (13 member countries: Belgium, Denmark, Finland, France, Germany, Italy, the Netherlands,  Norway, Russia, Spain, Sweden, Switzerland, and the UK; and 6 associate countries: Austria, the Czech Republic, Israel, Poland, Portugal and South Africa).
+Some 10,000 scientists visit this particle accelerator each year, conducting upwards of 2,000 experiments and producing around 1,800 scientific publications.
+
+
+== History ==
+Inaugurated in September 1994, it has an annual operating budget of around 100 million euros, employs around 700 people and is host to more than 10,000 visiting scientists each year.
+The ESRF was the world's first third generation synchrotron when it opened for user operation in 1994. 
+In 2009, the ESRF began a major refurbishment programme that, at term, has seen its performances increase by 100-fold. In 2015, the facility built an 8000 m2 extension to the original experimental hall, a new data centre and introduced an ambitious detector development programme. The ESRF's X-rays are 100 billion times brighter than hospital X-rays produced for medical radiographies. 
+The second stage of the refurbishment programme included a new improved storage ring - the Extremely Brilliant Source (ESRF-EBS). Planning started in 2015 with works spanning the years 2018-2020. With EBS, the ESRF improved its X-ray intensity by a factor of 100, or 10,000 billion times more powerful than X-rays used in the medical field. ESRF-EBS became the first fourth-generation high-energy synchrotron in the world.
+The first electron beam tests for ESRF-EBS began on November 28, 2019.  The facility reopened to users on August 25, 2020.
+
+
+== General description ==
+
+The ESRF physical plant consists of two main buildings: the experimental hall, containing the 844 metre circumference storage ring and 46 tangential beamlines; and a block of laboratories, preparation suites and offices. The linear accelerator electron gun and smaller booster ring used to bring the beam to an operating energy of 6 GeV are constructed within the main ring. 
+Research at the ESRF focuses, in large part, on the use of X-ray radiation in fields as diverse as protein crystallography, earth science, paleontology, materials science, chemistry and physics. Facilities such as the ESRF offer a flux, energy range and resolution unachievable with conventional (laboratory) radiation sources.
+
+
+== Study results ==
+In 2014, ancient books destroyed by the eruption of Mount Vesuvius in 79 AD were read for the first time in the ESRF. These 1840 fragments were reduced to the status of charred cylinders.
+In 2015, scientists from the University of Sheffield used the ESRF's X-rays to study the blue and white feathers of the jay, and found that the birds use well-controlled changes to the nanostructure of their feathers to create the vivid colours of their plumage. This research opened new possibilities for creating non-fading, synthetic colours for paints and clothing.
+In July 2016, a team of South African researchers scanned a complete fossilized skeleton of a small dinosaur discovered in 2005 in South Africa and more than 200 million years old. The dentition of heterodontosauridae, when scanned, revealed palate bones less than a millimeter thick.
+On December 6, 2017, the journal Nature unveiled the discovery at the European synchrotron of a new species of dinosaur with surprising characteristics that lived about 72 million years ago. It is a biped, with some features of a velociraptor, an ostrich and a swan, with a crocodile-like muzzle and penguin-like wings. With a height of about 1.2 meters (4 ft) and with killer claws, it could hunt his prey on the ground or by swimming in the water, which is a novelty for scientists in the study of dinosaurs.
+In November 2021, researchers demonstrated a novel X-ray imaging technique, "HiP-CT", for 3D cellular-resolution scans of whole organs, using the ESRF's "Extremely Brilliant Source". The published online Human Organ Atlas includes the lungs from a donor who died with COVID-19.
+In October 2024, First Light Fusion, in collaboration with the University of Oxford's Department of Engineering Science, performed an experiment on inertial fusion on the ID19 beamline to investigate the formation and transit of shock waves through some of First Light Fusion’s amplifiers.
+
+
+== Access ==
+The ESRF site forms part of the "Polygone Scientifique", lying at the confluence of the rivers Drac and Isère about 1.5 km from the centre of Grenoble. It is served by Grenoble tramway system and local bus lines of Semitag (C6, 22 and 54). It is served by Grenoble–Isère Airport and Lyon–Saint-Exupéry Airport.
+The ESRF shares its site with several other institutions including the Institut Laue-Langevin (ILL), the European Molecular Biology Laboratory (EMBL) and the Institut de biologie structurale. The Centre national de la recherche scientifique (CNRS) has an institute across the road.
+
+
+== People ==
+Roderick MacKinnon, Nobel Prize in Chemistry 2003, have carried out experiments on beamline ID13.
+Venki Ramakrishnan, Thomas A. Steitz, and Ada Yonath, Nobel Prize in Chemistry 2009, have used macromolecular crystallography beamlines (ID14-1, -2, -4; and ID29) at the ESRF.
+Brian Kobilka and Robert Lefkowitz, Nobel Prize in Chemistry 2012, have carried out experiments mainly on beamline ID13.
+Sine Larsen (1943–2025), Danish chemist and crystallographer was a scientific research director and the first female director of the ESRF
+
+
+== See also ==
+List of Synchrotron Radiation Facilities
+European Research Area (ERA)
+TANGO (control system originally developed at the ESRF)
+The African Light Source (AfLS)
+
+
+== References ==
+
+
+== External links ==
+
+ESRF.fr
+Lightsources.org
+24 hours at the X-ray factory by Richard Van Noorden on Nature
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fermat's_principle-0.md b/data/en.wikipedia.org/wiki/Fermat's_principle-0.md
index 1c436f922..3dc8d529f 100644
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+date_saved: "2026-05-05T16:29:02.905060+00:00"
 instance: "kb-cron"
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diff --git a/data/en.wikipedia.org/wiki/Fermat's_principle-1.md b/data/en.wikipedia.org/wiki/Fermat's_principle-1.md
index f58fc181c..2482ad98f 100644
--- a/data/en.wikipedia.org/wiki/Fermat's_principle-1.md
+++ b/data/en.wikipedia.org/wiki/Fermat's_principle-1.md
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 source: "https://en.wikipedia.org/wiki/Fermat's_principle"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T10:55:11.341862+00:00"
+date_saved: "2026-05-05T16:29:02.905060+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Fermat's_principle-2.md b/data/en.wikipedia.org/wiki/Fermat's_principle-2.md
index 91aab235d..a4394e054 100644
--- a/data/en.wikipedia.org/wiki/Fermat's_principle-2.md
+++ b/data/en.wikipedia.org/wiki/Fermat's_principle-2.md
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 source: "https://en.wikipedia.org/wiki/Fermat's_principle"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T10:55:11.341862+00:00"
+date_saved: "2026-05-05T16:29:02.905060+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Fermat's_principle-3.md b/data/en.wikipedia.org/wiki/Fermat's_principle-3.md
index fb919c9e5..ee44ac59e 100644
--- a/data/en.wikipedia.org/wiki/Fermat's_principle-3.md
+++ b/data/en.wikipedia.org/wiki/Fermat's_principle-3.md
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 source: "https://en.wikipedia.org/wiki/Fermat's_principle"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T10:55:11.341862+00:00"
+date_saved: "2026-05-05T16:29:02.905060+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Fermat's_principle-4.md b/data/en.wikipedia.org/wiki/Fermat's_principle-4.md
index d0fa83e3e..db9207de4 100644
--- a/data/en.wikipedia.org/wiki/Fermat's_principle-4.md
+++ b/data/en.wikipedia.org/wiki/Fermat's_principle-4.md
@@ -4,7 +4,7 @@ chunk: 5/6
 source: "https://en.wikipedia.org/wiki/Fermat's_principle"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T10:55:11.341862+00:00"
+date_saved: "2026-05-05T16:29:02.905060+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Fermat's_principle-5.md b/data/en.wikipedia.org/wiki/Fermat's_principle-5.md
index d118064d3..4048dbdfa 100644
--- a/data/en.wikipedia.org/wiki/Fermat's_principle-5.md
+++ b/data/en.wikipedia.org/wiki/Fermat's_principle-5.md
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 source: "https://en.wikipedia.org/wiki/Fermat's_principle"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T10:55:11.341862+00:00"
+date_saved: "2026-05-05T16:29:02.905060+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem-0.md b/data/en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem-0.md
new file mode 100644
index 000000000..5f48644f4
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem-0.md
@@ -0,0 +1,491 @@
+---
+title: "Fermi–Pasta–Ulam–Tsingou problem"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:04.197066+00:00"
+instance: "kb-cron"
+---
+
+In physics, the Fermi–Pasta–Ulam–Tsingou (FPUT) problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi–Pasta–Ulam–Tsingou recurrence (or Fermi–Pasta–Ulam recurrence) – instead of the expected ergodic behavior. This came as a surprise, as Enrico Fermi, certainly, expected the system to thermalize in a fairly short time. That is, it was expected for all vibrational modes to eventually appear with equal strength, as per the equipartition theorem, or, more generally, the ergodic hypothesis. Yet here was a system that appeared to evade the ergodic hypothesis. Although the recurrence is easily observed, it eventually became apparent that over much, much longer time periods, the system does eventually thermalize. Multiple competing theories have been proposed to explain the behavior of the system, and it remains a topic of active research.
+The original intent was to find a physics problem worthy of numerical simulation on the then-new MANIAC computer. Fermi felt that thermalization would pose such a challenge. As such, it represents one of the earliest uses of digital computers in mathematical research; simultaneously, the unexpected results launched the study of nonlinear systems.
+
+== The FPUT experiment ==
+
+In the summer of 1953 Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou conducted computer simulations of a vibrating string that included a non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third).  They found that the behavior of the system was quite different from what intuition would have led them to expect. Enrico Fermi thought that after many iterations, the system would exhibit thermalization, an ergodic behavior in which the influence of the initial modes of vibration fade and the system becomes more or less random with all modes excited more or less equally.  Instead, the system exhibited a very complicated quasi-periodic behavior.  They published their results in a Los Alamos technical report in 1955.  Enrico Fermi died in 1954, so that this technical report was published after his death.
+In 2020, National Security Science magazine featured an article on Tsingou that included her commentary and historical reflections on the FPUT problem. In the article, Tsingou states "I remember sitting there one day with Pasta and Ulam," as they brainstormed "some problems we could do on the computer, some really mathematical problems." They tried several things, but, eventually, "they came up with this vibrating string."
+The FPUT experiment was important both in showing the complexity of nonlinear system behavior and the value of computer simulation in analyzing systems.
+
+=== Name change ===
+The original paper names Fermi, Pasta, and Ulam as authors (although Fermi died before the report was written) with an acknowledgement to Tsingou for her work in programming the MANIAC simulations. Mary Tsingou's contributions to the FPUT problem were largely ignored by the community until Thierry Dauxois (2008) published additional information regarding the development and called for the problem to be renamed to grant her attribution as well.
+
+== The FPUT lattice system ==
+Fermi, Pasta, Ulam, and Tsingou simulated the vibrating string by solving the following discrete system of nearest-neighbor coupled oscillators. We follow the explanation as given in Richard Palais's article. Let there be N oscillators representing a string of length 
+  
+    
+      
+        ℓ
+      
+    
+    {\displaystyle \ell }
+  
+ with equilibrium positions 
+  
+    
+      
+        
+          p
+          
+            j
+          
+        
+        =
+        j
+        h
+        ,
+         
+        j
+        =
+        0
+        ,
+        …
+        ,
+        N
+        −
+        1
+      
+    
+    {\displaystyle p_{j}=jh,\ j=0,\dots ,N-1}
+  
+, where 
+  
+    
+      
+        h
+        =
+        ℓ
+        
+          /
+        
+        (
+        N
+        −
+        1
+        )
+      
+    
+    {\displaystyle h=\ell /(N-1)}
+  
+ is the lattice spacing. Then the position of the j-th oscillator as a function of time is 
+  
+    
+      
+        
+          X
+          
+            j
+          
+        
+        (
+        t
+        )
+        =
+        
+          p
+          
+            j
+          
+        
+        +
+        
+          x
+          
+            j
+          
+        
+        (
+        t
+        )
+      
+    
+    {\displaystyle X_{j}(t)=p_{j}+x_{j}(t)}
+  
+, so that 
+  
+    
+      
+        
+          x
+          
+            j
+          
+        
+        (
+        t
+        )
+      
+    
+    {\displaystyle x_{j}(t)}
+  
+ gives the displacement from equilibrium. FPUT used the following equations of motion:
+
+  
+    
+      
+        m
+        
+          
+            
+              
+                x
+                ¨
+              
+            
+          
+          
+            j
+          
+        
+        =
+        k
+        (
+        
+          x
+          
+            j
+            +
+            1
+          
+        
+        +
+        
+          x
+          
+            j
+            −
+            1
+          
+        
+        −
+        2
+        
+          x
+          
+            j
+          
+        
+        )
+        [
+        1
+        +
+        α
+        (
+        
+          x
+          
+            j
+            +
+            1
+          
+        
+        −
+        
+          x
+          
+            j
+            −
+            1
+          
+        
+        )
+        ]
+        .
+      
+    
+    {\displaystyle m{\ddot {x}}_{j}=k(x_{j+1}+x_{j-1}-2x_{j})[1+\alpha (x_{j+1}-x_{j-1})].}
+  
+
+This is just Newton's second law for the j-th particle. The first factor 
+  
+    
+      
+        k
+        (
+        
+          x
+          
+            j
+            +
+            1
+          
+        
+        +
+        
+          x
+          
+            j
+            −
+            1
+          
+        
+        −
+        2
+        
+          x
+          
+            j
+          
+        
+        )
+      
+    
+    {\displaystyle k(x_{j+1}+x_{j-1}-2x_{j})}
+  
+ is just the usual Hooke's law form for the force. The factor with 
+  
+    
+      
+        α
+      
+    
+    {\displaystyle \alpha }
+  
+ is the nonlinear force. We can rewrite this in terms of continuum quantities by defining 
+  
+    
+      
+        c
+        =
+        
+          
+            κ
+            
+              /
+            
+            ρ
+          
+        
+      
+    
+    {\displaystyle c={\sqrt {\kappa /\rho }}}
+  
+ to be the wave speed, where 
+  
+    
+      
+        κ
+        =
+        k
+        
+          /
+        
+        h
+      
+    
+    {\displaystyle \kappa =k/h}
+  
+ is the Young's modulus for the string, and 
+  
+    
+      
+        ρ
+        =
+        m
+        
+          /
+        
+        
+          h
+          
+            3
+          
+        
+      
+    
+    {\displaystyle \rho =m/h^{3}}
+  
+ is the density:
+
+  
+    
+      
+        
+          
+            
+              
+                x
+                ¨
+              
+            
+          
+          
+            j
+          
+        
+        =
+        
+          
+            
+              c
+              
+                2
+              
+            
+            
+              h
+              
+                2
+              
+            
+          
+        
+        (
+        
+          x
+          
+            j
+            +
+            1
+          
+        
+        +
+        
+          x
+          
+            j
+            −
+            1
+          
+        
+        −
+        2
+        
+          x
+          
+            j
+          
+        
+        )
+        [
+        1
+        +
+        α
+        (
+        
+          x
+          
+            j
+            +
+            1
+          
+        
+        −
+        
+          x
+          
+            j
+            −
+            1
+          
+        
+        )
+        ]
+        .
+      
+    
+    {\displaystyle {\ddot {x}}_{j}={\frac {c^{2}}{h^{2}}}(x_{j+1}+x_{j-1}-2x_{j})[1+\alpha (x_{j+1}-x_{j-1})].}
+  
+
+== Connection to the KdV equation ==
+The continuum limit of the governing equations for the string (with the quadratic force term) is the Korteweg–de Vries equation (KdV equation.)  The discovery of this relationship and of the soliton solutions of the KdV equation by Martin David Kruskal and Norman Zabusky in 1965 was an important step forward in nonlinear system research. We reproduce below a derivation of this limit; as found in Palais's article. To write the lattice equation
+
+  
+    
+      
+        
+          
+            
+              
+                x
+                ¨
+              
+            
+          
+          
+            j
+          
+        
+        =
+        
+          
+            
+              c
+              
+                2
+              
+            
+            
+              h
+              
+                2
+              
+            
+          
+        
+        (
+        
+          x
+          
+            j
+            +
+            1
+          
+        
+        +
+        
+          x
+          
+            j
+            −
+            1
+          
+        
+        −
+        2
+        
+          x
+          
+            j
+          
+        
+        )
+        [
+        1
+        +
+        α
+        (
+        
+          x
+          
+            j
+            +
+            1
+          
+        
+        −
+        
+          x
+          
+            j
+            −
+            1
+          
+        
+        )
+        ]
+        ,
+      
+    
+    {\displaystyle {\ddot {x}}_{j}={\frac {c^{2}}{h^{2}}}(x_{j+1}+x_{j-1}-2x_{j})[1+\alpha (x_{j+1}-x_{j-1})],}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem-1.md b/data/en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem-1.md
new file mode 100644
index 000000000..71546709a
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem-1.md
@@ -0,0 +1,1001 @@
+---
+title: "Fermi–Pasta–Ulam–Tsingou problem"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:04.197066+00:00"
+instance: "kb-cron"
+---
+
+in the "continuum form", we first define 
+  
+    
+      
+        u
+        (
+        x
+        ,
+        t
+        )
+      
+    
+    {\displaystyle u(x,t)}
+  
+ to be the displacement of the string at position 
+  
+    
+      
+        x
+      
+    
+    {\displaystyle x}
+  
+ and time 
+  
+    
+      
+        t
+      
+    
+    {\displaystyle t}
+  
+. We'll then want a correspondence so that 
+  
+    
+      
+        u
+        (
+        
+          p
+          
+            j
+          
+        
+        ,
+        t
+        )
+      
+    
+    {\displaystyle u(p_{j},t)}
+  
+ is 
+  
+    
+      
+        
+          x
+          
+            j
+          
+        
+        (
+        t
+        )
+      
+    
+    {\displaystyle x_{j}(t)}
+  
+, that is,
+
+  
+    
+      
+        
+          (
+          
+            
+              
+                
+                  x
+                  
+                    j
+                    +
+                    1
+                  
+                
+                +
+                
+                  x
+                  
+                    j
+                    −
+                    1
+                  
+                
+                −
+                2
+                
+                  x
+                  
+                    j
+                  
+                
+              
+              
+                h
+                
+                  2
+                
+              
+            
+          
+          )
+        
+        =
+        
+          
+            
+              u
+              (
+              x
+              +
+              h
+              ,
+              t
+              )
+              +
+              u
+              (
+              x
+              −
+              h
+              ,
+              t
+              )
+              −
+              2
+              u
+              (
+              x
+              ,
+              t
+              )
+            
+            
+              h
+              
+                2
+              
+            
+          
+        
+        ,
+      
+    
+    {\displaystyle \left({\frac {x_{j+1}+x_{j-1}-2x_{j}}{h^{2}}}\right)={\frac {u(x+h,t)+u(x-h,t)-2u(x,t)}{h^{2}}},}
+  
+
+for small 
+  
+    
+      
+        h
+      
+    
+    {\displaystyle h}
+  
+. Using Taylor's theorem, 
+
+  
+    
+      
+        u
+        (
+        x
+        ±
+        h
+        ,
+        t
+        )
+        =
+        u
+        (
+        x
+        ,
+        t
+        )
+        ±
+        h
+        
+          u
+          
+            x
+          
+        
+        (
+        x
+        ,
+        t
+        )
+        +
+        
+          
+            
+              h
+              
+                2
+              
+            
+            2
+          
+        
+        
+          u
+          
+            x
+            x
+          
+        
+        (
+        x
+        ,
+        t
+        )
+        ±
+        
+          
+            
+              h
+              
+                3
+              
+            
+            6
+          
+        
+        
+          u
+          
+            x
+            x
+            x
+          
+        
+        (
+        x
+        ,
+        t
+        )
+        +
+        
+          
+            
+              h
+              
+                4
+              
+            
+            24
+          
+        
+        
+          u
+          
+            x
+            x
+            x
+            x
+          
+        
+        (
+        x
+        ,
+        t
+        )
+        ±
+        
+          
+            
+              h
+              
+                5
+              
+            
+            120
+          
+        
+        
+          u
+          
+            x
+            x
+            x
+            x
+            x
+          
+        
+        (
+        x
+        ,
+        t
+        )
+        +
+        O
+        (
+        
+          h
+          
+            6
+          
+        
+        )
+        ,
+      
+    
+    {\displaystyle u(x\pm h,t)=u(x,t)\pm hu_{x}(x,t)+{\frac {h^{2}}{2}}u_{xx}(x,t)\pm {\frac {h^{3}}{6}}u_{xxx}(x,t)+{\frac {h^{4}}{24}}u_{xxxx}(x,t)\pm {\frac {h^{5}}{120}}u_{xxxxx}(x,t)+O(h^{6}),}
+  
+
+the above equation can be rewritten as
+
+  
+    
+      
+        
+          (
+          
+            
+              
+                
+                  x
+                  
+                    j
+                    +
+                    1
+                  
+                
+                +
+                
+                  x
+                  
+                    j
+                    −
+                    1
+                  
+                
+                −
+                2
+                
+                  x
+                  
+                    j
+                  
+                
+              
+              
+                h
+                
+                  2
+                
+              
+            
+          
+          )
+        
+        =
+        
+          u
+          
+            x
+            x
+          
+        
+        (
+        x
+        ,
+        t
+        )
+        +
+        
+          (
+          
+            
+              
+                h
+                
+                  2
+                
+              
+              12
+            
+          
+          )
+        
+        
+          u
+          
+            x
+            x
+            x
+            x
+          
+        
+        (
+        x
+        ,
+        t
+        )
+        +
+        O
+        (
+        
+          h
+          
+            4
+          
+        
+        )
+        .
+      
+    
+    {\displaystyle \left({\frac {x_{j+1}+x_{j-1}-2x_{j}}{h^{2}}}\right)=u_{xx}(x,t)+\left({\frac {h^{2}}{12}}\right)u_{xxxx}(x,t)+O(h^{4}).}
+  
+
+Similarly, the second term in the third factor is
+
+  
+    
+      
+        α
+        (
+        
+          x
+          
+            j
+            +
+            1
+          
+        
+        −
+        
+          x
+          
+            j
+            −
+            1
+          
+        
+        )
+        =
+        2
+        α
+        h
+        
+          u
+          
+            x
+          
+        
+        (
+        x
+        ,
+        t
+        )
+        +
+        
+          (
+          
+            
+              
+                α
+                
+                  h
+                  
+                    3
+                  
+                
+              
+              3
+            
+          
+          )
+        
+        
+          u
+          
+            x
+            x
+            x
+          
+        
+        (
+        x
+        ,
+        t
+        )
+        +
+        O
+        (
+        
+          h
+          
+            5
+          
+        
+        )
+        .
+      
+    
+    {\displaystyle \alpha (x_{j+1}-x_{j-1})=2\alpha hu_{x}(x,t)+\left({\frac {\alpha h^{3}}{3}}\right)u_{xxx}(x,t)+O(h^{5}).}
+  
+
+Thus, the FPUT system is
+
+  
+    
+      
+        
+          
+            1
+            
+              c
+              
+                2
+              
+            
+          
+        
+        
+          u
+          
+            t
+            t
+          
+        
+        −
+        
+          u
+          
+            x
+            x
+          
+        
+        =
+        (
+        2
+        α
+        h
+        )
+        
+          u
+          
+            x
+          
+        
+        
+          u
+          
+            x
+            x
+          
+        
+        +
+        
+          (
+          
+            
+              
+                h
+                
+                  2
+                
+              
+              12
+            
+          
+          )
+        
+        
+          u
+          
+            x
+            x
+            x
+            x
+          
+        
+        +
+        O
+        (
+        α
+        
+          h
+          
+            2
+          
+        
+        ,
+        
+          h
+          
+            4
+          
+        
+        )
+        .
+      
+    
+    {\displaystyle {\frac {1}{c^{2}}}u_{tt}-u_{xx}=(2\alpha h)u_{x}u_{xx}+\left({\frac {h^{2}}{12}}\right)u_{xxxx}+O(\alpha h^{2},h^{4}).}
+  
+
+If one were to keep terms up to O(h) only and assume that 
+  
+    
+      
+        2
+        α
+        h
+      
+    
+    {\displaystyle 2\alpha h}
+  
+ approaches a limit, the resulting equation is one which develops shocks, which is not observed. Thus one keeps the O(h2) term as well:
+
+  
+    
+      
+        
+          
+            1
+            
+              c
+              
+                2
+              
+            
+          
+        
+        
+          u
+          
+            t
+            t
+          
+        
+        −
+        
+          u
+          
+            x
+            x
+          
+        
+        =
+        (
+        2
+        α
+        h
+        )
+        
+          u
+          
+            x
+          
+        
+        
+          u
+          
+            x
+            x
+          
+        
+        +
+        
+          (
+          
+            
+              
+                h
+                
+                  2
+                
+              
+              12
+            
+          
+          )
+        
+        
+          u
+          
+            x
+            x
+            x
+            x
+          
+        
+        .
+      
+    
+    {\displaystyle {\frac {1}{c^{2}}}u_{tt}-u_{xx}=(2\alpha h)u_{x}u_{xx}+\left({\frac {h^{2}}{12}}\right)u_{xxxx}.}
+  
+
+We now make the following substitutions, motivated by the decomposition of traveling-wave solutions (of the ordinary wave equation, to which this reduces when 
+  
+    
+      
+        α
+        ,
+        h
+      
+    
+    {\displaystyle \alpha ,h}
+  
+ vanish) into left- and right-moving waves, so that we only consider a right-moving wave. Let 
+  
+    
+      
+        ξ
+        =
+        x
+        −
+        c
+        t
+        ,
+         
+        τ
+        =
+        (
+        α
+        h
+        )
+        c
+        t
+        ,
+         
+        y
+        (
+        ξ
+        ,
+        τ
+        )
+        =
+        u
+        (
+        x
+        ,
+        t
+        )
+      
+    
+    {\displaystyle \xi =x-ct,\ \tau =(\alpha h)ct,\ y(\xi ,\tau )=u(x,t)}
+  
+. Under this change of coordinates, the equation becomes
+
+  
+    
+      
+        
+          y
+          
+            ξ
+            τ
+          
+        
+        −
+        
+          (
+          
+            
+              
+                α
+                h
+              
+              2
+            
+          
+          )
+        
+        
+          y
+          
+            τ
+            τ
+          
+        
+        =
+        −
+        
+          y
+          
+            ξ
+          
+        
+        
+          y
+          
+            ξ
+            ξ
+          
+        
+        −
+        
+          (
+          
+            
+              h
+              
+                24
+                α
+              
+            
+          
+          )
+        
+        
+          y
+          
+            ξ
+            ξ
+            ξ
+            ξ
+          
+        
+        .
+      
+    
+    {\displaystyle y_{\xi \tau }-\left({\frac {\alpha h}{2}}\right)y_{\tau \tau }=-y_{\xi }y_{\xi \xi }-\left({\frac {h}{24\alpha }}\right)y_{\xi \xi \xi \xi }.}
+  
+
+To take the continuum limit, assume that 
+  
+    
+      
+        α
+        
+          /
+        
+        h
+      
+    
+    {\displaystyle \alpha /h}
+  
+ tends to a constant, and 
+  
+    
+      
+        α
+        ,
+        h
+      
+    
+    {\displaystyle \alpha ,h}
+  
+ tend to zero. If we take 
+  
+    
+      
+        δ
+        =
+        
+          lim
+          
+            h
+            →
+            0
+          
+        
+        
+          
+            h
+            
+              /
+            
+            (
+            24
+            α
+            )
+          
+        
+      
+    
+    {\displaystyle \delta =\lim _{h\to 0}{\sqrt {h/(24\alpha )}}}
+  
+, then
+
+  
+    
+      
+        
+          y
+          
+            ξ
+            τ
+          
+        
+        =
+        −
+        
+          y
+          
+            ξ
+          
+        
+        
+          y
+          
+            ξ
+            ξ
+          
+        
+        −
+        
+          δ
+          
+            2
+          
+        
+        
+          y
+          
+            ξ
+            ξ
+            ξ
+            ξ
+          
+        
+        .
+      
+    
+    {\displaystyle y_{\xi \tau }=-y_{\xi }y_{\xi \xi }-\delta ^{2}y_{\xi \xi \xi \xi }.}
+  
+
+Taking 
+  
+    
+      
+        v
+        =
+        
+          y
+          
+            ξ
+          
+        
+      
+    
+    {\displaystyle v=y_{\xi }}
+  
+ results in the KdV equation:
+
+  
+    
+      
+        
+          v
+          
+            τ
+          
+        
+        +
+        v
+        
+          v
+          
+            ξ
+          
+        
+        +
+        
+          δ
+          
+            2
+          
+        
+        
+          v
+          
+            ξ
+            ξ
+            ξ
+          
+        
+        =
+        0.
+      
+    
+    {\displaystyle v_{\tau }+vv_{\xi }+\delta ^{2}v_{\xi \xi \xi }=0.}
+  
+
+Zabusky and Kruskal argued that soliton solutions of the KdV equation passing through one another without affecting the asymptotic shapes explained the quasi-periodicity of the waves in the FPUT experiment. In short, thermalization could not occur because of a certain "soliton symmetry" in the system, which broke ergodicity.
+A similar set of manipulations (and approximations) lead to the Toda lattice, which is also famous for being a completely integrable system. It, too, has soliton solutions, the Lax pairs, and so also can be used to argue for the lack of ergodicity in the FPUT model.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem-2.md b/data/en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem-2.md
new file mode 100644
index 000000000..f79b1c83c
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem-2.md
@@ -0,0 +1,131 @@
+---
+title: "Fermi–Pasta–Ulam–Tsingou problem"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:04.197066+00:00"
+instance: "kb-cron"
+---
+
+== Routes to thermalization ==
+In 1966, Félix Izrailev and Boris Chirikov proposed that the system will thermalize, if a sufficient amount of initial energy is provided. The idea here is that the non-linearity changes the dispersion relation, allowing resonant interactions to take place that will bleed energy from one mode to another. A review of such models can be found in Roberto Livi et al. Yet, in 1970, Joseph Ford and Gary H. Lunsford insist that mixing can be observed even with arbitrarily small initial energies. There is a long and complex history of approaches to the problem, see Thierry Dauxois (2008) for a (partial) survey.
+Recent work by Miguel Onorato et al. demonstrates a very interesting route to thermalization. Rewriting the FPUT model in terms of normal modes, the non-linear term expresses itself as a three-mode interaction (using the language of statistical mechanics, this could be called a "three-phonon interaction".) It is, however, not a resonant interaction, and is thus not able to spread energy from one mode to another; it can only generate the FPUT recurrence. The three-phonon interaction cannot thermalize the system.
+A key insight, however, is that these modes are combinations of "free" and "bound" modes. That is, higher harmonics are "bound" to the fundamental, much in the same way that the higher harmonics in solutions to the KdV equation are bound to the fundamental. They do not have any dynamics of their own, and are instead phase-locked to the fundamental. Thermalization, if present, can only be among the free modes.
+To obtain the free modes, a canonical transformation can be applied that removes all modes that are not free (that do not engage in resonant interactions). Doing so for the FPUT system results in oscillator modes that have a four-wave interaction (the three-wave interaction has been removed). These quartets do interact resonantly, i.e. do mix together four modes at a time. Oddly, though, when the FPUT chain has only 16, 32 or 64 nodes in it, these quartets are isolated from one-another. Any given mode belongs to only one quartet, and energy cannot bleed from one quartet to another. Continuing on to higher orders of interaction, there is a six-wave interaction that is resonant; furthermore, every mode participates in at least two different six-wave interactions. In other words, all of the modes become interconnected, and energy will transfer between all of the different modes.
+The three-wave interaction is of strength 
+  
+    
+      
+        1
+        
+          /
+        
+        α
+      
+    
+    {\displaystyle 1/\alpha }
+  
+ (the same 
+  
+    
+      
+        α
+      
+    
+    {\displaystyle \alpha }
+  
+ as in prior sections, above). The four-wave interaction is of strength 
+  
+    
+      
+        1
+        
+          /
+        
+        
+          α
+          
+            2
+          
+        
+      
+    
+    {\displaystyle 1/\alpha ^{2}}
+  
+ and the six-wave interaction is of strength 
+  
+    
+      
+        1
+        
+          /
+        
+        
+          α
+          
+            4
+          
+        
+      
+    
+    {\displaystyle 1/\alpha ^{4}}
+  
+. Based on general principles from correlation of interactions (stemming from the BBGKY hierarchy) one expects the thermalization time to run as the square of the interaction. Thus, the original FPUT lattice (of size 16, 32 or 64) will eventually thermalize, on a time scale of order 
+  
+    
+      
+        1
+        
+          /
+        
+        
+          α
+          
+            8
+          
+        
+      
+    
+    {\displaystyle 1/\alpha ^{8}}
+  
+: clearly, this becomes a very long time for weak interactions 
+  
+    
+      
+        α
+        ≪
+        1
+      
+    
+    {\displaystyle \alpha \ll 1}
+  
+; meanwhile, the FPUT recurrence will appear to run unabated.  This particular result holds for these particular lattice sizes; the resonant four-wave or six-wave interactions for different lattice sizes may or may not mix together modes (because the Brillouin zones are of a different size, and so the combinatorics of which wave-vectors can sum to zero is altered.) Generic procedures for obtaining canonical transformations that linearize away the bound modes remain a topic of active research.
+However, a recent study 
+found that there are divergences in the canonical transformation used to remove the three-wave interactions due to the presence of small denominators. These small denominators become more prominent when the lower modes are excited, and are more significant as the system size is increased. These results also show an indication that there could be a stochasticity threshold in the 
+  
+    
+      
+        α
+      
+    
+    {\displaystyle \alpha }
+  
+-Fermi–Pasta–Ulam–Tsingou system.
+
+== References ==
+
+== Further reading ==
+Dauxois, Thierry (2008). "Fermi, Pasta, Ulam, and a mysterious lady". Physics Today. 6 (1): 55–57. arXiv:0801.1590. Bibcode:2008PhT....61a..55D. doi:10.1063/1.2835154. S2CID 118607235.
+Fermi, E.; Pasta, J.; Ulam, S. (1955). "Studies of Nonlinear Problems" (PDF). Document LA-1940. Los Alamos National Laboratory.
+Grant, Virginia (2020). "We thank Miss Mary Tsingou". National Security Science. Winter 2020: 36–43.
+Zabusky, N. J.; Kruskal, M. D. (1965). "Interactions of solitons in a collisionless plasma and the recurrence of initial states". Physical Review Letters. 15 (6): 240–243. Bibcode:1965PhRvL..15..240Z. doi:10.1103/PhysRevLett.15.240.
+Palais, R. (1997). "The Symmetries of Solitons" (PDF). Bulletin of the American Mathematical Society. 34 (4): 339–403. arXiv:dg-ga/9708004. doi:10.1090/S0273-0979-97-00732-5. MR 1462745. S2CID 14550937.
+Dauxois, T.; Ruffo, S. (2008). "Fermi–Pasta–Ulam nonlinear lattice oscillations". Scholarpedia. 3 (8): 5538. Bibcode:2008SchpJ...3.5538D. doi:10.4249/scholarpedia.5538.
+Gallavotti, G., ed. (2008). The Fermi–Pasta–Ulam Problem: A Status Report. Lecture Notes in Physics. Vol. 728. Springer. ISBN 978-3-540-72994-5.
+Porter, M. A.; Zabusky, N. J.; Hu, B.; Campbell, D. K. (2009). "Fermi, Pasta, Ulam and the Birth of Experimental Mathematics" (PDF). American Scientist. 97 (3): 214–221. doi:10.1511/2009.78.214.
+Onorato, M.; Vozella, L.; Proment, D.; Lvov, Y. (2015). "Route to thermalization in the α-Fermi–Pasta–Ulam system" (PDF). Proceedings of the National Academy of Sciences of the United States of America. 112 (14): 4208–4213. arXiv:1402.1603. Bibcode:2015PNAS..112.4208O. doi:10.1073/pnas.1404397112. PMC 4394280. PMID 25805822.
+Ganapa, Santhosh (2023). "Quasiperiodicity in the α-Fermi–Pasta–Ulam–Tsingou problem revisited: An approach using ideas from wave turbulence". Chaos: An Interdisciplinary Journal of Nonlinear Science. 33 (9). American Institute of Physics Publishing. arXiv:2303.10297. Bibcode:2023Chaos..33i3102G. doi:10.1063/5.0154157. PMID 37656916.
+
+== External links ==
+"Fermi Pasta Ulam: the paradox that launched scientific computing".
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_equations-0.md b/data/en.wikipedia.org/wiki/Fresnel_equations-0.md
new file mode 100644
index 000000000..1d2a69720
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fresnel_equations-0.md
@@ -0,0 +1,341 @@
+---
+title: "Fresnel equations"
+chunk: 1/8
+source: "https://en.wikipedia.org/wiki/Fresnel_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:05.464676+00:00"
+instance: "kb-cron"
+---
+
+The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by French engineer and physicist Augustin-Jean Fresnel () who was the first to understand that light is a transverse wave, when no one realized that the waves were electric and magnetic fields. For the first time, polarization could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the s and p polarizations incident upon a material interface.
+
+== Overview ==
+When light strikes the interface between a medium with refractive index n1 and a second medium with refractive index n2, both reflection and refraction of the light may occur. The Fresnel equations give the ratio of the reflected wave's electric field to the incident wave's electric field, and the ratio of the transmitted wave's electric field to the incident wave's electric field, for each of two components of polarization. (The magnetic fields can also be related using similar coefficients.) These ratios are generally complex, describing not only the relative amplitudes but also the phase shifts at the interface.
+The equations assume the interface between the media is flat and that the media are homogeneous and isotropic. The incident light is assumed to be a plane wave, which is sufficient to solve any problem since any incident light field can be decomposed into plane waves and polarizations.
+
+=== S and P polarizations ===
+
+There are two sets of Fresnel coefficients for two different linear polarization  components of the incident wave. Since any polarization state can be resolved into a combination of two orthogonal linear polarizations, this is sufficient for any problem. Likewise, unpolarized (or "randomly polarized") light has an equal amount of power in each of two linear polarizations.
+The s polarization refers to polarization of a wave's electric field normal to the plane of incidence (the z direction in the derivation below); then the magnetic field is in the plane of incidence. The p polarization refers to polarization of the electric field in the plane of incidence (the xy plane in the derivation below); then the magnetic field is normal to the plane of incidence. The names "s" and "p" for the polarization components refer to German "senkrecht" (perpendicular or normal) and "parallel" (parallel to the plane of incidence).
+Although the reflection and transmission are dependent on polarization, at normal incidence (θ = 0) there is no distinction between them so all polarization states are governed by a single set of Fresnel coefficients (and another special case is mentioned below in which that is true).
+
+== Configuration ==
+
+In the diagram, an incident plane wave in the direction of the ray IO strikes the interface between two media of refractive indices n1 and n2 at point O. Part of the wave is reflected in the direction  OR, and part refracted in the direction OT. The angles that the incident, reflected and refracted rays make to the normal of the interface are given as θi, θr and θt, respectively. The relationship between these angles is given by the law of reflection:
+  
+    
+      
+        
+          θ
+          
+            
+              i
+            
+          
+        
+        =
+        
+          θ
+          
+            
+              r
+            
+          
+        
+        ,
+      
+    
+    {\displaystyle \theta _{\mathrm {i} }=\theta _{\mathrm {r} },}
+  
+and Snell's law:
+  
+    
+      
+        
+          n
+          
+            1
+          
+        
+        sin
+        ⁡
+        
+          θ
+          
+            
+              i
+            
+          
+        
+        =
+        
+          n
+          
+            2
+          
+        
+        sin
+        ⁡
+        
+          θ
+          
+            
+              t
+            
+          
+        
+        .
+      
+    
+    {\displaystyle n_{1}\sin \theta _{\mathrm {i} }=n_{2}\sin \theta _{\mathrm {t} }.}
+  
+
+The behavior of light striking the interface is explained by considering the electric and magnetic fields that constitute an electromagnetic wave, and the laws of electromagnetism, as shown below. The ratio of waves' electric field (or magnetic field) amplitudes are obtained, but in practice one is more often interested in formulae which determine power coefficients, since power (or irradiance) is what can be directly measured at optical frequencies. The power of a wave is generally proportional to the square of the electric (or magnetic) field amplitude.
+
+== Power (intensity) reflection and transmission coefficients ==
+
+We call the fraction of the incident power that is reflected from the interface the reflectance (or reflectivity, or power reflection coefficient) R, and the fraction that is refracted into the second medium is called the transmittance (or transmissivity, or power transmission coefficient) T. Note that these are what would be measured right at each side of an interface and do not account for attenuation of a wave in an absorbing medium following transmission or reflection.
+The reflectance for s-polarized light is
+
+  
+    
+      
+        
+          R
+          
+            
+              s
+            
+          
+        
+        =
+        
+          
+            |
+            
+              
+                
+                  
+                    Z
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                  −
+                  
+                    Z
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        t
+                      
+                    
+                  
+                
+                
+                  
+                    Z
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                  +
+                  
+                    Z
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        t
+                      
+                    
+                  
+                
+              
+            
+            |
+          
+          
+            2
+          
+        
+        ,
+      
+    
+    {\displaystyle R_{\mathrm {s} }=\left|{\frac {Z_{2}\cos \theta _{\mathrm {i} }-Z_{1}\cos \theta _{\mathrm {t} }}{Z_{2}\cos \theta _{\mathrm {i} }+Z_{1}\cos \theta _{\mathrm {t} }}}\right|^{2},}
+  
+
+while the reflectance for p-polarized light is
+
+  
+    
+      
+        
+          R
+          
+            
+              p
+            
+          
+        
+        =
+        
+          
+            |
+            
+              
+                
+                  
+                    Z
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        t
+                      
+                    
+                  
+                  −
+                  
+                    Z
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                
+                
+                  
+                    Z
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        t
+                      
+                    
+                  
+                  +
+                  
+                    Z
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                
+              
+            
+            |
+          
+          
+            2
+          
+        
+        ,
+      
+    
+    {\displaystyle R_{\mathrm {p} }=\left|{\frac {Z_{2}\cos \theta _{\mathrm {t} }-Z_{1}\cos \theta _{\mathrm {i} }}{Z_{2}\cos \theta _{\mathrm {t} }+Z_{1}\cos \theta _{\mathrm {i} }}}\right|^{2},}
+  
+
+where Z1 and Z2 are the wave impedances of media 1 and 2, respectively.
+We assume that the media are non-magnetic (i.e., μ1 = μ2 = μ0), which is typically a good approximation at optical frequencies (and for transparent media at other frequencies). Then the wave impedances are determined solely by the refractive indices n1 and n2:
+
+  
+    
+      
+        
+          Z
+          
+            i
+          
+        
+        =
+        
+          
+            
+              Z
+              
+                0
+              
+            
+            
+              n
+              
+                i
+              
+            
+          
+        
+        
+        ,
+      
+    
+    {\displaystyle Z_{i}={\frac {Z_{0}}{n_{i}}}\,,}
+  
+
+where Z0 is the impedance of free space and i = 1, 2. Making this substitution, we obtain equations using the refractive indices:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_equations-1.md b/data/en.wikipedia.org/wiki/Fresnel_equations-1.md
new file mode 100644
index 000000000..933b716eb
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fresnel_equations-1.md
@@ -0,0 +1,728 @@
+---
+title: "Fresnel equations"
+chunk: 2/8
+source: "https://en.wikipedia.org/wiki/Fresnel_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:05.464676+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          R
+          
+            
+              s
+            
+          
+        
+        =
+        
+          
+            |
+            
+              
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                  −
+                  
+                    n
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        t
+                      
+                    
+                  
+                
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                  +
+                  
+                    n
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        t
+                      
+                    
+                  
+                
+              
+            
+            |
+          
+          
+            2
+          
+        
+        =
+        
+          
+            |
+            
+              
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                  −
+                  
+                    n
+                    
+                      2
+                    
+                  
+                  
+                    
+                      1
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              
+                                
+                                  n
+                                  
+                                    1
+                                  
+                                
+                                
+                                  n
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                            sin
+                            ⁡
+                            
+                              θ
+                              
+                                
+                                  i
+                                
+                              
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                  +
+                  
+                    n
+                    
+                      2
+                    
+                  
+                  
+                    
+                      1
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              
+                                
+                                  n
+                                  
+                                    1
+                                  
+                                
+                                
+                                  n
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                            sin
+                            ⁡
+                            
+                              θ
+                              
+                                
+                                  i
+                                
+                              
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+            |
+          
+          
+            2
+          
+        
+        
+        ,
+      
+    
+    {\displaystyle R_{\mathrm {s} }=\left|{\frac {n_{1}\cos \theta _{\mathrm {i} }-n_{2}\cos \theta _{\mathrm {t} }}{n_{1}\cos \theta _{\mathrm {i} }+n_{2}\cos \theta _{\mathrm {t} }}}\right|^{2}=\left|{\frac {n_{1}\cos \theta _{\mathrm {i} }-n_{2}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{\mathrm {i} }\right)^{2}}}}{n_{1}\cos \theta _{\mathrm {i} }+n_{2}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{\mathrm {i} }\right)^{2}}}}}\right|^{2}\!,}
+  
+
+  
+    
+      
+        
+          R
+          
+            
+              p
+            
+          
+        
+        =
+        
+          
+            |
+            
+              
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        t
+                      
+                    
+                  
+                  −
+                  
+                    n
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        t
+                      
+                    
+                  
+                  +
+                  
+                    n
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                
+              
+            
+            |
+          
+          
+            2
+          
+        
+        =
+        
+          
+            |
+            
+              
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  
+                    
+                      1
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              
+                                
+                                  n
+                                  
+                                    1
+                                  
+                                
+                                
+                                  n
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                            sin
+                            ⁡
+                            
+                              θ
+                              
+                                
+                                  i
+                                
+                              
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                  
+                  −
+                  
+                    n
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  
+                    
+                      1
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              
+                                
+                                  n
+                                  
+                                    1
+                                  
+                                
+                                
+                                  n
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                            sin
+                            ⁡
+                            
+                              θ
+                              
+                                
+                                  i
+                                
+                              
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                  
+                  +
+                  
+                    n
+                    
+                      2
+                    
+                  
+                  cos
+                  ⁡
+                  
+                    θ
+                    
+                      
+                        i
+                      
+                    
+                  
+                
+              
+            
+            |
+          
+          
+            2
+          
+        
+        
+        .
+      
+    
+    {\displaystyle R_{\mathrm {p} }=\left|{\frac {n_{1}\cos \theta _{\mathrm {t} }-n_{2}\cos \theta _{\mathrm {i} }}{n_{1}\cos \theta _{\mathrm {t} }+n_{2}\cos \theta _{\mathrm {i} }}}\right|^{2}=\left|{\frac {n_{1}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{\mathrm {i} }\right)^{2}}}-n_{2}\cos \theta _{\mathrm {i} }}{n_{1}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{\mathrm {i} }\right)^{2}}}+n_{2}\cos \theta _{\mathrm {i} }}}\right|^{2}\!.}
+  
+
+The second form of each equation is derived from the first by eliminating θt using Snell's law and trigonometric identities.
+As a consequence of conservation of energy, one can find the transmitted power (or more correctly, irradiance: power per unit area) simply as the portion of the incident power that isn't reflected: 
+
+  
+    
+      
+        
+          T
+          
+            
+              s
+            
+          
+        
+        =
+        1
+        −
+        
+          R
+          
+            
+              s
+            
+          
+        
+      
+    
+    {\displaystyle T_{\mathrm {s} }=1-R_{\mathrm {s} }}
+  
+
+and
+
+  
+    
+      
+        
+          T
+          
+            
+              p
+            
+          
+        
+        =
+        1
+        −
+        
+          R
+          
+            
+              p
+            
+          
+        
+      
+    
+    {\displaystyle T_{\mathrm {p} }=1-R_{\mathrm {p} }}
+  
+
+Note that all such intensities are measured in terms of a wave's irradiance in the direction normal to the interface; this is also what is measured in typical experiments. That number could be obtained from irradiances in the direction of an incident or reflected wave (given by the magnitude of a wave's Poynting vector) multiplied by cos θ for a wave at an angle θ to the normal direction (or equivalently, taking the dot product of the Poynting vector with the unit vector normal to the interface). This complication can be ignored in the case of the reflection coefficient, since cos θi = cos θr, so that the ratio of reflected to incident irradiance in the wave's direction is the same as in the direction normal to the interface.
+Although these relationships describe the basic physics, in many practical applications one is concerned with "natural light" that can be described as unpolarized. That means that there is an equal amount of power in the s and p polarizations, so that the effective reflectivity of the material is just the average of the two reflectivities:
+
+  
+    
+      
+        
+          R
+          
+            
+              e
+              f
+              f
+            
+          
+        
+        =
+        
+          
+            1
+            2
+          
+        
+        
+          (
+          
+            
+              R
+              
+                
+                  s
+                
+              
+            
+            +
+            
+              R
+              
+                
+                  p
+                
+              
+            
+          
+          )
+        
+        .
+      
+    
+    {\displaystyle R_{\mathrm {eff} }={\frac {1}{2}}\left(R_{\mathrm {s} }+R_{\mathrm {p} }\right).}
+  
+
+For low-precision applications involving unpolarized light, such as computer graphics, rather than rigorously computing the effective reflection coefficient for each angle, Schlick's approximation is often used.
+
+=== Special cases ===
+
+==== Normal incidence ====
+For the case of normal incidence, θi = θt = 0, and there is no distinction between s and p polarization.  Thus, the reflectance simplifies to
+
+  
+    
+      
+        
+          R
+          
+            0
+          
+        
+        =
+        
+          
+            |
+            
+              
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  −
+                  
+                    n
+                    
+                      2
+                    
+                  
+                
+                
+                  
+                    n
+                    
+                      1
+                    
+                  
+                  +
+                  
+                    n
+                    
+                      2
+                    
+                  
+                
+              
+            
+            |
+          
+          
+            2
+          
+        
+        
+        .
+      
+    
+    {\displaystyle R_{0}=\left|{\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right|^{2}\,.}
+  
+
+For common glass (n2 ≈ 1.5) surrounded by air (n1 = 1), the power reflectance at normal incidence can be seen to be about 4%, or 8% accounting for both sides of a glass pane.
+
+==== Brewster's angle ====
+
+At a dielectric interface from  n1 to n2, there is a particular angle of incidence at which Rp goes to zero and a p-polarised incident wave is purely refracted, thus all reflected light is s-polarised. This angle is known as Brewster's angle, and is around 56° for n1 = 1 and n2 = 1.5 (typical glass).
+
+==== Total internal reflection ====
+
+When light travelling in a denser medium strikes the surface of a less dense medium (i.e., n1 > n2), beyond a particular incidence angle known as the critical angle, all light is reflected and Rs = Rp = 1. This phenomenon, known as total internal reflection, occurs at incidence angles for which Snell's law predicts that the sine of the angle of refraction would exceed unity (whereas in fact sin θ ≤ 1 for all real θ). For glass with n = 1.5 surrounded by air, the critical angle is approximately 42°.
+
+==== 45° incidence ====
+Reflection at 45° incidence is very commonly used for making 90° turns. For the case of light traversing from a less dense medium into a denser one at 45° incidence (θ = 45°), it follows algebraically from the above equations that Rp equals the square of Rs:
+
+  
+    
+      
+        
+          R
+          
+            p
+          
+        
+        =
+        
+          R
+          
+            s
+          
+          
+            2
+          
+        
+      
+    
+    {\displaystyle R_{\text{p}}=R_{\text{s}}^{2}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_equations-2.md b/data/en.wikipedia.org/wiki/Fresnel_equations-2.md
new file mode 100644
index 000000000..116c88b17
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fresnel_equations-2.md
@@ -0,0 +1,521 @@
+---
+title: "Fresnel equations"
+chunk: 3/8
+source: "https://en.wikipedia.org/wiki/Fresnel_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:05.464676+00:00"
+instance: "kb-cron"
+---
+
+This can be used to either verify the consistency of the measurements of Rs and Rp, or to derive one of them when the other is known. This relationship is only valid for the simple case of a single plane interface between two homogeneous materials, not for films on substrates, where a more complex analysis is required.
+Measurements of Rs and Rp at 45° can be used to estimate the reflectivity at normal incidence. The "average of averages" obtained by calculating first the arithmetic as well as the geometric average of Rs and Rp, and then averaging these two averages again arithmetically, gives a value for R0 with an error of less than about 3% for most common optical materials. This is useful because measurements at normal incidence can be difficult to achieve in an experimental setup since the incoming beam and the detector will obstruct each other. However, since the dependence of Rs and Rp on the angle of incidence for angles below 10° is very small, a measurement at about 5° will usually be a good approximation for normal incidence, while allowing for a separation of the incoming and reflected beam.
+
+== Complex amplitude reflection and transmission coefficients ==
+The above equations relating powers (which could be measured with a photometer for instance) are derived from the Fresnel equations which solve the physical problem in terms of electromagnetic field complex amplitudes, i.e., considering phase shifts in addition to their amplitudes. Those underlying equations supply generally complex-valued ratios of those EM fields and may take several different forms, depending on the formalism used. The complex amplitude coefficients for reflection and transmission are usually represented by lower case r and t (whereas the power coefficients are capitalized). As before, we are assuming the magnetic permeability, µ of both media to be equal to the permeability of free space µ0 as is essentially true of all dielectrics at optical frequencies.
+
+In the following equations and graphs, we adopt the following conventions. For s polarization, the reflection coefficient r is defined as the ratio of the reflected wave's complex electric field amplitude to that of the incident wave, whereas for p polarization r is the ratio of the waves complex magnetic field amplitudes (or equivalently, the negative of the ratio of their electric field amplitudes). The transmission coefficient t is the ratio of the transmitted wave's complex electric field amplitude to that of the incident wave, for either polarization. The coefficients r and t are generally different between the s and p polarizations, and even at normal incidence (where the designations s and p do not even apply!) the sign of r is reversed depending on whether the wave is considered to be s or p polarized, an artifact of the adopted sign convention (see graph for an air-glass interface at 0° incidence).
+The equations consider a plane wave incident on a plane interface at angle of incidence 
+  
+    
+      
+        
+          θ
+          
+            
+              i
+            
+          
+        
+      
+    
+    {\displaystyle \theta _{\mathrm {i} }}
+  
+, a wave reflected at angle 
+  
+    
+      
+        
+          θ
+          
+            
+              r
+            
+          
+        
+        =
+        
+          θ
+          
+            
+              i
+            
+          
+        
+      
+    
+    {\displaystyle \theta _{\mathrm {r} }=\theta _{\mathrm {i} }}
+  
+, and a wave transmitted at angle 
+  
+    
+      
+        
+          θ
+          
+            
+              t
+            
+          
+        
+      
+    
+    {\displaystyle \theta _{\mathrm {t} }}
+  
+. In the case of an interface into an absorbing material (where n is complex) or total internal reflection, the angle of transmission does not generally evaluate to a real number. In that case, however, meaningful results can be obtained using formulations of these relationships in which trigonometric functions and geometric angles are avoided; the inhomogeneous waves launched into the second medium cannot be described using a single propagation angle.
+Using this convention,
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  r
+                  
+                    s
+                  
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      
+                        n
+                        
+                          1
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          i
+                        
+                      
+                      −
+                      
+                        n
+                        
+                          2
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          t
+                        
+                      
+                    
+                    
+                      
+                        n
+                        
+                          1
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          i
+                        
+                      
+                      +
+                      
+                        n
+                        
+                          2
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          t
+                        
+                      
+                    
+                  
+                
+                ,
+              
+            
+            
+              
+                
+                  t
+                  
+                    s
+                  
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      2
+                      
+                        n
+                        
+                          1
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          i
+                        
+                      
+                    
+                    
+                      
+                        n
+                        
+                          1
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          i
+                        
+                      
+                      +
+                      
+                        n
+                        
+                          2
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          t
+                        
+                      
+                    
+                  
+                
+                ,
+              
+            
+            
+              
+                
+                  r
+                  
+                    p
+                  
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      
+                        n
+                        
+                          2
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          i
+                        
+                      
+                      −
+                      
+                        n
+                        
+                          1
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          t
+                        
+                      
+                    
+                    
+                      
+                        n
+                        
+                          2
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          i
+                        
+                      
+                      +
+                      
+                        n
+                        
+                          1
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          t
+                        
+                      
+                    
+                  
+                
+                ,
+              
+            
+            
+              
+                
+                  t
+                  
+                    p
+                  
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      2
+                      
+                        n
+                        
+                          1
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          i
+                        
+                      
+                    
+                    
+                      
+                        n
+                        
+                          2
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          i
+                        
+                      
+                      +
+                      
+                        n
+                        
+                          1
+                        
+                      
+                      cos
+                      ⁡
+                      
+                        θ
+                        
+                          t
+                        
+                      
+                    
+                  
+                
+                .
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}r_{\text{s}}&={\frac {n_{1}\cos \theta _{\text{i}}-n_{2}\cos \theta _{\text{t}}}{n_{1}\cos \theta _{\text{i}}+n_{2}\cos \theta _{\text{t}}}},\\[3pt]t_{\text{s}}&={\frac {2n_{1}\cos \theta _{\text{i}}}{n_{1}\cos \theta _{\text{i}}+n_{2}\cos \theta _{\text{t}}}},\\[3pt]r_{\text{p}}&={\frac {n_{2}\cos \theta _{\text{i}}-n_{1}\cos \theta _{\text{t}}}{n_{2}\cos \theta _{\text{i}}+n_{1}\cos \theta _{\text{t}}}},\\[3pt]t_{\text{p}}&={\frac {2n_{1}\cos \theta _{\text{i}}}{n_{2}\cos \theta _{\text{i}}+n_{1}\cos \theta _{\text{t}}}}.\end{aligned}}}
+  
+
+For the case where the magnetic permeabilities are non-negligible, the equations change such that every appearance of 
+  
+    
+      
+        
+          n
+          
+            i
+          
+        
+      
+    
+    {\displaystyle n_{i}}
+  
+ is replaced by 
+  
+    
+      
+        
+          n
+          
+            i
+          
+        
+        
+          /
+        
+        
+          μ
+          
+            i
+          
+        
+      
+    
+    {\displaystyle n_{i}/\mu _{i}}
+  
+ (for both 
+  
+    
+      
+        i
+        =
+        1
+        ,
+        2
+      
+    
+    {\displaystyle i=1,2}
+  
+).
+One can see that ts = rs + 1 and ⁠n2/n1⁠tp = rp + 1. One can write very similar equations applying to the ratio of the waves' magnetic fields, but comparison of the electric fields is more conventional.
+Because the reflected and incident waves propagate in the same medium and make the same angle with the normal to the surface, the power reflection coefficient R is just the squared magnitude of r: 
+
+  
+    
+      
+        R
+        =
+        
+          |
+        
+        r
+        
+          
+            |
+          
+          
+            2
+          
+        
+        .
+      
+    
+    {\displaystyle R=|r|^{2}.}
+  
+
+On the other hand, calculation of the power transmission coefficient T is less straightforward, since the light travels in different directions in the two media. What's more, the wave impedances in the two media differ; power (irradiance) is given by the square of the electric field amplitude divided by the characteristic impedance of the medium (or by the square of the magnetic field multiplied by the characteristic impedance). This results in:
+
+  
+    
+      
+        T
+        =
+        
+          
+            
+              
+                n
+                
+                  2
+                
+              
+              cos
+              ⁡
+              
+                θ
+                
+                  t
+                
+              
+            
+            
+              
+                n
+                
+                  1
+                
+              
+              cos
+              ⁡
+              
+                θ
+                
+                  i
+                
+              
+            
+          
+        
+        
+          |
+        
+        t
+        
+          
+            |
+          
+          
+            2
+          
+        
+      
+    
+    {\displaystyle T={\frac {n_{2}\cos \theta _{\text{t}}}{n_{1}\cos \theta _{\text{i}}}}|t|^{2}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_equations-3.md b/data/en.wikipedia.org/wiki/Fresnel_equations-3.md
new file mode 100644
index 000000000..6e6f000c5
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fresnel_equations-3.md
@@ -0,0 +1,190 @@
+---
+title: "Fresnel equations"
+chunk: 4/8
+source: "https://en.wikipedia.org/wiki/Fresnel_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:05.464676+00:00"
+instance: "kb-cron"
+---
+
+using the above definition of t. The introduced factor of ⁠n2/n1⁠ is the reciprocal of the ratio of the media's wave impedances. The cos(θ) factors adjust the waves' powers so they are reckoned in the direction normal to the interface, for both the incident and transmitted waves, so that full power transmission corresponds to T = 1.
+In the case of total internal reflection where the power transmission T is zero, t nevertheless describes the electric field (including its phase) just beyond the interface. This is an evanescent field which does not propagate as a wave (thus T = 0) but has nonzero values very close to the interface. The phase shift of the reflected wave on total internal reflection can similarly be obtained from the phase angles of rp and rs (whose magnitudes are unity in this case). These phase shifts are different for  s and p waves, which is the well-known principle by which total internal reflection is used to effect polarization transformations.
+
+=== Alternative forms ===
+In the above formula for rs, if we put 
+  
+    
+      
+        
+          n
+          
+            2
+          
+        
+        =
+        
+          n
+          
+            1
+          
+        
+        sin
+        ⁡
+        
+          θ
+          
+            i
+          
+        
+        
+          /
+        
+        sin
+        ⁡
+        
+          θ
+          
+            t
+          
+        
+      
+    
+    {\displaystyle n_{2}=n_{1}\sin \theta _{\text{i}}/\sin \theta _{\text{t}}}
+  
+ (Snell's law) and multiply the numerator and denominator by ⁠1/n1⁠ sin θt, we obtain 
+
+  
+    
+      
+        
+          r
+          
+            s
+          
+        
+        =
+        −
+        
+          
+            
+              sin
+              ⁡
+              (
+              
+                θ
+                
+                  i
+                
+              
+              −
+              
+                θ
+                
+                  t
+                
+              
+              )
+            
+            
+              sin
+              ⁡
+              (
+              
+                θ
+                
+                  i
+                
+              
+              +
+              
+                θ
+                
+                  t
+                
+              
+              )
+            
+          
+        
+        .
+      
+    
+    {\displaystyle r_{\text{s}}=-{\frac {\sin(\theta _{\text{i}}-\theta _{\text{t}})}{\sin(\theta _{\text{i}}+\theta _{\text{t}})}}.}
+  
+
+If we do likewise with the formula for rp, the result is easily shown to be equivalent to 
+
+  
+    
+      
+        
+          r
+          
+            p
+          
+        
+        =
+        
+          
+            
+              tan
+              ⁡
+              (
+              
+                θ
+                
+                  i
+                
+              
+              −
+              
+                θ
+                
+                  t
+                
+              
+              )
+            
+            
+              tan
+              ⁡
+              (
+              
+                θ
+                
+                  i
+                
+              
+              +
+              
+                θ
+                
+                  t
+                
+              
+              )
+            
+          
+        
+        .
+      
+    
+    {\displaystyle r_{\text{p}}={\frac {\tan(\theta _{\text{i}}-\theta _{\text{t}})}{\tan(\theta _{\text{i}}+\theta _{\text{t}})}}.}
+  
+
+These formulas  are known respectively as Fresnel's sine law and Fresnel's tangent law. Although at normal incidence these expressions reduce to 0/0, one can see that they yield the correct results in the limit as θi → 0.
+
+== Multiple surfaces ==
+When light makes multiple reflections between two or more parallel surfaces, the multiple beams of light generally interfere with one another, resulting in net transmission and reflection amplitudes that depend on the light's wavelength. The interference, however, is seen only when the surfaces are at distances comparable to or smaller than the light's coherence length, which for ordinary white light is few micrometers; it can be much larger for light from a laser.
+An example of interference between reflections is the iridescent colours seen in a soap bubble or in thin oil films on water. Applications include Fabry–Pérot interferometers, antireflection coatings, and optical filters. A quantitative analysis of these effects is based on the Fresnel equations, but with additional calculations to account for interference.
+The transfer-matrix method, or Rouard's recursive method can be used to solve multiple-surface problems.
+
+== History ==
+
+In 1808, Étienne-Louis Malus discovered that when a ray of light was reflected off a non-metallic surface at the appropriate angle, it behaved like one of the two rays emerging from a doubly-refractive calcite crystal. He later coined the term polarization to describe this behavior. In 1815, the dependence of the polarizing angle on the refractive index was determined experimentally by David Brewster. But the reason for that dependence was such a deep mystery that in late 1817, Thomas Young was moved to write:
+
+[T]he great difficulty of all, which is to assign a sufficient reason for the reflection or nonreflection of a polarised ray, will probably long remain, to mortify the vanity of an ambitious philosophy, completely unresolved by any theory.
+In 1821, however, Augustin-Jean Fresnel derived results equivalent to his sine and tangent laws (above), by modeling light waves as transverse elastic waves with vibrations perpendicular to what had previously been called the plane of polarization. Fresnel promptly confirmed by experiment that the equations correctly predicted the direction of polarization of the reflected beam when the incident beam was polarized at 45° to the plane of incidence, for light incident from air onto glass or water; in particular, the equations gave the correct polarization at Brewster's angle. The experimental confirmation was reported in a "postscript" to the work in which Fresnel first revealed his theory that light waves, including "unpolarized" waves, were purely transverse.
+Details of Fresnel's derivation, including the modern forms of the sine law and tangent law, were given later, in a memoir read to the French Academy of Sciences in January 1823. That derivation combined conservation of energy with continuity of the tangential vibration at the interface, but failed to allow for any condition on the normal component of vibration. The first derivation from electromagnetic principles was given by Hendrik Lorentz in 1875.
+In the same memoir of January 1823, Fresnel found that for angles of incidence greater than the critical angle, his formulas for the reflection coefficients (rs and rp) gave complex values with unit magnitudes. Noting that the magnitude, as usual, represented the ratio of peak amplitudes, he guessed that the argument represented the phase shift, and verified the hypothesis experimentally. The verification involved
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_equations-4.md b/data/en.wikipedia.org/wiki/Fresnel_equations-4.md
new file mode 100644
index 000000000..1b0246be5
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fresnel_equations-4.md
@@ -0,0 +1,222 @@
+---
+title: "Fresnel equations"
+chunk: 5/8
+source: "https://en.wikipedia.org/wiki/Fresnel_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:05.464676+00:00"
+instance: "kb-cron"
+---
+
+calculating the angle of incidence that would introduce a total phase difference of 90° between the s and p components, for various numbers of total internal reflections at that angle (generally there were two solutions),
+subjecting light to that number of total internal reflections at that angle of incidence, with an initial linear polarization at 45° to the plane of incidence, and
+checking that the final polarization was circular.
+Thus he finally had a quantitative theory for what we now call the Fresnel rhomb — a device that he had been using in experiments, in one form or another, since 1817 (see Fresnel rhomb § History).
+The success of the complex reflection coefficient inspired James MacCullagh and Augustin-Louis Cauchy, beginning in 1836, to analyze reflection from metals by using the Fresnel equations with a complex refractive index.
+Four weeks before he presented his completed theory of total internal reflection and the rhomb, Fresnel submitted a memoir  in which he introduced the needed terms linear polarization, circular polarization, and elliptical polarization, and in which he explained optical rotation as a species of birefringence: linearly-polarized light can be resolved into two circularly-polarized components rotating in opposite directions, and if these propagate at different speeds, the phase difference between them — hence the orientation of their linearly-polarized resultant — will vary continuously with distance.
+Thus Fresnel's interpretation of the complex values of his reflection coefficients marked the confluence of several streams of his research and, arguably, the essential completion of his reconstruction of physical optics on the transverse-wave hypothesis (see Augustin-Jean Fresnel).
+
+== Derivation ==
+Here we systematically derive the above relations from electromagnetic premises.
+
+=== Material parameters ===
+In order to compute meaningful Fresnel coefficients, we must assume that the medium is (approximately) linear and homogeneous. If the medium is also isotropic, the four field vectors E, B, D, H  are related by
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  D
+                
+              
+              
+                
+                =
+                ϵ
+                
+                  E
+                
+              
+            
+            
+              
+                
+                  B
+                
+              
+              
+                
+                =
+                μ
+                
+                  H
+                
+                
+                ,
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}\mathbf {D} &=\epsilon \mathbf {E} \\\mathbf {B} &=\mu \mathbf {H} \,,\end{aligned}}}
+  
+
+where ϵ and μ are scalars, known respectively as the (electric) permittivity and the (magnetic) permeability of the medium. For vacuum, these have the values ϵ0 and μ0, respectively. Hence we define the relative permittivity (or dielectric constant) ϵrel = ϵ/ϵ0, and the relative permeability μrel = μ/μ0.
+In optics it is common to assume that the medium is non-magnetic, so that μrel = 1. For ferromagnetic materials at radio/microwave frequencies, larger values of μrel must be taken into account. But, for optically transparent media, and for all other materials at optical frequencies (except possible metamaterials), μrel is indeed very close to 1; that is, μ ≈ μ0.
+In optics, one usually knows the refractive index n of the medium, which is the ratio of the speed of light in vacuum (c) to the speed of light in the medium. In the analysis of partial reflection and transmission, one is also interested in the electromagnetic wave impedance Z, which is the ratio of the amplitude of E to the amplitude of H. It is therefore desirable to express n and Z in terms of ϵ and μ, and thence to relate Z to n. The last-mentioned relation, however, will make it convenient to derive the reflection coefficients in terms of the wave admittance Y, which is the reciprocal of the wave impedance Z.
+In the case of uniform plane sinusoidal waves, the wave impedance or admittance is known as the intrinsic impedance or admittance of the medium. This case is the one for which the Fresnel coefficients are to be derived.
+
+=== Electromagnetic plane waves ===
+In a uniform plane sinusoidal electromagnetic wave, the electric field E has the form
+
+where Ek is the (constant) complex amplitude vector, i is the imaginary unit, k is the wave vector (whose magnitude k is the angular wavenumber), r is the position vector, ω is the angular frequency, t is time, and it is understood that the real part of the expression is the physical field.  The value of the expression is unchanged if the position r varies in a direction normal to k; hence k is normal to the wavefronts.
+To advance the phase by the angle ϕ, we replace ωt by ωt + ϕ (that is, we replace −ωt by −ωt − ϕ), with the result that the (complex) field is multiplied by e−iϕ. So a phase advance is equivalent to multiplication by a complex constant with a negative argument. This becomes more obvious when the field (1) is factored as Ek eik⋅re−iωt, where the last factor contains the time-dependence. That factor also implies that differentiation w.r.t. time corresponds to multiplication by −iω. 
+If ℓ is the component of r in the direction of k, the field (1) can be written Ek ei(kℓ−ωt).  If the argument of ei(⋯) is to be constant,  ℓ must increase at the velocity 
+  
+    
+      
+        ω
+        
+          /
+        
+        k
+        
+        ,
+        
+      
+    
+    {\displaystyle \omega /k\,,\,}
+  
+ known as the phase velocity (vp). This in turn is equal to 
+  
+    
+      
+        c
+        
+          /
+        
+        n
+      
+    
+    {\displaystyle c/n}
+  
+. Solving for k gives
+
+As usual, we drop the time-dependent factor e−iωt, which is understood to multiply every complex field quantity. The electric field for a uniform plane sine wave will then be represented by the location-dependent phasor
+
+For fields of that form, Faraday's law and the Maxwell-Ampère law respectively reduce to 
+
+  
+    
+      
+        
+          
+            
+              
+                ω
+                
+                  B
+                
+              
+              
+                
+                =
+                
+                  k
+                
+                ×
+                
+                  E
+                
+              
+            
+            
+              
+                ω
+                
+                  D
+                
+              
+              
+                
+                =
+                −
+                
+                  k
+                
+                ×
+                
+                  H
+                
+                
+                .
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}\omega \mathbf {B} &=\mathbf {k} \times \mathbf {E} \\\omega \mathbf {D} &=-\mathbf {k} \times \mathbf {H} \,.\end{aligned}}}
+  
+
+Putting B = μH and D = ϵE, as above, we can eliminate B and D to obtain equations in only E and H:
+
+  
+    
+      
+        
+          
+            
+              
+                ω
+                μ
+                
+                  H
+                
+              
+              
+                
+                =
+                
+                  k
+                
+                ×
+                
+                  E
+                
+              
+            
+            
+              
+                ω
+                ϵ
+                
+                  E
+                
+              
+              
+                
+                =
+                −
+                
+                  k
+                
+                ×
+                
+                  H
+                
+                
+                .
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}\omega \mu \mathbf {H} &=\mathbf {k} \times \mathbf {E} \\\omega \epsilon \mathbf {E} &=-\mathbf {k} \times \mathbf {H} \,.\end{aligned}}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_equations-5.md b/data/en.wikipedia.org/wiki/Fresnel_equations-5.md
new file mode 100644
index 000000000..c40e485e1
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fresnel_equations-5.md
@@ -0,0 +1,551 @@
+---
+title: "Fresnel equations"
+chunk: 6/8
+source: "https://en.wikipedia.org/wiki/Fresnel_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:05.464676+00:00"
+instance: "kb-cron"
+---
+
+If the material parameters ϵ and μ are real (as in a lossless dielectric), these equations show that k, E, H  form a right-handed orthogonal triad, so that the same equations apply to the magnitudes of the respective vectors. Taking the magnitude equations and substituting from (2), we obtain
+
+  
+    
+      
+        
+          
+            
+              
+                μ
+                c
+                H
+              
+              
+                
+                =
+                n
+                E
+              
+            
+            
+              
+                ϵ
+                c
+                E
+              
+              
+                
+                =
+                n
+                H
+                
+                ,
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}\mu cH&=nE\\\epsilon cE&=nH\,,\end{aligned}}}
+  
+
+where H and E are the magnitudes of H and E. Multiplying the last two equations gives
+
+Dividing (or cross-multiplying) the same two equations gives H = YE, where
+
+This is the intrinsic admittance.
+From (4) we obtain the phase velocity 
+  
+    
+      
+        c
+        
+          /
+        
+        n
+        =
+        1
+        
+          
+            /
+          
+        
+        
+        
+          
+            μ
+            ϵ
+            
+          
+        
+      
+    
+    {\displaystyle c/n=1{\big /}\!{\sqrt {\mu \epsilon \,}}}
+  
+. For vacuum this reduces to 
+  
+    
+      
+        c
+        =
+        1
+        
+          
+            /
+          
+        
+        
+        
+          
+            
+              μ
+              
+                0
+              
+            
+            
+              ϵ
+              
+                0
+              
+            
+          
+        
+      
+    
+    {\displaystyle c=1{\big /}\!{\sqrt {\mu _{0}\epsilon _{0}}}}
+  
+. Dividing the second result by the first gives
+
+  
+    
+      
+        n
+        =
+        
+          
+            
+              μ
+              
+                rel
+              
+            
+            
+              ϵ
+              
+                rel
+              
+            
+          
+        
+        
+        .
+      
+    
+    {\displaystyle n={\sqrt {\mu _{\text{rel}}\epsilon _{\text{rel}}}}\,.}
+  
+
+For a non-magnetic medium (the usual case), this becomes ⁠
+  
+    
+      
+        n
+        =
+        
+          
+            
+              ϵ
+              
+                rel
+              
+            
+          
+        
+      
+    
+    {\displaystyle n={\sqrt {\epsilon _{\text{rel}}}}}
+  
+⁠.
+(Taking the reciprocal of (5), we find that the intrinsic impedance is 
+  
+    
+      
+        Z
+        =
+        
+          
+            μ
+            
+              /
+            
+            ϵ
+          
+        
+      
+    
+    {\textstyle Z={\sqrt {\mu /\epsilon }}}
+  
+. In vacuum this takes the value 
+  
+    
+      
+        
+          Z
+          
+            0
+          
+        
+        =
+        
+          
+            
+              μ
+              
+                0
+              
+            
+            
+              /
+            
+            
+              ϵ
+              
+                0
+              
+            
+          
+        
+        
+        ≈
+        377
+        
+        Ω
+        
+        ,
+      
+    
+    {\textstyle Z_{0}={\sqrt {\mu _{0}/\epsilon _{0}}}\,\approx 377\,\Omega \,,}
+  
+ known as the impedance of free space. By division, 
+  
+    
+      
+        Z
+        
+          /
+        
+        
+          Z
+          
+            0
+          
+        
+        =
+        
+          
+            
+              μ
+              
+                rel
+              
+            
+            
+              /
+            
+            
+              ϵ
+              
+                rel
+              
+            
+          
+        
+      
+    
+    {\textstyle Z/Z_{0}={\sqrt {\mu _{\text{rel}}/\epsilon _{\text{rel}}}}}
+  
+. For a non-magnetic medium, this becomes 
+  
+    
+      
+        Z
+        =
+        
+          Z
+          
+            0
+          
+        
+        
+          
+            /
+          
+        
+        
+        
+          
+            
+              ϵ
+              
+                rel
+              
+            
+          
+        
+        =
+        
+          Z
+          
+            0
+          
+        
+        
+          /
+        
+        n
+        .
+      
+    
+    {\displaystyle Z=Z_{0}{\big /}\!{\sqrt {\epsilon _{\text{rel}}}}=Z_{0}/n.}
+  
+)
+
+=== Wave vectors ===
+
+In Cartesian coordinates (x, y, z), let the region y < 0 have refractive index n1, intrinsic admittance Y1, etc., and let the region y > 0 have refractive index n2, intrinsic admittance Y2, etc. Then the xz plane is the interface, and the y axis is normal to the interface (see diagram). Let i and j (in bold roman type) be the unit vectors in the x and y directions, respectively. Let the plane of incidence be the xy plane (the plane of the page), with the angle of incidence θi measured from j towards i. Let the angle of refraction, measured in the same sense, be θt, where the subscript t stands for transmitted (reserving  r for reflected).
+In the absence of Doppler shifts, ω does not change on reflection or refraction. Hence, by (2), the magnitude of the wave vector is proportional to the refractive index.
+So, for a given ω, if we redefine k as the magnitude of the wave vector in the reference medium (for which n = 1), then the wave vector has magnitude n1k in the first medium (region y < 0 in the diagram) and magnitude n2k in the second medium. From the magnitudes and the geometry, we find that the wave vectors are
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  
+                    k
+                  
+                  
+                    i
+                  
+                
+              
+              
+                
+                =
+                
+                  n
+                  
+                    1
+                  
+                
+                k
+                (
+                
+                  i
+                
+                sin
+                ⁡
+                
+                  θ
+                  
+                    i
+                  
+                
+                +
+                
+                  j
+                
+                cos
+                ⁡
+                
+                  θ
+                  
+                    i
+                  
+                
+                )
+              
+            
+            
+              
+                
+                  
+                    k
+                  
+                  
+                    r
+                  
+                
+              
+              
+                
+                =
+                
+                  n
+                  
+                    1
+                  
+                
+                k
+                (
+                
+                  i
+                
+                sin
+                ⁡
+                
+                  θ
+                  
+                    i
+                  
+                
+                −
+                
+                  j
+                
+                cos
+                ⁡
+                
+                  θ
+                  
+                    i
+                  
+                
+                )
+              
+            
+            
+              
+                
+                  
+                    k
+                  
+                  
+                    t
+                  
+                
+              
+              
+                
+                =
+                
+                  n
+                  
+                    2
+                  
+                
+                k
+                (
+                
+                  i
+                
+                sin
+                ⁡
+                
+                  θ
+                  
+                    t
+                  
+                
+                +
+                
+                  j
+                
+                cos
+                ⁡
+                
+                  θ
+                  
+                    t
+                  
+                
+                )
+              
+            
+            
+              
+              
+                
+                =
+                k
+                (
+                
+                  i
+                
+                
+                
+                  n
+                  
+                    1
+                  
+                
+                sin
+                ⁡
+                
+                  θ
+                  
+                    i
+                  
+                
+                +
+                
+                  j
+                
+                
+                
+                  n
+                  
+                    2
+                  
+                
+                cos
+                ⁡
+                
+                  θ
+                  
+                    t
+                  
+                
+                )
+                
+                ,
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}\mathbf {k} _{\text{i}}&=n_{1}k(\mathbf {i} \sin \theta _{\text{i}}+\mathbf {j} \cos \theta _{\text{i}})\\[.5ex]\mathbf {k} _{\text{r}}&=n_{1}k(\mathbf {i} \sin \theta _{\text{i}}-\mathbf {j} \cos \theta _{\text{i}})\\[.5ex]\mathbf {k} _{\text{t}}&=n_{2}k(\mathbf {i} \sin \theta _{\text{t}}+\mathbf {j} \cos \theta _{\text{t}})\\&=k(\mathbf {i} \,n_{1}\sin \theta _{\text{i}}+\mathbf {j} \,n_{2}\cos \theta _{\text{t}})\,,\end{aligned}}}
+  
+
+where the last step uses Snell's law. The corresponding dot products in the phasor form (3) are
+
+Hence:
+
+=== s components ===
+For the s polarization, the E field is parallel to the z axis and may therefore be described by its component in the z direction. Let the reflection and transmission coefficients be rs and ts, respectively. Then, if the incident E field is taken to have unit amplitude, the phasor form (3) of its z-component is
+
+and the reflected and transmitted fields, in the same form, are
+
+Under the sign convention used in this article, a positive reflection or transmission coefficient is one that preserves the direction of the transverse field, meaning (in this context) the field normal to the plane of incidence. For the s polarization, that means the E field. If the incident, reflected, and transmitted E fields (in the above equations) are in the z-direction ("out of the page"), then the respective H fields are in the directions of the red arrows, since k, E, H form a right-handed orthogonal triad. The H fields may therefore be described by their components in the directions of those arrows, denoted by Hi, Hr, Ht. Then, since H = YE,
+
+At the interface, by the usual interface conditions for electromagnetic fields, the tangential components of the E and H fields must be continuous; that is,
+
+When we substitute from equations (8) to (10) and then from (7), the exponential factors cancel out, so that the interface conditions reduce to the simultaneous equations
+
+which are easily solved for rs and ts, yielding
+
+and
+
+At normal incidence (θi = θt = 0), indicated by an additional subscript 0, these results become
+
+and
+
+At grazing incidence (θi → 90°), we have cos θi → 0, hence rs → −1 and ts → 0.
+
+=== p components ===
+For the p polarization, the incident, reflected, and transmitted E fields are parallel to the red arrows and may therefore be described by their components in the directions of those arrows. Let those components be Ei, Er, Et  (redefining the symbols for the new context). Let the reflection and transmission coefficients be rp and tp. Then, if the incident E field is taken to have unit amplitude, we have
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_equations-6.md b/data/en.wikipedia.org/wiki/Fresnel_equations-6.md
new file mode 100644
index 000000000..638869460
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fresnel_equations-6.md
@@ -0,0 +1,224 @@
+---
+title: "Fresnel equations"
+chunk: 7/8
+source: "https://en.wikipedia.org/wiki/Fresnel_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:05.464676+00:00"
+instance: "kb-cron"
+---
+
+If the E fields are in the directions of the red arrows, then, in order for k, E, H to form a right-handed orthogonal triad, the respective H fields must be in the −z-direction ("into the page") and may therefore be described by their components in that direction. This is consistent with the adopted sign convention, namely that a positive reflection or transmission coefficient is one that preserves the direction of the transverse field (the H field in the case of the p polarization). The agreement of the other field with the red arrows reveals an alternative definition of the sign convention: that a positive reflection or transmission coefficient is one for which the field vector in the plane of incidence points towards the same medium before and after reflection or transmission.
+So, for the incident, reflected, and transmitted H fields, let the respective components in the −z-direction be Hi, Hr, Ht. Then, since H = YE,
+
+At the interface, the tangential components of the E and H fields must be continuous; that is,
+
+When we substitute from equations (17) and (18) and then from (7), the exponential factors again cancel out, so that the interface conditions reduce to
+
+Solving for rp and tp, we find
+
+and
+
+At normal incidence (θi = θt = 0) indicated by an additional subscript 0, these results become
+
+and
+
+At grazing incidence (θi → 90°), we again have cos θi → 0, hence rp → −1 and tp → 0.
+Comparing (23) and (24) with (15) and (16), we see that at normal incidence, under the adopted sign convention, the transmission coefficients for the two polarizations are equal, whereas the reflection coefficients have equal magnitudes but opposite signs. While this clash of signs is a disadvantage of the convention, the attendant advantage is that the signs agree at grazing incidence.
+
+=== Power ratios (reflectivity and transmissivity) ===
+The Poynting vector for a wave is a vector whose component in any direction is the irradiance (power per unit area) of that wave on a surface perpendicular to that direction. For a plane sinusoidal wave the Poynting vector is ⁠1/2⁠‍Re{E × H∗}, where E and H are due only to the wave in question, and the asterisk denotes complex conjugation. Inside a lossless dielectric (the usual case), E and H are in phase, and at right angles to each other and to the wave vector k; so, for s polarization, using the z and xy components of E and H  respectively (or for p polarization, using the xy and −z components of E and H), the irradiance in the direction of k is given simply by EH/2, which is E2/2Z in a medium of intrinsic impedance Z = 1/Y. To compute the irradiance in the direction normal to the interface, as we shall require in the definition of the power transmission coefficient, we could use only the x component (rather than the full xy component) of H or E or, equivalently, simply multiply EH/2 by the proper geometric factor, obtaining (E2/2Z)cos θ.
+From equations (13) and (21), taking squared magnitudes, we find that the reflectivity (ratio of reflected power to incident power) is
+
+for the s polarization, and
+
+for the p polarization. Note that when comparing the powers of two such waves in the same medium and with the same cos θ, the impedance and geometric factors mentioned above are identical and cancel out. But in computing the power transmission (below), these factors must be taken into account.
+The simplest way to obtain the power transmission coefficient (transmissivity, the ratio of transmitted power to incident power in the direction normal to the interface, i.e. the y direction) is to use R + T = 1 (conservation of energy). In this way we find
+
+for the s polarization, and
+
+for the p polarization.
+In the case of an interface between two lossless media (for which ϵ and μ are real and positive), one can obtain these results directly using the squared magnitudes of the amplitude transmission coefficients that we found earlier in equations (14) and (22). But, for given amplitude (as noted above), the component of the Poynting vector in the y direction is proportional to the geometric factor cos θ and inversely proportional to the wave impedance Z. Applying these corrections to each wave, we obtain two ratios multiplying the square of the amplitude transmission coefficient:
+
+for the s polarization, and
+
+for the p polarization. The last two equations apply only to lossless dielectrics, and only at incidence angles smaller than the critical angle (beyond which, of course, T = 0).
+For unpolarized light:
+
+  
+    
+      
+        T
+        =
+        
+          
+            1
+            2
+          
+        
+        (
+        
+          T
+          
+            s
+          
+        
+        +
+        
+          T
+          
+            p
+          
+        
+        )
+      
+    
+    {\displaystyle T={1 \over 2}(T_{s}+T_{p})}
+  
+
+  
+    
+      
+        R
+        =
+        
+          
+            1
+            2
+          
+        
+        (
+        
+          R
+          
+            s
+          
+        
+        +
+        
+          R
+          
+            p
+          
+        
+        )
+      
+    
+    {\displaystyle R={1 \over 2}(R_{s}+R_{p})}
+  
+
+where 
+  
+    
+      
+        R
+        +
+        T
+        =
+        1
+      
+    
+    {\displaystyle R+T=1}
+  
+.
+
+=== Equal refractive indices ===
+From equations (4) and (5), we see that two dissimilar media will have the same refractive index, but different admittances, if the ratio of their permeabilities is the inverse of the ratio of their permittivities. In that unusual situation we have θt = θi (that is, the transmitted ray is undeviated), so that the cosines in equations (13), (14), (21), (22), and (25) to (28) cancel out, and all the reflection and transmission ratios become independent of the angle of incidence; in other words, the ratios for normal incidence become applicable to all angles of incidence. When extended to spherical reflection or scattering, this results in the Kerker effect for Mie scattering.
+
+=== Non-magnetic media ===
+Since the Fresnel equations were developed for optics, they are usually given for non-magnetic materials. Dividing (4) by (5)) yields
+
+  
+    
+      
+        Y
+        =
+        
+          
+            n
+            
+              
+              c
+              μ
+              
+            
+          
+        
+        
+        .
+      
+    
+    {\displaystyle Y={\frac {n}{\,c\mu \,}}\,.}
+  
+
+For non-magnetic media we can substitute the vacuum permeability μ0 for μ, so that
+
+  
+    
+      
+        
+          Y
+          
+            1
+          
+        
+        =
+        
+          
+            
+              n
+              
+                1
+              
+            
+            
+              
+              c
+              
+                μ
+                
+                  0
+                
+              
+            
+          
+        
+         
+         
+        ;
+         
+         
+         
+        
+          Y
+          
+            2
+          
+        
+        =
+        
+          
+            
+              n
+              
+                2
+              
+            
+            
+              
+              c
+              
+                μ
+                
+                  0
+                
+              
+            
+          
+        
+        
+        ;
+      
+    
+    {\displaystyle Y_{1}={\frac {n_{1}}{\,c\mu _{0}}}~~;~~~Y_{2}={\frac {n_{2}}{\,c\mu _{0}}}\,;}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_equations-7.md b/data/en.wikipedia.org/wiki/Fresnel_equations-7.md
new file mode 100644
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fresnel_equations-7.md
@@ -0,0 +1,67 @@
+---
+title: "Fresnel equations"
+chunk: 8/8
+source: "https://en.wikipedia.org/wiki/Fresnel_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:05.464676+00:00"
+instance: "kb-cron"
+---
+
+that is, the admittances are simply proportional to the corresponding refractive indices. When we make these substitutions in equations (13) to (16) and equations (21) to (26), the factor cμ0 cancels out. For the amplitude coefficients we obtain:
+
+For the case of normal incidence these reduce to:
+
+The power reflection coefficients become:
+
+The power transmissions can then be found from T = 1 − R.
+
+=== Brewster's angle ===
+For equal permeabilities (e.g., non-magnetic media), if θi and θt are complementary, we can substitute sin θt for cos θi, and sin θi for cos θt, so that the numerator in equation (31) becomes n2‍sin θt − n1‍sin θi, which is zero (by Snell's law). Hence rp = 0  and only the s-polarized component is reflected. This is what happens at the Brewster angle. Substituting cos θi for sin θt in Snell's law, we readily obtain
+
+for Brewster's angle.
+
+=== Equal permittivities ===
+Although it is not encountered in practice, the equations can also apply to the case of two media with a common permittivity but different refractive indices due to different permeabilities. From equations (4) and (5), if ϵ is fixed instead of μ, then Y becomes inversely proportional to n, with the result that the subscripts 1 and 2 in equations (29) to (38) are interchanged (due to the additional step of multiplying the numerator and denominator by n1n2). Hence, in (29) and (31), the expressions for rs and rp in terms of refractive indices will be interchanged, so that Brewster's angle (39) will give rs = 0 instead of rp = 0, and any beam reflected at that angle will be p-polarized instead of s-polarized. Similarly, Fresnel's sine law will apply to the p polarization instead of the s polarization, and his tangent law to the s polarization instead of the p polarization.
+This switch of polarizations has an analog in the old mechanical theory of light waves (see § History, above). One could predict reflection coefficients that agreed with observation by supposing (like Fresnel) that different refractive indices were due to different densities and that the vibrations were normal to what was then called the plane of polarization, or by supposing (like MacCullagh and Neumann) that different refractive indices were due to different elasticities and that the vibrations were parallel to that plane. Thus the condition of equal permittivities and unequal permeabilities, although not realistic, is of some historical interest.
+
+== See also ==
+Jones calculus
+Polarization mixing
+Index-matching material
+Field and power quantities
+Fresnel rhomb, Fresnel's apparatus to produce circularly polarised light
+Reflection loss
+Specular reflection
+Schlick's approximation
+Snell's window
+X-ray reflectivity
+Plane of incidence
+Reflections of signals on conducting lines
+
+== Notes ==
+
+== References ==
+
+== Sources ==
+M. Born and E. Wolf, 1970, Principles of Optics, 4th Ed., Oxford: Pergamon Press.
+J.Z. Buchwald, 1989, The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century, University of Chicago Press, ISBN 0-226-07886-8.
+R.E. Collin, 1966, Foundations for Microwave Engineering, Tokyo: McGraw-Hill.
+O. Darrigol, 2012, A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford, ISBN 978-0-19-964437-7.
+A. Fresnel, 1866 (ed. H. de Senarmont, E. Verdet, and L. Fresnel), Oeuvres complètes d'Augustin Fresnel, Paris: Imprimerie Impériale (3 vols., 1866–70), vol. 1 (1866).
+Griffiths, David J. (2017). "Chapter 9.3: Electromagnetic Waves in Matter". Introduction to Electrodynamics (4th ed.). Cambridge University Press. ISBN 978-1-108-42041-9.
+E. Hecht, 1987, Optics, 2nd Ed., Addison Wesley, ISBN 0-201-11609-X.
+E. Hecht, 2002, Optics, 4th Ed., Addison Wesley, ISBN 0-321-18878-0.
+F.A. Jenkins and H.E. White, 1976, Fundamentals of Optics, 4th Ed., New York: McGraw-Hill, ISBN 0-07-032330-5.
+H. Lloyd, 1834, "Report on the progress and present state of physical optics", Report of the Fourth Meeting of the British Association for the Advancement of Science (held at Edinburgh in 1834), London: J. Murray, 1835, pp. 295–413.
+W. Whewell, 1857, History of the Inductive Sciences: From the Earliest to the Present Time, 3rd Ed., London: J.W. Parker & Son, vol. 2.
+E. T. Whittaker, 1910, A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century, London: Longmans, Green, & Co.
+
+== External links ==
+Fresnel Equations – Wolfram.
+Fresnel equations calculator
+FreeSnell – Free software computes the optical properties of multilayer materials.
+Thinfilm – Web interface for calculating optical properties of thin films and multilayer materials (reflection & transmission coefficients, ellipsometric parameters Psi & Delta).
+Simple web interface for calculating single-interface reflection and refraction angles and strengths.
+Reflection and transmittance for two dielectrics – Mathematica interactive webpage that shows the relations between index of refraction and reflection.
+A self-contained first-principles derivation of the transmission and reflection probabilities from a multilayer with complex indices of refraction.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_rhomb-0.md b/data/en.wikipedia.org/wiki/Fresnel_rhomb-0.md
new file mode 100644
index 000000000..b5a6e73b3
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+++ b/data/en.wikipedia.org/wiki/Fresnel_rhomb-0.md
@@ -0,0 +1,26 @@
+---
+title: "Fresnel rhomb"
+chunk: 1/5
+source: "https://en.wikipedia.org/wiki/Fresnel_rhomb"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:06.796995+00:00"
+instance: "kb-cron"
+---
+
+A Fresnel rhomb is an optical prism that introduces a 90° phase difference between two perpendicular components of polarization, by means of two total internal reflections. If the incident beam is linearly polarized at 45° to the plane of incidence and reflection, the emerging beam is circularly polarized, and vice versa. If the incident beam is linearly polarized at some other inclination, the emerging beam is elliptically polarized with one principal axis in the plane of reflection, and vice versa.
+The rhomb usually takes the form of a right parallelepiped, or in other words, a solid with six parallelogram faces (a square is to a cube as a parallelogram is to a parallelepiped). If the incident ray is perpendicular to one of the smaller rectangular faces, the angle of incidence and reflection at both of the longer faces is equal to the acute angle of the parallelogram. This angle is chosen so that each reflection introduces a phase difference of 45° between the components polarized parallel and perpendicular to the plane of reflection. For a given, sufficiently high refractive index, there are two angles meeting this criterion; for example, an index of 1.5 requires an angle of 50.2° or 53.3°.
+Conversely, if the angle of incidence and reflection is fixed, the phase difference introduced by the rhomb depends only on its refractive index, which typically varies only slightly over the visible spectrum. Thus the rhomb functions as if it were a wideband quarter-wave plate –  in contrast to a conventional birefringent (doubly-refractive) quarter-wave plate, whose phase difference is more sensitive to the frequency (color) of the light. The material of which the rhomb is made –  usually glass –  is specifically not birefringent.
+The Fresnel rhomb is named after its inventor, the French physicist Augustin-Jean Fresnel, who developed the device in stages between 1817 and 1823. During that time he deployed it in crucial experiments involving polarization, birefringence, and optical rotation, all of which contributed to the eventual acceptance of his transverse-wave theory of light.
+
+== Operation ==
+Incident electromagnetic waves (such as light) consist of transverse vibrations in the electric and magnetic fields; these are proportional to and at right angles to each other and may therefore be represented by (say) the electric field alone. When striking an interface, the electric field oscillations can be resolved into two perpendicular components, known as the s and p components, which are parallel to the surface and the plane of incidence, respectively; in other words, the s and p components are respectively square and parallel to the plane of incidence.
+Light passing through a Fresnel rhomb undergoes two total internal reflections at the same carefully chosen angle of incidence. After one such reflection, the p component is advanced by 1/8 of a cycle (45°; π/4 radians) relative to the s component. With two such reflections, a relative phase shift of 1/4 of a cycle (90°; π/2) is obtained. The word relative is critical: as the wavelength is very small compared with the dimensions of typical apparatus, the individual phase advances suffered by the s and p components are not readily observable, but the difference between them is easily observable through its effect on the state of polarization of the emerging light.
+If the incoming light is linearly polarized (plane-polarized), the s and p components are initially in phase; hence, after two reflections, "the p component is 90° ahead in phase", so that the polarization of the emerging light is elliptical with principal axes in the s and p directions (Fig. 1). Similarly, if the incoming light is elliptically polarized with axes in the s and p directions, the emerging light is linearly polarized.
+In the special case in which the incoming s and p components not only are in phase but also have equal magnitudes, the initial linear polarization is at 45° to the plane of incidence and reflection, and the final elliptical polarization is circular. If the circularly polarized light is inspected through an analyzer (second polarizer), it seems to have been completely "depolarized", because its observed brightness is independent of the orientation of the analyzer. But if this light is processed by a second rhomb, it is repolarized at 45° to the plane of reflection in that rhomb –  a property not shared by ordinary 
+(unpolarized) light.
+
+== Related devices ==
+For a general input polarization, the net effect of the rhomb is identical to that of a birefringent (doubly-refractive) quarter-wave plate, except that a simple birefringent plate gives the desired 90° separation at a single frequency, and not (even approximately) at widely different frequencies, whereas the phase separation given by the rhomb depends on its refractive index, which varies only slightly over a wide frequency range (see Dispersion). Two Fresnel rhombs can be used in tandem (usually cemented to avoid reflections at their interface) to achieve the function of a half-wave plate. The tandem arrangement, unlike a single Fresnel rhomb, has the additional feature that the emerging beam can be collinear with the original incident beam.
+
+== Theory ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Fresnel_rhomb-1.md b/data/en.wikipedia.org/wiki/Fresnel_rhomb-1.md
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index 000000000..61931aa6b
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Fresnel_rhomb-1.md
@@ -0,0 +1,60 @@
+---
+title: "Fresnel rhomb"
+chunk: 2/5
+source: "https://en.wikipedia.org/wiki/Fresnel_rhomb"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:06.796995+00:00"
+instance: "kb-cron"
+---
+
+In order to specify the phase shift on reflection, we must choose a sign convention for the reflection coefficient, which is the ratio of the reflected amplitude to the incident amplitude. In the case of the s components, for which the incident and reflected vibrations are both normal (perpendicular) to the plane of incidence, the obvious choice is to say that a positive reflection coefficient, corresponding to zero phase shift, is one for which the incident and reflected fields have the same direction (no reversal; no "inversion"). In the case of the p components, this article adopts the convention that a positive reflection coefficient is one for which the incident and reflected fields are inclined towards the same medium. We may then cover both cases by saying that a positive reflection coefficient is one for which the direction of the field vector normal to the plane of incidence (the electric vector for the s polarization, or the magnetic vector for the p polarization) is unchanged by the reflection. (But the reader should be warned that some authors use a different convention for the p components, with the result that the stated phase shift differs by 180° from the value given here.)
+With the chosen sign convention, the phase advances on total internal reflection, for the s and p components, are respectively given by
+
+and
+
+where θi is the angle of incidence, and n is the refractive index of the internal (optically denser) medium relative to the external (optically rarer) medium. (Some authors, however, use the reciprocal refractive index, so that their expressions for the phase shifts look different from the above.)
+
+The phase advance of the p component relative to the s component is then given by
+
+  
+    
+      
+        δ
+        =
+        
+          δ
+          
+            p
+            
+          
+        
+        −
+        
+          δ
+          
+            s
+          
+        
+        .
+      
+    
+    {\displaystyle \delta =\delta _{p\!}-\delta _{s}.}
+  
+
+This is plotted in black in Fig. 2, for angles of incidence exceeding the critical angle, for three values of the refractive index. It can be seen that a refractive index of 1.45 is not enough to give a 45° phase difference, whereas a refractive index of 1.5 is enough (by a slim margin) to give a 45° phase difference at two angles of incidence: about 50.2° and 53.3°.
+For θi greater than the critical angle, the phase shifts on total reflection are deduced from complex values of the reflection coefficients. For completeness, Fig. 2 also shows the phase shifts on partial reflection, for θi less than the critical angle. In the latter case, the reflection coefficients for the s and p components are real, and are conveniently expressed by Fresnel's sine law
+
+and Fresnel's tangent law
+
+where θi is the angle of incidence and θt is the angle of refraction (with subscript t for transmitted), and the sign of the latter result is a function of the convention described above. (We can now see a disadvantage of that convention, namely that the two coefficients have opposite signs as we approach normal incidence; the corresponding advantage is that they have the same signs at grazing incidence.)
+By Fresnel's sine law, rs is positive for all angles of incidence with a transmitted ray (since θt > θi for dense-to-rare incidence), giving a phase shift δs of zero. But, by his tangent law, rp is negative for small angles (that is, near normal incidence), and changes sign at Brewster's angle, where  θi and θt are complementary. Thus the phase shift δp is 180° for small θi but switches to 0° at Brewster's angle. Combining the complementarity with Snell's law yields θi = arctan(1/n) as Brewster's angle for dense-to-rare incidence.
+That completes the information needed to plot δs and δp for all angles of incidence in Fig. 2, in which δp is in red and δs in blue. On the angle-of-incidence scale (horizontal axis), Brewster's angle is where δp (red) falls from 180° to 0°, and the critical angle is where both δp and δs (red and blue) start to rise again. To the left of the critical angle is the region of partial reflection; here both reflection coefficients are real (phase 0° or 180°) with magnitudes less than 1. To the right of the critical angle is the region of total reflection; there both reflection coefficients are complex with magnitudes equal to 1.
+In Fig. 2, the phase difference δ is computed by a final subtraction; but there are other ways of expressing it. Fresnel himself, in 1823, gave a formula for cos δ. Born and Wolf (1970, p. 50) derive an expression for tan(δ/2), and find its maximum analytically.
+(For derivations of Eqs. (1) to (4) above, see Total internal reflection, especially § Derivation of evanescent wave and § Phase shifts.)
+
+== History ==
+
+=== Background ===
+Augustin-Jean Fresnel came to the study of total internal reflection through his research on polarization. In 1811, François Arago discovered that polarized light was apparently "depolarized" in an orientation-dependent and color-dependent manner when passed through a slice of birefringent crystal: the emerging light showed colors when viewed through an analyzer (second polarizer). Chromatic polarization, as this phenomenon came to be called, was more thoroughly investigated in 1812 by Jean-Baptiste Biot. In 1813, Biot established that one case studied by Arago, namely quartz cut perpendicular to its optic axis, was actually a gradual rotation of the plane of polarization with distance. He went on to discover that certain liquids, including turpentine (térébenthine), shared this property (see Optical rotation).
+In 1816, Fresnel offered his first attempt at a wave-based theory of chromatic polarization. Without (yet) explicitly invoking transverse waves, this theory treated the light as consisting of two perpendicularly polarized components.
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+---
+title: "Fresnel rhomb"
+chunk: 3/5
+source: "https://en.wikipedia.org/wiki/Fresnel_rhomb"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:06.796995+00:00"
+instance: "kb-cron"
+---
+
+=== Stage 1: Coupled prisms (1817) ===
+In 1817, Fresnel noticed that plane-polarized light seemed to be partly depolarized by total internal reflection, if initially polarized at an acute angle to the plane of incidence.  By including total internal reflection in a chromatic-polarization experiment, he found that the apparently depolarized light was a mixture of components polarized parallel and perpendicular to the plane of incidence, and that the total reflection introduced a phase difference between them. Choosing an appropriate angle of incidence (not yet exactly specified) gave a phase difference of 1/8 of a cycle. Two such reflections from the "parallel faces" of "two coupled prisms" gave a phase difference of 1/4 of a cycle. In that case, if the light was initially polarized at 45° to the plane of incidence and reflection, it appeared to be completely depolarized after the two reflections. These findings were reported in a memoir submitted and read to the French Academy of Sciences in November 1817.
+In a "supplement" dated January 1818, Fresnel reported that optical rotation could be emulated by passing the polarized light through a pair of "coupled prisms", followed by an ordinary birefringent lamina sliced parallel to its axis, with the axis at 45° to the plane of reflection of the prisms, followed by a second pair of prisms at 90° to the first. This was the first experimental evidence of a mathematical relation between optical rotation and birefringence.
+
+=== Stage 2: Parallelepiped (1818) ===
+The memoir of November 1817  bears the undated marginal note: "I have since replaced these two coupled prisms by a parallelepiped in glass." A dated reference to the parallelepiped form – the form that we would now recognize as a Fresnel rhomb – is found in a memoir which Fresnel read to the Academy on 30 March 1818, and which was subsequently lost until 1846. In that memoir, Fresnel reported that if polarized light was fully "depolarized" by a rhomb, its properties were not further modified by a subsequent passage through an optically rotating medium, whether that medium was a crystal or a liquid or even his own emulator; for example, the light retained its ability to be repolarized by a second rhomb.
+
+=== Interlude (1818–1822) ===
+
+As an engineer of bridges and roads, and as a proponent of the wave theory of light, Fresnel was still an outsider to the physics establishment when he presented his parallelepiped in March 1818. But he was increasingly difficult to ignore. In April 1818 he claimed priority for the Fresnel integrals. In July he submitted the great memoir on diffraction that immortalized his name in elementary physics textbooks. In 1819 came the announcement of the prize for the memoir on diffraction, the publication of the Fresnel–Arago laws, and the presentation of Fresnel's proposal to install "stepped lenses" in lighthouses.
+In 1821, Fresnel derived formulae equivalent to his sine and tangent laws (Eqs. (3) and (4), above) by modeling light waves as transverse elastic waves with vibrations perpendicular to what had previously been called the plane of polarization. Using old experimental data, he promptly confirmed that the equations correctly predicted the direction of polarization of the reflected beam when the incident beam was polarized at 45° to the plane of incidence, for light incident from air onto glass or water. The experimental confirmation was reported in a "postscript" to the work in which Fresnel expounded his mature theory of chromatic polarization, introducing transverse waves. Details of the derivation were given later, in a memoir read to the academy in January 1823. The derivation combined conservation of energy with continuity of the tangential vibration at the interface, but failed to allow for any condition on the normal component of vibration. (The first derivation from electromagnetic principles was given by Hendrik Lorentz in 1875.)
+Meanwhile, by April 1822, Fresnel accounted for the directions and polarizations of the refracted rays in birefringent crystals of the biaxial class –  a feat that won the admiration of Pierre-Simon Laplace.
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+---
+title: "Fresnel rhomb"
+chunk: 4/5
+source: "https://en.wikipedia.org/wiki/Fresnel_rhomb"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:06.796995+00:00"
+instance: "kb-cron"
+---
+
+=== Use in experiments (1822–1823) ===
+In a memoir on stress-induced birefringence (now called photoelasticity) read in September 1822, Fresnel reported an experiment involving a row of glass prisms with their refracting angles in alternating directions, and with two half-prisms at the ends, making the whole assembly rectangular. When the prisms facing the same way were compressed in a vise, objects viewed through the length of the assembly appeared double. At the end of this memoir he proposed a variation of the experiment, involving a Fresnel rhomb, for the purpose of verifying that optical rotation is a form of birefringence: he predicted that if the compressed glass prisms were replaced by (unstressed) monocrystalline quartz prisms with the same direction of optical rotation and with their optic axes aligned along the row, an object seen by looking along the common optic axis would give two images, which would seem unpolarized if viewed through an analyzer alone; but if viewed through a Fresnel rhomb, they would be polarized at ±45° to the plane of reflection.
+Confirmation of this prediction was reported in a memoir read in December 1822, in which Fresnel coined the terms linear polarization, circular polarization, and elliptical polarization. In the experiment, the Fresnel rhomb revealed that the two images were circularly polarized in opposite directions, and the separation of the images showed that the different (circular) polarizations propagated at different speeds. To obtain a visible separation, Fresnel needed only one 14°–152°–14° prism and two half-prisms. He found, however, that the separation was improved if the glass half-prisms were replaced by quartz half-prisms whose direction of optical rotation was opposite to that of the 14°–152°–14° prism.
+Thus, although we now think of the Fresnel rhomb primarily as a device for converting between linear and circular polarization, it was not until the memoir of December 1822 that Fresnel himself could describe it in those terms.
+In the same memoir, Fresnel explained optical rotation by noting that linearly-polarized light could be resolved into two circularly-polarized components rotating in opposite directions. If these components propagated at slightly different speeds (as he had demonstrated for quartz), then the phase difference between them –  and therefore the orientation of their linearly-polarized resultant –  would vary continuously with distance.
+
+=== Stage 3: Calculation of angles (1823) ===
+The concept of circular polarization was useful in the memoir of January 1823, containing the detailed derivations of the sine and tangent laws: in that same memoir, Fresnel found that for angles of incidence greater than the critical angle, the resulting reflection coefficients were complex with unit magnitude. Noting that the magnitude represented the amplitude ratio as usual, he guessed that the argument represented the phase shift, and verified the hypothesis by experiment. The verification involved
+
+calculating the angle of incidence that would introduce a total phase difference of 90° between the s and p components, for various numbers of total internal reflections at that angle (generally there were two solutions),
+subjecting light to that number of total internal reflections at that angle of incidence, with an initial linear polarization at 45° to the plane of incidence, and
+checking that the final polarization was circular.
+This procedure was necessary because, with the technology of the time, one could not measure the s and p phase-shifts directly, and one could not measure an arbitrary degree of ellipticality of polarization, such as might be caused by the difference between the phase shifts. But one could verify that the polarization was circular, because the brightness of the light was then insensitive to the orientation of the analyzer.
+For glass with a refractive index of 1.51, Fresnel calculated that a 45° phase difference between the two reflection coefficients (hence a 90° difference after two reflections) required an angle of incidence of 48°37' or 54°37'. He cut a rhomb to the latter angle and found that it performed as expected. Thus the specification of the Fresnel rhomb was completed.
+Similarly, Fresnel calculated and verified the angle of incidence that would give a 90° phase difference after three reflections at the same angle, and four reflections at the same angle. In each case there were two solutions, and in each case he reported that the larger angle of incidence gave an accurate circular polarization (for an initial linear polarization at 45° to the plane of reflection). For the case of three reflections he also tested the smaller angle, but found that it gave some coloration due to the proximity of the critical angle and its slight dependence on wavelength. (Compare Fig. 2 above, which shows that the phase difference δ is more sensitive to the refractive index for smaller angles of incidence.)
+For added confidence, Fresnel predicted and verified that four total internal reflections at 68°27' would give an accurate circular polarization if two of the reflections had water as the external medium while the other two had air, but not if the reflecting surfaces were all wet or all dry.
+
+=== Significance ===
+In summary, the invention of the rhomb was not a single event in Fresnel's career, but a process spanning a large part of it. Arguably, the calculation of the phase shift on total internal reflection marked not only the completion of his theory of the rhomb, but also the essential completion of his reconstruction of physical optics on the transverse-wave hypothesis (see Augustin-Jean Fresnel).
+The calculation of the phase shift was also a landmark in the application of complex numbers. Leonhard Euler had pioneered the use of complex exponents in solutions of ordinary differential equations, on the understanding that the real part of the solution was the relevant part. But Fresnel's treatment of total internal reflection seems to have been the first occasion on which a physical meaning was attached to the argument of a complex number. According to Salomon Bochner,
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+---
+title: "Fresnel rhomb"
+chunk: 5/5
+source: "https://en.wikipedia.org/wiki/Fresnel_rhomb"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:06.796995+00:00"
+instance: "kb-cron"
+---
+
+We think that this was the first time that complex numbers or any other mathematical objects which are "nothing-but-symbols" were put into the center of an interpretative context of "reality", and it is an extraordinary fact that this interpretation, although the first of its kind, stood up so well to verification by experiment and to the later "maxwellization" of the entire theory. In very loose terms one can say that this was the first time in which "nature" was abstracted from "pure" mathematics, that is from a mathematics which had not been previously abstracted from nature itself.
+
+== See also ==
+
+== Notes ==
+
+== References ==
+
+== Bibliography ==
+S. Bochner (June 1963), "The significance of some basic mathematical conceptions for physics", Isis, vol. 54, no. 2, pp. 179–205; jstor.org/stable/228537.
+M. Born and E. Wolf, 1970, Principles of Optics, 4th ed., Oxford: Pergamon Press.
+J. Z. Buchwald, 1989, The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century, University of Chicago Press, ISBN 0-226-07886-8.
+O. Darrigol, 2012, A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford, ISBN 978-0-19-964437-7.
+A. Fresnel, 1866 (ed. H. de Senarmont, E. Verdet, and L. Fresnel), Oeuvres complètes d'Augustin Fresnel, Paris: Imprimerie Impériale (3 vols., 1866–1870), vol. 1 (1866) (in French).
+E. Hecht, 2002, Optics, 4th ed., Addison Wesley, ISBN 0-321-18878-0.
+F. A. Jenkins and H. E. White, 1976, Fundamentals of Optics, 4th ed., New York: McGraw-Hill, ISBN 0-07-032330-5.
+N. Kipnis, 1991, History of the Principle of Interference of Light, Basel: Birkhäuser, ISBN 978-3-0348-9717-4.
+H. Lloyd, 1834, "Report on the progress and present state of physical optics", Report of the Fourth Meeting of the British Association for the Advancement of Science (held at Edinburgh in 1834), London: J. Murray, 1835, pp. 295–413.
+J. A. Stratton, 1941, Electromagnetic Theory, New York: McGraw-Hill.
+W. Whewell, 1857, History of the Inductive Sciences: From the Earliest to the Present Time, 3rd ed., London: J. W. Parker & Son, vol. 2.
+E. T. Whittaker, 1910, A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century, London: Longmans, Green, & Co.
+
+== External links ==
+For some photographs of (antique) Fresnel rhombs, see T. B. Greenslade, Jr., "Fresnel's rhomb", Instruments for Natural Philosophy, Kenyon College (Gambier, OH), accessed 4 March 2018; archived 28 August 2017. (Erratum, confirmed by the author: The words "at Brewster's angle" should be deleted.)
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diff --git a/data/en.wikipedia.org/wiki/Golden_age_of_cosmology-0.md b/data/en.wikipedia.org/wiki/Golden_age_of_cosmology-0.md
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diff --git a/data/en.wikipedia.org/wiki/Golden_age_of_physics-0.md b/data/en.wikipedia.org/wiki/Golden_age_of_physics-0.md
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+---
+title: "Golden age of physics"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Golden_age_of_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:11.940874+00:00"
+instance: "kb-cron"
+---
+
+A golden age of physics appears to have been delineated for certain periods of progress in the physics sciences, and this includes the previous and current developments of cosmology and astronomy. Each "golden age" introduces significant advancements in theoretical and experimental methods. Discernible time periods marking a "golden age" of advancements are, for example, the development of mechanics under Galileo (1564–1642) and Isaac Newton (1642–1727). Another small epoch seen as a golden age is the unification of electricity, magnetism, and optics because of 19th century notables, including Michael Faraday, James Clerk Maxwell, and others.
+Significant advancements in methods of investigation were introduced for celestial mechanics, which includes realizing a universal gravitational force, with the introduction of the telescope. Basing mechanics on experimental results was possible with the development of devices that could measure time, and tools for measuring distance. The advances in electromagnetism in the 19th century enamored physicists, as another golden age closed, and there was a reluctance to perceive further advancement. Hence, the progress of one era, termed a "golden age" has appeared to mark the completion of physics as a science. Yet, this perception has turned out to be erroneous. For example, around 1980, Stephen Hawking predicted the end of theoretical physics within 20 years. Around 2001, he amended his prediction to twenty years more from that year. Steven Weinberg predicts a unified physics by 2050. Tadeusz Lulek, Barbara Lulek, and A. Wal – the authors of a 2001 book – believed themselves to be at the beginning of a new "golden age of physics".
+Paul Davies notes that whilst "many elderly scientists" may regard the first 30 years of the 20th century as a golden age of physics, historians may well, instead, regard it to be the dawning days of "the New Physics".
+When Paul Dirac received the J. Robert Oppenheimer Memorial Prize in 1969, said
+
+I can thank the fact that I was born at just the right time. A few years older or younger, I would have missed the opportunity... One might call the period from 1925 onward for a few years the Golden Age of Physics when our basic ideas were developing very rapidly and there was plenty of work for everyone to do.
+The golden age of physics was the 19th century. According to Emilio Segrè, in Italy it came to an end in the 18th century, after the time of Alessandro Volta.  He reported in his autobiography that Enrico Fermi felt that it was coming to an end in 1933.  A golden age of physics began with the simultaneous discovery of the principle of the conservation of energy in the mid-19th century.  A golden age of physics was the years 1925 to 1927.  The golden age of nonlinear physics was the period from 1950 to 1970, encompassing the Fermi–Pasta–Ulam–Tsingou problem and others.  This followed the golden age of nuclear physics, which had spanned the two decades from the mid-1930s to the mid-1950s.  A golden age of physics started at the end of the 1920s.
+The golden age of physics cabinets was the 18th century, with the rise of such lecturer-demonstrators as John Keill, John Theophilus Desaguliers, and William Whiston, who all invented new physics apparatus for their lectures.
+
+
+== See also ==
+Golden age of general relativity
+Golden age of cosmology
+Golden age (metaphor)
+
+
+== References ==
+
+
+=== Reference bibliography ===
+Amaldi, Edoardo (1998). "The Case of Physics". In Giovanni Battimelli; Giovanni Paoloni (eds.). 20th century physics: essays and recollections : a selection of historical writings. World Scientific. ISBN 978-981-02-2369-4.
+Brenni, Paolo (2002). "Jean Antoine Nollet and Physics Instruments". In Lewis Pyenson; Jean-François Gauvin (eds.). The art of teaching physics: the eighteenth-century demonstration apparatus of Jean Antoine Nollet. Les éditions du Septentrion. ISBN 978-2-89448-320-6.
+Cook, Norman D. (2006). Models of the atomic nucleus: with interactive software. Vol. 1. Birkhäuser. ISBN 978-3-540-28569-4.
+Davies, Paul (1992). The new physics. Cambridge University Press. ISBN 978-0-521-43831-5.
+Mitra, Asoke Nath (2009). India in the world of physics: then and now. History of science, philosophy, and culture in Indian civilization: Theories of natural and life sciences. Vol. 1. Pearson Education India. ISBN 978-81-317-1579-6.
+Prigogine, Ilya; Stengers, Isabelle (1984). Order out of chaos: man's new dialogue with nature. Vol. 2. Bantam Books. ISBN 978-0-553-34082-2.
+Sandbothe, Mike (2001). The temporalization of time: basic tendencies in modern debate on time in philosophy and science. Rowman & Littlefield. ISBN 978-0-7425-1290-0.
+Segrè, Emilio (1993). A mind always in motion: the autobiography of Emilio Segrè. University of California Press. ISBN 978-0-520-07627-3.
+Van Name, F. W. (1962). "The Golden Age of Physics". Modern physics (2nd ed.). Prentice-Hall.
+Wilhelm, I (2008). "The Ethics of Research: The Responsibility of the Researcher". In S. Gunn; A. William; Michele Masellis (eds.). Concepts and Practice of Humanitarian Medicine. Springer. ISBN 978-0-387-72263-4.
+Lulek, Tadeusz; Lulek, Barbara; Wal, A. (May 2001). Symmetry and Structural Properties of Condensed Matter, Proceedings of the Sixth's International School of Theoretical Physics. World Scientific Publishing Company, Inc. pp. 13 to 23 (Chap. 1). ISBN 978-981-02-4569-6. Download available from Google Books.
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diff --git a/data/en.wikipedia.org/wiki/High_Voltage_Engineering_Corporation-0.md b/data/en.wikipedia.org/wiki/High_Voltage_Engineering_Corporation-0.md
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+---
+title: "High Voltage Engineering Corporation"
+chunk: 1/5
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+tags: "science, encyclopedia"
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+instance: "kb-cron"
+---
+
+High Voltage Engineering Corporation (HVEC) was an American manufacturer of particle accelerators and one of the first venture capital-backed startups.
+HVEC originated at MIT, where physicist Robert Van de Graaff invented a high-voltage electrostatic particle accelerator and his colleague John Trump miniaturized it for cancer radiotherapy. In 1946, Trump organized a company to manufacture these machines, recruiting Van de Graaff and Denis Robinson as co-founders. Production began in a Cambridge automobile garage.
+The company's early medical devices gave way to large research accelerators after Sputnik-era government funding transformed the market for scientific instruments. For two decades, HVEC accelerators were the dominant platform for nuclear physics; in the 1970s, nearly 70 percent of experimental papers relied on HVEC machines. The company built 471 accelerators between 1946 and 1981. They were installed at hospitals, universities, and national laboratories in 30 countries, and some remain in active research use.
+Using these instruments, HVEC subsidiaries introduced new uses of accelerator beams. Ion Physics Corporation demonstrated that ion implantation could precisely control transistor characteristics, a technique now essential to integrated circuit fabrication. Electronized Chemicals Corporation developed methods to crosslink plastics with electron beams, producing the heat-shrink tubing now ubiquitous in electrical wiring.
+HVEC was one of the first two startups backed by the American Research & Development Corporation, the first modern venture capital fund. By 1960, it was the fund's most successful investment, and its returns helped demonstrate the viability of venture investing in start-ups. After federal science funding contracted in the late 1960s, HVEC ceased accelerator production and reorganized as a conglomerate. The company was taken private in 1988 and filed for bankruptcy in 2005.
+
+== History ==
+
+=== Founding and early development ===
+
+High Voltage Engineering Corporation accelerators originated with the electrostatic generator designed by MIT physicist Robert J. Van de Graaff. In an effort to split the atom, Van de Graaff devised a electrostatic method to accelerate and direct charged particles at high voltages. While constructing a high-voltage prototype accelerator in the early 1930s, Van de Graaff patented several technologies that would form part of the future company's technology base.
+MIT professor John G. Trump, an apprentice of Van de Graaff, focused on making the generators useful for cancer radiotherapy. In the 1930s, few hospitals could afford radium sources, available x-ray sources were insufficiently powerful, and both methods damaged healthy tissues. Trump proposed that the unlimited, controllable beam output of Van de Graaff devices could make treatment affordable and safer. He built a series of compact "supervoltage" (>1-megavolt) x-ray generators for local cancer hospitals and secured further patents for the smaller generators.
+Returning from his World War II leave, Trump received requests from several British hospitals for new cancer generators and decided a company could better fulfill further orders. He recruited Van de Graaff to serve as co-founder and chief scientist. Neither professor wished to leave MIT, so Trump brought in British physicist Denis M. Robinson as a third co-founder and president. In 1946, Trump approached his wartime colleague, MIT President Karl Compton, about supporting the venture. Compton had recently founded the American Research and Development Corporation (ARD) to spur the formation of new post-war industries. He introduced the founders to ARD's president, Georges Doriot.
+Doriot predicted the cancer treatment machines would be a commercial failure. Nevertheless, he perceived HVEC's leaders to be technically capable, and Compton persuaded him that ARD should have a startup with clear human benefits. Among more than 400 applications, Doriot selected the firm among ARD's first three investments. He offered the founders $200,000 in initial capitalization, leaving half the equity to them and their staff consultants. Compton arranged for HVEC to exclusively license MIT's Van de Graaff and Trump patents. Both Compton and Doriot served on the new company's board.
+
+=== Supervoltage cancer therapy ===
+Working from an auto garage near Harvard Square, HVEC began building Trump's gas-insulated Van de Graaff generators for hospitals and manufacturers. In 1947, the first orders came from several British hospitals for HVEC's compact 2-megavolt machines. The company was among the first to make artificial radiation sources commercially available for cancer treatment.
+After three years, HVEC had delivered 17 particle accelerators, employed 140 people, and negotiated $2 million in sales (equivalent to $27.1 million in 2025), eclipsing its competitors' products and undercutting them on price. Nevertheless, the company faced severe financial difficulties in its early years. On several occasions, technical problems brought HVEC to within days of exhausting both money and credit.
+By the mid-1950s, successor technologies like cobalt-60 machines built by General Electric began dominating hospital orders, offering simpler operation and lower maintenance costs. Although HVEC remained in the medical market until 1969, the company increasingly focused on redesigning its generators for research and industrial applications.
+
+=== Pivot to scientific instruments ===
+ HVEC had originally built products for clients in cancer therapy and industrial radiography, but its machines proved valuable for basic research. The company's proximity to MIT research gave it unique advantages in understanding accelerator requirements. Van de Graaff, Trump, and fellow board member William Buechner regularly consulted with physicists pushing the boundaries of nuclear structure studies, translating experimental needs into engineering specifications.
+In 1949, Brookhaven National Laboratory commissioned HVEC to build a 4 MeV Van de Graaff particle injector for its planned high-energy Cosmotron accelerator. When completed in 1953, the Cosmotron became the first accelerator to exceed billion-electronvolt potentials. HVEC's standard 2 MV accelerators also found nuclear science customers, including the Naval Research Laboratory and European universities.
+In 1951, HVEC adopted a Trump-designed MIT accelerator as a research accelerator prototype. This single-stage "CN" model was the first mass-produced research accelerator. CN machines operated at voltages up to 6.5 megavolts and established HVEC's reputation for reliability in nuclear research applications. In 1954, Canada's Chalk River Laboratories asked HVEC to modify the CN into higher-voltage tandem accelerator, yielding a highly profitable product line that sustained the company for fifteen years.
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+---
+title: "High Voltage Engineering Corporation"
+chunk: 2/5
+source: "https://en.wikipedia.org/wiki/High_Voltage_Engineering_Corporation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:14.539653+00:00"
+instance: "kb-cron"
+---
+
+In the push for large research accelerators, HVEC outgrew the space available in its Cambridge auto garage. The company opened a production plant on Route 128 in Burlington, Massachusetts in 1957. At the recommendation of board member Doriot, the company also opened a Dutch subsidiary, High Voltage Engineering Europa, to supply accelerators in the European common market.
+Western reaction to the 1957 launch of Sputnik transformed the commercial opportunities for nuclear instrumentation. Laboratories had typically built their own accelerators from scratch. After Sputnik, the Atomic Energy Commission and National Science Foundation generously funded university and national laboratory purchases of research particle accelerators. HVEC's reliable, manufactured machines became the preferred instrument. Over fifteen years, HVEC sold 55 tandem accelerators to research laboratories in seven countries, selling each for $1–3 million. By the mid-1970s, nearly 70% of papers in experimental nuclear physics relied on data from HVEC accelerators.
+HVEC entered the 1960s as the nation's leading manufacturer of particle accelerators and was the single best investment ARD had made. Annual sales climbed from $1 million in 1954 to $17 million in 1962. At the time of its public listing on the New York Stock Exchange in 1963, HVEC was more than 40% of ARD's portfolio assets, having grown ARD's original $0.2M investment to $13.2 million.
+
+=== The Transuranium bet ===
+
+Already chief scientist, Van de Graaff joined HVEC full-time in 1960. He worked with colleagues to introduce the industrial core transformer. Focused on scientific hypothesis at the frontier of the field, he championed development of the company's most ambitious accelerator. Theoretical models predicted an "island of stability" of superheavy elements—heavy atoms that would resist rapid radioactive decay despite lying beyond uranium on the periodic table. Van de Graaff believed that stable superheavy elements could provide nuclear fuel for long-distance space missions or enable compact nuclear weapons, making superheavy ion synthesis the top priority for accelerator research.
+The proposed 20-megavolt Transuranium Accelerator (XTU) pushed HVEC accelerators towards this frontier. HVEC invested more than $4.6 million in two XTU prototypes (equivalent to $44.4 million in 2025). Anticipating that laboratories would compete to acquire machines capable of historic discoveries, leadership adopted a "build first and seek customers later" approach.
+During the XTU's construction in 1967–68, federal support for basic nuclear physics declined sharply. The Vietnam War and Great Society programs drew resources away from fundamental research. Simultaneously, the discovery of sub-atomic quarks put the high-energy frontier of physics research beyond the reach of Van de Graaff accelerators. By the time the XTU passed preliminary tests the following year, the U.S. Atomic Energy Commission had said it would not fund purchases.  One month later, HVEC announced it was mothballing the XTU and closing the Van de Graaff Research Laboratory in Burlington.
+The market failure of the XTU coincided with new competitive pressures. Operational difficulties with HVEC's Emperor tandems further damaged the company's competitive position. Laboratories reported technical problems with the Emperor requiring costly component replacements. In 1965, fellow physicist and former HVEC consultant Ray Herb founded the National Electrostatics Corporation. The company's durable Pelletron charging technology became the favored platform for federally-funded accelerator research. HVEC sold its final two Emperor models to French national laboratories in 1973.
+
+=== Diversification and decline ===
+The ensuing financial crisis prompted a major strategic transition. In 1970, HVEC's losses represented 31 percent of total stockholder investment. The company laid off 100 employees and suspended many research programs, citing insufficient federal funding for basic physics research. That year also marked a leadership transition: Pascal Levesque, head of the profitable HVEC subsidiary Electronized Chemicals Corporation, became president and chief executive, while departing president Denis Robinson assumed the chairmanship held by Trump.
+Under new management, HVEC diversified into industrial applications of its accelerator technologies. By 1972, the company had reorganized as a miniconglomerate with more than ten subsidiaries manufacturing plastics, power equipment, and radiation processing systems—products enabled by particle accelerators rather than particle accelerators themselves. The diversification strategy yielded several commercially successful products. Electronized Chemicals Corporation's heat-shrink tubing, made by electron-beam crosslinking of polyethylene, became ubiquitous in electrical wiring. The technology enabled modern wire harnesses in automobiles and aircraft, where compact, reliable insulation was essential. Ion Physics Corporation introduced radiation-based ion implantation, enabling precise control of transistor characteristics in integrated circuits. HVEC closed Ion Physics in 1971, but became standard practice throughout the global semiconductor industry by the late 1970s. While research accelerators had once generated 70 percent of sales, industrial products now accounted for 80 percent.
+Despite the strategic pivot, HVEC struggled to achieve sustained profitability. Its subsidiaries faced intense competition from larger conglomerates. In 1981, HVEC divested from its accelerator manufacturing business. Two years later, it sold its Burlington manufacturing plant. The company refocused on smaller industrial products including specialty plastics, wire, industrial instruments, and electrical connectors.  Through the 1980s, HVEC progressively sold these product lines to other manufacturing conglomerates.
+In 1988, private equity firm Hyde Park Partners bid to take HVEC private at roughly twice its prevailing share price. Though Levesque resisted, shareholders accepted the offer in 1989. Hyde Park dismissed existing management, sold remaining real estate, and relocated the headquarters to Charlestown, Massachusetts. The company filed for bankruptcy in 2005. Since 2019, corporate remnants have been held by Oak Point Partners.
+
+=== Venture capital legacy ===
+HVEC was among the first three investments of ARD, the first modern venture capital fund. By 1960, it was ARD's largest and most successful asset, having grown the original $200,000 investment to $13.2 million. These returns sustained ARD through its early years and enabled its 1957 investment in Digital Equipment Corporation. The latter's eventual $355 million return established the now-standard model where exceptional returns from a single investment justify a venture fund's diversified portfolio of high-risk bets.
+The company also embodied ARD's innovative methods of investing: active participation in management, selection for scientific talent, and focus on technology-intensive industries where technical barriers provided durable profitability. Barron's described HVEC as "an ideal example of the way [ARD] likes to work."
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+---
+title: "High Voltage Engineering Corporation"
+chunk: 3/5
+source: "https://en.wikipedia.org/wiki/High_Voltage_Engineering_Corporation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:14.539653+00:00"
+instance: "kb-cron"
+---
+
+== Technology ==
+HVEC manufactured approximately 471 particle accelerators between 1946 and 1981. Its former European subsidiary, High Voltage Engineering Europa, produced another 93 between 1958 and 2005. Over 25 years, the company's Van de Graaff product lines evolved from 2.5-metre (8.2 ft) compact medical X-ray generators to 24.5-metre (80 ft) tandem accelerators for nuclear physics research. HVEC also developed the insulating core transformer, a new high-voltage direct current generator that found applications in industrial radiation processing. These products enabled commercial development of electron-beam sterilization, radiation crosslinking of polymers, and ion implantation for semiconductor manufacturing.
+
+=== Medical equipment ===
+
+HVEC's first product line targeted cancer treatment, an application that demonstrated the practical value of controlled particle acceleration for medicine. Between 1948 and 1969, the company manufactured compact 2-megavolt electron accelerators designed for hospital radiotherapy departments. These 8-foot-long generators could be operated by technicians and nurses, making radiation therapy accessible beyond major research hospitals. During their production run, 35 U.S. hospitals and eight hospitals abroad installed the machines for cancer treatment.
+The generators addressed significant limitations in available cancer treatments. Traditional radiotherapy relied on radium sources, which were expensive, scarce, and produced uncontrolled radiation that damaged healthy tissue surrounding tumors. Low-voltage (0.25 MV) x-ray devices were available, but lacked sufficient penetration to treat deep tumors and caused violent skin reactions. HVEC's 1- and 2-MV Van de Graaff accelerators generated artificial X-rays that could be precisely aimed and modulated, allowing physicians to target deep-seated tumors while minimizing exposure to surrounding organs. The beam energy could be adjusted to match tumor depth, and therapy could be spread across multiple sessions to reduce side effects.
+HVEC also supported medical research. Several HVEC machines were used in joint research programs between the Lahey Clinic and Trump's MIT laboratory, where physicians developed rotation techniques that delivered radiation from multiple angles to concentrate dosage on tumors while limiting any single beam path through healthy tissue. These protocols became standard practice in radiation oncology. In 1954, HVEC and MIT completed a compact linear accelerator for the University of Chicago's Argonne Cancer Research Hospital, capable of producing electrons at variable energies from 10 to 50 million electron volts.  This research instrument enabled experiments in high-energy radiation therapy that informed treatment protocols.
+By the mid-1950s, however, cobalt-60 therapy machines manufactured by General Electric began displacing electron accelerators in hospital purchasing. The cobalt sources, a byproduct of nuclear reactor use, offered simpler operation and lower maintenance costs, though with less precise energy control. HVEC exited the medical device market in 1969, as its competitive advantages shifted toward research and industrial applications where beam controllability justified higher complexity.
+
+=== Industrial radiography ===
+During World War II, Van de Graaff had used the compact generator invented with Trump to detect defects in ship hulls and ordnance for the U.S. Navy. Drawing on this application, HVEC produced 2-MeV industrial X-ray generators for non-destructive testing of manufactured goods. These units, capable of detecting flaws in thick steel sections, weighed more than two tons and were designed to operate in industrial facilities.
+HVEC adapted these generators to output electron beams, selling a line of industrial radiography equipment and also renting sterilization services to other companies. In 1957, Ethicon, a medical subsidiary of Johnson & Johnson, purchased an HVEC linear accelerator to sterilize surgical sutures, the first commercial medial product to use radiation processing.
+Sales of e-beam processing machines picked up after HVEC introduced insulating core transformers. ICTs, operating in the lower-voltage 300 keV to 2.5 MeV range, were used for crosslinking polyethylene and other polymers. W. R. Grace's Cryovac division used radiation crosslinking to produce heat-shrinkable materials for food packaging. Other companies purchased ICTs for extended to wire and cable insulation, rubber vulcanization, auto paint, textile modification, and semiconductors.
+
+As HVEC shifted into conglomerate model, its subsidiary Electronized Chemicals Corporation began producing in-house products with HVEC devices. By 1960, ECC had introduced product lines in heat-shrink tubing, shrink wrap, and cross-linked wiring.
+In the late 1970s, piggybacking on research projects led by John Trump, HVEC expanded into environmental applications of electron beam technology. In 1980, the company received a $1 million contract from Miami-Dade County for electron beam equipment to disinfect wastewater before discharge to sanitary landfills. The company also received contracts to expand a prototype sewage sludge treatment plant for the Massachusetts Metropolitan District Commission and to develop an electron beam system for poultry feed disinfection.
+
+=== Research accelerators ===
+
+HVEC's entry into high-energy research accelerators began in 1949 with its 4 MV Cosmotron particle injector. By 1951, HVEC had begun producing its single-ended CN series that became the first mass-produced research accelerators.
+The CN design was based on a vertical accelerator at MIT designed by John Trump. It employed resistor grading in both column and tube structure, field-shaping column hoops, and high-pressure insulating gas mixtures of nitrogen and carbon dioxide. Operating in a single stage at terminal voltages up to 6.5 megavolts, the 26 CN models manufactured by HVEC reliable platforms for light-ion nuclear physics experiments. However, fundamental physics questions, particularly the structure of heavier nuclei, demanded higher particle energies than a single-stage Van de Graaff accelerator could reach.
+
+==== The tandem principle ====
+The solution emerged from a charge-reversal concept proposed demonstrated by Nobel laureate Luis Alvarez in 1951. Rather than accelerate positive ions from ground to a high-voltage terminal, the tandem accelerator begins with negative ions. These particles accelerate toward a positive terminal, where a thin foil or gas stripper removes multiple electrons, converting them to positive ions. The now-positive particles accelerate away from the terminal back to ground potential. This double acceleration effectively multiplies the particle energy without requiring proportionally higher terminal voltages. A negative hydrogen ion accelerated through a 5 megavolt tandem emerges with 10 megavolts of kinetic energy.
+After commissioning tandem production in 1954, Atomic Energy of Canada Limited placed HVEC's first tandem order in September 1956 for $0.92M (equivalent to $10.89M in 2025). The machine achieved first beam at HVEC's Burlington facility in June 1958.
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+---
+title: "High Voltage Engineering Corporation"
+chunk: 4/5
+source: "https://en.wikipedia.org/wiki/High_Voltage_Engineering_Corporation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:14.539653+00:00"
+instance: "kb-cron"
+---
+
+==== Tandem models ====
+Between 1958 and 1973, HVEC manufactured 55 tandem accelerators in four progressively larger models. Each generation opened new experiments with heavier ions, higher energies, and previously inaccessible nuclear reactions.
+The EN model became the production workhorse. First installed at Chalk River in 1959, it was the first large accelerator to use pure sulfur hexafluoride as insulating gas, which allowed higher voltages in a smaller tank. Its commercial viability depended on two developments: sufficiently intense negative ion sources (developed at Chalk River and Wisconsin) and HVEC's invention of the inclined-field acceleration tube, which solved the voltage breakdown problem that had plagued earlier long tubes. HVEC built 30 EN units for institutions across seven countries. At Chalk River, researchers used the EN to discover quasi-molecular states—transient configurations where colliding nuclei briefly orbit each other before separating.
+The FN model ("King") extended terminal voltages to 9 megavolts in its "Super FN" variant. The first went to Los Alamos in October 1963. HVEC sold 17 FN units to laboratories including Rutgers, Florida State, Stanford, and national research institutes in France and Romania.
+The MP model ("Emperor"), a much larger model commissioned by the Atomic Energy Commission in 1962, employed an "open truss" column structure—beams fabricated from alternating steel and glass plates bonded with epoxy—that supported a substantially larger terminal while maintaining electrical insulation. The first MP, installed at Yale in 1963, operated consistently at 10–11 megavolts; a later installation at Strasbourg reached 18. At these energies, electron stripping becomes highly efficient. A uranium ion passing through the terminal can lose more than 20 electrons, enabling heavy-ion fusion experiments impossible with earlier machines. Advances in gamma-ray spectroscopy combined with MP tandems enabled precision measurements of nuclear structure. HVEC manufactured 10 MP units between 1965 and 1973 for institutions including the University of Minnesota, Chalk River, and the Max Planck Institute in Heidelberg.
+The XTU ("Holy Roman Emperor") was designed for superheavy element synthesis. Theoretical models predicted an "island of stability" beyond element 110 where nuclei would resist rapid decay. The XTU's 20-megavolt rating would accelerate uranium ions to nearly one billion electron volts—enough to overcome Coulomb barriers in heavy-element fusion. Two prototypes operated solely on a test basis at Burlington before the project was cancelled. One later sold to Italy's national laboratory at Legnaro in 1979.
+
+Sources: Bromley 1974
+
+=== Insulated core transformer ===
+By the early 1950s, Van de Graaff recognized that electrostatic accelerators would eventually require higher currents than his belt-charged system could deliver. Rather than abandon direct current power, he conceived a novel voltage-generating principle that replaced his electrostatic charging belt with magnetic flux as the means of transforming power to high-voltage direct current. Van de Graaff filed a patent for his single-phase insulating core transformer (ICT) accelerator design in 1957, which was issued in 1965. HVEC engineers subsequently developed a three-phase version that proved commercially viable.
+The ICT found particular success in industrial radiation processing applications. By 1967, the technology had gained recognition as an important source of high-voltage DC power for particle acceleration in industrial settings, with HVEC offering ICT power supplies for low-voltage electron beams alongside their belt-charged accelerators. ICT accelerators in the 300 keV to 1-million-volt range were installed on industrial processing lines for crosslinking plastic film and tubing, pasteurizing food, and sterilizing pharmaceuticals. ICTs continued to be used for crosslinking wire and cable jacketing and shrinkable films, operating in the 300 keV to 2.5 MeV energy range
+
+== Subsidiaries ==
+Following declining earnings in 1965, HVEC reorganized into profit centers and established three wholly owned subsidiaries to diversify beyond particle accelerators. After U.S. orders for new accelerators ceased in the early 1970s, HVEC transformed into a miniconglomerate with more than ten subsidiaries, and industrial products from these units accounted for 80 percent of company revenues by 1972.
+
+=== High Voltage Engineering Europa ===
+
+In 1958, HVEC established High Voltage Engineering Europa (HVEE) in Amersfoort, Netherlands to supply accelerators to the European common market.  The subsidiary was created in response to demand for accelerators in the European common market and export-controlled markets. HVEE manufactured HVEC's lower-voltage Van de Graaff accelerators for industries in the European common market, as well as insulated-core transformer power supplies for low-voltage electron beams.
+According to production records compiled through 2004, HVEE manufactured 93 accelerators across various voltage ranges, mostly in the 0.5–2 MV range. HVEE also produced smaller numbers of higher-voltage systems, including three accelerators in the 5–7 MV range and one in the 4-5 MV range.
+High Voltage Engineering Europa continued operations after its parent company's bankruptcy. HVEE produced low-voltage  1–5 MV, solid-state voltage generators with the trade names Tandetron and Singletron, originally designed by the General Ionix Corporation in Massachusetts. Having shifted away from belt-charged accelerators, HVEE's lower voltage accelerators now incorporate newer charging technologies.
+
+=== Applied Radiation Corporation ===
+In June 1960, High Voltage Engineering Corporation acquired Applied Radiation Corporation (ARCO) of Walnut Creek, California through a stock exchange. ARCO manufactured a line of linear accelerators with uses complementing those of HVEC's existing Van de Graaff accelerators. Applied Radiation was established as a separate subsidiary under its existing management, though its sales operations were integrated with HVEC's broader organization.
+The acquisition, however, would prove short-lived due to antitrust concerns. At the time, HVEC dominated the market for research accelerators, controlling an 80 percent share of orders. In April 1963, the Federal Trade Commission issued a consent decree requiring HVEC to divest itself of Applied Radiation Corporation. This forced divestiture reflected FTC concerns about concentration in the particle accelerator manufacturing industry, as both firms competed for research and industrial accelerator clients.
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+---
+title: "High Voltage Engineering Corporation"
+chunk: 5/5
+source: "https://en.wikipedia.org/wiki/High_Voltage_Engineering_Corporation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:14.539653+00:00"
+instance: "kb-cron"
+---
+
+=== Electronized Chemicals Corporation ===
+In 1943, Arno Brasch and Wolfgang Huber built a bespoke particle accelerator in Brooklyn, New York to irradiate foods, finding they could sterilize foods without affecting their taste. Brash and Huber founded Electronized Chemicals Corporation to explore methods for cold sterilization. HVEC acquired their company in 1957 and began to broadly explore radiation processing of materials.
+Using HVEC's electron beam technology at a facility adjoining the HVEC Burlington plant, ECC's new operation in Burlington rented irridiation services to a variety of industries. It developed methods to irradiate and crosslink polymers. After Raychem pioneered a cross-linking method using low-voltage radiation in 1957, Electronized Chemicals followed it into the manufacture of heat-shrink tubing. In 1985, the business was acquired by 3M, which continues to manufacture heat-shrink tubing a factory in Chelmsford, Massachusetts.
+
+=== Ion Physics Corporation ===
+Ion Physics Corporation (IPC), an HVEC subsidiary, conducted the first commercial research in ion implantation, a technique that became essential to semiconductor manufacturing worldwide.
+IPC originated in 1959 as a joint venture with B.F. Goodrich to develop ion propulsion for spacecraft. The venture delivered an experimental ion engine to the Jet Propulsion Laboratory for testing. After HVEC bought out Goodrich in 1962, the subsidiary was renamed Ion Physics Corporation and pivoted toward ion bombardment techniques for fabricating solar cells and other semiconductor devices. Using Van de Graaff accelerators to implant ions into silicon wafers, IPC achieved several advances by the mid-1960s: a new efficiency record for silicon solar cells, the first bipolar transistor made from ion-implanted junctions, and annealing processes to repair crystal damage caused by bombardment.
+In 1969, Fairchild Semiconductor contracted with HVEC for a low-energy ion accelerator. Peter Rose, HVEC's research director, built a functional prototype in six weeks from stockroom parts. The machine demonstrated that ion implantation could precisely control the placement and quantity of dopant atoms in silicon—offering finer control over transistor characteristics than traditional diffusion techniques.
+IPC itself failed to commercialize the technology. After three executives resigned in late 1969, Rose was appointed president, but the subsidiary continued to struggle. In 1971, Rose left to found Extrion Corporation with HVEC backing and IPC closed the same year. Extrion became the dominant manufacturer of ion implanters. By the late 1970s, ion implantation was standard practice throughout the semiconductor industry, enabling the MOS integrated circuits that would dominate late twentieth-century electronics.
+
+=== High Voltage Power Corporation ===
+In July 1968, High Voltage Engineering Corporation and Reynolds Metals Company announced they would form a joint venture partnership to develop, produce, and sell gas-insulated systems for transmission of electric power.  The venture, High Voltage Power Corporation, aimed to commercialize technology for underground electric power transmission. HVEC president Denis Robinson noted increasing need by bury transmission lines underground for technological, economic, and aesthetic reasons, and emphasizing that compressed gas offered unique advantages for transmitting large amounts of power at high voltages with increased reliability at lower cost. Each company held a 50% interest in the venture, with Reynolds providing funds and technical research while HVEC contributed its patents, licenses, and know-how. The development work was carried out at HVEC's Burlington factory.
+The subsidiary's products included insulating-core reactors for nuclear power plants and gas-insulated transmission systems for electrical utilities, based on Van de Graaff's insulating-core transformer invention. However, by 1974, High Voltage Power Corp. losses were consuming 60-75% of HVEC's cash flow despite generating only $1.5-2 million in annual sales, leading HVEC to divest from the subsidiary.
+
+== Legacy ==
+
+=== Scientific instrumentation ===
+HVEC represented a shift in how experimental physics acquired its tools. Before the company's founding, laboratories typically built accelerators from scratch; HVEC's mass-produced instruments made reliable high-voltage machines available to institutions without in-house engineering capacity. The result was a rapid expansion of experimental nuclear physics. At the field's peak in the mid-1970s, nearly 70 percent of published papers relied on data from HVEC accelerators.
+Presidential science adviser D. Allan Bromley, who worked with the first HVEC tandem at Chalk River, called the machines "superb nuclear science instruments." In a 1984 assessment, he concluded that "of all the accelerators yet devised in nuclear science I believe that a very strong case can be made that the large tandems span the greatest range and scope of physics."
+
+=== Accelerator mass spectrometry ===
+HVEC tandems enabled accelerator mass spectrometry (AMS), a technique that transformed radiocarbon dating and created new applications across multiple fields.
+In May 1977, researchers at the University of Rochester used an HVEC MP tandem to demonstrate that carbon-14 atoms could be detected directly in milligram-scale samples—compared to the 10–100 grams required by conventional decay counting. The tandem configuration exploited a key property: nitrogen-14, the primary interference in conventional dating, forms no stable negative ions and cannot survive acceleration through the system, eliminating a major source of contamination.
+The reduction in sample size made radiocarbon dating applicable to precious artifacts and specimens where destructive sampling had been prohibitive. Tandem machines also extended the practical range of radiocarbon dating from approximately 40,000 to potentially 100,000 years. Beyond radiocarbon applications, AMS expanded into hydrology, geoscience, biomedicine, archaeology, and paleoclimatology.
+
+=== Commercial applications ===
+According to a 2010 survey, the three primary uses of the 26,000 low-energy particle accelerators operating worldwide are radiotherapy (44%), ion implantation (41%), and industrial processing (9%). HVEC made foundational contributions to all three.
+The company's compact Van de Graaff generators were among the first artificial radiation sources commercially available for cancer treatment. Radiation physicist Milford Schulz called them "truly milestones in the progress of radiotherapy." The first medical linear accelerator—now the dominant technology in cancer treatment—was assembled at Stanford using a retrofitted HVEC machine.
+Ion implantation, pioneered at HVEC's Ion Physics Corporation, became standard practice in semiconductor manufacturing by the late 1970s. The technique enabled MOS integrated circuits that dominate modern electronics. Radiation crosslinking, developed at Electronized Chemicals Corporation, produced heat-shrink tubing and films now ubiquitous in electrical wiring and food packaging.
+
+=== Continuing research use ===
+
+Although HVEC ceased accelerator production in 1981, many of its machines remain active in nuclear physics research. Several have operated continuously for more than 50 years. Beyond AMS, active accelerators are used for nuclear astrophysics (studying neutron-induced reactions relevant to stellar nucleosynthesis), ion beam analysis, radiation effects testing, and ion-atom collision physics. Four remain at U.S. national laboratories: Argonne, Brookhaven, Lawrence Livermore, and Sandia.
+High Voltage Engineering Europa, the former Dutch subsidiary, continues manufacturing electrostatic accelerators for research and industrial applications.
+
+== Notes ==
+
+== Citations ==
+
+== Sources ==
+
+== External links ==
+List of active research accelerators from the International Atomic Energy Agency
+High Voltage Engineering Corporation Bulletin PA (1958), via Duke University
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-0.md b/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-0.md
index 816989aa4..047e9966e 100644
--- a/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-0.md
+++ b/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-0.md
@@ -4,7 +4,7 @@ chunk: 1/4
 source: "https://en.wikipedia.org/wiki/History_of_ESPCI_Paris"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T16:15:15.630694+00:00"
+date_saved: "2026-05-05T16:29:17.123366+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-1.md b/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-1.md
index ebc3e16d3..79700d54e 100644
--- a/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-1.md
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@@ -4,7 +4,7 @@ chunk: 2/4
 source: "https://en.wikipedia.org/wiki/History_of_ESPCI_Paris"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T16:15:15.630694+00:00"
+date_saved: "2026-05-05T16:29:17.123366+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-2.md b/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-2.md
index 75322d5d9..64402744f 100644
--- a/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-2.md
+++ b/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-2.md
@@ -4,7 +4,7 @@ chunk: 3/4
 source: "https://en.wikipedia.org/wiki/History_of_ESPCI_Paris"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T16:15:15.630694+00:00"
+date_saved: "2026-05-05T16:29:17.123366+00:00"
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diff --git a/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-3.md b/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-3.md
index c773b7a42..4f6ede3ff 100644
--- a/data/en.wikipedia.org/wiki/History_of_ESPCI_Paris-3.md
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 source: "https://en.wikipedia.org/wiki/History_of_ESPCI_Paris"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T16:15:15.630694+00:00"
+date_saved: "2026-05-05T16:29:17.123366+00:00"
 instance: "kb-cron"
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diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-0.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-0.md
new file mode 100644
index 000000000..a07b559db
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+---
+title: "History of Lorentz transformations"
+chunk: 1/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval 
+  
+    
+      
+        −
+        
+          x
+          
+            0
+          
+          
+            2
+          
+        
+        +
+        ⋯
+        +
+        
+          x
+          
+            n
+          
+          
+            2
+          
+        
+      
+    
+    {\displaystyle -x_{0}^{2}+\cdots +x_{n}^{2}}
+  
+ and the Minkowski inner product 
+  
+    
+      
+        −
+        
+          x
+          
+            0
+          
+        
+        
+          y
+          
+            0
+          
+        
+        +
+        ⋯
+        +
+        
+          x
+          
+            n
+          
+        
+        
+          y
+          
+            n
+          
+        
+      
+    
+    {\displaystyle -x_{0}y_{0}+\cdots +x_{n}y_{n}}
+  
+.
+In mathematics, transformations equivalent to what was later known as Lorentz transformations in various dimensions were discussed in the 19th century in relation to the theory of quadratic forms, hyperbolic geometry, Möbius geometry, and sphere geometry, which is connected to the fact that the group of motions in hyperbolic space, the Möbius group or projective special linear group, and the Laguerre group are isomorphic to the Lorentz group.
+In physics, Lorentz transformations became known at the beginning of the 20th century, when it was discovered that they exhibit the symmetry of Maxwell's equations. Subsequently, they became fundamental to all of physics, because they formed the basis of special relativity in which they exhibit the symmetry of Minkowski spacetime, making the speed of light invariant between different inertial frames. They relate the spacetime coordinates of two arbitrary inertial frames of reference with constant relative speed v. In one frame, the position of an event is given by x,y,z and time t, while in the other frame the same event has coordinates x′,y′,z′ and t′.
+
+== Mathematical prehistory ==
+Using the coefficients of a symmetric matrix g, the associated bilinear form, and a linear transformations in terms of transformation matrix A, the Lorentz transformation is given if the following conditions are satisfied:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  
+                    
+                      
+                        −
+                        
+                          x
+                          
+                            0
+                          
+                          
+                            2
+                          
+                        
+                        +
+                        ⋯
+                        +
+                        
+                          x
+                          
+                            n
+                          
+                          
+                            2
+                          
+                        
+                      
+                      
+                        
+                        =
+                        −
+                        
+                          x
+                          
+                            0
+                          
+                          
+                            ′
+                            2
+                          
+                        
+                        +
+                        ⋯
+                        +
+                        
+                          x
+                          
+                            n
+                          
+                          
+                            ′
+                            2
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+                        
+                      
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+                    
+                      
+                        −
+                        
+                          x
+                          
+                            0
+                          
+                        
+                        
+                          y
+                          
+                            0
+                          
+                        
+                        +
+                        ⋯
+                        +
+                        
+                          x
+                          
+                            n
+                          
+                        
+                        
+                          y
+                          
+                            n
+                          
+                        
+                      
+                      
+                        
+                        =
+                        −
+                        
+                          x
+                          
+                            0
+                          
+                          
+                            ′
+                          
+                        
+                        
+                          y
+                          
+                            0
+                          
+                          
+                            ′
+                          
+                        
+                        +
+                        ⋯
+                        +
+                        
+                          x
+                          
+                            n
+                          
+                          
+                            ′
+                          
+                        
+                        
+                          y
+                          
+                            n
+                          
+                          
+                            ′
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+                        
+                      
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+                
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+                      
+                        
+                          
+                            x
+                          
+                          ′
+                        
+                        =
+                        
+                          A
+                        
+                        ⋅
+                        
+                          x
+                        
+                      
+                    
+                    
+                      
+                        
+                          x
+                        
+                        =
+                        
+                          
+                            A
+                          
+                          
+                            −
+                            1
+                          
+                        
+                        ⋅
+                        
+                          
+                            x
+                          
+                          ′
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+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  
+                    
+                      
+                        
+                          
+                            
+                              
+                                
+                                  g
+                                
+                                ⋅
+                                
+                                  
+                                    A
+                                  
+                                  
+                                    
+                                      T
+                                    
+                                  
+                                
+                                ⋅
+                                
+                                  g
+                                
+                              
+                              
+                                
+                                =
+                                
+                                  
+                                    A
+                                  
+                                  
+                                    −
+                                    1
+                                  
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+                            
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+                                
+                                  
+                                    A
+                                  
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+                                      T
+                                    
+                                  
+                                
+                                ⋅
+                                
+                                  g
+                                
+                                ⋅
+                                
+                                  A
+                                
+                              
+                              
+                                
+                                =
+                                
+                                  g
+                                
+                              
+                            
+                            
+                              
+                                
+                                  A
+                                
+                                ⋅
+                                
+                                  g
+                                
+                                ⋅
+                                
+                                  
+                                    A
+                                  
+                                  
+                                    
+                                      T
+                                    
+                                  
+                                
+                              
+                              
+                                
+                                =
+                                
+                                  g
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  g
+                
+                =
+                
+                  
+                    d
+                    i
+                    a
+                    g
+                  
+                
+                (
+                −
+                1
+                ,
+                1
+                ,
+                …
+                ,
+                1
+                )
+              
+            
+            
+              
+                det
+                
+                  A
+                
+                =
+                ±
+                1
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\begin{aligned}-x_{0}^{2}+\cdots +x_{n}^{2}&=-x_{0}^{\prime 2}+\dots +x_{n}^{\prime 2}\\-x_{0}y_{0}+\cdots +x_{n}y_{n}&=-x_{0}^{\prime }y_{0}^{\prime }+\cdots +x_{n}^{\prime }y_{n}^{\prime }\end{aligned}}\\\hline {\begin{matrix}\mathbf {x} '=\mathbf {A} \cdot \mathbf {x} \\\mathbf {x} =\mathbf {A} ^{-1}\cdot \mathbf {x} '\end{matrix}}\\\hline {\begin{matrix}{\begin{aligned}\mathbf {g} \cdot \mathbf {A} ^{\mathrm {T} }\cdot \mathbf {g} &=\mathbf {A} ^{-1}\\\mathbf {A} ^{\rm {T}}\cdot \mathbf {g} \cdot \mathbf {A} &=\mathbf {g} \\\mathbf {A} \cdot \mathbf {g} \cdot \mathbf {A} ^{\mathrm {T} }&=\mathbf {g} \end{aligned}}\end{matrix}}\\\hline \mathbf {g} ={\rm {diag}}(-1,1,\dots ,1)\\\det \mathbf {A} =\pm 1\end{matrix}}}
+  
+
+It forms an indefinite orthogonal group called the Lorentz group O(1,n), while the case det A=+1 forms the restricted Lorentz group SO(1,n). The quadratic form becomes the Lorentz interval in terms of an indefinite quadratic form of Minkowski space (being a special case of pseudo-Euclidean space), and the associated bilinear form becomes the Minkowski inner product. Long before the advent of special relativity it was used in topics such as the Cayley–Klein metric, hyperboloid model and other models of hyperbolic geometry, computations of elliptic functions and integrals, transformation of indefinite quadratic forms, squeeze mappings of the hyperbola, group theory, Möbius transformations, spherical wave transformation, transformation of the Sine-Gordon equation, Biquaternion algebra, split-complex numbers, Clifford algebra, and others.
+
+== Electrodynamics and special relativity ==
+
+=== Overview ===
+In the special relativity, Lorentz transformations exhibit the symmetry of Minkowski spacetime by using a constant c as the speed of light, and a parameter v as the relative velocity between two inertial reference frames. Using the above conditions, the Lorentz transformation in 3+1 dimensions assume the form:
+
+  
+    
+      
+        
+          
+            
+              
+                −
+                
+                  c
+                  
+                    2
+                  
+                
+                
+                  t
+                  
+                    2
+                  
+                
+                +
+                
+                  x
+                  
+                    2
+                  
+                
+                +
+                
+                  y
+                  
+                    2
+                  
+                
+                +
+                
+                  z
+                  
+                    2
+                  
+                
+                =
+                −
+                
+                  c
+                  
+                    2
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+                
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+                  t
+                  
+                    ′
+                    2
+                  
+                
+                +
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+                  x
+                  
+                    ′
+                    2
+                  
+                
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+                
+                  y
+                  
+                    ′
+                    2
+                  
+                
+                +
+                
+                  z
+                  
+                    ′
+                    2
+                  
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            t
+                            ′
+                          
+                        
+                        
+                          
+                          =
+                          γ
+                          
+                            (
+                            
+                              t
+                              −
+                              x
+                              
+                                
+                                  v
+                                  
+                                    c
+                                    
+                                      2
+                                    
+                                  
+                                
+                              
+                            
+                            )
+                          
+                        
+                      
+                      
+                        
+                          
+                            x
+                            ′
+                          
+                        
+                        
+                          
+                          =
+                          γ
+                          (
+                          x
+                          −
+                          v
+                          t
+                          )
+                        
+                      
+                      
+                        
+                          
+                            y
+                            ′
+                          
+                        
+                        
+                          
+                          =
+                          y
+                        
+                      
+                      
+                        
+                          
+                            z
+                            ′
+                          
+                        
+                        
+                          
+                          =
+                          z
+                        
+                      
+                    
+                  
+                  |
+                
+                
+                  
+                    
+                      
+                        t
+                      
+                      
+                        
+                        =
+                        γ
+                        
+                          (
+                          
+                            
+                              t
+                              ′
+                            
+                            +
+                            x
+                            
+                              
+                                v
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                    
+                      
+                        x
+                      
+                      
+                        
+                        =
+                        γ
+                        (
+                        
+                          x
+                          ′
+                        
+                        +
+                        v
+                        
+                          t
+                          ′
+                        
+                        )
+                      
+                    
+                    
+                      
+                        y
+                      
+                      
+                        
+                        =
+                        
+                          y
+                          ′
+                        
+                      
+                    
+                    
+                      
+                        z
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+                      
+                        
+                        =
+                        
+                          z
+                          ′
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+                  
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+              
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+        
+        ⇒
+        
+          
+            
+              
+                (
+                c
+                
+                  t
+                  ′
+                
+                +
+                
+                  x
+                  ′
+                
+                )
+              
+              
+                
+                =
+                (
+                c
+                t
+                +
+                x
+                )
+                
+                  
+                    
+                      
+                        c
+                        +
+                        v
+                      
+                      
+                        c
+                        −
+                        v
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                (
+                c
+                
+                  t
+                  ′
+                
+                −
+                
+                  x
+                  ′
+                
+                )
+              
+              
+                
+                =
+                (
+                c
+                t
+                −
+                x
+                )
+                
+                  
+                    
+                      
+                        c
+                        −
+                        v
+                      
+                      
+                        c
+                        +
+                        v
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}-c^{2}t^{2}+x^{2}+y^{2}+z^{2}=-c^{2}t^{\prime 2}+x^{\prime 2}+y^{\prime 2}+z^{\prime 2}\\\hline \left.{\begin{aligned}t'&=\gamma \left(t-x{\frac {v}{c^{2}}}\right)\\x'&=\gamma (x-vt)\\y'&=y\\z'&=z\end{aligned}}\right|{\begin{aligned}t&=\gamma \left(t'+x{\frac {v}{c^{2}}}\right)\\x&=\gamma (x'+vt')\\y&=y'\\z&=z'\end{aligned}}\end{matrix}}\Rightarrow {\begin{aligned}(ct'+x')&=(ct+x){\sqrt {\frac {c+v}{c-v}}}\\(ct'-x')&=(ct-x){\sqrt {\frac {c-v}{c+v}}}\end{aligned}}}
+  
+
+In physics, analogous transformations have been introduced by Voigt (1887) related to an incompressible medium, and by Heaviside (1888), Thomson (1889), Searle (1896) and Lorentz (1892, 1895) who analyzed Maxwell's equations. They were completed by Larmor (1897, 1900) and Lorentz (1899, 1904), and brought into their modern form by Poincaré (1905) who gave the transformation the name of Lorentz. Eventually, Einstein (1905) showed in his development of special relativity that the transformations follow from the principle of relativity and constant light speed alone by modifying the traditional concepts of space and time, without requiring a mechanical aether in contradistinction to Lorentz and Poincaré. Minkowski (1907–1908) used them to argue that space and time are inseparably connected as spacetime.
+Regarding special representations of the Lorentz transformations: Minkowski (1907–1908) and Sommerfeld (1909) used imaginary trigonometric functions, Frank (1909) and Varićak (1910) used hyperbolic functions, Bateman and Cunningham (1909–1910) used spherical wave transformations, Herglotz (1909–10) used Möbius transformations, Plummer (1910) and Gruner (1921) used trigonometric Lorentz boosts, Ignatowski (1910) derived the transformations without light speed postulate, Noether (1910) and Klein (1910) as well Conway (1911) and Silberstein (1911) used Biquaternions, Ignatowski (1910/11), Herglotz (1911), and others used vector transformations valid in arbitrary directions, Borel (1913–14) used Cayley–Hermite parameter,
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-1.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-1.md
new file mode 100644
index 000000000..ce29b5a43
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-1.md
@@ -0,0 +1,1131 @@
+---
+title: "History of Lorentz transformations"
+chunk: 2/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+=== Voigt (1887) ===
+Woldemar Voigt (1887) developed a transformation in connection with the Doppler effect and an incompressible medium, being in modern notation:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            ξ
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          
+                            x
+                            
+                              1
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+                          −
+                          ϰ
+                          t
+                        
+                      
+                      
+                        
+                          
+                            η
+                            
+                              1
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+                        
+                        
+                          
+                          =
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+                      
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+                            
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+                        
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+                          =
+                          
+                            z
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+                        
+                      
+                      
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+                        
+                          
+                          =
+                          t
+                          −
+                          
+                            
+                              
+                                ϰ
+                                
+                                  x
+                                  
+                                    1
+                                  
+                                
+                              
+                              
+                                ω
+                                
+                                  2
+                                
+                              
+                            
+                          
+                        
+                      
+                      
+                        
+                          q
+                        
+                        
+                          
+                          =
+                          
+                            
+                              1
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+                              
+                                
+                                  
+                                    ϰ
+                                    
+                                      2
+                                    
+                                  
+                                  
+                                    ω
+                                    
+                                      2
+                                    
+                                  
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                  |
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+              
+              
+                
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+                        
+                          x
+                          
+                            ′
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+                        
+                      
+                      
+                        
+                        =
+                        x
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+                        v
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+                      
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+                        =
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+                      
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+                    
+                      
+                        
+                          z
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            z
+                            γ
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+                        
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        t
+                        −
+                        
+                          
+                            
+                              v
+                              x
+                            
+                            
+                              c
+                              
+                                2
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+                            
+                          
+                        
+                      
+                    
+                    
+                      
+                        
+                          
+                            1
+                            γ
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            1
+                            −
+                            
+                              
+                                
+                                  v
+                                  
+                                    2
+                                  
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}\xi _{1}&=x_{1}-\varkappa t\\\eta _{1}&=y_{1}q\\\zeta _{1}&=z_{1}q\\\tau &=t-{\frac {\varkappa x_{1}}{\omega ^{2}}}\\q&={\sqrt {1-{\frac {\varkappa ^{2}}{\omega ^{2}}}}}\end{aligned}}\right|&{\begin{aligned}x^{\prime }&=x-vt\\y^{\prime }&={\frac {y}{\gamma }}\\z^{\prime }&={\frac {z}{\gamma }}\\t^{\prime }&=t-{\frac {vx}{c^{2}}}\\{\frac {1}{\gamma }}&={\sqrt {1-{\frac {v^{2}}{c^{2}}}}}\end{aligned}}\end{matrix}}}
+  
+
+If the right-hand sides of his equations are multiplied by γ they are the modern Lorentz transformation. In Voigt's theory the speed of light is invariant, but his transformations mix up a relativistic boost together with a rescaling of space-time. Optical phenomena in free space are scale, conformal, and Lorentz invariant, so the combination is invariant too. For instance, Lorentz transformations can be extended by using factor 
+  
+    
+      
+        l
+      
+    
+    {\displaystyle l}
+  
+:
+
+  
+    
+      
+        
+          x
+          
+            ′
+          
+        
+        =
+        γ
+        l
+        
+          (
+          
+            x
+            −
+            v
+            t
+          
+          )
+        
+        ,
+        
+        
+          y
+          
+            ′
+          
+        
+        =
+        l
+        y
+        ,
+        
+        
+          z
+          
+            ′
+          
+        
+        =
+        l
+        z
+        ,
+        
+        
+          t
+          
+            ′
+          
+        
+        =
+        γ
+        l
+        
+          (
+          
+            t
+            −
+            x
+            
+              
+                v
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle x^{\prime }=\gamma l\left(x-vt\right),\quad y^{\prime }=ly,\quad z^{\prime }=lz,\quad t^{\prime }=\gamma l\left(t-x{\frac {v}{c^{2}}}\right)}
+  
+.
+l=1/γ gives the Voigt transformation, l=1 the Lorentz transformation. But scale transformations are not a symmetry of all the laws of nature, only of electromagnetism, so these transformations cannot be used to formulate a principle of relativity in general. It was demonstrated by Poincaré and Einstein that one has to set l=1 in order to make the above transformation symmetric and to form a group as required by the relativity principle, therefore the Lorentz transformation is the only viable choice.
+
+Voigt sent his 1887 paper to Lorentz in 1908, and that was acknowledged in 1909: In a paper "Über das Doppler'sche Princip", published in 1887 (Gött. Nachrichten, p. 41) and which to my regret has escaped my notice all these years, Voigt has applied to equations of the form (7) (§ 3 of this book) [namely 
+  
+    
+      
+        Δ
+        Ψ
+        −
+        
+          
+            
+              1
+              
+                c
+                
+                  2
+                
+              
+            
+          
+        
+        
+          
+            
+              
+                
+                  ∂
+                  
+                    2
+                  
+                
+                Ψ
+              
+              
+                ∂
+                
+                  t
+                  
+                    2
+                  
+                
+              
+            
+          
+        
+        =
+        0
+      
+    
+    {\displaystyle \Delta \Psi -{\tfrac {1}{c^{2}}}{\tfrac {\partial ^{2}\Psi }{\partial t^{2}}}=0}
+  
+] a transformation equivalent to the formulae (287) and (288) [namely 
+  
+    
+      
+        
+          x
+          
+            ′
+          
+        
+        =
+        γ
+        l
+        
+          (
+          
+            x
+            −
+            v
+            t
+          
+          )
+        
+        ,
+         
+        
+          y
+          
+            ′
+          
+        
+        =
+        l
+        y
+        ,
+         
+        
+          z
+          
+            ′
+          
+        
+        =
+        l
+        z
+        ,
+         
+        
+          t
+          
+            ′
+          
+        
+        =
+        γ
+        l
+        
+          (
+          
+            t
+            −
+            
+              
+                
+                  v
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+            
+            x
+          
+          )
+        
+      
+    
+    {\displaystyle x^{\prime }=\gamma l\left(x-vt\right),\ y^{\prime }=ly,\ z^{\prime }=lz,\ t^{\prime }=\gamma l\left(t-{\tfrac {v}{c^{2}}}x\right)}
+  
+]. The idea of the transformations used above (and in § 44) might therefore have been borrowed from Voigt and the proof that it does not alter the form of the equations for the free ether is contained in his paper.
+Also Hermann Minkowski said in 1908 that the transformations which play the main role in the principle of relativity were first examined by Voigt in 1887. Voigt responded in the same paper by saying that his theory was based on an elastic theory of light, not an electromagnetic one. However, he concluded that some results were actually the same.
+
+=== Heaviside (1888), Thomson (1889), Searle (1896) ===
+In 1888, Oliver Heaviside investigated the properties of charges in motion according to Maxwell's electrodynamics. He calculated, among other things, anisotropies in the electric field of moving bodies represented by this formula:
+
+  
+    
+      
+        
+          E
+        
+        =
+        
+          (
+          
+            
+              
+                q
+                
+                  r
+                
+              
+              
+                r
+                
+                  2
+                
+              
+            
+          
+          )
+        
+        
+          
+            (
+            
+              1
+              −
+              
+                
+                  
+                    
+                      v
+                      
+                        2
+                      
+                    
+                    
+                      sin
+                      
+                        2
+                      
+                    
+                    ⁡
+                    θ
+                  
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+            
+            )
+          
+          
+            −
+            3
+            
+              /
+            
+            2
+          
+        
+      
+    
+    {\displaystyle \mathrm {E} =\left({\frac {q\mathrm {r} }{r^{2}}}\right)\left(1-{\frac {v^{2}\sin ^{2}\theta }{c^{2}}}\right)^{-3/2}}
+  
+.
+Consequently, Joseph John Thomson (1889) found a way to substantially simplify calculations concerning moving charges by using the following mathematical transformation (like other authors such as Lorentz or Larmor, also Thomson implicitly used the Galilean transformation z-vt in his equation):
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          z
+                        
+                        
+                          
+                          =
+                          
+                            
+                              {
+                              
+                                1
+                                −
+                                
+                                  
+                                    
+                                      ω
+                                      
+                                        2
+                                      
+                                    
+                                    
+                                      v
+                                      
+                                        2
+                                      
+                                    
+                                  
+                                
+                              
+                              }
+                            
+                            
+                              
+                                1
+                                2
+                              
+                            
+                          
+                          
+                            z
+                            ′
+                          
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          z
+                          
+                            ∗
+                          
+                        
+                        =
+                        z
+                        −
+                        v
+                        t
+                      
+                      
+                        
+                        =
+                        
+                          
+                            
+                              z
+                              ′
+                            
+                            γ
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}z&=\left\{1-{\frac {\omega ^{2}}{v^{2}}}\right\}^{\frac {1}{2}}z'\end{aligned}}\right|&{\begin{aligned}z^{\ast }=z-vt&={\frac {z'}{\gamma }}\end{aligned}}\end{matrix}}}
+  
+
+Thereby, inhomogeneous electromagnetic wave equations are transformed into a Poisson equation. Eventually, George Frederick Charles Searle noted in (1896) that Heaviside's expression leads to a deformation of electric fields which he called "Heaviside-Ellipsoid" of axial ratio
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                        
+                          
+                            
+                              α
+                            
+                          
+                          :
+                          1
+                          :
+                          1
+                        
+                      
+                      
+                        
+                          α
+                          =
+                        
+                        
+                          1
+                          −
+                          
+                            
+                              
+                                u
+                                
+                                  2
+                                
+                              
+                              
+                                v
+                                
+                                  2
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                      
+                        
+                          
+                            1
+                            γ
+                          
+                        
+                        :
+                        1
+                        :
+                        1
+                      
+                    
+                    
+                      
+                        
+                          
+                            1
+                            
+                              γ
+                              
+                                2
+                              
+                            
+                          
+                        
+                      
+                      
+                        
+                        =
+                        1
+                        −
+                        
+                          
+                            
+                              v
+                              
+                                2
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}&{\sqrt {\alpha }}:1:1\\\alpha =&1-{\frac {u^{2}}{v^{2}}}\end{aligned}}\right|&{\begin{aligned}&{\frac {1}{\gamma }}:1:1\\{\frac {1}{\gamma ^{2}}}&=1-{\frac {v^{2}}{c^{2}}}\end{aligned}}\end{matrix}}}
+  
+
+=== Lorentz (1892, 1895) ===
+In order to explain the aberration of light and the result of the Fizeau experiment in accordance with Maxwell's equations, Lorentz in 1892 developed a model ("Lorentz ether theory") in which the aether is completely motionless, and the speed of light in the aether is constant in all directions. In order to calculate the optics of moving bodies, Lorentz introduced the following quantities to transform from the aether system into a moving system (it's unknown whether he was influenced by Voigt, Heaviside, and Thomson)
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            
+                              x
+                            
+                          
+                        
+                        
+                          
+                          =
+                          
+                            
+                              V
+                              
+                                
+                                  V
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  p
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          x
+                        
+                      
+                      
+                        
+                          
+                            t
+                            ′
+                          
+                        
+                        
+                          
+                          =
+                          t
+                          −
+                          
+                            
+                              ε
+                              V
+                            
+                          
+                          
+                            
+                              x
+                            
+                          
+                        
+                      
+                      
+                        
+                          ε
+                        
+                        
+                          
+                          =
+                          
+                            
+                              p
+                              
+                                
+                                  V
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  p
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          x
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        γ
+                        
+                          x
+                          
+                            ∗
+                          
+                        
+                        =
+                        γ
+                        (
+                        x
+                        −
+                        v
+                        t
+                        )
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        t
+                        −
+                        
+                          
+                            
+                              
+                                γ
+                                
+                                  2
+                                
+                              
+                              v
+                              
+                                x
+                                
+                                  ∗
+                                
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                        =
+                        
+                          γ
+                          
+                            2
+                          
+                        
+                        
+                          (
+                          
+                            t
+                            −
+                            
+                              
+                                
+                                  v
+                                  x
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                    
+                      
+                        γ
+                        
+                          
+                            v
+                            c
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            v
+                            
+                              
+                                c
+                                
+                                  2
+                                
+                              
+                              −
+                              
+                                v
+                                
+                                  2
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}{\mathfrak {x}}&={\frac {V}{\sqrt {V^{2}-p^{2}}}}x\\t'&=t-{\frac {\varepsilon }{V}}{\mathfrak {x}}\\\varepsilon &={\frac {p}{\sqrt {V^{2}-p^{2}}}}\end{aligned}}\right|&{\begin{aligned}x^{\prime }&=\gamma x^{\ast }=\gamma (x-vt)\\t^{\prime }&=t-{\frac {\gamma ^{2}vx^{\ast }}{c^{2}}}=\gamma ^{2}\left(t-{\frac {vx}{c^{2}}}\right)\\\gamma {\frac {v}{c}}&={\frac {v}{\sqrt {c^{2}-v^{2}}}}\end{aligned}}\end{matrix}}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-10.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-10.md
new file mode 100644
index 000000000..570765860
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-10.md
@@ -0,0 +1,1241 @@
+---
+title: "History of Lorentz transformations"
+chunk: 11/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  x
+                  
+                    2
+                  
+                
+                +
+                
+                  y
+                  
+                    2
+                  
+                
+                −
+                
+                  z
+                  
+                    2
+                  
+                
+                −
+                1
+                =
+                0
+              
+            
+            
+              
+                
+                  
+                    
+                      
+                        
+                          
+                            δ
+                            a
+                          
+                          
+                            
+                            =
+                            
+                              λ
+                              
+                                2
+                              
+                            
+                            +
+                            
+                              μ
+                              
+                                2
+                              
+                            
+                            +
+                            
+                              ν
+                              
+                                2
+                              
+                            
+                            −
+                            
+                              ρ
+                              
+                                2
+                              
+                            
+                            ,
+                          
+                          
+                            δ
+                            b
+                          
+                          
+                            
+                            =
+                            2
+                            (
+                            λ
+                            μ
+                            +
+                            ν
+                            ρ
+                            )
+                            ,
+                          
+                          
+                            δ
+                            c
+                          
+                          
+                            
+                            =
+                            −
+                            2
+                            (
+                            λ
+                            ν
+                            +
+                            μ
+                            ρ
+                            )
+                            ,
+                          
+                        
+                        
+                          
+                            δ
+                            
+                              a
+                              ′
+                            
+                          
+                          
+                            
+                            =
+                            2
+                            (
+                            λ
+                            μ
+                            −
+                            ν
+                            ρ
+                            )
+                            ,
+                          
+                          
+                            δ
+                            
+                              b
+                              ′
+                            
+                          
+                          
+                            
+                            =
+                            −
+                            
+                              λ
+                              
+                                2
+                              
+                            
+                            +
+                            
+                              μ
+                              
+                                2
+                              
+                            
+                            +
+                            
+                              ν
+                              
+                                2
+                              
+                            
+                            −
+                            
+                              ρ
+                              
+                                2
+                              
+                            
+                            ,
+                          
+                          
+                            δ
+                            
+                              c
+                              ′
+                            
+                          
+                          
+                            
+                            =
+                            2
+                            (
+                            λ
+                            ρ
+                            −
+                            μ
+                            ν
+                            )
+                            ,
+                          
+                        
+                        
+                          
+                            δ
+                            
+                              a
+                              ″
+                            
+                          
+                          
+                            
+                            =
+                            2
+                            (
+                            λ
+                            ν
+                            −
+                            μ
+                            ρ
+                            )
+                            ,
+                          
+                          
+                            δ
+                            
+                              b
+                              ″
+                            
+                          
+                          
+                            
+                            =
+                            2
+                            (
+                            λ
+                            ρ
+                            +
+                            μ
+                            ν
+                            )
+                            ,
+                          
+                          
+                            δ
+                            
+                              c
+                              ″
+                            
+                          
+                          
+                            
+                            =
+                            −
+                            
+                              (
+                              
+                                
+                                  λ
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  μ
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  ν
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  ρ
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            ,
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  (
+                  
+                    δ
+                    =
+                    
+                      λ
+                      
+                        2
+                      
+                    
+                    +
+                    
+                      μ
+                      
+                        2
+                      
+                    
+                    −
+                    
+                      ρ
+                      
+                        2
+                      
+                    
+                    −
+                    
+                      ν
+                      
+                        2
+                      
+                    
+                  
+                  )
+                
+              
+            
+            
+              
+                λ
+                =
+                ν
+                =
+                0
+                →
+                
+                  Hyperbolic rotation
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}x^{2}+y^{2}-z^{2}-1=0\\\hline {\scriptstyle {\begin{aligned}\delta a&=\lambda ^{2}+\mu ^{2}+\nu ^{2}-\rho ^{2},&\delta b&=2(\lambda \mu +\nu \rho ),&\delta c&=-2(\lambda \nu +\mu \rho ),\\\delta a'&=2(\lambda \mu -\nu \rho ),&\delta b'&=-\lambda ^{2}+\mu ^{2}+\nu ^{2}-\rho ^{2},&\delta c'&=2(\lambda \rho -\mu \nu ),\\\delta a''&=2(\lambda \nu -\mu \rho ),&\delta b''&=2(\lambda \rho +\mu \nu ),&\delta c''&=-\left(\lambda ^{2}+\mu ^{2}+\nu ^{2}+\rho ^{2}\right),\end{aligned}}}\\\left(\delta =\lambda ^{2}+\mu ^{2}-\rho ^{2}-\nu ^{2}\right)\\\lambda =\nu =0\rightarrow {\text{Hyperbolic rotation}}\end{matrix}}}
+  
+
+In four dimensions:
+
+  
+    
+      
+        
+          
+            
+              
+                F
+                =
+                
+                  
+                    (
+                    
+                      
+                        x
+                        
+                          1
+                        
+                      
+                      −
+                      
+                        x
+                        
+                          2
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                +
+                
+                  
+                    (
+                    
+                      
+                        y
+                        
+                          1
+                        
+                      
+                      −
+                      
+                        y
+                        
+                          2
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                +
+                
+                  
+                    (
+                    
+                      
+                        z
+                        
+                          1
+                        
+                      
+                      −
+                      
+                        z
+                        
+                          2
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                −
+                
+                  
+                    (
+                    
+                      
+                        t
+                        
+                          1
+                        
+                      
+                      −
+                      
+                        t
+                        
+                          2
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+              
+            
+            
+              
+                
+                  
+                    
+                      
+                        
+                          
+                          
+                            
+                              (
+                              
+                                
+                                  μ
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  ν
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  α
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            cos
+                            ⁡
+                            φ
+                            +
+                            
+                              (
+                              
+                                
+                                  λ
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  β
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  γ
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                          
+                          
+                          
+                            
+                            −
+                            (
+                            α
+                            β
+                            +
+                            λ
+                            μ
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            −
+                            ν
+                            sin
+                            ⁡
+                            φ
+                            −
+                            γ
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                        
+                        
+                          
+                          
+                            
+                            −
+                            (
+                            α
+                            β
+                            +
+                            λ
+                            μ
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            −
+                            ν
+                            sin
+                            ⁡
+                            φ
+                            +
+                            γ
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                          
+                          
+                            
+                              (
+                              
+                                
+                                  μ
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  ν
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  β
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            cos
+                            ⁡
+                            φ
+                            +
+                            
+                              (
+                              
+                                
+                                  μ
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  α
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  γ
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                          
+                        
+                        
+                          
+                          
+                            
+                            −
+                            (
+                            α
+                            γ
+                            +
+                            λ
+                            ν
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            +
+                            μ
+                            sin
+                            ⁡
+                            φ
+                            −
+                            β
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                          
+                          
+                            
+                            −
+                            (
+                            β
+                            μ
+                            +
+                            μ
+                            ν
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            +
+                            λ
+                            sin
+                            ⁡
+                            φ
+                            +
+                            α
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                        
+                        
+                          
+                          
+                            
+                            (
+                            γ
+                            μ
+                            −
+                            β
+                            ν
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            +
+                            α
+                            sin
+                            ⁡
+                            φ
+                            −
+                            λ
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                          
+                          
+                            
+                            −
+                            (
+                            α
+                            ν
+                            −
+                            λ
+                            γ
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            +
+                            β
+                            sin
+                            ⁡
+                            φ
+                            −
+                            μ
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                        
+                        
+                          
+                        
+                        
+                          
+                          
+                            
+                            
+                            −
+                            (
+                            α
+                            γ
+                            +
+                            λ
+                            ν
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            +
+                            μ
+                            sin
+                            ⁡
+                            φ
+                            +
+                            β
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                          
+                          
+                            
+                            
+                            (
+                            β
+                            ν
+                            −
+                            μ
+                            ν
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            +
+                            α
+                            sin
+                            ⁡
+                            φ
+                            −
+                            λ
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                        
+                        
+                          
+                          
+                            
+                            
+                            −
+                            (
+                            β
+                            μ
+                            +
+                            μ
+                            ν
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            −
+                            λ
+                            sin
+                            ⁡
+                            φ
+                            −
+                            α
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                          
+                          
+                            
+                            
+                            (
+                            λ
+                            γ
+                            −
+                            α
+                            ν
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            +
+                            β
+                            sin
+                            ⁡
+                            φ
+                            −
+                            μ
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                        
+                        
+                          
+                          
+                            
+                            
+                              (
+                              
+                                
+                                  λ
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  μ
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  γ
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            cos
+                            ⁡
+                            φ
+                            +
+                            
+                              (
+                              
+                                
+                                  ν
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  α
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  β
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                          
+                          
+                          
+                            
+                            
+                            (
+                            α
+                            μ
+                            −
+                            β
+                            λ
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            +
+                            γ
+                            sin
+                            ⁡
+                            φ
+                            −
+                            ν
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                        
+                        
+                          
+                          
+                            
+                            
+                            (
+                            β
+                            γ
+                            −
+                            α
+                            μ
+                            )
+                            (
+                            cos
+                            ⁡
+                            φ
+                            −
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                            )
+                            +
+                            γ
+                            sin
+                            ⁡
+                            φ
+                            −
+                            ν
+                            sh
+                            ⁡
+                            
+                              θ
+                            
+                          
+                          
+                          
+                            
+                            
+                            −
+                            
+                              (
+                              
+                                
+                                  α
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  β
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  γ
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            cos
+                            ⁡
+                            φ
+                            +
+                            
+                              (
+                              
+                                
+                                  λ
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  μ
+                                  
+                                    2
+                                  
+                                
+                                +
+                                
+                                  ν
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            ch
+                            ⁡
+                            
+                              θ
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  (
+                  
+                    
+                      α
+                      
+                        2
+                      
+                    
+                    +
+                    
+                      β
+                      
+                        2
+                      
+                    
+                    +
+                    
+                      γ
+                      
+                        2
+                      
+                    
+                    −
+                    
+                      λ
+                      
+                        2
+                      
+                    
+                    −
+                    
+                      μ
+                      
+                        2
+                      
+                    
+                    −
+                    
+                      ν
+                      
+                        2
+                      
+                    
+                    =
+                    −
+                    1
+                  
+                  )
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}F=\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}+\left(z_{1}-z_{2}\right)^{2}-\left(t_{1}-t_{2}\right)^{2}\\\hline {\scriptstyle {\begin{aligned}&\left(\mu ^{2}+\nu ^{2}-\alpha ^{2}\right)\cos \varphi +\left(\lambda ^{2}-\beta ^{2}-\gamma ^{2}\right)\operatorname {ch} {\theta }&&-(\alpha \beta +\lambda \mu )(\cos \varphi -\operatorname {ch} {\theta })-\nu \sin \varphi -\gamma \operatorname {sh} {\theta }\\&-(\alpha \beta +\lambda \mu )(\cos \varphi -\operatorname {ch} {\theta })-\nu \sin \varphi +\gamma \operatorname {sh} {\theta }&&\left(\mu ^{2}+\nu ^{2}-\beta ^{2}\right)\cos \varphi +\left(\mu ^{2}-\alpha ^{2}-\gamma ^{2}\right)\operatorname {ch} {\theta }\\&-(\alpha \gamma +\lambda \nu )(\cos \varphi -\operatorname {ch} {\theta })+\mu \sin \varphi -\beta \operatorname {sh} {\theta }&&-(\beta \mu +\mu \nu )(\cos \varphi -\operatorname {ch} {\theta })+\lambda \sin \varphi +\alpha \operatorname {sh} {\theta }\\&(\gamma \mu -\beta \nu )(\cos \varphi -\operatorname {ch} {\theta })+\alpha \sin \varphi -\lambda \operatorname {sh} {\theta }&&-(\alpha \nu -\lambda \gamma )(\cos \varphi -\operatorname {ch} {\theta })+\beta \sin \varphi -\mu \operatorname {sh} {\theta }\\\\&\quad -(\alpha \gamma +\lambda \nu )(\cos \varphi -\operatorname {ch} {\theta })+\mu \sin \varphi +\beta \operatorname {sh} {\theta }&&\quad (\beta \nu -\mu \nu )(\cos \varphi -\operatorname {ch} {\theta })+\alpha \sin \varphi -\lambda \operatorname {sh} {\theta }\\&\quad -(\beta \mu +\mu \nu )(\cos \varphi -\operatorname {ch} {\theta })-\lambda \sin \varphi -\alpha \operatorname {sh} {\theta }&&\quad (\lambda \gamma -\alpha \nu )(\cos \varphi -\operatorname {ch} {\theta })+\beta \sin \varphi -\mu \operatorname {sh} {\theta }\\&\quad \left(\lambda ^{2}+\mu ^{2}-\gamma ^{2}\right)\cos \varphi +\left(\nu ^{2}-\alpha ^{2}-\beta ^{2}\right)\operatorname {ch} {\theta }&&\quad (\alpha \mu -\beta \lambda )(\cos \varphi -\operatorname {ch} {\theta })+\gamma \sin \varphi -\nu \operatorname {sh} {\theta }\\&\quad (\beta \gamma -\alpha \mu )(\cos \varphi -\operatorname {ch} {\theta })+\gamma \sin \varphi -\nu \operatorname {sh} {\theta }&&\quad -\left(\alpha ^{2}+\beta ^{2}+\gamma ^{2}\right)\cos \varphi +\left(\lambda ^{2}+\mu ^{2}+\nu ^{2}\right)\operatorname {ch} {\theta }\end{aligned}}}\\\left(\alpha ^{2}+\beta ^{2}+\gamma ^{2}-\lambda ^{2}-\mu ^{2}-\nu ^{2}=-1\right)\end{matrix}}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-11.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-11.md
new file mode 100644
index 000000000..6e3fb2684
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-11.md
@@ -0,0 +1,273 @@
+---
+title: "History of Lorentz transformations"
+chunk: 12/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+=== Gruner (1921) – Trigonometric Lorentz boosts ===
+In order to simplify the graphical representation of Minkowski space, Paul Gruner (1921) (with the aid of Josef Sauter) developed what is now called Loedel diagrams, using the following relations:
+
+  
+    
+      
+        
+          
+            
+              
+                v
+                =
+                α
+                ⋅
+                c
+                ;
+                
+                β
+                =
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        α
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                sin
+                ⁡
+                φ
+                =
+                α
+                ;
+                
+                β
+                =
+                
+                  
+                    1
+                    
+                      cos
+                      ⁡
+                      φ
+                    
+                  
+                
+                ;
+                
+                α
+                β
+                =
+                tan
+                ⁡
+                φ
+              
+            
+            
+              
+                
+                  x
+                  ′
+                
+                =
+                
+                  
+                    x
+                    
+                      cos
+                      ⁡
+                      φ
+                    
+                  
+                
+                −
+                t
+                ⋅
+                tan
+                ⁡
+                φ
+                ,
+                
+                
+                  t
+                  ′
+                
+                =
+                
+                  
+                    t
+                    
+                      cos
+                      ⁡
+                      φ
+                    
+                  
+                
+                −
+                x
+                ⋅
+                tan
+                ⁡
+                φ
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}v=\alpha \cdot c;\quad \beta ={\frac {1}{\sqrt {1-\alpha ^{2}}}}\\\sin \varphi =\alpha ;\quad \beta ={\frac {1}{\cos \varphi }};\quad \alpha \beta =\tan \varphi \\\hline x'={\frac {x}{\cos \varphi }}-t\cdot \tan \varphi ,\quad t'={\frac {t}{\cos \varphi }}-x\cdot \tan \varphi \end{matrix}}}
+  
+
+In another paper Gruner used the alternative relations:
+
+  
+    
+      
+        
+          
+            
+              
+                α
+                =
+                
+                  
+                    v
+                    c
+                  
+                
+                ;
+                 
+                β
+                =
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        α
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ;
+              
+            
+            
+              
+                cos
+                ⁡
+                θ
+                =
+                α
+                =
+                
+                  
+                    v
+                    c
+                  
+                
+                ;
+                 
+                sin
+                ⁡
+                θ
+                =
+                
+                  
+                    1
+                    β
+                  
+                
+                ;
+                 
+                cot
+                ⁡
+                θ
+                =
+                α
+                ⋅
+                β
+              
+            
+            
+              
+                
+                  x
+                  ′
+                
+                =
+                
+                  
+                    x
+                    
+                      sin
+                      ⁡
+                      θ
+                    
+                  
+                
+                −
+                t
+                ⋅
+                cot
+                ⁡
+                θ
+                ,
+                
+                
+                  t
+                  ′
+                
+                =
+                
+                  
+                    t
+                    
+                      sin
+                      ⁡
+                      θ
+                    
+                  
+                
+                −
+                x
+                ⋅
+                cot
+                ⁡
+                θ
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}\alpha ={\frac {v}{c}};\ \beta ={\frac {1}{\sqrt {1-\alpha ^{2}}}};\\\cos \theta =\alpha ={\frac {v}{c}};\ \sin \theta ={\frac {1}{\beta }};\ \cot \theta =\alpha \cdot \beta \\\hline x'={\frac {x}{\sin \theta }}-t\cdot \cot \theta ,\quad t'={\frac {t}{\sin \theta }}-x\cdot \cot \theta \end{matrix}}}
+  
+
+== See also ==
+Derivations of the Lorentz transformations
+History of special relativity
+
+== References ==
+
+=== Historical mathematical sources ===
+ Learning materials related to History of Topics in Special Relativity/mathsource at Wikiversity
+
+=== Historical relativity sources ===
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-12.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-12.md
new file mode 100644
index 000000000..de6948c2f
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-12.md
@@ -0,0 +1,30 @@
+---
+title: "History of Lorentz transformations"
+chunk: 13/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+Abraham, M. (1905). "§ 42. Die Lichtzeit in einem gleichförmig bewegten System" . Theorie der Elektrizität: Elektromagnetische Theorie der Strahlung. Leipzig: Teubner. Bateman, Harry (1910) [1909]. "The Transformation of the Electrodynamical Equations" . Proceedings of the London Mathematical Society. 8: 223–264. doi:10.1112/plms/s2-8.1.223. Bateman, Harry (1912) [1910]. "Some geometrical theorems connected with Laplace's equation and the equation of wave motion". American Journal of Mathematics. 34 (3): 325–360. doi:10.2307/2370223. JSTOR 2370223. Borel, Émile (1914). Introduction Geometrique à quelques Théories Physiques. Paris: Gauthier-Villars. Brill, J. (1925). "Note on the Lorentz group". Mathematical Proceedings of the Cambridge Philosophical Society. 22 (5): 630–632. Bibcode:1925PCPS...22..630B. doi:10.1017/S030500410000949X. S2CID 121117536. Bucherer, A. H. (1904). Mathematische Einführung in die Elektronentheorie. Leipzig: Teubner. Bucherer, A. H. (1908), "Messungen an Becquerelstrahlen. Die experimentelle Bestätigung der Lorentz-Einsteinschen Theorie. (Measurements of Becquerel rays. The Experimental Confirmation of the Lorentz-Einstein Theory)", Physikalische Zeitschrift, 9 (22): 758–762. For Minkowski's and Voigt's statements see p. 762. Cartan, Élie (1912). "Sur les groupes de transformation de contact et la Cinématique nouvelle". Société de Mathématique the France – Comptes Rendus des Séances: 23. Cohn, Emil (1904a), "Zur Elektrodynamik bewegter Systeme I" [On the Electrodynamics of Moving Systems I], Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, 1904/2 (40): 1294–1303
+Cohn, Emil (1904b), "Zur Elektrodynamik bewegter Systeme II" [On the Electrodynamics of Moving Systems II], Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, 1904/2 (43): 1404–1416
+Conway, A. W. (1911). "On the application of quaternions to some recent developments of electrical theory". Proceedings of the Royal Irish Academy, Section A. 29: 1–9. Cunningham, Ebenezer (1910) [1909]. "The principle of Relativity in Electrodynamics and an Extension Thereof" . Proceedings of the London Mathematical Society. 8: 77–98. doi:10.1112/plms/s2-8.1.77. Einstein, Albert (1905), "Zur Elektrodynamik bewegter Körper" (PDF), Annalen der Physik, 322 (10): 891–921, Bibcode:1905AnP...322..891E, doi:10.1002/andp.19053221004. See also: English translation. Frank, Philipp (1909). "Die Stellung des Relativitätsprinzips im System der Mechanik und Elektrodynamik". Wiener Sitzungsberichte IIA. 118: 373–446. hdl:2027/mdp.39015073682224. Frank, Philipp; Rothe, Hermann (1911). "Über die Transformation der Raum-Zeitkoordinaten von ruhenden auf bewegte Systeme". Annalen der Physik. 339 (5): 825–855. Bibcode:1911AnP...339..825F. doi:10.1002/andp.19113390502. Frank, Philipp; Rothe, Hermann (1912). "Zur Herleitung der Lorentztransformation". Physikalische Zeitschrift. 13: 750–753. Gans, Richard (1905), "H. A. Lorentz. Elektromagnetische Vorgänge" [H.A. Lorentz: Electromagnetic Phenomena], Beiblätter zu den Annalen der Physik, 29 (4): 168–170
+Gruner, Paul & Sauter, Josef (1921a). "Représentation géométrique élémentaire des formules de la théorie de la relativité" [Elementary geometric representation of the formulas of the special theory of relativity]. Archives des sciences physiques et naturelles. 5. 3: 295–296. Gruner, Paul (1921b). "Eine elementare geometrische Darstellung der Transformationsformeln der speziellen Relativitätstheorie" [An elementary geometrical representation of the transformation formulas of the special theory of relativity]. Physikalische Zeitschrift. 22: 384–385. Heaviside, Oliver (1889), "On the Electromagnetic Effects due to the Motion of Electrification through a Dielectric", Philosophical Magazine, 5, 27 (167): 324–339, doi:10.1080/14786448908628362
+Herglotz, Gustav (1910) [1909], "Über den vom Standpunkt des Relativitätsprinzips aus als starr zu bezeichnenden Körper" [Wikisource translation: On bodies that are to be designated as "rigid" from the standpoint of the relativity principle], Annalen der Physik, 336 (2): 393–415, Bibcode:1910AnP...336..393H, doi:10.1002/andp.19103360208
+Herglotz, G. (1911). "Über die Mechanik des deformierbaren Körpers vom Standpunkte der Relativitätstheorie". Annalen der Physik. 341 (13): 493–533. Bibcode:1911AnP...341..493H. doi:10.1002/andp.19113411303.; English translation by David Delphenich: On the mechanics of deformable bodies from the standpoint of relativity theory. Ignatowsky, W. v. (1910). "Einige allgemeine Bemerkungen über das Relativitätsprinzip" . Physikalische Zeitschrift. 11: 972–976. Ignatowski, W. v. (1911) [1910]. "Das Relativitätsprinzip" . Archiv der Mathematik und Physik. 18: 17–40. Ignatowski, W. v. (1911). "Eine Bemerkung zu meiner Arbeit: "Einige allgemeine Bemerkungen zum Relativitätsprinzip"" . Physikalische Zeitschrift. 12: 779. Klein, F. (1908). Hellinger, E. (ed.). Elementarmethematik vom höheren Standpunkte aus. Teil I. Vorlesung gehalten während des Wintersemesters 1907-08. Leipzig: Teubner. Klein, Felix (1921) [1910]. "Über die geometrischen Grundlagen der Lorentzgruppe". Gesammelte Mathematische Abhandlungen . Vol. 1. pp. 533–552. doi:10.1007/978-3-642-51960-4_31 (inactive 12 July 2025). ISBN 978-3-642-51898-0. {{cite book}}: ISBN / Date incompatibility (help)CS1 maint: DOI inactive as of July 2025 (link)
+Klein, F.; Sommerfeld A. (1910). Noether, Fr. (ed.). Über die Theorie des Kreisels. Heft IV. Leipzig: Teuber. Klein, F. (1911). Hellinger, E. (ed.). Elementarmethematik vom höheren Standpunkte aus. Teil I (Second Edition). Vorlesung gehalten während des Wintersemesters 1907-08. Leipzig: Teubner. hdl:2027/mdp.39015068187817. Larmor, Joseph (1897), "On a Dynamical Theory of the Electric and Luminiferous Medium, Part 3, Relations with material media" , Philosophical Transactions of the Royal Society, 190: 205–300, Bibcode:1897RSPTA.190..205L, doi:10.1098/rsta.1897.0020
+Larmor, Joseph (1929) [1897], "On a Dynamical Theory of the Electric and Luminiferous Medium. Part 3: Relations with material media", Mathematical and Physical Papers: Volume II, Cambridge University Press, pp. 2–132, ISBN 978-1-107-53640-1 {{citation}}: ISBN / Date incompatibility (help) (Reprint of Larmor (1897) with new annotations by Larmor.)
+Larmor, Joseph (1900), Aether and Matter , Cambridge University Press
+Larmor, Joseph (1904a). "On the intensity of the natural radiation from moving bodies and its mechanical reaction". Philosophical Magazine. 7 (41): 578–586. doi:10.1080/14786440409463149. Larmor, Joseph (1904b). "On the ascertained Absence of Effects of Motion through the Aether, in relation to the Constitution of Matter, and on the FitzGerald-Lorentz Hypothesis" . Philosophical Magazine. 7 (42): 621–625. doi:10.1080/14786440409463156. Lorentz, Hendrik Antoon (1892a), "La Théorie electromagnétique de Maxwell et son application aux corps mouvants", Archives Néerlandaises des Sciences Exactes et Naturelles, 25: 363–552
+Lorentz, Hendrik Antoon (1892b), "De relatieve beweging van de aarde en den aether" [The Relative Motion of the Earth and the Aether], Zittingsverlag Akad. V. Wet., 1: 74–79
+Lorentz, Hendrik Antoon (1895), Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern  [Attempt of a Theory of Electrical and Optical Phenomena in Moving Bodies], Leiden: E.J. Brill
+Lorentz, Hendrik Antoon (1899), "Simplified Theory of Electrical and Optical Phenomena in Moving Systems" , Proceedings of the Royal Netherlands Academy of Arts and Sciences, 1: 427–442, Bibcode:1898KNAB....1..427L
+Lorentz, Hendrik Antoon (1904), "Electromagnetic phenomena in a system moving with any velocity smaller than that of light" , Proceedings of the Royal Netherlands Academy of Arts and Sciences, 6: 809–831, Bibcode:1903KNAB....6..809L
+Lorentz, Hendrik Antoon (1916) [1915], The theory of electrons and its applications to the phenomena of light and radiant heat, Leipzig & Berlin: B.G. Teubner
+Minkowski, Hermann (1915) [1907], "Das Relativitätsprinzip" , Annalen der Physik, 352 (15): 927–938, Bibcode:1915AnP...352..927M, doi:10.1002/andp.19153521505
+Minkowski, Hermann (1908) [1907], "Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern"  [The Fundamental Equations for Electromagnetic Processes in Moving Bodies], Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse: 53–111
+Minkowski, Hermann (1909) [1908], "Space and Time" , Physikalische Zeitschrift, 10: 75–88
+Müller, Hans Robert (1948). "Zyklographische Betrachtung der Kinematik der speziellen Relativitätstheorie". Monatshefte für Mathematik und Physik. 52 (4): 337–353. doi:10.1007/BF01525338. S2CID 120150204. Plummer, H.C.K. (1910), "On the Theory of Aberration and the Principle of Relativity", Monthly Notices of the Royal Astronomical Society, 40 (3): 252–266, Bibcode:1910MNRAS..70..252P, doi:10.1093/mnras/70.3.252
+Poincaré, Henri (1900), "La théorie de Lorentz et le principe de réaction" , Archives Néerlandaises des Sciences Exactes et Naturelles, 5: 252–278. See also the English translation. Poincaré, Henri (1906) [1904], "The Principles of Mathematical Physics" , Congress of arts and science, universal exposition, St. Louis, 1904, vol. 1, Boston and New York: Houghton, Mifflin and Company, pp.
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+---
+title: "History of Lorentz transformations"
+chunk: 14/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+604–622
+Poincaré, Henri (1905), "Sur la dynamique de l'électron"  [On the Dynamics of the Electron], Comptes Rendus, 140: 1504–1508
+Poincaré, Henri (1906) [1905], "Sur la dynamique de l'électron"  [On the Dynamics of the Electron], Rendiconti del Circolo Matematico di Palermo, 21: 129–176, Bibcode:1906RCMP...21..129P, doi:10.1007/BF03013466, hdl:2027/uiug.30112063899089, S2CID 120211823
+Poincaré, Henri (1921) [1912]. "Rapport sur les travaux de M. Cartan (fait à la Faculté des sciences de l'Université de Paris)". Acta Mathematica. 38 (1): 137–145. doi:10.1007/bf02392064. Written by Poincaré in 1912, printed in Acta Mathematica in 1914 though belatedly published in 1921. Searle, George Frederick Charles (1897), "On the Steady Motion of an Electrified Ellipsoid" , Philosophical Magazine, 5, 44 (269): 329–341, doi:10.1080/14786449708621072
+Silberstein, L. (1912) [1911], "Quaternionic form of relativity", The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 23 (137): 790–809, doi:10.1080/14786440508637276
+Sommerfeld, A. (1909), "Über die Zusammensetzung der Geschwindigkeiten in der Relativtheorie" [Wikisource translation: On the Composition of Velocities in the Theory of Relativity], Verh. Dtsch. Phys. Ges., 21: 577–582
+Thomson, Joseph John (1889), "On the Magnetic Effects produced by Motion in the Electric Field" , Philosophical Magazine, 5, 28 (170): 1–14, doi:10.1080/14786448908619821
+Varićak, V. (1910), "Anwendung der Lobatschefskijschen Geometrie in der Relativtheorie"  [Application of Lobachevskian Geometry in the Theory of Relativity], Physikalische Zeitschrift, 11: 93–6
+Varičak, V. (1912), "Über die nichteuklidische Interpretation der Relativtheorie"  [On the Non-Euclidean Interpretation of the Theory of Relativity], Jahresbericht der Deutschen Mathematiker-Vereinigung, 21: 103–127
+Voigt, Woldemar (1887), "Ueber das Doppler'sche Princip"  [On the Principle of Doppler], Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen (2): 41–51
+Wien, Wilhelm (1904). "Zur Elektronentheorie" . Physikalische Zeitschrift. 5 (14): 393–395.
\ No newline at end of file
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+---
+title: "History of Lorentz transformations"
+chunk: 15/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+=== Secondary sources ===
+
+Baccetti, Valentina; Tate, Kyle; Visser, Matt (2012). "Inertial frames without the relativity principle". Journal of High Energy Physics. 2012 (5): 119. arXiv:1112.1466. Bibcode:2012JHEP...05..119B. doi:10.1007/JHEP05(2012)119. S2CID 118695037.
+Bachmann, P. (1898). Die Arithmetik der quadratischen Formen. Erste Abtheilung. Leipzig: B.G. Teubner.
+Bachmann, P. (1923). Die Arithmetik der quadratischen Formen. Zweite Abtheilung. Leipzig: B.G. Teubner.
+Barnett, J. H. (2004). "Enter, stage center: The early drama of the hyperbolic functions" (PDF). Mathematics Magazine. 77 (1): 15–30. doi:10.1080/0025570x.2004.11953223. S2CID 121088132.
+Bôcher, Maxim (1907). "Quadratic forms". Introduction to higher algebra. New York: Macmillan.
+Bondi, Hermann (1964). Relativity and Common Sense. New York: Doubleday & Company.
+Bonola, R. (1912). Non-Euclidean geometry: A critical and historical study of its development. Chicago: Open Court.
+Brown, Harvey R. (2001), "The origins of length contraction: I. The FitzGerald-Lorentz deformation hypothesis", American Journal of Physics, 69 (10): 1044–1054, arXiv:gr-qc/0104032, Bibcode:2001AmJPh..69.1044B, doi:10.1119/1.1379733, S2CID 2945585 See also "Michelson, FitzGerald and Lorentz: the origins of relativity revisited", Online.
+Cartan, É.; Study, E. (1908). "Nombres complexes". Encyclopédie des Sciences Mathématiques Pures et Appliquées. 1 (1): 328–468.
+Cartan, É.; Fano, G. (1955) [1915]. "La théorie des groupes continus et la géométrie". Encyclopédie des Sciences Mathématiques Pures et Appliquées. 3 (1): 39–43. (Only pages 1–21 were published in 1915, the entire article including pp. 39–43 concerning the groups of Laguerre and Lorentz was posthumously published in 1955 in Cartan's collected papers, and was reprinted in the Encyclopédie in 1991.)
+Coolidge, Julian (1916). A treatise on the circle and the sphere. Oxford: Clarendon Press.
+Darrigol, Olivier (2000), Electrodynamics from Ampère to Einstein, Oxford: Oxford Univ. Press, ISBN 978-0-19-850594-5
+Darrigol, Olivier (2005), "The Genesis of the theory of relativity" (PDF), Séminaire Poincaré, 1: 1–22, Bibcode:2006eins.book....1D, doi:10.1007/3-7643-7436-5_1, ISBN 978-3-7643-7435-8{{citation}}:  CS1 maint: work parameter with ISBN (link)
+Dickson, L.E. (1923). History of the theory of numbers, Volume III, Quadratic and higher forms. Washington: Washington Carnegie Institution of Washington.
+Fjelstad, P. (1986). "Extending special relativity via the perplex numbers". American Journal of Physics. 54 (5): 416–422. Bibcode:1986AmJPh..54..416F. doi:10.1119/1.14605.
+Girard, P. R. (1984). "The quaternion group and modern physics". European Journal of Physics. 5 (1): 25–32. Bibcode:1984EJPh....5...25G. doi:10.1088/0143-0807/5/1/007. S2CID 250775753.
+Gray, J. (1979). "Non-euclidean geometry—A re-interpretation". Historia Mathematica. 6 (3): 236–258. doi:10.1016/0315-0860(79)90124-1.
+Gray, J.; Scott W. (1997). "Introduction" (PDF). Trois suppléments sur la découverte des fonctions fuchsiennes (PDF). Berlin. pp. 7–28.{{cite book}}:  CS1 maint: location missing publisher (link)
+Hawkins, Thomas (2013). "The Cayley–Hermite problem and matrix algebra". The Mathematics of Frobenius in Context: A Journey Through 18th to 20th Century Mathematics. Springer. ISBN 978-1461463337.
+Janssen, Michel (1995), A Comparison between Lorentz's Ether Theory and Special Relativity in the Light of the Experiments of Trouton and Noble (Thesis)
+Kastrup, H. A. (2008). "On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics". Annalen der Physik. 520 (9–10): 631–690. arXiv:0808.2730. Bibcode:2008AnP...520..631K. doi:10.1002/andp.200810324. S2CID 12020510.
+Katzir, Shaul (2005), "Poincaré's Relativistic Physics: Its Origins and Nature", Physics in Perspective, 7 (3): 268–292, Bibcode:2005PhP.....7..268K, doi:10.1007/s00016-004-0234-y, S2CID 14751280
+Klein, F. (1897) [1896]. The Mathematical Theory of the Top. New York: Scribner.
+Klein, Felix; Blaschke, Wilhelm (1926). Vorlesungen über höhere Geometrie. Berlin: Springer.
+von Laue, M. (1921). Die Relativitätstheorie, Band 1 (fourth edition of "Das Relativitätsprinzip" ed.). Vieweg.; First edition 1911, second expanded edition 1913, third expanded edition 1919.
+Lorente, M. (2003). "Representations of classical groups on the lattice and its application to the field theory on discrete space-time". Symmetries in Science. VI: 437–454. arXiv:hep-lat/0312042. Bibcode:2003hep.lat..12042L.
+Macrossan, M. N. (1986), "A Note on Relativity Before Einstein", The British Journal for the Philosophy of Science, 37 (2): 232–234, CiteSeerX 10.1.1.679.5898, doi:10.1093/bjps/37.2.232
+Madelung, E. (1922). Die mathematischen Hilfsmittel des Physikers. Berlin: Springer.
+Majerník, V. (1986). "Representation of relativistic quantities by trigonometric functions". American Journal of Physics. 54 (6): 536–538. Bibcode:1986AmJPh..54..536M. doi:10.1119/1.14557.
+Meyer, W.F. (1899). "Invariantentheorie". Encyclopädie der Mathematischen Wissenschaften. 1 (1): 322–455.
+Miller, Arthur I. (1981), Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, ISBN 978-0-201-04679-3
+Møller, C. (1955) [1952]. The theory of relativity. Oxford Clarendon Press.
+Müller, Emil (1910). "Die verschiedenen Koordinatensysteme". Encyclopädie der Mathematischen Wissenschaften. 3.1.1: 596–770.
+Musen, P. (1970). "A Discussion of Hill's Method of Secular Perturbations...". Celestial Mechanics. 2 (1): 41–59. Bibcode:1970CeMec...2...41M. doi:10.1007/BF01230449. hdl:2060/19700018328. S2CID 122335532.
+Naimark, M. A. (2014) [1964]. Linear Representations of the Lorentz Group. Oxford. ISBN 978-1483184982.{{cite book}}:  CS1 maint: location missing publisher (link)
+Pacheco, R. (2008). "Bianchi–Bäcklund transforms and dressing actions, revisited". Geometriae Dedicata. 146 (1): 85–99. arXiv:0808.4138. doi:10.1007/s10711-009-9427-5. S2CID 14356965.
+Pais, Abraham (1982), Subtle is the Lord: The Science and the Life of Albert Einstein, New York: Oxford University Press, ISBN 978-0-19-520438-4
+Pauli, Wolfgang (1921), "Die Relativitätstheorie", Encyclopädie der Mathematischen Wissenschaften, 5 (2): 539–776 In English: Pauli, W. (1981) [1921]. Theory of Relativity. Vol. 165. Dover Publications. ISBN 978-0-486-64152-2.
+Penrose, R.; Rindler W. (1984), Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields, Cambridge University Press, ISBN 978-0521337076
+Plummer, H. C. (1910), "On the Theory of Aberration and the Principle of Relativity", Monthly Notices of the Royal Astronomical Society, 70 (3): 252–266, Bibcode:1910MNRAS..70..252P, doi:10.1093/mnras/70.3.252
+Ratcliffe, J. G. (1994). "Hyperbolic geometry". Foundations of Hyperbolic Manifolds. New York. pp. 56–104. ISBN 978-0387943480.{{cite book}}:  CS1 maint: location missing publisher (link)
+Reynolds, W. F. (1993). "Hyperbolic geometry on a hyperboloid". The American Mathematical Monthly. 100 (5): 442–455. doi:10.1080/00029890.1993.11990430. JSTOR 2324297. S2CID 124088818.
+Rindler, W. (2013) [1969]. Essential Relativity: Special, General, and Cosmological. Springer. ISBN 978-1475711356.
+Robinson, E.A. (1990). Einstein's relativity in metaphor and mathematics. Prentice Hall. ISBN 9780132464970.
+Rosenfeld, B.A. (1988). A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space. New York: Springer. ISBN 978-1441986801.
+Rothe, H. (1916). "Systeme geometrischer Analyse". Encyclopädie der Mathematischen Wissenschaften. 3.1.1: 1282–1425.
+Schottenloher, M. (2008). A Mathematical Introduction to Conformal Field Theory. Springer. ISBN 978-3540706908.
+Silberstein, L. (1914). The Theory of Relativity. London: Macmillan.
+Sobczyk, G. (1995). "The Hyperbolic Number Plane". The College Mathematics Journal. 26 (4): 268–280. doi:10.2307/2687027. JSTOR 2687027.
+Sommerville, D. M. L. Y. (1911). Bibliography of non-Euclidean geometry. London: London Pub. by Harrison for the University of St. Andrews.
+Synge, J. L. (1956), Relativity: The Special Theory, North Holland
+Synge, J.L. (1972). "Quaternions, Lorentz transformations, and the Conway–Dirac–Eddington matrices". Communications of the Dublin Institute for Advanced Studies. 21.
+Terng, C. L. & Uhlenbeck, K. (2000). "Geometry of solitons" (PDF). Notices of the AMS. 47 (1): 17–25.
+Touma, J. R.; Tremaine, S. & Kazandjian, M. V. (2009). "Gauss's method for secular dynamics, softened". Monthly Notices of the Royal Astronomical Society. 394 (2): 1085–1108. arXiv:0811.2812. Bibcode:2009MNRAS.394.1085T. doi:10.1111/j.1365-2966.2009.14409.x. S2CID 14531003.
+Volk, O. (1976). "Miscellanea from the history of celestial mechanics". Celestial Mechanics. 14 (3): 365–382. Bibcode:1976CeMec..14..365V. doi:10.1007/bf01228523. S2CID 122955645.
+Walter, Scott A. (1999). "Minkowski, mathematicians, and the mathematical theory of relativity". In H. Goenner; J. Renn; J. Ritter; T. Sauer (eds.). The Expanding Worlds of General Relativity. Einstein Studies. Vol. 7. Boston: Birkhäuser. pp. 45–86. ISBN 978-0-8176-4060-6.
+Walter, Scott A. (1999b). "The non-Euclidean style of Minkowskian relativity". In J. Gray (ed.). The Symbolic Universe: Geometry and Physics. Oxford: Oxford University Press. pp. 91–127.
+Walter, Scott A. (2018). "Figures of Light in the Early History of Relativity (1905–1914)". In Rowe D.; Sauer T.; Walter S. (eds.). Beyond Einstein. Einstein Studies. Vol. 14. New York: Birkhäuser. pp. 3–50. doi:10.1007/978-1-4939-7708-6_1. ISBN 978-1-4939-7708-6. S2CID 31840179.
+
+== External links ==
+Mathpages: 1.4 The Relativity of Light
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-2.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-2.md
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+---
+title: "History of Lorentz transformations"
+chunk: 3/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+where x* is the Galilean transformation x-vt. Except the additional γ in the time transformation, this is the complete Lorentz transformation. While t is the "true" time for observers resting in the aether, t′ is an auxiliary variable only for calculating processes for moving systems. It is also important that Lorentz and later also Larmor formulated this transformation in two steps. At first an implicit Galilean transformation, and later the expansion into the "fictitious" electromagnetic system with the aid of the Lorentz transformation. In order to explain the negative result of the Michelson–Morley experiment, he (1892b) introduced the additional hypothesis that also intermolecular forces are affected in a similar way and introduced length contraction in his theory (without proof as he admitted). The same hypothesis had been made previously by George FitzGerald in 1889 based on Heaviside's work. While length contraction was a real physical effect for Lorentz, he considered the time transformation only as a heuristic working hypothesis and a mathematical stipulation.
+In 1895, Lorentz further elaborated on his theory and introduced the "theorem of corresponding states". This theorem states that a moving observer (relative to the ether) in his "fictitious" field makes the same observations as a resting observers in his "real" field for velocities to first order in v/c. Lorentz showed that the dimensions of electrostatic systems in the ether and a moving frame are connected by this transformation:
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+                          
+                        
+                        =
+                        x
+                        −
+                        v
+                        t
+                      
+                      
+                        
+                        =
+                        
+                          
+                            
+                              x
+                              
+                                ′
+                              
+                            
+                            γ
+                          
+                        
+                      
+                    
+                    
+                      
+                        y
+                      
+                      
+                        
+                        =
+                        
+                          y
+                          
+                            ′
+                          
+                        
+                      
+                    
+                    
+                      
+                        z
+                      
+                      
+                        
+                        =
+                        
+                          z
+                          
+                            ′
+                          
+                        
+                      
+                    
+                    
+                      
+                        t
+                      
+                      
+                        
+                        =
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}x&=x^{\prime }{\sqrt {1-{\frac {{\mathfrak {p}}^{2}}{V^{2}}}}}\\y&=y^{\prime }\\z&=z^{\prime }\\t&=t^{\prime }\end{aligned}}\right|&{\begin{aligned}x^{\ast }=x-vt&={\frac {x^{\prime }}{\gamma }}\\y&=y^{\prime }\\z&=z^{\prime }\\t&=t^{\prime }\end{aligned}}\end{matrix}}}
+  
+
+For solving optical problems Lorentz used the following transformation, in which the modified time variable was called "local time" (German: Ortszeit) by him:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          x
+                        
+                        
+                          
+                          =
+                          
+                            x
+                          
+                          −
+                          
+                            
+                              
+                                p
+                              
+                            
+                            
+                              x
+                            
+                          
+                          t
+                        
+                      
+                      
+                        
+                          y
+                        
+                        
+                          
+                          =
+                          
+                            y
+                          
+                          −
+                          
+                            
+                              
+                                p
+                              
+                            
+                            
+                              y
+                            
+                          
+                          t
+                        
+                      
+                      
+                        
+                          z
+                        
+                        
+                          
+                          =
+                          
+                            z
+                          
+                          −
+                          
+                            
+                              
+                                p
+                              
+                            
+                            
+                              z
+                            
+                          
+                          t
+                        
+                      
+                      
+                        
+                          
+                            t
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          t
+                          −
+                          
+                            
+                              
+                                
+                                  
+                                    p
+                                  
+                                
+                                
+                                  x
+                                
+                              
+                              
+                                V
+                                
+                                  2
+                                
+                              
+                            
+                          
+                          x
+                          −
+                          
+                            
+                              
+                                
+                                  
+                                    p
+                                  
+                                
+                                
+                                  y
+                                
+                              
+                              
+                                V
+                                
+                                  2
+                                
+                              
+                            
+                          
+                          y
+                          −
+                          
+                            
+                              
+                                
+                                  
+                                    p
+                                  
+                                
+                                
+                                  z
+                                
+                              
+                              
+                                V
+                                
+                                  2
+                                
+                              
+                            
+                          
+                          z
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          x
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        x
+                        −
+                        
+                          v
+                          
+                            x
+                          
+                        
+                        t
+                      
+                    
+                    
+                      
+                        
+                          y
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        y
+                        −
+                        
+                          v
+                          
+                            y
+                          
+                        
+                        t
+                      
+                    
+                    
+                      
+                        
+                          z
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        z
+                        −
+                        
+                          v
+                          
+                            z
+                          
+                        
+                        t
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        t
+                        −
+                        
+                          
+                            
+                              v
+                              
+                                x
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                        
+                          x
+                          ′
+                        
+                        −
+                        
+                          
+                            
+                              v
+                              
+                                y
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                        
+                          y
+                          ′
+                        
+                        −
+                        
+                          
+                            
+                              v
+                              
+                                z
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                        
+                          z
+                          ′
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}x&=\mathrm {x} -{\mathfrak {p}}_{x}t\\y&=\mathrm {y} -{\mathfrak {p}}_{y}t\\z&=\mathrm {z} -{\mathfrak {p}}_{z}t\\t^{\prime }&=t-{\frac {{\mathfrak {p}}_{x}}{V^{2}}}x-{\frac {{\mathfrak {p}}_{y}}{V^{2}}}y-{\frac {{\mathfrak {p}}_{z}}{V^{2}}}z\end{aligned}}\right|&{\begin{aligned}x^{\prime }&=x-v_{x}t\\y^{\prime }&=y-v_{y}t\\z^{\prime }&=z-v_{z}t\\t^{\prime }&=t-{\frac {v_{x}}{c^{2}}}x'-{\frac {v_{y}}{c^{2}}}y'-{\frac {v_{z}}{c^{2}}}z'\end{aligned}}\end{matrix}}}
+  
+
+With this concept Lorentz could explain the Doppler effect, the aberration of light, and the Fizeau experiment.
+
+=== Larmor (1897, 1900) ===
+In 1897, Larmor extended the work of Lorentz and derived the following transformation
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            x
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          x
+                          
+                            ε
+                            
+                              
+                                1
+                                2
+                              
+                            
+                          
+                        
+                      
+                      
+                        
+                          
+                            y
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          y
+                        
+                      
+                      
+                        
+                          
+                            z
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          z
+                        
+                      
+                      
+                        
+                          
+                            t
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          t
+                          −
+                          v
+                          x
+                          
+                            /
+                          
+                          
+                            c
+                            
+                              2
+                            
+                          
+                        
+                      
+                      
+                        
+                          d
+                          
+                            t
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          d
+                          
+                            t
+                            
+                              ′
+                            
+                          
+                          
+                            ε
+                            
+                              −
+                              
+                                
+                                  1
+                                  2
+                                
+                              
+                            
+                          
+                        
+                      
+                      
+                        
+                          ε
+                        
+                        
+                          
+                          =
+                          
+                            
+                              (
+                              
+                                1
+                                −
+                                
+                                  v
+                                  
+                                    2
+                                  
+                                
+                                
+                                  /
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                              )
+                            
+                            
+                              −
+                              1
+                            
+                          
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          x
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        γ
+                        
+                          x
+                          
+                            ∗
+                          
+                        
+                        =
+                        γ
+                        (
+                        x
+                        −
+                        v
+                        t
+                        )
+                      
+                    
+                    
+                      
+                        
+                          y
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        y
+                      
+                    
+                    
+                      
+                        
+                          z
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        z
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        t
+                        −
+                        
+                          
+                            
+                              v
+                              
+                                x
+                                
+                                  ∗
+                                
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                        =
+                        t
+                        −
+                        
+                          
+                            
+                              v
+                              (
+                              x
+                              −
+                              v
+                              t
+                              )
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                      
+                    
+                    
+                      
+                        d
+                        
+                          t
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            
+                              d
+                              
+                                t
+                                
+                                  ′
+                                
+                              
+                            
+                            γ
+                          
+                        
+                      
+                    
+                    
+                      
+                        
+                          γ
+                          
+                            2
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            1
+                            
+                              1
+                              −
+                              
+                                
+                                  
+                                    v
+                                    
+                                      2
+                                    
+                                  
+                                  
+                                    c
+                                    
+                                      2
+                                    
+                                  
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}x_{1}&=x\varepsilon ^{\frac {1}{2}}\\y_{1}&=y\\z_{1}&=z\\t^{\prime }&=t-vx/c^{2}\\dt_{1}&=dt^{\prime }\varepsilon ^{-{\frac {1}{2}}}\\\varepsilon &=\left(1-v^{2}/c^{2}\right)^{-1}\end{aligned}}\right|&{\begin{aligned}x_{1}&=\gamma x^{\ast }=\gamma (x-vt)\\y_{1}&=y\\z_{1}&=z\\t^{\prime }&=t-{\frac {vx^{\ast }}{c^{2}}}=t-{\frac {v(x-vt)}{c^{2}}}\\dt_{1}&={\frac {dt^{\prime }}{\gamma }}\\\gamma ^{2}&={\frac {1}{1-{\frac {v^{2}}{c^{2}}}}}\end{aligned}}\end{matrix}}}
+  
+
+Larmor noted that if it is assumed that the constitution of molecules is electrical then the FitzGerald–Lorentz contraction is a consequence of this transformation, explaining the Michelson–Morley experiment. It's notable that Larmor was the first who recognized that some sort of time dilation is a consequence of this transformation as well, because "individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio 1/γ". Larmor wrote his electrodynamical equations and transformations neglecting terms of higher order than (v/c)2 – when his 1897 paper was reprinted in 1929, Larmor added the following comment in which he described how they can be made valid to all orders of v/c:
+
+Nothing need be neglected: the transformation is exact if v/c2 is replaced by εv/c2 in the equations and also in the change following from t to t′, as is worked out in Aether and Matter (1900), p. 168, and as Lorentz found it to be in 1904, thereby stimulating the modern schemes of intrinsic relational relativity.
+In line with that comment, in his book Aether and Matter published in 1900, Larmor used a modified local time t″=t′-εvx′/c2 instead of the 1897 expression t′=t-vx/c2 by replacing v/c2 with εv/c2, so that t″ is now identical to the one given by Lorentz in 1892, which he combined with a Galilean transformation for the x′, y′, z′, t′ coordinates:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            x
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          x
+                          −
+                          v
+                          t
+                        
+                      
+                      
+                        
+                          
+                            y
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          y
+                        
+                      
+                      
+                        
+                          
+                            z
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          z
+                        
+                      
+                      
+                        
+                          
+                            t
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          t
+                        
+                      
+                      
+                        
+                          
+                            t
+                            
+                              ′
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          
+                            t
+                            
+                              ′
+                            
+                          
+                          −
+                          ε
+                          v
+                          
+                            x
+                            
+                              ′
+                            
+                          
+                          
+                            /
+                          
+                          
+                            c
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          x
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        x
+                        −
+                        v
+                        t
+                      
+                    
+                    
+                      
+                        
+                          y
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        y
+                      
+                    
+                    
+                      
+                        
+                          z
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        z
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        t
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            ′
+                            ′
+                          
+                        
+                        =
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                        −
+                        
+                          
+                            
+                              
+                                γ
+                                
+                                  2
+                                
+                              
+                              v
+                              
+                                x
+                                
+                                  ′
+                                
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          γ
+                          
+                            2
+                          
+                        
+                        
+                          (
+                          
+                            t
+                            −
+                            
+                              
+                                
+                                  v
+                                  x
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}x^{\prime }&=x-vt\\y^{\prime }&=y\\z^{\prime }&=z\\t^{\prime }&=t\\t^{\prime \prime }&=t^{\prime }-\varepsilon vx^{\prime }/c^{2}\end{aligned}}\right|&{\begin{aligned}x^{\prime }&=x-vt\\y^{\prime }&=y\\z^{\prime }&=z\\t^{\prime }&=t\\t^{\prime \prime }=t^{\prime }-{\frac {\gamma ^{2}vx^{\prime }}{c^{2}}}&=\gamma ^{2}\left(t-{\frac {vx}{c^{2}}}\right)\end{aligned}}\end{matrix}}}
+  
+
+Larmor knew that the Michelson–Morley experiment was accurate enough to detect an effect of motion depending on the factor (v/c)2, and so he sought the transformations which were "accurate to second order" (as he put it). Thus he wrote the final transformations (where x′=x-vt and t″ as given above) as:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-3.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-3.md
new file mode 100644
index 000000000..8465574d6
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-3.md
@@ -0,0 +1,1378 @@
+---
+title: "History of Lorentz transformations"
+chunk: 4/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            x
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          
+                            ε
+                            
+                              
+                                1
+                                2
+                              
+                            
+                          
+                          
+                            x
+                            
+                              ′
+                            
+                          
+                        
+                      
+                      
+                        
+                          
+                            y
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          
+                            y
+                            
+                              ′
+                            
+                          
+                        
+                      
+                      
+                        
+                          
+                            z
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          
+                            z
+                            
+                              ′
+                            
+                          
+                        
+                      
+                      
+                        
+                          d
+                          
+                            t
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          
+                            ε
+                            
+                              −
+                              
+                                
+                                  1
+                                  2
+                                
+                              
+                            
+                          
+                          d
+                          
+                            t
+                            
+                              ′
+                              ′
+                            
+                          
+                          =
+                          
+                            ε
+                            
+                              −
+                              
+                                
+                                  1
+                                  2
+                                
+                              
+                            
+                          
+                          
+                            (
+                            
+                              d
+                              
+                                t
+                                
+                                  ′
+                                
+                              
+                              −
+                              
+                                
+                                  v
+                                  
+                                    c
+                                    
+                                      2
+                                    
+                                  
+                                
+                              
+                              ε
+                              d
+                              
+                                x
+                                
+                                  ′
+                                
+                              
+                            
+                            )
+                          
+                        
+                      
+                      
+                        
+                          
+                            t
+                            
+                              1
+                            
+                          
+                        
+                        
+                          
+                          =
+                          
+                            ε
+                            
+                              −
+                              
+                                
+                                  1
+                                  2
+                                
+                              
+                            
+                          
+                          
+                            t
+                            
+                              ′
+                            
+                          
+                          −
+                          
+                            
+                              v
+                              
+                                c
+                                
+                                  2
+                                
+                              
+                            
+                          
+                          
+                            ε
+                            
+                              
+                                1
+                                2
+                              
+                            
+                          
+                          
+                            x
+                            
+                              ′
+                            
+                          
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          x
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        γ
+                        
+                          x
+                          
+                            ′
+                          
+                        
+                        =
+                        γ
+                        (
+                        x
+                        −
+                        v
+                        t
+                        )
+                      
+                    
+                    
+                      
+                        
+                          y
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          y
+                          ′
+                        
+                        =
+                        y
+                      
+                    
+                    
+                      
+                        
+                          z
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          z
+                          ′
+                        
+                        =
+                        z
+                      
+                    
+                    
+                      
+                        d
+                        
+                          t
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            
+                              d
+                              
+                                t
+                                
+                                  ′
+                                  ′
+                                
+                              
+                            
+                            γ
+                          
+                        
+                        =
+                        
+                          
+                            1
+                            γ
+                          
+                        
+                        
+                          (
+                          
+                            d
+                            
+                              t
+                              
+                                ′
+                              
+                            
+                            −
+                            
+                              
+                                
+                                  
+                                    γ
+                                    
+                                      2
+                                    
+                                  
+                                  v
+                                  d
+                                  
+                                    x
+                                    
+                                      ′
+                                    
+                                  
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                        =
+                        γ
+                        
+                          (
+                          
+                            d
+                            t
+                            −
+                            
+                              
+                                
+                                  v
+                                  d
+                                  x
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            
+                              t
+                              
+                                ′
+                              
+                            
+                            γ
+                          
+                        
+                        −
+                        
+                          
+                            
+                              γ
+                              v
+                              
+                                x
+                                
+                                  ′
+                                
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                        =
+                        γ
+                        
+                          (
+                          
+                            t
+                            −
+                            
+                              
+                                
+                                  v
+                                  x
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}x_{1}&=\varepsilon ^{\frac {1}{2}}x^{\prime }\\y_{1}&=y^{\prime }\\z_{1}&=z^{\prime }\\dt_{1}&=\varepsilon ^{-{\frac {1}{2}}}dt^{\prime \prime }=\varepsilon ^{-{\frac {1}{2}}}\left(dt^{\prime }-{\frac {v}{c^{2}}}\varepsilon dx^{\prime }\right)\\t_{1}&=\varepsilon ^{-{\frac {1}{2}}}t^{\prime }-{\frac {v}{c^{2}}}\varepsilon ^{\frac {1}{2}}x^{\prime }\end{aligned}}\right|&{\begin{aligned}x_{1}&=\gamma x^{\prime }=\gamma (x-vt)\\y_{1}&=y'=y\\z_{1}&=z'=z\\dt_{1}&={\frac {dt^{\prime \prime }}{\gamma }}={\frac {1}{\gamma }}\left(dt^{\prime }-{\frac {\gamma ^{2}vdx^{\prime }}{c^{2}}}\right)=\gamma \left(dt-{\frac {vdx}{c^{2}}}\right)\\t_{1}&={\frac {t^{\prime }}{\gamma }}-{\frac {\gamma vx^{\prime }}{c^{2}}}=\gamma \left(t-{\frac {vx}{c^{2}}}\right)\end{aligned}}\end{matrix}}}
+  
+
+by which he arrived at the complete Lorentz transformation. Larmor showed that Maxwell's equations were invariant under this two-step transformation, "to second order in v/c" – it was later shown by Lorentz (1904) and Poincaré (1905) that they are indeed invariant under this transformation to all orders in v/c.
+Larmor gave credit to Lorentz in two papers published in 1904, in which he used the term "Lorentz transformation" for Lorentz's first order transformations of coordinates and field configurations:
+
+p. 583: [..] Lorentz's transformation for passing from the field of activity of a stationary electrodynamic material system to that of one moving with uniform velocity of translation through the aether. p. 585: [..] the Lorentz transformation has shown us what is not so immediately obvious [..]  p. 622: [..] the transformation first developed by Lorentz: namely, each point in space is to have its own origin from which time is measured, its "local time" in Lorentz's phraseology, and then the values of the electric and magnetic vectors [..] at all points in the aether between the molecules in the system at rest, are the same as those of the vectors [..] at the corresponding points in the convected system at the same local times.
+
+=== Lorentz (1899, 1904) ===
+Also Lorentz extended his theorem of corresponding states in 1899. First he wrote a transformation equivalent to the one from 1892 (again, x* must be replaced by x-vt):
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            x
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          
+                            
+                              V
+                              
+                                
+                                  V
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  
+                                    
+                                      p
+                                    
+                                  
+                                  
+                                    x
+                                  
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          x
+                        
+                      
+                      
+                        
+                          
+                            y
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          y
+                        
+                      
+                      
+                        
+                          
+                            z
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          z
+                        
+                      
+                      
+                        
+                          
+                            t
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          t
+                          −
+                          
+                            
+                              
+                                
+                                  
+                                    p
+                                  
+                                
+                                
+                                  x
+                                
+                              
+                              
+                                
+                                  V
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  
+                                    
+                                      p
+                                    
+                                  
+                                  
+                                    x
+                                  
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          x
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          x
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        γ
+                        
+                          x
+                          
+                            ∗
+                          
+                        
+                        =
+                        γ
+                        (
+                        x
+                        −
+                        v
+                        t
+                        )
+                      
+                    
+                    
+                      
+                        
+                          y
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        y
+                      
+                    
+                    
+                      
+                        
+                          z
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        z
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        t
+                        −
+                        
+                          
+                            
+                              
+                                γ
+                                
+                                  2
+                                
+                              
+                              v
+                              
+                                x
+                                
+                                  ∗
+                                
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                        =
+                        
+                          γ
+                          
+                            2
+                          
+                        
+                        
+                          (
+                          
+                            t
+                            −
+                            
+                              
+                                
+                                  v
+                                  x
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}x^{\prime }&={\frac {V}{\sqrt {V^{2}-{\mathfrak {p}}_{x}^{2}}}}x\\y^{\prime }&=y\\z^{\prime }&=z\\t^{\prime }&=t-{\frac {{\mathfrak {p}}_{x}}{V^{2}-{\mathfrak {p}}_{x}^{2}}}x\end{aligned}}\right|&{\begin{aligned}x^{\prime }&=\gamma x^{\ast }=\gamma (x-vt)\\y^{\prime }&=y\\z^{\prime }&=z\\t^{\prime }&=t-{\frac {\gamma ^{2}vx^{\ast }}{c^{2}}}=\gamma ^{2}\left(t-{\frac {vx}{c^{2}}}\right)\end{aligned}}\end{matrix}}}
+  
+
+Then he introduced a factor ε of which he said he has no means of determining it, and modified his transformation as follows (where the above value of t′ has to be inserted):
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          x
+                        
+                        
+                          
+                          =
+                          
+                            
+                              ε
+                              k
+                            
+                          
+                          
+                            x
+                            
+                              ′
+                              ′
+                            
+                          
+                        
+                      
+                      
+                        
+                          y
+                        
+                        
+                          
+                          =
+                          ε
+                          
+                            y
+                            
+                              ′
+                              ′
+                            
+                          
+                        
+                      
+                      
+                        
+                          z
+                        
+                        
+                          
+                          =
+                          ε
+                          
+                            x
+                            
+                              ′
+                              ′
+                            
+                          
+                        
+                      
+                      
+                        
+                          
+                            t
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          k
+                          ε
+                          
+                            t
+                            
+                              ′
+                              ′
+                            
+                          
+                        
+                      
+                      
+                        
+                          k
+                        
+                        
+                          
+                          =
+                          
+                            
+                              V
+                              
+                                
+                                  V
+                                  
+                                    2
+                                  
+                                
+                                −
+                                
+                                  
+                                    
+                                      p
+                                    
+                                  
+                                  
+                                    x
+                                  
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          x
+                          
+                            ∗
+                          
+                        
+                        =
+                        x
+                        −
+                        v
+                        t
+                      
+                      
+                        
+                        =
+                        
+                          
+                            ε
+                            γ
+                          
+                        
+                        
+                          x
+                          
+                            ′
+                            ′
+                          
+                        
+                      
+                    
+                    
+                      
+                        y
+                      
+                      
+                        
+                        =
+                        ε
+                        
+                          y
+                          
+                            ′
+                            ′
+                          
+                        
+                      
+                    
+                    
+                      
+                        z
+                      
+                      
+                        
+                        =
+                        ε
+                        
+                          z
+                          
+                            ′
+                            ′
+                          
+                        
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                        =
+                        
+                          γ
+                          
+                            2
+                          
+                        
+                        
+                          (
+                          
+                            t
+                            −
+                            
+                              
+                                
+                                  v
+                                  x
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                      
+                        
+                        =
+                        γ
+                        ε
+                        
+                          t
+                          
+                            ′
+                            ′
+                          
+                        
+                      
+                    
+                    
+                      
+                        γ
+                      
+                      
+                        
+                        =
+                        
+                          
+                            1
+                            
+                              1
+                              −
+                              
+                                
+                                  
+                                    v
+                                    
+                                      2
+                                    
+                                  
+                                  
+                                    c
+                                    
+                                      2
+                                    
+                                  
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}x&={\frac {\varepsilon }{k}}x^{\prime \prime }\\y&=\varepsilon y^{\prime \prime }\\z&=\varepsilon x^{\prime \prime }\\t^{\prime }&=k\varepsilon t^{\prime \prime }\\k&={\frac {V}{\sqrt {V^{2}-{\mathfrak {p}}_{x}^{2}}}}\end{aligned}}\right|&{\begin{aligned}x^{\ast }=x-vt&={\frac {\varepsilon }{\gamma }}x^{\prime \prime }\\y&=\varepsilon y^{\prime \prime }\\z&=\varepsilon z^{\prime \prime }\\t^{\prime }=\gamma ^{2}\left(t-{\frac {vx}{c^{2}}}\right)&=\gamma \varepsilon t^{\prime \prime }\\\gamma &={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}\end{aligned}}\end{matrix}}}
+  
+
+This is equivalent to the complete Lorentz transformation when solved for x″ and t″ and with ε=1. Like Larmor, Lorentz noticed in 1899 also some sort of time dilation effect in relation to the frequency of oscillating electrons "that in S the time of vibrations be kε times as great as in S0", where S0 is the aether frame.
+In 1904 he rewrote the equations in the following form by setting l=1/ε (again, x* must be replaced by x-vt):
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            x
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          k
+                          l
+                          x
+                        
+                      
+                      
+                        
+                          
+                            y
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          l
+                          y
+                        
+                      
+                      
+                        
+                          
+                            z
+                            
+                              ′
+                            
+                          
+                        
+                        
+                          
+                          =
+                          l
+                          z
+                        
+                      
+                      
+                        
+                          
+                            t
+                            ′
+                          
+                        
+                        
+                          
+                          =
+                          
+                            
+                              l
+                              k
+                            
+                          
+                          t
+                          −
+                          k
+                          l
+                          
+                            
+                              w
+                              
+                                c
+                                
+                                  2
+                                
+                              
+                            
+                          
+                          x
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          x
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        γ
+                        l
+                        
+                          x
+                          
+                            ∗
+                          
+                        
+                        =
+                        γ
+                        l
+                        (
+                        x
+                        −
+                        v
+                        t
+                        )
+                      
+                    
+                    
+                      
+                        
+                          y
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        l
+                        y
+                      
+                    
+                    
+                      
+                        
+                          z
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        l
+                        z
+                      
+                    
+                    
+                      
+                        
+                          t
+                          
+                            ′
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            
+                              l
+                              t
+                            
+                            γ
+                          
+                        
+                        −
+                        
+                          
+                            
+                              γ
+                              l
+                              v
+                              
+                                x
+                                
+                                  ∗
+                                
+                              
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                        
+                        =
+                        γ
+                        l
+                        
+                          (
+                          
+                            t
+                            −
+                            
+                              
+                                
+                                  v
+                                  x
+                                
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}x^{\prime }&=klx\\y^{\prime }&=ly\\z^{\prime }&=lz\\t'&={\frac {l}{k}}t-kl{\frac {w}{c^{2}}}x\end{aligned}}\right|&{\begin{aligned}x^{\prime }&=\gamma lx^{\ast }=\gamma l(x-vt)\\y^{\prime }&=ly\\z^{\prime }&=lz\\t^{\prime }&={\frac {lt}{\gamma }}-{\frac {\gamma lvx^{\ast }}{c^{2}}}=\gamma l\left(t-{\frac {vx}{c^{2}}}\right)\end{aligned}}\end{matrix}}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-4.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-4.md
new file mode 100644
index 000000000..dab85f155
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-4.md
@@ -0,0 +1,665 @@
+---
+title: "History of Lorentz transformations"
+chunk: 5/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+Under the assumption that l=1 when v=0, he demonstrated that l=1 must be the case at all velocities, therefore length contraction can only arise in the line of motion. So by setting the factor l to unity, Lorentz's transformations now assumed the same form as Larmor's and are now completed. Unlike Larmor, who restricted himself to show the covariance of Maxwell's equations to second order, Lorentz tried to widen its covariance to all orders in v/c. He also derived the correct formulas for the velocity dependence of electromagnetic mass, and concluded that the transformation formulas must apply to all forces of nature, not only electrical ones. However, he didn't achieve full covariance of the transformation equations for charge density and velocity. When the 1904 paper was reprinted in 1913, Lorentz therefore added the following remark:
+
+One will notice that in this work the transformation equations of Einstein’s Relativity Theory have not quite been attained. [..] On this circumstance depends the clumsiness of many of the further considerations in this work.
+Lorentz's 1904 transformation was cited and used by Alfred Bucherer in July 1904:
+
+  
+    
+      
+        
+          x
+          
+            ′
+          
+        
+        =
+        
+          
+            s
+          
+        
+        x
+        ,
+        
+        
+          y
+          
+            ′
+          
+        
+        =
+        y
+        ,
+        
+        
+          z
+          
+            ′
+          
+        
+        =
+        z
+        ,
+        
+        
+          t
+          ′
+        
+        =
+        
+          
+            t
+            
+              s
+            
+          
+        
+        −
+        
+          
+            s
+          
+        
+        
+          
+            u
+            
+              v
+              
+                2
+              
+            
+          
+        
+        x
+        ,
+        
+        s
+        =
+        1
+        −
+        
+          
+            
+              u
+              
+                2
+              
+            
+            
+              v
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\displaystyle x^{\prime }={\sqrt {s}}x,\quad y^{\prime }=y,\quad z^{\prime }=z,\quad t'={\frac {t}{\sqrt {s}}}-{\sqrt {s}}{\frac {u}{v^{2}}}x,\quad s=1-{\frac {u^{2}}{v^{2}}}}
+  
+
+or by Wilhelm Wien in July 1904:
+
+  
+    
+      
+        x
+        =
+        k
+        
+          x
+          ′
+        
+        ,
+        
+        y
+        =
+        
+          y
+          ′
+        
+        ,
+        
+        z
+        =
+        
+          z
+          ′
+        
+        ,
+        
+        
+          t
+          ′
+        
+        =
+        k
+        t
+        −
+        
+          
+            v
+            
+              k
+              
+                c
+                
+                  2
+                
+              
+            
+          
+        
+        x
+      
+    
+    {\displaystyle x=kx',\quad y=y',\quad z=z',\quad t'=kt-{\frac {v}{kc^{2}}}x}
+  
+
+or by Emil Cohn in November 1904 (setting the speed of light to unity):
+
+  
+    
+      
+        x
+        =
+        
+          
+            
+              x
+              
+                0
+              
+            
+            k
+          
+        
+        ,
+        
+        y
+        =
+        
+          y
+          
+            0
+          
+        
+        ,
+        
+        z
+        =
+        
+          z
+          
+            0
+          
+        
+        ,
+        
+        t
+        =
+        k
+        
+          t
+          
+            0
+          
+        
+        ,
+        
+        
+          t
+          
+            1
+          
+        
+        =
+        
+          t
+          
+            0
+          
+        
+        −
+        w
+        ⋅
+        
+          r
+          
+            0
+          
+        
+        ,
+        
+        
+          k
+          
+            2
+          
+        
+        =
+        
+          
+            1
+            
+              1
+              −
+              
+                w
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle x={\frac {x_{0}}{k}},\quad y=y_{0},\quad z=z_{0},\quad t=kt_{0},\quad t_{1}=t_{0}-w\cdot r_{0},\quad k^{2}={\frac {1}{1-w^{2}}}}
+  
+
+or by Richard Gans in February 1905:
+
+  
+    
+      
+        
+          x
+          
+            ′
+          
+        
+        =
+        k
+        x
+        ,
+        
+        
+          y
+          
+            ′
+          
+        
+        =
+        y
+        ,
+        
+        
+          z
+          
+            ′
+          
+        
+        =
+        z
+        ,
+        
+        
+          t
+          ′
+        
+        =
+        
+          
+            t
+            k
+          
+        
+        −
+        
+          
+            
+              k
+              w
+              x
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+        ,
+        
+        
+          k
+          
+            2
+          
+        
+        =
+        
+          
+            
+              c
+              
+                2
+              
+            
+            
+              
+                c
+                
+                  2
+                
+              
+              −
+              
+                w
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle x^{\prime }=kx,\quad y^{\prime }=y,\quad z^{\prime }=z,\quad t'={\frac {t}{k}}-{\frac {kwx}{c^{2}}},\quad k^{2}={\frac {c^{2}}{c^{2}-w^{2}}}}
+  
+
+=== Poincaré (1900, 1905) ===
+
+==== Local time ====
+Neither Lorentz or Larmor gave a clear physical interpretation of the origin of local time. However, Henri Poincaré in 1900 commented on the origin of Lorentz's "wonderful invention" of local time. He remarked that it arose when clocks in a moving reference frame are synchronised by exchanging signals which are assumed to travel with the same speed 
+  
+    
+      
+        c
+      
+    
+    {\displaystyle c}
+  
+ in both directions, which lead to what is nowadays called relativity of simultaneity, although Poincaré's calculation does not involve length contraction or time dilation. In order to synchronise the clocks here on Earth (the x*, t* frame) a light signal from one clock (at the origin) is sent to another (at x*), and is sent back. It's supposed that the Earth is moving with speed v in the x-direction (= x*-direction) in some rest system (x, t) (i.e. the luminiferous aether system for Lorentz and Larmor). The time of flight outwards is
+
+  
+    
+      
+        δ
+        
+          t
+          
+            a
+          
+        
+        =
+        
+          
+            
+              x
+              
+                ∗
+              
+            
+            
+              (
+              
+                c
+                −
+                v
+              
+              )
+            
+          
+        
+      
+    
+    {\displaystyle \delta t_{a}={\frac {x^{\ast }}{\left(c-v\right)}}}
+  
+
+and the time of flight back is
+
+  
+    
+      
+        δ
+        
+          t
+          
+            b
+          
+        
+        =
+        
+          
+            
+              x
+              
+                ∗
+              
+            
+            
+              (
+              
+                c
+                +
+                v
+              
+              )
+            
+          
+        
+      
+    
+    {\displaystyle \delta t_{b}={\frac {x^{\ast }}{\left(c+v\right)}}}
+  
+.
+The elapsed time on the clock when the signal is returned is δta+δtb and the time t*=(δta+δtb)/2 is ascribed to the moment when the light signal reached the distant clock. In the rest frame the time t=δta is ascribed to that same instant. Some algebra gives the relation between the different time coordinates ascribed to the moment of reflection. Thus
+
+  
+    
+      
+        
+          t
+          
+            ∗
+          
+        
+        =
+        t
+        −
+        
+          
+            
+              
+                γ
+                
+                  2
+                
+              
+              v
+              
+                x
+                
+                  ∗
+                
+              
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\displaystyle t^{\ast }=t-{\frac {\gamma ^{2}vx^{*}}{c^{2}}}}
+  
+
+identical to Lorentz (1892). By dropping the factor γ2 under the assumption that 
+  
+    
+      
+        
+          
+            
+              
+                v
+                
+                  2
+                
+              
+              
+                c
+                
+                  2
+                
+              
+            
+          
+        
+        ≪
+        1
+      
+    
+    {\displaystyle {\tfrac {v^{2}}{c^{2}}}\ll 1}
+  
+, Poincaré gave the result t*=t-vx*/c2, which is the form used by Lorentz in 1895.
+Similar physical interpretations of local time were later given by Emil Cohn (1904) and Max Abraham (1905).
+
+==== Lorentz transformation ====
+On June 5, 1905 (published June 9) Poincaré formulated transformation equations which are algebraically equivalent to those of Larmor and Lorentz and gave them the modern form:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  x
+                  
+                    ′
+                  
+                
+              
+              
+                
+                =
+                k
+                l
+                (
+                x
+                +
+                ε
+                t
+                )
+              
+            
+            
+              
+                
+                  y
+                  
+                    ′
+                  
+                
+              
+              
+                
+                =
+                l
+                y
+              
+            
+            
+              
+                
+                  z
+                  
+                    ′
+                  
+                
+              
+              
+                
+                =
+                l
+                z
+              
+            
+            
+              
+                
+                  t
+                  ′
+                
+              
+              
+                
+                =
+                k
+                l
+                (
+                t
+                +
+                ε
+                x
+                )
+              
+            
+            
+              
+                k
+              
+              
+                
+                =
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        ε
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}x^{\prime }&=kl(x+\varepsilon t)\\y^{\prime }&=ly\\z^{\prime }&=lz\\t'&=kl(t+\varepsilon x)\\k&={\frac {1}{\sqrt {1-\varepsilon ^{2}}}}\end{aligned}}}
+  
+.
+Apparently Poincaré was unaware of Larmor's contributions, because he only mentioned Lorentz and therefore used for the first time the name "Lorentz transformation". Poincaré set the speed of light to unity, pointed out the group characteristics of the transformation by setting l=1, and modified/corrected Lorentz's derivation of the equations of electrodynamics in some details in order to fully satisfy the principle of relativity, i.e. making them fully Lorentz covariant.
+In July 1905 (published in January 1906) Poincaré showed in detail how the transformations and electrodynamic equations are a consequence of the principle of least action; he demonstrated in more detail the group characteristics of the transformation, which he called Lorentz group, and he showed that the combination x2+y2+z2-t2 is invariant. He noticed that the Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing 
+  
+    
+      
+        c
+        t
+        
+          
+            −
+            1
+          
+        
+      
+    
+    {\displaystyle ct{\sqrt {-1}}}
+  
+ as a fourth imaginary coordinate, and he used an early form of four-vectors. He also formulated the velocity addition formula, which he had already derived in unpublished letters to Lorentz from May 1905:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-5.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-5.md
new file mode 100644
index 000000000..914f619a5
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-5.md
@@ -0,0 +1,1485 @@
+---
+title: "History of Lorentz transformations"
+chunk: 6/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          ξ
+          ′
+        
+        =
+        
+          
+            
+              ξ
+              +
+              ε
+            
+            
+              1
+              +
+              ξ
+              ε
+            
+          
+        
+        ,
+         
+        
+          η
+          ′
+        
+        =
+        
+          
+            η
+            
+              k
+              (
+              1
+              +
+              ξ
+              ε
+              )
+            
+          
+        
+      
+    
+    {\displaystyle \xi '={\frac {\xi +\varepsilon }{1+\xi \varepsilon }},\ \eta '={\frac {\eta }{k(1+\xi \varepsilon )}}}
+  
+.
+
+=== Einstein (1905) – Special relativity ===
+On June 30, 1905 (published September 1905) Einstein published what is now called special relativity and gave a new derivation of the transformation, which was based only on the principle of relativity and the principle of the constancy of the speed of light. While Lorentz considered "local time" to be a mathematical stipulation device for explaining the Michelson-Morley experiment, Einstein showed that the coordinates given by the Lorentz transformation were in fact the inertial coordinates of relatively moving frames of reference. For quantities of first order in v/c this was also done by Poincaré in 1900, while Einstein derived the complete transformation by this method. Unlike Lorentz and Poincaré who still distinguished between real time in the aether and apparent time for moving observers, Einstein showed that the transformations applied to the kinematics of moving frames.
+The notation for this transformation is equivalent to Poincaré's of 1905, except that Einstein didn't set the speed of light to unity:
+
+  
+    
+      
+        
+          
+            
+              
+                τ
+              
+              
+                
+                =
+                β
+                
+                  (
+                  
+                    t
+                    −
+                    
+                      
+                        v
+                        
+                          V
+                          
+                            2
+                          
+                        
+                      
+                    
+                    x
+                  
+                  )
+                
+              
+            
+            
+              
+                ξ
+              
+              
+                
+                =
+                β
+                (
+                x
+                −
+                v
+                t
+                )
+              
+            
+            
+              
+                η
+              
+              
+                
+                =
+                y
+              
+            
+            
+              
+                ζ
+              
+              
+                
+                =
+                z
+              
+            
+            
+              
+                β
+              
+              
+                
+                =
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              v
+                              V
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}\tau &=\beta \left(t-{\frac {v}{V^{2}}}x\right)\\\xi &=\beta (x-vt)\\\eta &=y\\\zeta &=z\\\beta &={\frac {1}{\sqrt {1-\left({\frac {v}{V}}\right)^{2}}}}\end{aligned}}}
+  
+
+Einstein also defined the velocity addition formula:
+
+  
+    
+      
+        
+          
+            
+              
+                x
+                =
+                
+                  
+                    
+                      
+                        w
+                        
+                          ξ
+                        
+                      
+                      +
+                      v
+                    
+                    
+                      1
+                      +
+                      
+                        
+                          
+                            v
+                            
+                              w
+                              
+                                ξ
+                              
+                            
+                          
+                          
+                            V
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                
+                t
+                ,
+                 
+                y
+                =
+                
+                  
+                    
+                      1
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              v
+                              V
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                    
+                      1
+                      +
+                      
+                        
+                          
+                            v
+                            
+                              w
+                              
+                                ξ
+                              
+                            
+                          
+                          
+                            V
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                
+                
+                  w
+                  
+                    η
+                  
+                
+                t
+              
+            
+            
+              
+                
+                  U
+                  
+                    2
+                  
+                
+                =
+                
+                  
+                    (
+                    
+                      
+                        
+                          d
+                          x
+                        
+                        
+                          d
+                          t
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                +
+                
+                  
+                    (
+                    
+                      
+                        
+                          d
+                          y
+                        
+                        
+                          d
+                          t
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                ,
+                 
+                
+                  w
+                  
+                    2
+                  
+                
+                =
+                
+                  w
+                  
+                    ξ
+                  
+                  
+                    2
+                  
+                
+                +
+                
+                  w
+                  
+                    η
+                  
+                  
+                    2
+                  
+                
+                ,
+                 
+                α
+                =
+                arctg
+                ⁡
+                
+                  
+                    
+                      w
+                      
+                        y
+                      
+                    
+                    
+                      w
+                      
+                        x
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                U
+                =
+                
+                  
+                    
+                      
+                        (
+                        
+                          
+                            v
+                            
+                              2
+                            
+                          
+                          +
+                          
+                            w
+                            
+                              2
+                            
+                          
+                          +
+                          2
+                          v
+                          w
+                          cos
+                          ⁡
+                          α
+                        
+                        )
+                      
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              
+                                v
+                                w
+                                sin
+                                ⁡
+                                α
+                              
+                              V
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                    
+                      1
+                      +
+                      
+                        
+                          
+                            v
+                            w
+                            cos
+                            ⁡
+                            α
+                          
+                          
+                            V
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+        
+          |
+          
+            
+              
+                
+                  
+                    
+                      
+                        
+                          u
+                          
+                            x
+                          
+                        
+                        −
+                        v
+                      
+                      
+                        1
+                        −
+                        
+                          
+                            
+                              
+                                u
+                                
+                                  x
+                                
+                              
+                              v
+                            
+                            
+                              V
+                              
+                                2
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                  =
+                  
+                    u
+                    
+                      ξ
+                    
+                  
+                
+              
+              
+                
+                  
+                    
+                      
+                        u
+                        
+                          y
+                        
+                      
+                      
+                        β
+                        
+                          (
+                          
+                            1
+                            −
+                            
+                              
+                                
+                                  
+                                    u
+                                    
+                                      x
+                                    
+                                  
+                                  v
+                                
+                                
+                                  V
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                  
+                  =
+                  
+                    u
+                    
+                      η
+                    
+                  
+                
+              
+              
+                
+                  
+                    
+                      
+                        u
+                        
+                          z
+                        
+                      
+                      
+                        β
+                        
+                          (
+                          
+                            1
+                            −
+                            
+                              
+                                
+                                  
+                                    u
+                                    
+                                      x
+                                    
+                                  
+                                  v
+                                
+                                
+                                  V
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                  
+                  =
+                  
+                    u
+                    
+                      ζ
+                    
+                  
+                
+              
+            
+          
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}x={\frac {w_{\xi }+v}{1+{\frac {vw_{\xi }}{V^{2}}}}}t,\ y={\frac {\sqrt {1-\left({\frac {v}{V}}\right)^{2}}}{1+{\frac {vw_{\xi }}{V^{2}}}}}w_{\eta }t\\U^{2}=\left({\frac {dx}{dt}}\right)^{2}+\left({\frac {dy}{dt}}\right)^{2},\ w^{2}=w_{\xi }^{2}+w_{\eta }^{2},\ \alpha =\operatorname {arctg} {\frac {w_{y}}{w_{x}}}\\U={\frac {\sqrt {\left(v^{2}+w^{2}+2vw\cos \alpha \right)-\left({\frac {vw\sin \alpha }{V}}\right)^{2}}}{1+{\frac {vw\cos \alpha }{V^{2}}}}}\end{matrix}}\left|{\begin{matrix}{\frac {u_{x}-v}{1-{\frac {u_{x}v}{V^{2}}}}}=u_{\xi }\\{\frac {u_{y}}{\beta \left(1-{\frac {u_{x}v}{V^{2}}}\right)}}=u_{\eta }\\{\frac {u_{z}}{\beta \left(1-{\frac {u_{x}v}{V^{2}}}\right)}}=u_{\zeta }\end{matrix}}\right.}
+  
+
+and the light aberration formula:
+
+  
+    
+      
+        cos
+        ⁡
+        
+          φ
+          ′
+        
+        =
+        
+          
+            
+              cos
+              ⁡
+              φ
+              −
+              
+                
+                  v
+                  V
+                
+              
+            
+            
+              1
+              −
+              
+                
+                  v
+                  V
+                
+              
+              cos
+              ⁡
+              φ
+            
+          
+        
+      
+    
+    {\displaystyle \cos \varphi '={\frac {\cos \varphi -{\frac {v}{V}}}{1-{\frac {v}{V}}\cos \varphi }}}
+  
+
+=== Minkowski (1907–1908) – Spacetime ===
+The work on the principle of relativity by Lorentz, Einstein, Planck, together with Poincaré's four-dimensional approach, were further elaborated and combined with the hyperboloid model by Hermann Minkowski in 1907 and 1908. Minkowski particularly reformulated electrodynamics in a four-dimensional way (Minkowski spacetime). For instance, he wrote x, y, z, it in the form x1, x2, x3, x4. By defining ψ as the angle of rotation around the z-axis, the Lorentz transformation assumes the form (with c=1):
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  x
+                  
+                    1
+                  
+                  ′
+                
+              
+              
+                
+                =
+                
+                  x
+                  
+                    1
+                  
+                
+              
+            
+            
+              
+                
+                  x
+                  
+                    2
+                  
+                  ′
+                
+              
+              
+                
+                =
+                
+                  x
+                  
+                    2
+                  
+                
+              
+            
+            
+              
+                
+                  x
+                  
+                    3
+                  
+                  ′
+                
+              
+              
+                
+                =
+                
+                  x
+                  
+                    3
+                  
+                
+                cos
+                ⁡
+                i
+                ψ
+                +
+                
+                  x
+                  
+                    4
+                  
+                
+                sin
+                ⁡
+                i
+                ψ
+              
+            
+            
+              
+                
+                  x
+                  
+                    4
+                  
+                  ′
+                
+              
+              
+                
+                =
+                −
+                
+                  x
+                  
+                    3
+                  
+                
+                sin
+                ⁡
+                i
+                ψ
+                +
+                
+                  x
+                  
+                    4
+                  
+                
+                cos
+                ⁡
+                i
+                ψ
+              
+            
+            
+              
+                cos
+                ⁡
+                i
+                ψ
+              
+              
+                
+                =
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        q
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}x'_{1}&=x_{1}\\x'_{2}&=x_{2}\\x'_{3}&=x_{3}\cos i\psi +x_{4}\sin i\psi \\x'_{4}&=-x_{3}\sin i\psi +x_{4}\cos i\psi \\\cos i\psi &={\frac {1}{\sqrt {1-q^{2}}}}\end{aligned}}}
+  
+
+Even though Minkowski used the imaginary number iψ, he for once directly used the tangens hyperbolicus in the equation for velocity
+
+  
+    
+      
+        −
+        i
+        tan
+        ⁡
+        i
+        ψ
+        =
+        
+          
+            
+              
+                e
+                
+                  ψ
+                
+              
+              −
+              
+                e
+                
+                  −
+                  ψ
+                
+              
+            
+            
+              
+                e
+                
+                  ψ
+                
+              
+              +
+              
+                e
+                
+                  −
+                  ψ
+                
+              
+            
+          
+        
+        =
+        q
+      
+    
+    {\displaystyle -i\tan i\psi ={\frac {e^{\psi }-e^{-\psi }}{e^{\psi }+e^{-\psi }}}=q}
+  
+ with 
+  
+    
+      
+        ψ
+        =
+        
+          
+            1
+            2
+          
+        
+        ln
+        ⁡
+        
+          
+            
+              1
+              +
+              q
+            
+            
+              1
+              −
+              q
+            
+          
+        
+      
+    
+    {\displaystyle \psi ={\frac {1}{2}}\ln {\frac {1+q}{1-q}}}
+  
+.
+Minkowski's expression can also by written as ψ=atanh(q) and was later called rapidity. He also wrote the Lorentz transformation in matrix form:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  x
+                  
+                    1
+                  
+                  
+                    2
+                  
+                
+                +
+                
+                  x
+                  
+                    2
+                  
+                  
+                    2
+                  
+                
+                +
+                
+                  x
+                  
+                    3
+                  
+                  
+                    2
+                  
+                
+                +
+                
+                  x
+                  
+                    4
+                  
+                  
+                    2
+                  
+                
+                =
+                
+                  x
+                  
+                    1
+                  
+                  
+                    ′
+                    2
+                  
+                
+                +
+                
+                  x
+                  
+                    2
+                  
+                  
+                    ′
+                    2
+                  
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+                +
+                
+                  x
+                  
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+                  
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+                    ′
+                    2
+                  
+                
+                +
+                
+                  x
+                  
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+                  
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+                    2
+                  
+                
+              
+            
+            
+              
+                
+                  (
+                  
+                    
+                      x
+                      
+                        1
+                      
+                      
+                        ′
+                      
+                    
+                    =
+                    
+                      x
+                      ′
+                    
+                    ,
+                     
+                    
+                      x
+                      
+                        2
+                      
+                      
+                        ′
+                      
+                    
+                    =
+                    
+                      y
+                      ′
+                    
+                    ,
+                     
+                    
+                      x
+                      
+                        3
+                      
+                      
+                        ′
+                      
+                    
+                    =
+                    
+                      z
+                      ′
+                    
+                    ,
+                     
+                    
+                      x
+                      
+                        4
+                      
+                      
+                        ′
+                      
+                    
+                    =
+                    i
+                    
+                      t
+                      ′
+                    
+                  
+                  )
+                
+              
+            
+            
+              
+                −
+                
+                  x
+                  
+                    2
+                  
+                
+                −
+                
+                  y
+                  
+                    2
+                  
+                
+                −
+                
+                  z
+                  
+                    2
+                  
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+                +
+                
+                  t
+                  
+                    2
+                  
+                
+                =
+                −
+                
+                  x
+                  
+                    ′
+                    2
+                  
+                
+                −
+                
+                  y
+                  
+                    ′
+                    2
+                  
+                
+                −
+                
+                  z
+                  
+                    ′
+                    2
+                  
+                
+                +
+                
+                  t
+                  
+                    ′
+                    2
+                  
+                
+              
+            
+            
+              
+                
+                  x
+                  
+                    h
+                  
+                
+                =
+                
+                  α
+                  
+                    h
+                    1
+                  
+                
+                
+                  x
+                  
+                    1
+                  
+                  
+                    ′
+                  
+                
+                +
+                
+                  α
+                  
+                    h
+                    2
+                  
+                
+                
+                  x
+                  
+                    2
+                  
+                  
+                    ′
+                  
+                
+                +
+                
+                  α
+                  
+                    h
+                    3
+                  
+                
+                
+                  x
+                  
+                    3
+                  
+                  
+                    ′
+                  
+                
+                +
+                
+                  α
+                  
+                    h
+                    4
+                  
+                
+                
+                  x
+                  
+                    4
+                  
+                  
+                    ′
+                  
+                
+              
+            
+            
+              
+                
+                  A
+                
+                =
+                
+                  
+                    |
+                    
+                      
+                        
+                          
+                            
+                              α
+                              
+                                11
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                12
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                13
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                14
+                              
+                            
+                          
+                        
+                        
+                          
+                            
+                              α
+                              
+                                21
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                22
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                23
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                24
+                              
+                            
+                          
+                        
+                        
+                          
+                            
+                              α
+                              
+                                31
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                32
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                33
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                34
+                              
+                            
+                          
+                        
+                        
+                          
+                            
+                              α
+                              
+                                41
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                42
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                43
+                              
+                            
+                            ,
+                          
+                          
+                            
+                              α
+                              
+                                44
+                              
+                            
+                          
+                        
+                      
+                    
+                    |
+                  
+                  ,
+                   
+                  
+                    
+                      
+                        
+                          
+                            
+                              
+                                
+                                  A
+                                
+                                ¯
+                              
+                            
+                          
+                          
+                            A
+                          
+                        
+                        
+                          
+                          =
+                          1
+                        
+                      
+                      
+                        
+                          
+                            
+                              (
+                              
+                                det
+                                
+                                  A
+                                
+                              
+                              )
+                            
+                            
+                              2
+                            
+                          
+                        
+                        
+                          
+                          =
+                          1
+                        
+                      
+                      
+                        
+                          det
+                          
+                            A
+                          
+                        
+                        
+                          
+                          =
+                          1
+                        
+                      
+                      
+                        
+                          
+                            α
+                            
+                              44
+                            
+                          
+                        
+                        
+                          
+                          >
+                          0
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}=x_{1}^{\prime 2}+x_{2}^{\prime 2}+x_{3}^{\prime 2}+x_{4}^{\prime 2}\\\left(x_{1}^{\prime }=x',\ x_{2}^{\prime }=y',\ x_{3}^{\prime }=z',\ x_{4}^{\prime }=it'\right)\\-x^{2}-y^{2}-z^{2}+t^{2}=-x^{\prime 2}-y^{\prime 2}-z^{\prime 2}+t^{\prime 2}\\\hline x_{h}=\alpha _{h1}x_{1}^{\prime }+\alpha _{h2}x_{2}^{\prime }+\alpha _{h3}x_{3}^{\prime }+\alpha _{h4}x_{4}^{\prime }\\\mathrm {A} =\mathrm {\left|{\begin{matrix}\alpha _{11},&\alpha _{12},&\alpha _{13},&\alpha _{14}\\\alpha _{21},&\alpha _{22},&\alpha _{23},&\alpha _{24}\\\alpha _{31},&\alpha _{32},&\alpha _{33},&\alpha _{34}\\\alpha _{41},&\alpha _{42},&\alpha _{43},&\alpha _{44}\end{matrix}}\right|,\ {\begin{aligned}{\bar {\mathrm {A} }}\mathrm {A} &=1\\\left(\det \mathrm {A} \right)^{2}&=1\\\det \mathrm {A} &=1\\\alpha _{44}&>0\end{aligned}}} \end{matrix}}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-6.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-6.md
new file mode 100644
index 000000000..d893d63b5
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-6.md
@@ -0,0 +1,1082 @@
+---
+title: "History of Lorentz transformations"
+chunk: 7/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+As a graphical representation of the Lorentz transformation he introduced the Minkowski diagram, which became a standard tool in textbooks and research articles on relativity:
+
+=== Sommerfeld (1909) – Spherical trigonometry ===
+Using an imaginary rapidity such as Minkowski, Arnold Sommerfeld (1909) formulated the Lorentz boost and the relativistic velocity addition in terms of trigonometric functions and the spherical law of cosines:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            x
+                            ′
+                          
+                          =
+                        
+                        
+                          x
+                           
+                          cos
+                          ⁡
+                          φ
+                          +
+                          l
+                           
+                          sin
+                          ⁡
+                          φ
+                          ,
+                        
+                        
+                          
+                            y
+                            ′
+                          
+                          =
+                          y
+                        
+                      
+                      
+                        
+                          
+                            l
+                            ′
+                          
+                          =
+                        
+                        
+                          −
+                          x
+                           
+                          sin
+                          ⁡
+                          φ
+                          +
+                          l
+                           
+                          cos
+                          ⁡
+                          φ
+                          ,
+                        
+                        
+                          
+                            z
+                            ′
+                          
+                          =
+                          z
+                        
+                      
+                    
+                  
+                  }
+                
+              
+            
+            
+              
+                
+                  (
+                  
+                    tg
+                    ⁡
+                    φ
+                    =
+                    i
+                    β
+                    ,
+                     
+                    cos
+                    ⁡
+                    φ
+                    =
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                    ,
+                     
+                    sin
+                    ⁡
+                    φ
+                    =
+                    
+                      
+                        
+                          i
+                          β
+                        
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+            
+            
+              
+                β
+                =
+                
+                  
+                    1
+                    i
+                  
+                
+                tg
+                ⁡
+                
+                  (
+                  
+                    
+                      φ
+                      
+                        1
+                      
+                    
+                    +
+                    
+                      φ
+                      
+                        2
+                      
+                    
+                  
+                  )
+                
+                =
+                
+                  
+                    1
+                    i
+                  
+                
+                
+                  
+                    
+                      tg
+                      ⁡
+                      
+                        φ
+                        
+                          1
+                        
+                      
+                      +
+                      tg
+                      ⁡
+                      
+                        φ
+                        
+                          2
+                        
+                      
+                    
+                    
+                      1
+                      −
+                      tg
+                      ⁡
+                      
+                        φ
+                        
+                          1
+                        
+                      
+                      tg
+                      ⁡
+                      
+                        φ
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                =
+                
+                  
+                    
+                      
+                        β
+                        
+                          1
+                        
+                      
+                      +
+                      
+                        β
+                        
+                          2
+                        
+                      
+                    
+                    
+                      1
+                      +
+                      
+                        β
+                        
+                          1
+                        
+                      
+                      
+                        β
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                cos
+                ⁡
+                φ
+                =
+                cos
+                ⁡
+                
+                  φ
+                  
+                    1
+                  
+                
+                cos
+                ⁡
+                
+                  φ
+                  
+                    2
+                  
+                
+                −
+                sin
+                ⁡
+                
+                  φ
+                  
+                    1
+                  
+                
+                sin
+                ⁡
+                
+                  φ
+                  
+                    2
+                  
+                
+                cos
+                ⁡
+                α
+              
+            
+            
+              
+                
+                  v
+                  
+                    2
+                  
+                
+                =
+                
+                  
+                    
+                      
+                        v
+                        
+                          1
+                        
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        v
+                        
+                          2
+                        
+                        
+                          2
+                        
+                      
+                      +
+                      2
+                      
+                        v
+                        
+                          1
+                        
+                      
+                      
+                        v
+                        
+                          2
+                        
+                      
+                      cos
+                      ⁡
+                      α
+                      −
+                      
+                        
+                          1
+                          
+                            c
+                            
+                              2
+                            
+                          
+                        
+                      
+                      
+                        v
+                        
+                          1
+                        
+                        
+                          2
+                        
+                      
+                      
+                        v
+                        
+                          2
+                        
+                        
+                          2
+                        
+                      
+                      
+                        sin
+                        
+                          2
+                        
+                      
+                      ⁡
+                      α
+                    
+                    
+                      
+                        (
+                        
+                          1
+                          +
+                          
+                            
+                              1
+                              
+                                c
+                                
+                                  2
+                                
+                              
+                            
+                          
+                          
+                            v
+                            
+                              1
+                            
+                          
+                          
+                            v
+                            
+                              2
+                            
+                          
+                          cos
+                          ⁡
+                          α
+                        
+                        )
+                      
+                      
+                        2
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}\left.{\begin{array}{lrl}x'=&x\ \cos \varphi +l\ \sin \varphi ,&y'=y\\l'=&-x\ \sin \varphi +l\ \cos \varphi ,&z'=z\end{array}}\right\}\\\left(\operatorname {tg} \varphi =i\beta ,\ \cos \varphi ={\frac {1}{\sqrt {1-\beta ^{2}}}},\ \sin \varphi ={\frac {i\beta }{\sqrt {1-\beta ^{2}}}}\right)\\\hline \beta ={\frac {1}{i}}\operatorname {tg} \left(\varphi _{1}+\varphi _{2}\right)={\frac {1}{i}}{\frac {\operatorname {tg} \varphi _{1}+\operatorname {tg} \varphi _{2}}{1-\operatorname {tg} \varphi _{1}\operatorname {tg} \varphi _{2}}}={\frac {\beta _{1}+\beta _{2}}{1+\beta _{1}\beta _{2}}}\\\cos \varphi =\cos \varphi _{1}\cos \varphi _{2}-\sin \varphi _{1}\sin \varphi _{2}\cos \alpha \\v^{2}={\frac {v_{1}^{2}+v_{2}^{2}+2v_{1}v_{2}\cos \alpha -{\frac {1}{c^{2}}}v_{1}^{2}v_{2}^{2}\sin ^{2}\alpha }{\left(1+{\frac {1}{c^{2}}}v_{1}v_{2}\cos \alpha \right)^{2}}}\end{matrix}}}
+  
+
+=== Frank (1909) – Hyperbolic functions ===
+Hyperbolic functions were used by Philipp Frank (1909), who derived the Lorentz transformation using ψ as rapidity:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  x
+                  ′
+                
+                =
+                x
+                φ
+                (
+                a
+                )
+                
+                
+                  
+                    c
+                    h
+                  
+                
+                
+                ψ
+                +
+                t
+                φ
+                (
+                a
+                )
+                
+                
+                  
+                    s
+                    h
+                  
+                
+                
+                ψ
+              
+            
+            
+              
+                
+                  t
+                  ′
+                
+                =
+                −
+                x
+                φ
+                (
+                a
+                )
+                
+                
+                  
+                    s
+                    h
+                  
+                
+                
+                ψ
+                +
+                t
+                φ
+                (
+                a
+                )
+                
+                
+                  
+                    c
+                    h
+                  
+                
+                
+                ψ
+              
+            
+            
+              
+                
+                  
+                    t
+                    h
+                  
+                
+                
+                ψ
+                =
+                −
+                a
+                ,
+                 
+                
+                  
+                    s
+                    h
+                  
+                
+                
+                ψ
+                =
+                
+                  
+                    a
+                    
+                      1
+                      −
+                      
+                        a
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+                 
+                
+                  
+                    c
+                    h
+                  
+                
+                
+                ψ
+                =
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        a
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+                 
+                φ
+                (
+                a
+                )
+                =
+                1
+              
+            
+            
+              
+                
+                  x
+                  ′
+                
+                =
+                
+                  
+                    
+                      x
+                      −
+                      a
+                      t
+                    
+                    
+                      1
+                      −
+                      
+                        a
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+                 
+                
+                  y
+                  ′
+                
+                =
+                y
+                ,
+                 
+                
+                  z
+                  ′
+                
+                =
+                z
+                ,
+                 
+                
+                  t
+                  ′
+                
+                =
+                
+                  
+                    
+                      −
+                      a
+                      x
+                      +
+                      t
+                    
+                    
+                      1
+                      −
+                      
+                        a
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}x'=x\varphi (a)\,{\rm {ch}}\,\psi +t\varphi (a)\,{\rm {sh}}\,\psi \\t'=-x\varphi (a)\,{\rm {sh}}\,\psi +t\varphi (a)\,{\rm {ch}}\,\psi \\\hline {\rm {th}}\,\psi =-a,\ {\rm {sh}}\,\psi ={\frac {a}{\sqrt {1-a^{2}}}},\ {\rm {ch}}\,\psi ={\frac {1}{\sqrt {1-a^{2}}}},\ \varphi (a)=1\\\hline x'={\frac {x-at}{\sqrt {1-a^{2}}}},\ y'=y,\ z'=z,\ t'={\frac {-ax+t}{\sqrt {1-a^{2}}}}\end{matrix}}}
+  
+
+=== Bateman and Cunningham (1909–1910) – Spherical wave transformation ===
+In line with Sophus Lie's (1871) research on the relation between sphere transformations with an imaginary radius coordinate and 4D conformal transformations, it was pointed out by Bateman and Cunningham (1909–1910), that by setting u=ict as the imaginary fourth coordinates one can produce spacetime conformal transformations. Not only the quadratic form 
+  
+    
+      
+        λ
+        
+          (
+          
+            d
+            
+              x
+              
+                2
+              
+            
+            +
+            d
+            
+              y
+              
+                2
+              
+            
+            +
+            d
+            
+              z
+              
+                2
+              
+            
+            +
+            d
+            
+              u
+              
+                2
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle \lambda \left(dx^{2}+dy^{2}+dz^{2}+du^{2}\right)}
+  
+, but also Maxwells equations are covariant with respect to these transformations, irrespective of the choice of λ. These variants of conformal or Lie sphere transformations were called spherical wave transformations by Bateman. However, this covariance is restricted to certain areas such as electrodynamics, whereas the totality of natural laws in inertial frames is covariant under the Lorentz group. In particular, by setting λ=1 the Lorentz group SO(1,3) can be seen as a 10-parameter subgroup of the 15-parameter spacetime conformal group Con(1,3).
+Bateman (1910–12) also alluded to the identity between the Laguerre inversion and the Lorentz transformations. In general, the isomorphism between the Laguerre group and the Lorentz group was pointed out by Élie Cartan (1912, 1915–55), Henri Poincaré (1912–21) and others.
+
+=== Herglotz (1909/10) – Möbius transformation ===
+Following Felix Klein (1889–1897) and Fricke & Klein (1897) concerning the Cayley absolute, hyperbolic motion and its transformation, Gustav Herglotz (1909–10) classified the one-parameter Lorentz transformations as loxodromic, hyperbolic, parabolic and elliptic. The general case (on the left) and the hyperbolic case equivalent to Lorentz transformations or squeeze mappings are as follows:
+
+  
+    
+      
+        
+          
+          
+            
+              
+                
+                  
+                    z
+                    
+                      1
+                    
+                    
+                      2
+                    
+                  
+                  +
+                  
+                    z
+                    
+                      2
+                    
+                    
+                      2
+                    
+                  
+                  +
+                  
+                    z
+                    
+                      3
+                    
+                    
+                      2
+                    
+                  
+                  −
+                  
+                    z
+                    
+                      4
+                    
+                    
+                      2
+                    
+                  
+                  =
+                  0
+                
+              
+              
+                
+                  
+                    z
+                    
+                      1
+                    
+                  
+                  =
+                  x
+                  ,
+                   
+                  
+                    z
+                    
+                      2
+                    
+                  
+                  =
+                  y
+                  ,
+                   
+                  
+                    z
+                    
+                      3
+                    
+                  
+                  =
+                  z
+                  ,
+                   
+                  
+                    z
+                    
+                      4
+                    
+                  
+                  =
+                  t
+                
+              
+              
+                
+                  Z
+                  =
+                  
+                    
+                      
+                        
+                          z
+                          
+                            1
+                          
+                        
+                        +
+                        i
+                        
+                          z
+                          
+                            2
+                          
+                        
+                      
+                      
+                        
+                          z
+                          
+                            4
+                          
+                        
+                        −
+                        
+                          z
+                          
+                            3
+                          
+                        
+                      
+                    
+                  
+                  =
+                  
+                    
+                      
+                        x
+                        +
+                        i
+                        y
+                      
+                      
+                        t
+                        −
+                        z
+                      
+                    
+                  
+                  ,
+                   
+                  
+                    Z
+                    ′
+                  
+                  =
+                  
+                    
+                      
+                        
+                          x
+                          ′
+                        
+                        +
+                        i
+                        
+                          y
+                          ′
+                        
+                      
+                      
+                        
+                          t
+                          ′
+                        
+                        −
+                        
+                          z
+                          ′
+                        
+                      
+                    
+                  
+                
+              
+              
+                
+                  Z
+                  =
+                  
+                    
+                      
+                        α
+                        
+                          Z
+                          ′
+                        
+                        +
+                        β
+                      
+                      
+                        γ
+                        
+                          Z
+                          ′
+                        
+                        +
+                        δ
+                      
+                    
+                  
+                
+              
+            
+          
+          |
+        
+        
+          
+            
+              
+                Z
+                =
+                
+                  Z
+                  ′
+                
+                
+                  e
+                  
+                    ϑ
+                  
+                
+              
+            
+            
+              
+                
+                  
+                    
+                      
+                        x
+                      
+                      
+                        
+                        =
+                        
+                          x
+                          ′
+                        
+                        ,
+                      
+                      
+                        t
+                        −
+                        z
+                      
+                      
+                        
+                        =
+                        (
+                        
+                          t
+                          ′
+                        
+                        −
+                        
+                          z
+                          ′
+                        
+                        )
+                        
+                          e
+                          
+                            ϑ
+                          
+                        
+                      
+                    
+                    
+                      
+                        y
+                      
+                      
+                        
+                        =
+                        
+                          y
+                          ′
+                        
+                        ,
+                      
+                      
+                        t
+                        +
+                        z
+                      
+                      
+                        
+                        =
+                        (
+                        
+                          t
+                          ′
+                        
+                        +
+                        
+                          z
+                          ′
+                        
+                        )
+                        
+                          e
+                          
+                            −
+                            ϑ
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle \left.{\begin{matrix}z_{1}^{2}+z_{2}^{2}+z_{3}^{2}-z_{4}^{2}=0\\z_{1}=x,\ z_{2}=y,\ z_{3}=z,\ z_{4}=t\\Z={\frac {z_{1}+iz_{2}}{z_{4}-z_{3}}}={\frac {x+iy}{t-z}},\ Z'={\frac {x'+iy'}{t'-z'}}\\Z={\frac {\alpha Z'+\beta }{\gamma Z'+\delta }}\end{matrix}}\right|{\begin{matrix}Z=Z'e^{\vartheta }\\{\begin{aligned}x&=x',&t-z&=(t'-z')e^{\vartheta }\\y&=y',&t+z&=(t'+z')e^{-\vartheta }\end{aligned}}\end{matrix}}}
+  
+
+=== Varićak (1910) – Hyperbolic functions ===
+Following Sommerfeld (1909), hyperbolic functions were used by Vladimir Varićak in several papers starting from 1910, who represented the equations of special relativity on the basis of hyperbolic geometry in terms of Weierstrass coordinates. For instance, by setting l=ct and v/c=tanh(u) with u as rapidity he wrote the Lorentz transformation:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-7.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-7.md
new file mode 100644
index 000000000..0bf81ac63
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-7.md
@@ -0,0 +1,989 @@
+---
+title: "History of Lorentz transformations"
+chunk: 8/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  l
+                  ′
+                
+              
+              
+                
+                =
+                −
+                x
+                sh
+                ⁡
+                u
+                +
+                l
+                ch
+                ⁡
+                u
+                ,
+              
+            
+            
+              
+                
+                  x
+                  ′
+                
+              
+              
+                
+                =
+                x
+                ch
+                ⁡
+                u
+                −
+                l
+                sh
+                ⁡
+                u
+                ,
+              
+            
+            
+              
+                
+                  y
+                  ′
+                
+              
+              
+                
+                =
+                y
+                ,
+                
+                
+                  z
+                  ′
+                
+                =
+                z
+                ,
+              
+            
+            
+              
+                ch
+                ⁡
+                u
+              
+              
+                
+                =
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              v
+                              c
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}l'&=-x\operatorname {sh} u+l\operatorname {ch} u,\\x'&=x\operatorname {ch} u-l\operatorname {sh} u,\\y'&=y,\quad z'=z,\\\operatorname {ch} u&={\frac {1}{\sqrt {1-\left({\frac {v}{c}}\right)^{2}}}}\end{aligned}}}
+  
+
+and showed the relation of rapidity to the Gudermannian function and the angle of parallelism:
+
+  
+    
+      
+        
+          
+            v
+            c
+          
+        
+        =
+        th
+        ⁡
+        u
+        =
+        tg
+        ⁡
+        ψ
+        =
+        sin
+        ⁡
+        gd
+        ⁡
+        (
+        u
+        )
+        =
+        cos
+        ⁡
+        Π
+        (
+        u
+        )
+      
+    
+    {\displaystyle {\frac {v}{c}}=\operatorname {th} u=\operatorname {tg} \psi =\sin \operatorname {gd} (u)=\cos \Pi (u)}
+  
+
+He also related the velocity addition to the hyperbolic law of cosines:
+
+  
+    
+      
+        
+          
+            
+              
+                ch
+                ⁡
+                
+                  u
+                
+                =
+                ch
+                ⁡
+                
+                  
+                    u
+                    
+                      1
+                    
+                  
+                
+                c
+                ⁡
+                h
+                
+                  
+                    u
+                    
+                      2
+                    
+                  
+                
+                +
+                sh
+                ⁡
+                
+                  
+                    u
+                    
+                      1
+                    
+                  
+                
+                sh
+                ⁡
+                
+                  
+                    u
+                    
+                      2
+                    
+                  
+                
+                cos
+                ⁡
+                α
+              
+            
+            
+              
+                ch
+                ⁡
+                
+                  
+                    u
+                    
+                      i
+                    
+                  
+                
+                =
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              
+                                v
+                                
+                                  i
+                                
+                              
+                              c
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+                 
+                sh
+                ⁡
+                
+                  
+                    u
+                    
+                      i
+                    
+                  
+                
+                =
+                
+                  
+                    
+                      v
+                      
+                        i
+                      
+                    
+                    
+                      1
+                      −
+                      
+                        
+                          (
+                          
+                            
+                              
+                                v
+                                
+                                  i
+                                
+                              
+                              c
+                            
+                          
+                          )
+                        
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                v
+                =
+                
+                  
+                    
+                      v
+                      
+                        1
+                      
+                      
+                        2
+                      
+                    
+                    +
+                    
+                      v
+                      
+                        2
+                      
+                      
+                        2
+                      
+                    
+                    −
+                    
+                      
+                        (
+                        
+                          
+                            
+                              
+                                v
+                                
+                                  1
+                                
+                              
+                              
+                                v
+                                
+                                  2
+                                
+                              
+                            
+                            c
+                          
+                        
+                        )
+                      
+                      
+                        2
+                      
+                    
+                  
+                
+                 
+                
+                  (
+                  
+                    a
+                    =
+                    
+                      
+                        π
+                        2
+                      
+                    
+                  
+                  )
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}\operatorname {ch} {u}=\operatorname {ch} {u_{1}}\operatorname {c} h{u_{2}}+\operatorname {sh} {u_{1}}\operatorname {sh} {u_{2}}\cos \alpha \\\operatorname {ch} {u_{i}}={\frac {1}{\sqrt {1-\left({\frac {v_{i}}{c}}\right)^{2}}}},\ \operatorname {sh} {u_{i}}={\frac {v_{i}}{\sqrt {1-\left({\frac {v_{i}}{c}}\right)^{2}}}}\\v={\sqrt {v_{1}^{2}+v_{2}^{2}-\left({\frac {v_{1}v_{2}}{c}}\right)^{2}}}\ \left(a={\frac {\pi }{2}}\right)\end{matrix}}}
+  
+
+Subsequently, other authors such as E. T. Whittaker (1910) or Alfred Robb (1911, who coined the name rapidity) used similar expressions, which are still used in modern textbooks.
+
+=== Plummer (1910) – Trigonometric Lorentz boosts ===
+Henry Crozier Keating Plummer (1910) defined the Lorentz boost in terms of trigonometric functions
+
+  
+    
+      
+        
+          
+            
+              
+                τ
+                =
+                t
+                sec
+                ⁡
+                β
+                −
+                x
+                tan
+                ⁡
+                β
+                
+                  /
+                
+                U
+              
+            
+            
+              
+                ξ
+                =
+                x
+                sec
+                ⁡
+                β
+                −
+                U
+                t
+                tan
+                ⁡
+                β
+              
+            
+            
+              
+                η
+                =
+                y
+                ,
+                 
+                ζ
+                =
+                z
+                ,
+              
+            
+            
+              
+                sin
+                ⁡
+                β
+                =
+                v
+                
+                  /
+                
+                U
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}\tau =t\sec \beta -x\tan \beta /U\\\xi =x\sec \beta -Ut\tan \beta \\\eta =y,\ \zeta =z,\\\hline \sin \beta =v/U\end{matrix}}}
+  
+
+=== Ignatowski (1910) ===
+While earlier derivations and formulations of the Lorentz transformation relied from the outset on optics, electrodynamics, or the invariance of the speed of light, Vladimir Ignatowski (1910) showed that it is possible to use the principle of relativity (and related group theoretical principles) alone, in order to derive the following transformation between two inertial frames:
+
+  
+    
+      
+        
+          
+            
+              
+                d
+                
+                  x
+                  ′
+                
+              
+              
+                
+                =
+                p
+                 
+                d
+                x
+                −
+                p
+                q
+                 
+                d
+                t
+              
+            
+            
+              
+                d
+                
+                  t
+                  ′
+                
+              
+              
+                
+                =
+                −
+                p
+                q
+                n
+                 
+                d
+                x
+                +
+                p
+                 
+                d
+                t
+              
+            
+            
+              
+                p
+              
+              
+                
+                =
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        q
+                        
+                          2
+                        
+                      
+                      n
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}dx'&=p\ dx-pq\ dt\\dt'&=-pqn\ dx+p\ dt\\p&={\frac {1}{\sqrt {1-q^{2}n}}}\end{aligned}}}
+  
+
+The variable n can be seen as a space-time constant whose value has to be determined by experiment or taken from a known physical law such as electrodynamics. For that purpose, Ignatowski used the above-mentioned Heaviside ellipsoid representing a contraction of electrostatic fields by x/γ in the direction of motion. It can be seen that this is only consistent with Ignatowski's transformation when n=1/c2, resulting in p=γ and the Lorentz transformation. With n=0, no length changes arise and the Galilean transformation follows. Ignatowski's method was further developed and improved by Philipp Frank and Hermann Rothe (1911, 1912), with various authors developing similar methods in subsequent years.
+
+=== Noether (1910), Klein (1910) – Quaternions ===
+Felix Klein (1908) described Cayley's (1854) 4D quaternion multiplications as "Drehstreckungen" (orthogonal substitutions in terms of rotations leaving invariant a quadratic form up to a factor), and pointed out that the modern principle of relativity as provided by Minkowski is essentially only the consequent application of such Drehstreckungen, even though he didn't provide details.
+In an appendix to Klein's and Sommerfeld's "Theory of the top" (1910), Fritz Noether showed how to formulate hyperbolic rotations using biquaternions with 
+  
+    
+      
+        ω
+        =
+        
+          
+            −
+            1
+          
+        
+      
+    
+    {\displaystyle \omega ={\sqrt {-1}}}
+  
+, which he also related to the speed of light by setting ω2=-c2. He concluded that this is the principal ingredient for a rational representation of the group of Lorentz transformations:
+
+  
+    
+      
+        
+          
+            
+              
+                V
+                =
+                
+                  
+                    
+                      
+                        Q
+                        
+                          1
+                        
+                      
+                      v
+                      
+                        Q
+                        
+                          2
+                        
+                      
+                    
+                    
+                      
+                        T
+                        
+                          1
+                        
+                      
+                      
+                        T
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  X
+                  
+                    2
+                  
+                
+                +
+                
+                  Y
+                  
+                    2
+                  
+                
+                +
+                
+                  Z
+                  
+                    2
+                  
+                
+                +
+                
+                  ω
+                  
+                    2
+                  
+                
+                
+                  S
+                  
+                    2
+                  
+                
+                =
+                
+                  x
+                  
+                    2
+                  
+                
+                +
+                
+                  y
+                  
+                    2
+                  
+                
+                +
+                
+                  z
+                  
+                    2
+                  
+                
+                +
+                
+                  ω
+                  
+                    2
+                  
+                
+                
+                  s
+                  
+                    2
+                  
+                
+              
+            
+            
+              
+                
+                  
+                    
+                      
+                        V
+                      
+                      
+                        
+                        =
+                        X
+                        i
+                        +
+                        Y
+                        j
+                        +
+                        Z
+                        k
+                        +
+                        ω
+                        S
+                      
+                    
+                    
+                      
+                        v
+                      
+                      
+                        
+                        =
+                        x
+                        i
+                        +
+                        y
+                        j
+                        +
+                        z
+                        k
+                        +
+                        ω
+                        s
+                      
+                    
+                    
+                      
+                        
+                          Q
+                          
+                            1
+                          
+                        
+                      
+                      
+                        
+                        =
+                        (
+                        +
+                        A
+                        i
+                        +
+                        B
+                        j
+                        +
+                        C
+                        k
+                        +
+                        D
+                        )
+                        +
+                        ω
+                        (
+                        
+                          A
+                          ′
+                        
+                        i
+                        +
+                        
+                          B
+                          ′
+                        
+                        j
+                        +
+                        
+                          C
+                          ′
+                        
+                        k
+                        +
+                        
+                          D
+                          ′
+                        
+                        )
+                      
+                    
+                    
+                      
+                        
+                          Q
+                          
+                            2
+                          
+                        
+                      
+                      
+                        
+                        =
+                        (
+                        −
+                        A
+                        i
+                        −
+                        B
+                        j
+                        −
+                        C
+                        k
+                        +
+                        D
+                        )
+                        +
+                        ω
+                        (
+                        
+                          A
+                          ′
+                        
+                        i
+                        +
+                        
+                          B
+                          ′
+                        
+                        j
+                        +
+                        
+                          C
+                          ′
+                        
+                        k
+                        −
+                        
+                          D
+                          ′
+                        
+                        )
+                      
+                    
+                    
+                      
+                        
+                          T
+                          
+                            1
+                          
+                        
+                        
+                          T
+                          
+                            2
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          T
+                          
+                            1
+                          
+                          
+                            2
+                          
+                        
+                        =
+                        
+                          T
+                          
+                            2
+                          
+                          
+                            2
+                          
+                        
+                        =
+                        
+                          A
+                          
+                            2
+                          
+                        
+                        +
+                        
+                          B
+                          
+                            2
+                          
+                        
+                        +
+                        
+                          C
+                          
+                            2
+                          
+                        
+                        +
+                        
+                          D
+                          
+                            2
+                          
+                        
+                        +
+                        
+                          ω
+                          
+                            2
+                          
+                        
+                        
+                          (
+                          
+                            
+                              A
+                              
+                                ′
+                                2
+                              
+                            
+                            +
+                            
+                              B
+                              
+                                ′
+                                2
+                              
+                            
+                            +
+                            
+                              C
+                              
+                                ′
+                                2
+                              
+                            
+                            +
+                            
+                              D
+                              
+                                ′
+                                2
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}V={\frac {Q_{1}vQ_{2}}{T_{1}T_{2}}}\\\hline X^{2}+Y^{2}+Z^{2}+\omega ^{2}S^{2}=x^{2}+y^{2}+z^{2}+\omega ^{2}s^{2}\\\hline {\begin{aligned}V&=Xi+Yj+Zk+\omega S\\v&=xi+yj+zk+\omega s\\Q_{1}&=(+Ai+Bj+Ck+D)+\omega (A'i+B'j+C'k+D')\\Q_{2}&=(-Ai-Bj-Ck+D)+\omega (A'i+B'j+C'k-D')\\T_{1}T_{2}&=T_{1}^{2}=T_{2}^{2}=A^{2}+B^{2}+C^{2}+D^{2}+\omega ^{2}\left(A^{\prime 2}+B^{\prime 2}+C^{\prime 2}+D^{\prime 2}\right)\end{aligned}}\end{matrix}}}
+  
+
+Besides citing quaternion related standard works by Arthur Cayley (1854), Noether referred to the entries in Klein's encyclopedia by Eduard Study (1899) and the French version by Élie Cartan (1908). Cartan's version contains a description of Study's dual numbers, Clifford's biquaternions (including the choice 
+  
+    
+      
+        ω
+        =
+        
+          
+            −
+            1
+          
+        
+      
+    
+    {\displaystyle \omega ={\sqrt {-1}}}
+  
+ for hyperbolic geometry), and Clifford algebra, with references to Stephanos (1883), Buchheim (1884–85), Vahlen (1901–02) and others.
+Citing Noether, Klein himself published in August 1910 the following quaternion substitutions forming the group of Lorentz transformations:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-8.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-8.md
new file mode 100644
index 000000000..1e018f10b
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-8.md
@@ -0,0 +1,1795 @@
+---
+title: "History of Lorentz transformations"
+chunk: 9/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  
+                    
+                      
+                      
+                        
+                          (
+                          
+                            
+                              i
+                              
+                                1
+                              
+                            
+                            
+                              x
+                              ′
+                            
+                            +
+                            
+                              i
+                              
+                                2
+                              
+                            
+                            
+                              y
+                              ′
+                            
+                            +
+                            
+                              i
+                              
+                                3
+                              
+                            
+                            
+                              z
+                              ′
+                            
+                            +
+                            i
+                            c
+                            
+                              t
+                              ′
+                            
+                          
+                          )
+                        
+                      
+                    
+                    
+                      
+                      
+                        
+                        
+                        −
+                        
+                          (
+                          
+                            
+                              i
+                              
+                                1
+                              
+                            
+                            
+                              x
+                              
+                                0
+                              
+                            
+                            +
+                            
+                              i
+                              
+                                2
+                              
+                            
+                            
+                              y
+                              
+                                0
+                              
+                            
+                            +
+                            
+                              i
+                              
+                                3
+                              
+                            
+                            
+                              z
+                              
+                                0
+                              
+                            
+                            +
+                            i
+                            c
+                            
+                              t
+                              
+                                0
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                  
+                
+                =
+                
+                  
+                    
+                      [
+                      
+                        
+                          
+                            
+                            
+                              
+                                (
+                                
+                                  
+                                    i
+                                    
+                                      1
+                                    
+                                  
+                                  (
+                                  A
+                                  +
+                                  i
+                                  
+                                    A
+                                    ′
+                                  
+                                  )
+                                  +
+                                  
+                                    i
+                                    
+                                      2
+                                    
+                                  
+                                  (
+                                  B
+                                  +
+                                  i
+                                  
+                                    B
+                                    ′
+                                  
+                                  )
+                                  +
+                                  
+                                    i
+                                    
+                                      3
+                                    
+                                  
+                                  (
+                                  C
+                                  +
+                                  i
+                                  
+                                    C
+                                    ′
+                                  
+                                  )
+                                  +
+                                  
+                                    i
+                                    
+                                      4
+                                    
+                                  
+                                  (
+                                  D
+                                  +
+                                  i
+                                  
+                                    D
+                                    ′
+                                  
+                                  )
+                                
+                                )
+                              
+                            
+                          
+                          
+                            
+                            
+                              
+                              
+                              ⋅
+                              
+                                (
+                                
+                                  
+                                    i
+                                    
+                                      1
+                                    
+                                  
+                                  x
+                                  +
+                                  
+                                    i
+                                    
+                                      2
+                                    
+                                  
+                                  y
+                                  +
+                                  
+                                    i
+                                    
+                                      3
+                                    
+                                  
+                                  z
+                                  +
+                                  i
+                                  c
+                                  t
+                                
+                                )
+                              
+                            
+                          
+                          
+                            
+                            
+                              
+                              
+                              
+                              ⋅
+                              
+                                (
+                                
+                                  
+                                    i
+                                    
+                                      1
+                                    
+                                  
+                                  (
+                                  A
+                                  −
+                                  i
+                                  
+                                    A
+                                    ′
+                                  
+                                  )
+                                  +
+                                  
+                                    i
+                                    
+                                      2
+                                    
+                                  
+                                  (
+                                  B
+                                  −
+                                  i
+                                  
+                                    B
+                                    ′
+                                  
+                                  )
+                                  +
+                                  
+                                    i
+                                    
+                                      3
+                                    
+                                  
+                                  (
+                                  C
+                                  −
+                                  i
+                                  
+                                    C
+                                    ′
+                                  
+                                  )
+                                  −
+                                  (
+                                  D
+                                  −
+                                  i
+                                  
+                                    D
+                                    ′
+                                  
+                                  )
+                                
+                                )
+                              
+                            
+                          
+                        
+                      
+                      ]
+                    
+                    
+                      
+                        (
+                        
+                          
+                            A
+                            
+                              ′
+                              2
+                            
+                          
+                          +
+                          
+                            B
+                            
+                              ′
+                              2
+                            
+                          
+                          +
+                          
+                            C
+                            
+                              ′
+                              2
+                            
+                          
+                          +
+                          
+                            D
+                            
+                              ′
+                              2
+                            
+                          
+                        
+                        )
+                      
+                      −
+                      
+                        (
+                        
+                          
+                            A
+                            
+                              2
+                            
+                          
+                          +
+                          
+                            B
+                            
+                              2
+                            
+                          
+                          +
+                          
+                            C
+                            
+                              2
+                            
+                          
+                          +
+                          
+                            D
+                            
+                              2
+                            
+                          
+                        
+                        )
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  where
+                
+              
+            
+            
+              
+                A
+                
+                  A
+                  ′
+                
+                +
+                B
+                
+                  B
+                  ′
+                
+                +
+                C
+                
+                  C
+                  ′
+                
+                +
+                D
+                
+                  D
+                  ′
+                
+                =
+                0
+              
+            
+            
+              
+                
+                  A
+                  
+                    2
+                  
+                
+                +
+                
+                  B
+                  
+                    2
+                  
+                
+                +
+                
+                  C
+                  
+                    2
+                  
+                
+                +
+                
+                  D
+                  
+                    2
+                  
+                
+                >
+                
+                  A
+                  
+                    ′
+                    2
+                  
+                
+                +
+                
+                  B
+                  
+                    ′
+                    2
+                  
+                
+                +
+                
+                  C
+                  
+                    ′
+                    2
+                  
+                
+                +
+                
+                  D
+                  
+                    ′
+                    2
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\begin{aligned}&\left(i_{1}x'+i_{2}y'+i_{3}z'+ict'\right)\\&\quad -\left(i_{1}x_{0}+i_{2}y_{0}+i_{3}z_{0}+ict_{0}\right)\end{aligned}}={\frac {\left[{\begin{aligned}&\left(i_{1}(A+iA')+i_{2}(B+iB')+i_{3}(C+iC')+i_{4}(D+iD')\right)\\&\quad \cdot \left(i_{1}x+i_{2}y+i_{3}z+ict\right)\\&\quad \quad \cdot \left(i_{1}(A-iA')+i_{2}(B-iB')+i_{3}(C-iC')-(D-iD')\right)\end{aligned}}\right]}{\left(A^{\prime 2}+B^{\prime 2}+C^{\prime 2}+D^{\prime 2}\right)-\left(A^{2}+B^{2}+C^{2}+D^{2}\right)}}\\\hline {\text{where}}\\AA'+BB'+CC'+DD'=0\\A^{2}+B^{2}+C^{2}+D^{2}>A^{\prime 2}+B^{\prime 2}+C^{\prime 2}+D^{\prime 2}\end{matrix}}}
+  
+
+or in March 1911
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  g
+                  ′
+                
+                =
+                
+                  
+                    
+                      p
+                      g
+                      π
+                    
+                    M
+                  
+                
+              
+            
+            
+              
+                
+                  
+                    
+                      
+                        g
+                      
+                      
+                        
+                        =
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        c
+                        t
+                        +
+                        i
+                        x
+                        +
+                        j
+                        y
+                        +
+                        k
+                        z
+                      
+                    
+                    
+                      
+                        
+                          g
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        c
+                        
+                          t
+                          ′
+                        
+                        +
+                        i
+                        
+                          x
+                          ′
+                        
+                        +
+                        j
+                        
+                          y
+                          ′
+                        
+                        +
+                        k
+                        
+                          z
+                          ′
+                        
+                      
+                    
+                    
+                      
+                        p
+                      
+                      
+                        
+                        =
+                        (
+                        D
+                        +
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          D
+                          ′
+                        
+                        )
+                        +
+                        i
+                        (
+                        A
+                        +
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          A
+                          ′
+                        
+                        )
+                        +
+                        j
+                        (
+                        B
+                        +
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          B
+                          ′
+                        
+                        )
+                        +
+                        k
+                        (
+                        C
+                        +
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          C
+                          ′
+                        
+                        )
+                      
+                    
+                    
+                      
+                        π
+                      
+                      
+                        
+                        =
+                        (
+                        D
+                        −
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          D
+                          ′
+                        
+                        )
+                        −
+                        i
+                        (
+                        A
+                        −
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          A
+                          ′
+                        
+                        )
+                        −
+                        j
+                        (
+                        B
+                        −
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          B
+                          ′
+                        
+                        )
+                        −
+                        k
+                        (
+                        C
+                        −
+                        
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          C
+                          ′
+                        
+                        )
+                      
+                    
+                    
+                      
+                        M
+                      
+                      
+                        
+                        =
+                        
+                          (
+                          
+                            
+                              A
+                              
+                                2
+                              
+                            
+                            +
+                            
+                              B
+                              
+                                2
+                              
+                            
+                            +
+                            
+                              C
+                              
+                                2
+                              
+                            
+                            +
+                            
+                              D
+                              
+                                2
+                              
+                            
+                          
+                          )
+                        
+                        −
+                        
+                          (
+                          
+                            
+                              A
+                              
+                                ′
+                                2
+                              
+                            
+                            +
+                            
+                              B
+                              
+                                ′
+                                2
+                              
+                            
+                            +
+                            
+                              C
+                              
+                                ′
+                                2
+                              
+                            
+                            +
+                            
+                              D
+                              
+                                ′
+                                2
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                    
+                      
+                      
+                        A
+                        
+                          A
+                          ′
+                        
+                        +
+                        B
+                        
+                          B
+                          ′
+                        
+                        +
+                        C
+                        
+                          C
+                          ′
+                        
+                        +
+                        D
+                        
+                          D
+                          ′
+                        
+                        =
+                        0
+                      
+                    
+                    
+                      
+                      
+                        
+                          A
+                          
+                            2
+                          
+                        
+                        +
+                        
+                          B
+                          
+                            2
+                          
+                        
+                        +
+                        
+                          C
+                          
+                            2
+                          
+                        
+                        +
+                        
+                          D
+                          
+                            2
+                          
+                        
+                        >
+                        
+                          A
+                          
+                            ′
+                            2
+                          
+                        
+                        +
+                        
+                          B
+                          
+                            ′
+                            2
+                          
+                        
+                        +
+                        
+                          C
+                          
+                            ′
+                            2
+                          
+                        
+                        +
+                        
+                          D
+                          
+                            ′
+                            2
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}g'={\frac {pg\pi }{M}}\\\hline {\begin{aligned}g&={\sqrt {-1}}ct+ix+jy+kz\\g'&={\sqrt {-1}}ct'+ix'+jy'+kz'\\p&=(D+{\sqrt {-1}}D')+i(A+{\sqrt {-1}}A')+j(B+{\sqrt {-1}}B')+k(C+{\sqrt {-1}}C')\\\pi &=(D-{\sqrt {-1}}D')-i(A-{\sqrt {-1}}A')-j(B-{\sqrt {-1}}B')-k(C-{\sqrt {-1}}C')\\M&=\left(A^{2}+B^{2}+C^{2}+D^{2}\right)-\left(A^{\prime 2}+B^{\prime 2}+C^{\prime 2}+D^{\prime 2}\right)\\&AA'+BB'+CC'+DD'=0\\&A^{2}+B^{2}+C^{2}+D^{2}>A^{\prime 2}+B^{\prime 2}+C^{\prime 2}+D^{\prime 2}\end{aligned}}\end{matrix}}}
+  
+
+=== Conway (1911), Silberstein (1911) – Quaternions ===
+Arthur W. Conway in February 1911 explicitly formulated quaternionic Lorentz transformations of various electromagnetic quantities in terms of velocity λ:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  
+                    
+                      
+                        
+                          
+                            D
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            a
+                          
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          
+                            
+                              D
+                            
+                          
+                          ′
+                        
+                        
+                          
+                            a
+                          
+                          
+                            −
+                            1
+                          
+                        
+                      
+                    
+                    
+                      
+                        
+                          
+                            σ
+                          
+                        
+                      
+                      
+                        
+                        =
+                        
+                          a
+                        
+                        
+                          
+                            
+                              σ
+                            
+                          
+                          ′
+                        
+                        
+                          
+                            a
+                          
+                          
+                            −
+                            1
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                e
+                =
+                
+                  
+                    a
+                  
+                  
+                    −
+                    1
+                  
+                
+                
+                  e
+                  ′
+                
+                
+                  
+                    a
+                  
+                  
+                    −
+                    1
+                  
+                
+              
+            
+            
+              
+                a
+                =
+                
+                  
+                    (
+                    
+                      1
+                      −
+                      h
+                      
+                        c
+                        
+                          −
+                          1
+                        
+                      
+                      λ
+                    
+                    )
+                  
+                  
+                    
+                      1
+                      2
+                    
+                  
+                
+                
+                  
+                    (
+                    
+                      1
+                      +
+                      
+                        c
+                        
+                          −
+                          2
+                        
+                      
+                      
+                        λ
+                        
+                          2
+                        
+                      
+                    
+                    )
+                  
+                  
+                    −
+                    
+                      
+                        1
+                        4
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\begin{aligned}{\mathtt {D}}&=\mathbf {a} ^{-1}{\mathtt {D}}'\mathbf {a} ^{-1}\\{\mathtt {\sigma }}&=\mathbf {a} {\mathtt {\sigma }}'\mathbf {a} ^{-1}\end{aligned}}\\e=\mathbf {a} ^{-1}e'\mathbf {a} ^{-1}\\\hline a=\left(1-hc^{-1}\lambda \right)^{\frac {1}{2}}\left(1+c^{-2}\lambda ^{2}\right)^{-{\frac {1}{4}}}\end{matrix}}}
+  
+
+Also Ludwik Silberstein in November 1911 as well as in 1914, formulated the Lorentz transformation in terms of velocity v:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  q
+                  ′
+                
+                =
+                Q
+                q
+                Q
+              
+            
+            
+              
+                
+                  
+                    
+                      
+                        q
+                      
+                      
+                        
+                        =
+                        
+                          r
+                        
+                        +
+                        l
+                        =
+                        x
+                        i
+                        +
+                        y
+                        j
+                        +
+                        z
+                        k
+                        +
+                        ι
+                        c
+                        t
+                      
+                    
+                    
+                      
+                        q
+                      
+                      
+                        
+                          
+                          ′
+                        
+                        =
+                        
+                          
+                            r
+                          
+                          ′
+                        
+                        +
+                        
+                          l
+                          ′
+                        
+                        =
+                        
+                          x
+                          ′
+                        
+                        i
+                        +
+                        
+                          y
+                          ′
+                        
+                        j
+                        +
+                        
+                          z
+                          ′
+                        
+                        k
+                        +
+                        ι
+                        c
+                        
+                          t
+                          ′
+                        
+                      
+                    
+                    
+                      
+                        Q
+                      
+                      
+                        
+                        =
+                        
+                          
+                            1
+                            
+                              2
+                            
+                          
+                        
+                        
+                          (
+                          
+                            
+                              
+                                1
+                                +
+                                γ
+                              
+                            
+                            +
+                            
+                              u
+                            
+                            
+                              
+                                1
+                                −
+                                γ
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                    
+                      
+                      
+                        
+                        =
+                        cos
+                        ⁡
+                        α
+                        +
+                        
+                          u
+                        
+                        sin
+                        ⁡
+                        α
+                        =
+                        
+                          e
+                          
+                            α
+                            
+                              u
+                            
+                          
+                        
+                      
+                    
+                    
+                      
+                      
+                        
+                          {
+                          
+                            γ
+                            =
+                            
+                              
+                                (
+                                
+                                  1
+                                  −
+                                  
+                                    v
+                                    
+                                      2
+                                    
+                                  
+                                  
+                                    /
+                                  
+                                  
+                                    c
+                                    
+                                      2
+                                    
+                                  
+                                
+                                )
+                              
+                              
+                                −
+                                1
+                                
+                                  /
+                                
+                                2
+                              
+                            
+                            ,
+                             
+                            2
+                            α
+                            =
+                            arctg
+                            ⁡
+                             
+                            
+                              (
+                              
+                                ι
+                                
+                                  
+                                    v
+                                    c
+                                  
+                                
+                              
+                              )
+                            
+                          
+                          }
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}q'=QqQ\\\hline {\begin{aligned}q&=\mathbf {r} +l=xi+yj+zk+\iota ct\\q&'=\mathbf {r} '+l'=x'i+y'j+z'k+\iota ct'\\Q&={\frac {1}{\sqrt {2}}}\left({\sqrt {1+\gamma }}+\mathrm {u} {\sqrt {1-\gamma }}\right)\\&=\cos \alpha +\mathrm {u} \sin \alpha =e^{\alpha \mathrm {u} }\\&\left\{\gamma =\left(1-v^{2}/c^{2}\right)^{-1/2},\ 2\alpha =\operatorname {arctg} \ \left(\iota {\frac {v}{c}}\right)\right\}\end{aligned}}\end{matrix}}}
+  
+
+Silberstein cites Cayley (1854, 1855) and Study's encyclopedia entry (in the extended French version of Cartan in 1908), as well as the appendix of Klein's and Sommerfeld's book.
+
+=== Ignatowski (1910/11), Herglotz (1911), and others – Vector transformation ===
+
+Vladimir Ignatowski (1910, published 1911) showed how to reformulate the Lorentz transformation in order to allow for arbitrary velocities and coordinates:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  
+                    
+                      
+                        
+                          
+                            v
+                          
+                        
+                        =
+                        
+                          
+                            
+                              
+                                
+                                  
+                                    v
+                                  
+                                
+                                ′
+                              
+                              +
+                              (
+                              p
+                              −
+                              1
+                              )
+                              
+                                
+                                  
+                                    c
+                                  
+                                
+                                
+                                  0
+                                
+                              
+                              ⋅
+                              
+                                
+                                  
+                                    c
+                                  
+                                
+                                
+                                  0
+                                
+                              
+                              
+                                
+                                  
+                                    v
+                                  
+                                
+                                ′
+                              
+                              +
+                              p
+                              q
+                              
+                                
+                                  
+                                    c
+                                  
+                                
+                                
+                                  0
+                                
+                              
+                            
+                            
+                              p
+                              
+                                (
+                                
+                                  1
+                                  +
+                                  n
+                                  q
+                                  
+                                    
+                                      
+                                        c
+                                      
+                                    
+                                    
+                                      0
+                                    
+                                  
+                                  
+                                    
+                                      
+                                        v
+                                      
+                                    
+                                    ′
+                                  
+                                
+                                )
+                              
+                            
+                          
+                        
+                      
+                      
+                        
+                          |
+                          
+                            
+                              
+                                
+                                  
+                                    
+                                      
+                                        A
+                                      
+                                    
+                                    ′
+                                  
+                                
+                                
+                                  
+                                  =
+                                  
+                                    
+                                      A
+                                    
+                                  
+                                  +
+                                  (
+                                  p
+                                  −
+                                  1
+                                  )
+                                  
+                                    
+                                      
+                                        c
+                                      
+                                    
+                                    
+                                      0
+                                    
+                                  
+                                  ⋅
+                                  
+                                    
+                                      
+                                        c
+                                      
+                                    
+                                    
+                                      0
+                                    
+                                  
+                                  
+                                    
+                                      A
+                                    
+                                  
+                                  −
+                                  p
+                                  q
+                                  b
+                                  
+                                    
+                                      
+                                        c
+                                      
+                                    
+                                    
+                                      0
+                                    
+                                  
+                                
+                              
+                              
+                                
+                                  
+                                    b
+                                    ′
+                                  
+                                
+                                
+                                  
+                                  =
+                                  p
+                                  b
+                                  −
+                                  p
+                                  q
+                                  n
+                                  
+                                    
+                                      A
+                                    
+                                  
+                                  
+                                    
+                                      
+                                        c
+                                      
+                                    
+                                    
+                                      0
+                                    
+                                  
+                                
+                              
+                              
+                                
+                              
+                              
+                                
+                                  
+                                    
+                                      A
+                                    
+                                  
+                                
+                                
+                                  
+                                  =
+                                  
+                                    
+                                      
+                                        A
+                                      
+                                    
+                                    ′
+                                  
+                                  +
+                                  (
+                                  p
+                                  −
+                                  1
+                                  )
+                                  
+                                    
+                                      
+                                        c
+                                      
+                                    
+                                    
+                                      0
+                                    
+                                  
+                                  ⋅
+                                  
+                                    
+                                      
+                                        c
+                                      
+                                    
+                                    
+                                      0
+                                    
+                                  
+                                  
+                                    
+                                      
+                                        A
+                                      
+                                    
+                                    ′
+                                  
+                                  +
+                                  p
+                                  q
+                                  
+                                    b
+                                    ′
+                                  
+                                  
+                                    
+                                      
+                                        c
+                                      
+                                    
+                                    
+                                      0
+                                    
+                                  
+                                
+                              
+                              
+                                
+                                  b
+                                
+                                
+                                  
+                                  =
+                                  p
+                                  
+                                    b
+                                    ′
+                                  
+                                  +
+                                  p
+                                  q
+                                  n
+                                  
+                                    
+                                      
+                                        A
+                                      
+                                    
+                                    ′
+                                  
+                                  
+                                    
+                                      
+                                        c
+                                      
+                                    
+                                    
+                                      0
+                                    
+                                  
+                                
+                              
+                            
+                          
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  [
+                  
+                    
+                      
+                        v
+                      
+                    
+                    =
+                    
+                      u
+                    
+                    ,
+                     
+                    
+                      
+                        A
+                      
+                    
+                    =
+                    
+                      x
+                    
+                    ,
+                     
+                    b
+                    =
+                    t
+                    ,
+                     
+                    
+                      
+                        
+                          c
+                        
+                      
+                      
+                        0
+                      
+                    
+                    =
+                    
+                      
+                        
+                          v
+                        
+                        v
+                      
+                    
+                    ,
+                     
+                    p
+                    =
+                    γ
+                    ,
+                     
+                    n
+                    =
+                    
+                      
+                        1
+                        
+                          c
+                          
+                            2
+                          
+                        
+                      
+                    
+                  
+                  ]
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\begin{matrix}{\mathfrak {v}}={\frac {{\mathfrak {v}}'+(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {v}}'+pq{\mathfrak {c}}_{0}}{p\left(1+nq{\mathfrak {c}}_{0}{\mathfrak {v}}'\right)}}&\left|{\begin{aligned}{\mathfrak {A}}'&={\mathfrak {A}}+(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {A}}-pqb{\mathfrak {c}}_{0}\\b'&=pb-pqn{\mathfrak {A}}{\mathfrak {c}}_{0}\\\\{\mathfrak {A}}&={\mathfrak {A}}'+(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {A}}'+pqb'{\mathfrak {c}}_{0}\\b&=pb'+pqn{\mathfrak {A}}'{\mathfrak {c}}_{0}\end{aligned}}\right.\end{matrix}}\\\left[{\mathfrak {v}}=\mathbf {u} ,\ {\mathfrak {A}}=\mathbf {x} ,\ b=t,\ {\mathfrak {c}}_{0}={\frac {\mathbf {v} }{v}},\ p=\gamma ,\ n={\frac {1}{c^{2}}}\right]\end{matrix}}}
+  
+
+Gustav Herglotz (1911) also showed how to formulate the transformation in order to allow for arbitrary velocities and coordinates v=(vx, vy, vz) and r=(x, y, z):
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-9.md b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-9.md
new file mode 100644
index 000000000..bf83f6bd1
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Lorentz_transformations-9.md
@@ -0,0 +1,1555 @@
+---
+title: "History of Lorentz transformations"
+chunk: 10/15
+source: "https://en.wikipedia.org/wiki/History_of_Lorentz_transformations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:36.860372+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  original
+                
+              
+              
+                
+                  modern
+                
+              
+            
+            
+              
+                
+                  
+                  
+                    
+                      
+                        
+                          
+                            x
+                            
+                              0
+                            
+                          
+                        
+                        
+                          
+                          =
+                          x
+                          +
+                          α
+                          u
+                          (
+                          u
+                          x
+                          +
+                          v
+                          y
+                          +
+                          w
+                          z
+                          )
+                          −
+                          β
+                          u
+                          t
+                        
+                      
+                      
+                        
+                          
+                            y
+                            
+                              0
+                            
+                          
+                        
+                        
+                          
+                          =
+                          y
+                          +
+                          α
+                          v
+                          (
+                          u
+                          x
+                          +
+                          v
+                          y
+                          +
+                          w
+                          z
+                          )
+                          −
+                          β
+                          v
+                          t
+                        
+                      
+                      
+                        
+                          
+                            z
+                            
+                              0
+                            
+                          
+                        
+                        
+                          
+                          =
+                          z
+                          +
+                          α
+                          w
+                          (
+                          u
+                          x
+                          +
+                          v
+                          y
+                          +
+                          w
+                          z
+                          )
+                          −
+                          β
+                          w
+                          t
+                        
+                      
+                      
+                        
+                          
+                            t
+                            
+                              0
+                            
+                          
+                        
+                        
+                          
+                          =
+                          −
+                          β
+                          (
+                          u
+                          x
+                          +
+                          v
+                          y
+                          +
+                          w
+                          z
+                          )
+                          +
+                          β
+                          t
+                        
+                      
+                      
+                        
+                        
+                          α
+                          =
+                          
+                            
+                              1
+                              
+                                
+                                  
+                                    1
+                                    −
+                                    
+                                      s
+                                      
+                                        2
+                                      
+                                    
+                                  
+                                
+                                
+                                  (
+                                  
+                                    1
+                                    +
+                                    
+                                      
+                                        1
+                                        −
+                                        
+                                          s
+                                          
+                                            2
+                                          
+                                        
+                                      
+                                    
+                                  
+                                  )
+                                
+                              
+                            
+                          
+                          ,
+                           
+                          β
+                          =
+                          
+                            
+                              1
+                              
+                                1
+                                −
+                                
+                                  s
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                  |
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          x
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        x
+                        +
+                        α
+                        
+                          v
+                          
+                            x
+                          
+                        
+                        
+                          (
+                          
+                            
+                              v
+                              
+                                x
+                              
+                            
+                            x
+                            +
+                            
+                              v
+                              
+                                y
+                              
+                            
+                            y
+                            +
+                            
+                              v
+                              
+                                z
+                              
+                            
+                            z
+                          
+                          )
+                        
+                        −
+                        γ
+                        
+                          v
+                          
+                            x
+                          
+                        
+                        t
+                      
+                    
+                    
+                      
+                        
+                          y
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        y
+                        +
+                        α
+                        
+                          v
+                          
+                            y
+                          
+                        
+                        
+                          (
+                          
+                            
+                              v
+                              
+                                x
+                              
+                            
+                            x
+                            +
+                            
+                              v
+                              
+                                y
+                              
+                            
+                            y
+                            +
+                            
+                              v
+                              
+                                z
+                              
+                            
+                            z
+                          
+                          )
+                        
+                        −
+                        γ
+                        
+                          v
+                          
+                            y
+                          
+                        
+                        t
+                      
+                    
+                    
+                      
+                        
+                          z
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        z
+                        +
+                        α
+                        
+                          v
+                          
+                            z
+                          
+                        
+                        
+                          (
+                          
+                            
+                              v
+                              
+                                x
+                              
+                            
+                            x
+                            +
+                            
+                              v
+                              
+                                y
+                              
+                            
+                            y
+                            +
+                            
+                              v
+                              
+                                z
+                              
+                            
+                            z
+                          
+                          )
+                        
+                        −
+                        γ
+                        
+                          v
+                          
+                            z
+                          
+                        
+                        t
+                      
+                    
+                    
+                      
+                        
+                          t
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        −
+                        γ
+                        
+                          (
+                          
+                            
+                              v
+                              
+                                x
+                              
+                            
+                            x
+                            +
+                            
+                              v
+                              
+                                y
+                              
+                            
+                            y
+                            +
+                            
+                              v
+                              
+                                z
+                              
+                            
+                            z
+                          
+                          )
+                        
+                        +
+                        γ
+                        t
+                      
+                    
+                    
+                      
+                      
+                        α
+                        =
+                        
+                          
+                            
+                              γ
+                              
+                                2
+                              
+                            
+                            
+                              γ
+                              +
+                              1
+                            
+                          
+                        
+                        ,
+                         
+                        γ
+                        =
+                        
+                          
+                            1
+                            
+                              1
+                              −
+                              
+                                v
+                                
+                                  2
+                                
+                              
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{matrix}{\text{original}}&{\text{modern}}\\\hline \left.{\begin{aligned}x^{0}&=x+\alpha u(ux+vy+wz)-\beta ut\\y^{0}&=y+\alpha v(ux+vy+wz)-\beta vt\\z^{0}&=z+\alpha w(ux+vy+wz)-\beta wt\\t^{0}&=-\beta (ux+vy+wz)+\beta t\\&\alpha ={\frac {1}{{\sqrt {1-s^{2}}}\left(1+{\sqrt {1-s^{2}}}\right)}},\ \beta ={\frac {1}{\sqrt {1-s^{2}}}}\end{aligned}}\right|&{\begin{aligned}x'&=x+\alpha v_{x}\left(v_{x}x+v_{y}y+v_{z}z\right)-\gamma v_{x}t\\y'&=y+\alpha v_{y}\left(v_{x}x+v_{y}y+v_{z}z\right)-\gamma v_{y}t\\z'&=z+\alpha v_{z}\left(v_{x}x+v_{y}y+v_{z}z\right)-\gamma v_{z}t\\t'&=-\gamma \left(v_{x}x+v_{y}y+v_{z}z\right)+\gamma t\\&\alpha ={\frac {\gamma ^{2}}{\gamma +1}},\ \gamma ={\frac {1}{\sqrt {1-v^{2}}}}\end{aligned}}\end{matrix}}}
+  
+
+This was simplified using vector notation by Ludwik Silberstein (1911 on the left, 1914 on the right):
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  
+                    
+                      
+                        
+                          
+                            r
+                          
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        
+                          r
+                        
+                        +
+                        (
+                        γ
+                        −
+                        1
+                        )
+                        (
+                        
+                          r
+                          u
+                        
+                        )
+                        
+                          u
+                        
+                        +
+                        i
+                        β
+                        γ
+                        l
+                        u
+                      
+                    
+                    
+                      
+                        
+                          l
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        γ
+                        
+                          [
+                          
+                            l
+                            −
+                            i
+                            β
+                            (
+                            
+                              r
+                              u
+                            
+                            )
+                          
+                          ]
+                        
+                      
+                    
+                  
+                
+              
+              
+                
+                  
+                    
+                      
+                        
+                          
+                            r
+                          
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        
+                          r
+                        
+                        +
+                        
+                          [
+                          
+                            
+                              
+                                
+                                  γ
+                                  −
+                                  1
+                                
+                                
+                                  v
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                            (
+                            
+                              v
+                              r
+                            
+                            )
+                            −
+                            γ
+                            t
+                          
+                          ]
+                        
+                        
+                          v
+                        
+                      
+                    
+                    
+                      
+                        
+                          t
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        γ
+                        
+                          [
+                          
+                            t
+                            −
+                            
+                              
+                                1
+                                
+                                  c
+                                  
+                                    2
+                                  
+                                
+                              
+                            
+                            (
+                            
+                              v
+                              r
+                            
+                            )
+                          
+                          ]
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{array}{c|c}{\begin{aligned}\mathbf {r} '&=\mathbf {r} +(\gamma -1)(\mathbf {ru} )\mathbf {u} +i\beta \gamma lu\\l'&=\gamma \left[l-i\beta (\mathbf {ru} )\right]\end{aligned}}&{\begin{aligned}\mathbf {r} '&=\mathbf {r} +\left[{\frac {\gamma -1}{v^{2}}}(\mathbf {vr} )-\gamma t\right]\mathbf {v} \\t'&=\gamma \left[t-{\frac {1}{c^{2}}}(\mathbf {vr} )\right]\end{aligned}}\end{array}}}
+  
+
+Equivalent formulas were also given by Wolfgang Pauli (1921), with Erwin Madelung (1922) providing the matrix form
+
+  
+    
+      
+        
+          
+            
+              
+              
+                x
+              
+              
+                y
+              
+              
+                z
+              
+              
+                t
+              
+            
+            
+              
+                
+                  x
+                  ′
+                
+              
+              
+                1
+                −
+                
+                  
+                    
+                      v
+                      
+                        x
+                      
+                      
+                        2
+                      
+                    
+                    
+                      v
+                      
+                        2
+                      
+                    
+                  
+                
+                
+                  (
+                  
+                    1
+                    −
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+              
+                −
+                
+                  
+                    
+                      
+                        v
+                        
+                          x
+                        
+                      
+                      
+                        v
+                        
+                          y
+                        
+                      
+                    
+                    
+                      v
+                      
+                        2
+                      
+                    
+                  
+                
+                
+                  (
+                  
+                    1
+                    −
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+              
+                −
+                
+                  
+                    
+                      
+                        v
+                        
+                          x
+                        
+                      
+                      
+                        v
+                        
+                          z
+                        
+                      
+                    
+                    
+                      v
+                      
+                        2
+                      
+                    
+                  
+                
+                
+                  (
+                  
+                    1
+                    −
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+              
+                
+                  
+                    
+                      −
+                      
+                        v
+                        
+                          x
+                        
+                      
+                    
+                    
+                      1
+                      −
+                      
+                        β
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  y
+                  ′
+                
+              
+              
+                −
+                
+                  
+                    
+                      
+                        v
+                        
+                          x
+                        
+                      
+                      
+                        v
+                        
+                          y
+                        
+                      
+                    
+                    
+                      v
+                      
+                        2
+                      
+                    
+                  
+                
+                
+                  (
+                  
+                    1
+                    −
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+              
+                1
+                −
+                
+                  
+                    
+                      v
+                      
+                        y
+                      
+                      
+                        2
+                      
+                    
+                    
+                      v
+                      
+                        2
+                      
+                    
+                  
+                
+                
+                  (
+                  
+                    1
+                    −
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+              
+                −
+                
+                  
+                    
+                      
+                        v
+                        
+                          y
+                        
+                      
+                      
+                        v
+                        
+                          z
+                        
+                      
+                    
+                    
+                      v
+                      
+                        2
+                      
+                    
+                  
+                
+                
+                  (
+                  
+                    1
+                    −
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+              
+                
+                  
+                    
+                      −
+                      
+                        v
+                        
+                          y
+                        
+                      
+                    
+                    
+                      1
+                      −
+                      
+                        β
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  z
+                  ′
+                
+              
+              
+                −
+                
+                  
+                    
+                      
+                        v
+                        
+                          x
+                        
+                      
+                      
+                        v
+                        
+                          z
+                        
+                      
+                    
+                    
+                      v
+                      
+                        2
+                      
+                    
+                  
+                
+                
+                  (
+                  
+                    1
+                    −
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+              
+                −
+                
+                  
+                    
+                      
+                        v
+                        
+                          y
+                        
+                      
+                      
+                        v
+                        
+                          z
+                        
+                      
+                    
+                    
+                      v
+                      
+                        2
+                      
+                    
+                  
+                
+                
+                  (
+                  
+                    1
+                    −
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+              
+                1
+                −
+                
+                  
+                    
+                      v
+                      
+                        z
+                      
+                      
+                        2
+                      
+                    
+                    
+                      v
+                      
+                        2
+                      
+                    
+                  
+                
+                
+                  (
+                  
+                    1
+                    −
+                    
+                      
+                        1
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                  )
+                
+              
+              
+                
+                  
+                    
+                      −
+                      
+                        v
+                        
+                          z
+                        
+                      
+                    
+                    
+                      1
+                      −
+                      
+                        β
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+            
+              
+                
+                  t
+                  ′
+                
+              
+              
+                
+                  
+                    
+                      −
+                      
+                        v
+                        
+                          x
+                        
+                      
+                    
+                    
+                      
+                        c
+                        
+                          2
+                        
+                      
+                      
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+              
+                
+                  
+                    
+                      −
+                      
+                        v
+                        
+                          y
+                        
+                      
+                    
+                    
+                      
+                        c
+                        
+                          2
+                        
+                      
+                      
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+              
+                
+                  
+                    
+                      −
+                      
+                        v
+                        
+                          z
+                        
+                      
+                    
+                    
+                      
+                        c
+                        
+                          2
+                        
+                      
+                      
+                        
+                          1
+                          −
+                          
+                            β
+                            
+                              2
+                            
+                          
+                        
+                      
+                    
+                  
+                
+              
+              
+                
+                  
+                    1
+                    
+                      1
+                      −
+                      
+                        β
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{array}{c|c|c|c|c}&x&y&z&t\\\hline x'&1-{\frac {v_{x}^{2}}{v^{2}}}\left(1-{\frac {1}{\sqrt {1-\beta ^{2}}}}\right)&-{\frac {v_{x}v_{y}}{v^{2}}}\left(1-{\frac {1}{\sqrt {1-\beta ^{2}}}}\right)&-{\frac {v_{x}v_{z}}{v^{2}}}\left(1-{\frac {1}{\sqrt {1-\beta ^{2}}}}\right)&{\frac {-v_{x}}{\sqrt {1-\beta ^{2}}}}\\y'&-{\frac {v_{x}v_{y}}{v^{2}}}\left(1-{\frac {1}{\sqrt {1-\beta ^{2}}}}\right)&1-{\frac {v_{y}^{2}}{v^{2}}}\left(1-{\frac {1}{\sqrt {1-\beta ^{2}}}}\right)&-{\frac {v_{y}v_{z}}{v^{2}}}\left(1-{\frac {1}{\sqrt {1-\beta ^{2}}}}\right)&{\frac {-v_{y}}{\sqrt {1-\beta ^{2}}}}\\z'&-{\frac {v_{x}v_{z}}{v^{2}}}\left(1-{\frac {1}{\sqrt {1-\beta ^{2}}}}\right)&-{\frac {v_{y}v_{z}}{v^{2}}}\left(1-{\frac {1}{\sqrt {1-\beta ^{2}}}}\right)&1-{\frac {v_{z}^{2}}{v^{2}}}\left(1-{\frac {1}{\sqrt {1-\beta ^{2}}}}\right)&{\frac {-v_{z}}{\sqrt {1-\beta ^{2}}}}\\t'&{\frac {-v_{x}}{c^{2}{\sqrt {1-\beta ^{2}}}}}&{\frac {-v_{y}}{c^{2}{\sqrt {1-\beta ^{2}}}}}&{\frac {-v_{z}}{c^{2}{\sqrt {1-\beta ^{2}}}}}&{\frac {1}{\sqrt {1-\beta ^{2}}}}\end{array}}}
+  
+
+These formulas were called "general Lorentz transformation without rotation" by Christian Møller (1952), who in addition gave an even more general Lorentz transformation in which the Cartesian axes have different orientations, using a rotation operator 
+  
+    
+      
+        
+          
+            D
+          
+        
+      
+    
+    {\displaystyle {\mathfrak {D}}}
+  
+. In this case, v′=(v′x, v′y, v′z) is not equal to -v=(-vx, -vy, -vz), but the relation 
+  
+    
+      
+        
+          
+            v
+          
+          ′
+        
+        =
+        −
+        
+          
+            D
+          
+        
+        
+          v
+        
+      
+    
+    {\displaystyle \mathbf {v} '=-{\mathfrak {D}}\mathbf {v} }
+  
+ holds instead, with the result
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  
+                    
+                      
+                        
+                          
+                            x
+                          
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        
+                          
+                            
+                              D
+                            
+                          
+                          
+                            −
+                            1
+                          
+                        
+                        
+                          x
+                        
+                        −
+                        
+                          
+                            v
+                          
+                          ′
+                        
+                        
+                          {
+                          
+                            
+                              (
+                              
+                                γ
+                                −
+                                1
+                              
+                              )
+                            
+                            (
+                            
+                              x
+                              ⋅
+                              v
+                            
+                            )
+                            
+                              /
+                            
+                            
+                              v
+                              
+                                2
+                              
+                            
+                            −
+                            γ
+                            t
+                          
+                          }
+                        
+                      
+                    
+                    
+                      
+                        
+                          t
+                          ′
+                        
+                      
+                      
+                        
+                        =
+                        γ
+                        
+                          (
+                          
+                            t
+                            −
+                            (
+                            
+                              v
+                            
+                            ⋅
+                            
+                              x
+                            
+                            )
+                            
+                              /
+                            
+                            
+                              c
+                              
+                                2
+                              
+                            
+                          
+                          )
+                        
+                      
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{array}{c}{\begin{aligned}\mathbf {x} '&={\mathfrak {D}}^{-1}\mathbf {x} -\mathbf {v} '\left\{\left(\gamma -1\right)(\mathbf {x\cdot v} )/v^{2}-\gamma t\right\}\\t'&=\gamma \left(t-(\mathbf {v} \cdot \mathbf {x} )/c^{2}\right)\end{aligned}}\end{array}}}
+  
+
+=== Borel (1913–14) – Cayley–Hermite parameter ===
+Émile Borel (1913) started by demonstrating Euclidean motions using Euler-Rodrigues parameter in three dimensions, and Cayley's (1846) parameter in four dimensions. Then he demonstrated the connection to indefinite quadratic forms expressing hyperbolic motions and Lorentz transformations. In three dimensions:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-0.md b/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-0.md
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-0.md
@@ -0,0 +1,86 @@
+---
+title: "History of Maxwell's equations"
+chunk: 1/4
+source: "https://en.wikipedia.org/wiki/History_of_Maxwell's_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:43.403664+00:00"
+instance: "kb-cron"
+---
+
+By the first half of the 19th century, the understanding of electromagnetics had improved through many experiments and theoretical work. In the 1780s, Charles-Augustin de Coulomb established his law of electrostatics. In 1825, André-Marie Ampère published his force law. In 1831, Michael Faraday discovered electromagnetic induction through his experiments, and proposed lines of forces to describe it. In 1834, Emil Lenz solved the problem of the direction of the induction, and Franz Ernst Neumann wrote down the equation to calculate the induced force by change of magnetic flux. However, these experimental results and rules were not well organized and sometimes confusing to scientists. A comprehensive summary of the electrodynamic principles was needed.
+This work was done by James Clerk Maxwell through a series of papers published from the 1850s to the 1870s. In the 1850s, Maxwell was working at the University of Cambridge where he was impressed by Faraday's lines of forces concept. Faraday created this concept by impression of Roger Boscovich, a physicist that impacted Maxwell's work as well.  In 1856, he published his first paper in electromagnetism: On Faraday's Lines of Force. 
+He tried to use the analogy of incompressible fluid flow to model the magnetic lines of forces. Later, Maxwell moved to King's College London where he actually came into regular contact with Faraday, and became life-long friends. From 1861 to 1862, Maxwell published a series of four papers under the title of On Physical Lines of Force. 
+In these papers, he used mechanical models, such as rotating vortex tubes, to model the electromagnetic field.  He also modeled the vacuum as a kind of insulating elastic medium to account for the stress of the magnetic lines of force given by Faraday. These works had already laid the basis of the formulation of the Maxwell's equations. Moreover, the 1862 paper already derived the speed of light c from the expression of the velocity of the electromagnetic wave in relation to the vacuum constants. The final form of Maxwell's equations was published in 1865 A Dynamical Theory of the Electromagnetic Field,
+ in which the theory is formulated in strictly mathematical form. 
+In 1873, Maxwell published A Treatise on Electricity and Magnetism as a summary of his work on electromagnetism. In summary, Maxwell's equations successfully unified theories of light and electromagnetism, which is one of the great unifications in physics.
+Maxwell built a simple flywheel model of electromagnetism, and Boltzmann built an elaborate mechanical model ("Bicykel") based on Maxwell's flywheel model, which he used for lecture demonstrations. Figures are at the end of Boltzmann's 1891 book.
+
+Later, Oliver Heaviside studied Maxwell's A Treatise on Electricity and Magnetism and employed vector calculus to synthesize Maxwell's over 20 equations into the four recognizable ones which modern physicists use. Maxwell's equations also inspired Albert Einstein in developing the theory of special relativity.
+The experimental proof of Maxwell's equations was demonstrated by Heinrich Hertz in a series of experiments in the 1890s. 
+After that, Maxwell's equations were fully accepted by scientists.
+
+== Relationships among electricity, magnetism, and the speed of light ==
+The relationships amongst electricity, magnetism, and the speed of light can be summarized by the modern equation:
+
+  
+    
+      
+        c
+        =
+        
+          
+            1
+            
+              
+                μ
+                
+                  0
+                
+              
+              
+                ε
+                
+                  0
+                
+              
+            
+          
+        
+         
+        .
+      
+    
+    {\displaystyle c={\frac {1}{\sqrt {\mu _{0}\varepsilon _{0}}}}\ .}
+  
+
+The left-hand side is the speed of light and the right-hand side is a quantity related to the constants that appear in the equations governing electricity and magnetism. Although the right-hand side has units of velocity, it can be inferred from measurements of electric and magnetic forces, which involve no physical velocities. Therefore, establishing this relationship provided convincing evidence that light is an electromagnetic phenomenon.
+The discovery of this relationship started in 1855, when Wilhelm Eduard Weber and Rudolf Kohlrausch determined that there was a quantity related to electricity and magnetism, "the ratio of the absolute electromagnetic unit of charge to the absolute electrostatic unit of charge" (in modern language, the value 
+  
+    
+      
+        1
+        
+          /
+        
+        
+          
+            
+              μ
+              
+                0
+              
+            
+            
+              ε
+              
+                0
+              
+            
+          
+        
+      
+    
+    {\displaystyle 1/{\sqrt {\mu _{0}\varepsilon _{0}}}}
+  
+), and determined that it should have units of velocity. They then measured this ratio by an experiment which involved charging and discharging a Leyden jar and measuring the magnetic force from the discharge current, and found a value 3.107×108 m/s, remarkably close to the speed of light, which had recently been measured at 3.14×108 m/s by Hippolyte Fizeau in 1848 and at 2.98×108 m/s by Léon Foucault in 1850. However, Weber and Kohlrausch did not make the connection to the speed of light. Towards the end of 1861 while working on Part III of his paper On Physical Lines of Force, Maxwell travelled from Scotland to London and looked up Weber and Kohlrausch's results. He converted them into a format which was compatible with his own writings, and in doing so he established the connection to the speed of light and concluded that light is a form of electromagnetic radiation.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-1.md b/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-1.md
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-1.md
@@ -0,0 +1,121 @@
+---
+title: "History of Maxwell's equations"
+chunk: 2/4
+source: "https://en.wikipedia.org/wiki/History_of_Maxwell's_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:43.403664+00:00"
+instance: "kb-cron"
+---
+
+== The term Maxwell's equations ==
+The four modern Maxwell's equations can be found individually throughout his 1861 paper, derived theoretically using a molecular vortex model of Michael Faraday's "lines of force" and in conjunction with the experimental result of Weber and Kohlrausch. But it was not until 1884 that Oliver Heaviside, concurrently with similar work by Josiah Willard Gibbs and Heinrich Hertz, grouped the twenty equations together into a set of only four, via vector notation. This group of four equations was known variously as the Hertz–Heaviside equations and the Maxwell–Hertz equations, but are now universally known as Maxwell's equations. Heaviside's equations, which are taught in textbooks and universities as Maxwell's equations are not exactly the same as the ones due to Maxwell, and, in fact, the latter are more easily made to conform to quantum physics.
+This very subtle and paradoxical sounding situation can perhaps be most easily understood in terms of the similar situation that exists with respect to Newton's second law of motion: In textbooks and in classrooms the law 
+  
+    
+      
+        F
+        =
+        m
+        a
+      
+    
+    {\displaystyle F=ma}
+  
+ is attributed to  Newton, but Newton in fact wrote his second law as 
+  
+    
+      
+        F
+        =
+        
+          
+            
+              p
+              ˙
+            
+          
+        
+      
+    
+    {\displaystyle F={\dot {p}}}
+  
+. This is clearly visible in a glass case in the Wren Library of Trinity College, Cambridge, where Newton's manuscript is open to the relevant page, showing the equation 
+  
+    
+      
+        F
+        =
+        
+          
+            
+              p
+              ˙
+            
+          
+        
+      
+    
+    {\displaystyle F={\dot {p}}}
+  
+, where 
+  
+    
+      
+        
+          
+            
+              p
+              ˙
+            
+          
+        
+      
+    
+    {\displaystyle {\dot {p}}}
+  
+ is the time derivative of the momentum 
+  
+    
+      
+        p
+      
+    
+    {\displaystyle p}
+  
+. This seems a trivial enough fact until you realize that 
+  
+    
+      
+        F
+        =
+        
+          
+            
+              p
+              ˙
+            
+          
+        
+      
+    
+    {\displaystyle F={\dot {p}}}
+  
+ remains true in special relativity, without modification.
+Maxwell's contribution to science in producing these equations lies in the correction he made to Ampère's circuital law in his 1861 paper On Physical Lines of Force. He added the displacement current term to Ampère's circuital law and this enabled him to derive the electromagnetic wave equation in his later 1865 paper A Dynamical Theory of the Electromagnetic Field and to demonstrate the fact that light is an electromagnetic wave. This fact was later confirmed experimentally by Heinrich Hertz in 1887. The physicist Richard Feynman predicted that, "From a long view of the history of mankind, seen from, say, ten thousand years from now, there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade."
+The concept of fields was introduced by, among others, Faraday. Albert Einstein wrote:
+
+The precise formulation of the time-space laws was the work of Maxwell. Imagine his feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarized waves, and at the speed of light! To few men in the world has such an experience been vouchsafed ... it took physicists some decades to grasp the full significance of Maxwell's discovery, so bold was the leap that his genius forced upon the conceptions of his fellow workers. 
+Heaviside worked to eliminate the potentials (electric potential and magnetic potential) that Maxwell had used as the central concepts in his equations; this effort was somewhat controversial, though it was understood by 1884 that the potentials must propagate at the speed of light like the fields, unlike the concept of instantaneous action-at-a-distance like the then conception of gravitational potential.
+
+== On Physical Lines of Force ==
+
+The four equations we use today appeared separately in Maxwell's 1861 paper, On Physical Lines of Force:
+
+Equation (56) in Maxwell's 1861 paper is Gauss's law for magnetism, ∇ • B = 0.
+Equation (112) is Ampère's circuital law, with Maxwell's addition of displacement current. This may be the most remarkable contribution of Maxwell's work, enabling him to derive the electromagnetic wave equation in his 1865 paper A Dynamical Theory of the Electromagnetic Field, showing that light is an electromagnetic wave. This lent the equations their full significance with respect to understanding the nature of the phenomena he elucidated. (Kirchhoff derived the telegrapher's equations in 1857 without using displacement current, but he did use Poisson's equation and the equation of continuity, which are the mathematical ingredients of the displacement current. Nevertheless, believing his equations to be applicable only inside an electric wire, he cannot be credited with the discovery that light is an electromagnetic wave).
+Equation (115) is Gauss's law.
+Equation (54) expresses what Oliver Heaviside referred to as 'Faraday's law', which addresses the time-variant aspect of electromagnetic induction, but not the one induced by motion; Faraday's original flux law accounted for both. Maxwell deals with the motion-related aspect of electromagnetic induction, v × B, in equation (77), which is the same as equation (D) in Maxwell's original equations as listed below. It is expressed today as the force law equation, F  = q(E + v × B), which sits adjacent to Maxwell's equations and bears the name Lorentz force, even though Maxwell derived it when Lorentz was still a young boy.
+The difference between the B and the H vectors can be traced back to Maxwell's 1855 paper entitled On Faraday's Lines of Force which was read to the Cambridge Philosophical Society. The paper presented a simplified model of Faraday's work, and how the two phenomena were related. He reduced all of the current knowledge into a linked set of differential equations.
+
+It is later clarified in his concept of a sea of molecular vortices that appears in his 1861 paper On Physical Lines of Force. Within that context, H represented pure vorticity (spin), whereas B was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability µ to be a measure of the density of the vortex sea. Hence the relationship,
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-2.md b/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-2.md
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@@ -0,0 +1,84 @@
+---
+title: "History of Maxwell's equations"
+chunk: 3/4
+source: "https://en.wikipedia.org/wiki/History_of_Maxwell's_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:43.403664+00:00"
+instance: "kb-cron"
+---
+
+Magnetic induction current causes a magnetic current density B = μ H was essentially a rotational analogy to the linear electric current relationship,
+Electric convection current J = ρ v where ρ is electric charge density. B was seen as a kind of magnetic current of vortices aligned in their axial planes, with H being the circumferential velocity of the vortices. With µ representing vortex density, it follows that the product of µ with vorticity H leads to the magnetic field denoted as B.
+The electric current equation can be viewed as a convective current of electric charge that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the B vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse-square law force.
+The extension of the above considerations confirms that where B is to H, and where J is to ρ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that E is to D i.e. B parallels with E, whereas H parallels with D.
+
+== A Dynamical Theory of the Electromagnetic Field ==
+
+In 1865 Maxwell published "A dynamical theory of the electromagnetic field" in which he showed that light was an electromagnetic phenomenon. Confusion over the term "Maxwell's equations" sometimes arises because it has been used for a set of eight equations that appeared in Part III of Maxwell's 1865 paper "A dynamical theory of the electromagnetic field", entitled "General equations of the electromagnetic field", and this confusion is compounded by the writing of six of those eight equations as three separate equations (one for each of the Cartesian axes), resulting in twenty equations and twenty unknowns.
+The eight original Maxwell's equations can be written in the modern form of Heaviside's vector notation as follows:
+
+Notation
+
+H is the magnetizing field, which Maxwell called the magnetic intensity.
+
+J is the current density (with Jtot being the total current including displacement current).
+
+D is the displacement field (called the electric displacement by Maxwell).
+
+ρ is the free charge density (called the quantity of free electricity by Maxwell).
+
+A is the magnetic potential (called the angular impulse by Maxwell).
+
+E is called the electromotive force by Maxwell. The term electromotive force is nowadays used for voltage, but it is clear from the context that Maxwell's meaning corresponded more to the modern term electric field.
+
+ϕ is the electric potential (which Maxwell also called electric potential).
+
+σ is the electrical conductivity (Maxwell called the inverse of conductivity the specific resistance, what is now called the resistivity).
+Equation [D], with the  μv × H term, is effectively the Lorentz force, similarly to equation (77) of his 1861 paper (see above).
+When Maxwell derives the electromagnetic wave equation in his 1865 paper, he uses equation [D] to cater for electromagnetic induction rather than Faraday's law of induction which is used in modern textbooks. (Faraday's law itself does not appear among his equations.) However, Maxwell drops the  μ v × H term from equation [D] when he is deriving the electromagnetic wave equation, as he considers the situation only from the rest frame.
+
+== A Treatise on Electricity and Magnetism ==
+
+In A Treatise on Electricity and Magnetism, an 1873 treatise on electromagnetism written by James Clerk Maxwell, twelve general equations of the electromagnetic field are listed and these include the eight that are listed in the 1865 paper. His theoretical investigations of the electromagnetic field was guided by the notions of work, energy, potential, the principle of conservation of energy, and Lagrangian dynamics.  All the principal equations concerning Maxwell's electromagnetic theory are recapitulated in Chapter IX of Part IV. At the end of this chapter, all the equations are listed and set in quaternion form. The first two equations [A] and [B] relates the electric scalar potential and magnetic vector potential to the electric and magnetic fields. The third equation [C] relates the electromagnetic field to electromagnetic force. The rest of the equations [D] to [L] relates the electromagnetic field to material data: the current and charge densities as well as the material medium.
+Here the twelve Maxwell's equations have been given, respecting the original notations used by Maxwell. The only difference is that the vectors have been denoted using bold typeface instead of the original Fraktur typeface. For comparison Maxwell's equations in their original quaternion form and their vector form have been given. The 
+  
+    
+      
+        S
+        .
+      
+    
+    {\displaystyle S.}
+  
+ and 
+  
+    
+      
+        V
+        .
+      
+    
+    {\displaystyle V.}
+  
+ notations are used to denote the scalar and vector parts of quaternion product. 
+
+Unfamiliar notation
+
+G is the velocity of a point.
+
+C is total current.
+
+J is the intensity of magnetization.
+
+K is the current of conduction.
+
+Ψ is the electric potential.
+
+Ω is the magnetic potential.
+
+K is the dielectric constant.
+
+C is electrical conductivity.
+
+e is electric charge density.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-3.md b/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-3.md
new file mode 100644
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_Maxwell's_equations-3.md
@@ -0,0 +1,112 @@
+---
+title: "History of Maxwell's equations"
+chunk: 4/4
+source: "https://en.wikipedia.org/wiki/History_of_Maxwell's_equations"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:43.403664+00:00"
+instance: "kb-cron"
+---
+
+m is magnetic charge density.
+In the same chapter, Maxwell points out that the consequence of equation [A] is (in vector notation) 
+  
+    
+      
+        ∇
+        ⋅
+        
+          B
+        
+        =
+        0
+      
+    
+    {\displaystyle \nabla \cdot \mathbf {B} =0}
+  
+. Similarly, taking divergence of equation [E] gives conservation of electric charge, 
+  
+    
+      
+        ∇
+        ⋅
+        
+          C
+        
+        =
+        0
+      
+    
+    {\displaystyle \nabla \cdot \mathbf {C} =0}
+  
+, which, Maxwell points out, is true only if the total current includes the variation of electric displacement. Lastly, combining equation [A] and equation [E], the formula 
+  
+    
+      
+        
+          ∇
+          
+            2
+          
+        
+        
+          A
+        
+        =
+        4
+        π
+        μ
+        
+          C
+        
+      
+    
+    {\displaystyle \nabla ^{2}\mathbf {A} =4\pi \mu \mathbf {C} }
+  
+ is obtained which relates magnetic potential with current. Elsewhere in the Part I of the book, the electric potential is related to charge density as 
+  
+    
+      
+        
+          ∇
+          
+            2
+          
+        
+        Ψ
+        =
+        −
+        
+          
+            
+              4
+              π
+            
+            K
+          
+        
+        e
+      
+    
+    {\displaystyle \nabla ^{2}\Psi =-{\frac {4\pi }{K}}e}
+  
+ in the absence of motion. Presciently, Maxwell also mentions that although some of the equations could be combined to eliminate some quantities, the objective of his list was to express every relation of which there was any knowledge of, rather than to obtain compactness of mathematical formulae.
+
+== Relativity ==
+
+Maxwell's equations were an essential inspiration for the development of special relativity. Possibly the most important aspect was their denial of instantaneous action at a distance. Rather, according to them, forces are propagated at the velocity of light through the electromagnetic field.
+Maxwell's original equations are based on the idea that light travels through a sea of molecular vortices known as the "luminiferous aether", and that the speed of light has to be respective to the reference frame of this aether. Measurements designed to measure the speed of the Earth through the aether conflicted with this notion, though.
+A more theoretical approach was suggested by Hendrik Lorentz along with George FitzGerald and Joseph Larmor. Both Larmor (1897) and Lorentz (1899, 1904) ignored aether motion and derived the Lorentz transformation (so named by Henri Poincaré) as one under which Maxwell's equations were invariant. Poincaré (1900) analyzed the coordination of moving clocks by exchanging light signals. He also established the mathematical group property of the Lorentz transformation (Poincaré 1905). Sometimes this transformation is called the FitzGerald–Lorentz transformation or even the FitzGerald–Lorentz–Einstein transformation.
+Albert Einstein also dismissed the notion of the aether, and relied on Lorentz's conclusion about the fixed speed of light, independent of the velocity of the observer. He applied the FitzGerald–Lorentz transformation to kinematics, and not just Maxwell's equations. Maxwell's equations played a key role in Einstein's groundbreaking 1905 scientific paper on special relativity. For example, in the opening paragraph of his paper, he began his theory by noting that a description of an electric conductor moving with respect to a magnet must generate a consistent set of fields regardless of whether the force is calculated in the rest frame of the magnet or that of the conductor.
+The general theory of relativity has also had a close relationship with Maxwell's equations. For example, Theodor Kaluza and Oskar Klein in the 1920s showed that Maxwell's equations could be derived by extending general relativity into five physical dimensions. This strategy of using additional dimensions to unify different forces remains an active area of research in physics.
+
+== See also ==
+Classical electromagnetism and special relativity
+History of electromagnetic theory
+The Maxwellians
+
+== Notes ==
+
+== References ==
+
+Turnbull, Graham, ed. (29 October 2019). "Maxwell's Equations". Engineering and Technology History Wiki.
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+title: "History of classical field theory"
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+---
+
+In the history of physics, the concept of fields had its origins in the 18th century in a mathematical formulation of Newton's law of universal gravitation, but it was seen as deficient as it implied action at a distance. In 1852, Michael Faraday treated the magnetic field as a physical object, reasoning about lines of force. James Clerk Maxwell used Faraday's conceptualisation to help formulate his unification of electricity and magnetism in his field theory of electromagnetism.
+With Albert Einstein's special relativity and the Michelson–Morley experiment, it became clear that electromagnetic waves could travel in a vacuum without the need of a medium or luminiferous aether. Einstein also developed general relativity, in which spacetime was treated as a field and its curvature was the origin of the gravitational interactions, putting an end to action at a distance.
+In quantum field theory, fields become the fundamental objects of study, and particles are excitations of these fields. To differentiate from quantum field theory, previously developed field theories were called classical field theories.
+
+== Early mechanical explanations of forces ==
+
+=== Magnetism ===
+The first record of explanations of how magnets works comes from ancient Greece. Thinkers like Thales of Miletus, Aristotle and Diogenes Laertius considered that magnets were animated and should have a soul in order to move. Empedocles tried to provide a mechanical explanation of why magnets could influence each other by introducing the concept of "effluences" emanated by magnets. According to book Quaestiones by Alexander of Aphrodisias from about 200 AD, this was Empedocles view:
+On the reason why the lodestone attracts iron. Empedocles says that the iron is attracted to the stone by the effluences which issue from both, and because the pores of the stone are commensurate with the effluences from the iron. The effluences from the stone stir and disperse the air lying upon and obstructing the pores of the iron and when this is removed the iron is drawn on by a concerted outflow. As the effluences from the iron travel towards the pores of the stone,
+because they are commensurate with them and fit into them the iron itself follows and moves together with them.
+Democritus had a similar view as Empedocles but added that the effluences created a void. Metals and rocks could also contain void in order to be less or more attracted to magnets.
+This idea survived up to the Scientific Revolution. In 1664, René Descartes produced his theory of magnetism, in which the flow of effluences or effluvia rarified the air, creating differences in air pressure. According to Descartes, these effluvia circulated inside and around the magnet in closed loops.
+
+=== Gravitation ===
+
+In ancient times, Greek thinkers like Posidonius (1 BC) noticed a relation between the tides and the position of the Moon in the sky. He considered that light from the Moon had an influence on the tides.
+In the 9th century, Abu Ma'shar al-Balkhi (Latinized as Albumasar) wrote his book on The Great Introduction to the Science of Astrology (Kitāb al-madkhal al-kabīr) recorded the correlation between the tides and the Moon, noticing that there were two tides in a day. As there is no moonlight when the Moon is the opposite side of Earth, he proposed that the Moon had some intrinsic virtue that attracted the water. The Sun would have some of that virtue but less than the moon. This book was translated to Latin and was a reference for European medieval scholars. One writer that rejected this astrological reading was Robert Grosseteste who wrote On the Ebb and Flow of the Sea (Latin: Questio de fluxu et refluxu maris), written around 1227, in which he insisted that light from the Moon rarefied the air producing the tides. He explained the tides when the Moon is below the horizon as reflections from the celestial sphere. Two theories coexisted, the idea of light influencing the tides and Albumasar' virtue. Roger Bacon supported the idea of Grosseteste, Albertus Magnus supported a mix of both, and others like Jean Buridan hesitated between the two.
+In 17th century, Johannes Kepler who came up with the Kepler's laws of planetary motion, proposed the idea that the Sun emitted some sort of invisible "species" that traveled instantaneously and acted more strongly depending on the distance, size and density of the planet. Kepler considered that if the Sun rotated, it would create a whirlpool of species that drags all planets to orbit around it. The idea of the rotation of the Sun was confirmed by Galileo Galilei, but the frequency did not match Kepler's calculations. To explain the tides, Kepler considered that the species would behave similar to magnetic forces.
+Descartes rejected Kepler's theory and also constructed also a mechanical explanation of gravitation based on the ideas vortices, considering space continuous. Descartes pushed the Aristotelian idea of the plenum, considering that there was no void and the entirety of space was filled with corpuscles.
+
+== Newtonian gravitation ==
+
+=== Newtonian mechanics ===
+Before Newton, only a few mechanical explanations of gravity existed.
+In 1687, Newton's Principia in 1687 provided a framework with which to investigate the motion and forces. He introduced mathematical definition of gravitational force with his law of universal gravitation, in which the gravitational force between two bodies is directed along the line separating the bodies and its magnitude is proportional to the product of their masses, divided by the square of their distance apart.
+While Newton explanation of gravity was very successful in astronomy, it did not explain how it could act at a distance and instantaneously. Newton, considered action at a distance to be:
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+
+so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it.
+Gottfried Wilhelm Leibniz complained that Newtonian mechanics violated the metaphysics of continuity according to natura non facit saltus, in which every cause and effect should be connected to one another. Roger Joseph Boscovich rejected Leibniz take considering that bodies would have discontinuous changes in density at the boundaries and that if came into contact their velocities would change discontinuously.
+British empiricist like John Locke, George Locke and David Hume regarded Newton's second law of motion as sufficient, as it establishes a causal relation between force and acceleration.
+
+=== Beginning of aether theories ===
+
+To solve the issue of action at a distance, aether theories were developed. The aether was considered as a yet undetected medium and responsible agent for conducting the force. In a letter to Robert Boyle in 1679 Newton proposed an "aethereal substance" to explain gravity. Later in his work Opticks of 1717 he considered the aether to be made of impenetrable corpuscules. Newtonian aether was very dilute and elastic. Immanuel Kant considered Newton's aether inconsistent as requiring additional forces between corpuscles. Leibniz on the other hand considered a continuous medium.
+
+== Eulerian fluid dynamics ==
+
+An important development of field theories appeared with Leonhard Euler who expanded Newtonian mechanics in his work Mechanica of 1736. Euler work expanded on how to deal with rotations of rigid bodies, elasticity and fluid mechanics. To describe fluids he considered a flow velocity function (today called velocity field) defined at every point in space. However, this function was for a long time considered significantly different from that of the forces of gravitation as it was only defined inside a medium and thus was considered a real quantity. Modern science historian Mary Hesse attributed the origin of field theory to Euler flow velocity field.
+Euler also introduced between 1755 and 1759 the Lagrangian and Eulerian specifications for the flow that would be important to detach motion of particles from field properties.
+
+== Potential theory ==
+Joseph-Louis Lagrange is often cited for introducing the concept of a potential in 1777, and independently by Adrien-Marie Legendre (1784–1794) and Pierre-Simon Laplace (1782–1799). Lagrange noticed that he could introduce a gravitational potential to derive the gravitational force. This function was called a potential function by mathematician George Green 1828 and by Carl Friedrich Gauss in 1840 just as "potential".
+
+== Forces of electricity and magnetism ==
+Charles-Augustin de Coulomb showed in 1785 that the repulsive force between two electrically charged spheres obeys the same (up to a sign) force law as Newton's law of universal gravitation. In 1823, Siméon Denis Poisson introduced the Poisson's equation, explaining the electric forces in terms of an electric potential. The same year André-Marie Ampère showed that the force between infinitesimal lengths of current-carrying wires similarly obeys an inverse-square law such that the force is directed along the line of separation between the wire elements. These law suffered from the same problem of action-at-a-distance.
+
+=== Luminiferous aether ===
+In 1800, Thomas Young proved the wave nature of light using the double-slit experiment. This discovery led him in 1802 to consider the existence of luminiferous aether in which light traveled. Augustin-Jean Fresnel considered it to be an elastic medium. The motion of this aether were described mathematically by scientist like Claude-Louis Navier (in 1821) and Augustin-Louis Cauchy (in 1828) as discrete medium. About 1840, George Stokes and Lord Kelvin extended the formalism to describe a continuous aether using the idea of a potential theory. This development was important as it allowed to describe any deformable medium in terms of continuous functions.
+
+== Introduction of fields ==
+
+=== Faraday's lines of force ===
+
+Michael Faraday developed the concept of lines of force to describe electric and magnetic phenomena. In 1831, he writes
+
+By magnetic curves, I mean the lines of magnetic forces, however modified by the juxtaposition of poles, which would be depicted by iron filings; or those to which a very small magnetic needle would form a tangent."
+He provided a definition in 1845,
+
+But before I proceed to them, I will define the meaning I connect with certain terms which I shall have occasion to use: thus, by line of magnetic force, or magnetic line of force, or magnetic curve, I mean that exercise of magnetic force which is exerted in the lines usually called magnetic curves, and which equally exist as passing from or to magnetic poles, or forming concentric circles round an electric current. By line of electric force, I mean the force exerted in the lines joining two bodies, acting on each other according to the principles of static electric induction, which may also be either in curved or straight lines.
+In his work, he also coined the term "magnetic field" in this sense in 1845, which he later used frequently. He provided a clear definition in 1850, stating
+
+I will now endeavour to consider what the influence is which paramagnetic and diamagnetic bodies, viewed as conductors, exert upon the lines of force in a
+magnetic field. Any portion of space traversed by lines of magnetic power, may be taken as such a field, and there is probably no space without them. The condition of the field may vary in intensity of power. from place to place, either along the lines or across them; but it will be better to assume for the present consideration a field of equal force throughout, and I have formerly described how this may, for a certain limited space, be produced.
+Faraday did not conceive of this field as a mere mathematical construct for calculating the forces between particles—having only rudimentary mathematical training, he had no use for abstracting reality to make quantitative predictions. Instead he conjectured that there was force filling the space where electromagnetic fields were generated and reasoned qualitatively about these forces with lines of force:
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+Important to the definition of these lines is that they represent a determinate and unchanging amount of force. Though, therefore, their forms, as they exist between two or more centers or sources of power, may vary greatly, and also the space through which they may be traced, yet the sum of power contained in any one section of a given portion of the lines is exactly equal to the sum of power in any other section of the same lines, however altered in form or however convergent or divergent they may be at the second place.
+However, Faraday never used the term "electric field" explicitly. Nevertheless, Faraday's insights into the behavior of magnetic fields would prove invaluable for the development of electromagnetism and field theory.
+
+=== Kelvin's definition ===
+In 1845, Lord Kelvin formalized the mathematical similarities between the fields of electromagnetic phenomena and Joseph Fourier work on heat; and in 1847 between electric conduction and elasticity. These similarities led Lord Kelvin to propose a formal definition of magnetic field in 1851:Any space at every point of which there is a finite magnetic force is called ‘a field of magnetic force’ or (magnetic being understood) simply ‘a field of force,’ or sometimes ‘a magnetic field’.Kelvin also introduced the concept of a magnetic vector potential.
+
+=== Maxwell's electromagnetic field ===
+
+In 1864, James Clerk Maxwell published "A Dynamical Theory of the Electromagnetic Field" in which he compiled all known equations of electricity and magnetism. Maxwell's equations led to an electromagnetic wave equation with waves that propagated in vacuum at the speed of light. He describes his research as
+
+(3) The theory I propose may therefore be called a theory of the Electromagnetic Field, because it has to do with the space in the neighbourhood of the electric and magnetic bodies, and it may be called a Dynamical Theory, because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced
+
+(4) The electromagnetic field is that part of space which contains and surrounds bodies in electric or magnetic conditions
+In A Treatise on Electricity and Magnetism of 1873, he writes "the electric field is the portion of space in the neighbourhood of electrified bodies, considered with reference to electric phenomena." And for magnetic fields
+
+lt appears therefore that in the space surrounding a wire transmitting an electric current a magnet is acted on by forces dependent on the position of the wire and on the strength of the current. The space in which these forces act may therefore be considered as a magnetic field, and we may study it in the same way as we have already studied the field in the neighbourhood of ordinary magnets, by tracing the course of the lines of magnetic force, and measuring the intensity of the force at every point.
+Maxwell had to settle for the idea of a luminiferous aether. He wrote
+
+We have therefore some reason to believe, from the phenomena of light and
+heat, that there is an aethereal medium filling space and permeating bodies, capable of being set in motion and of transmitting that motion from one part to another, and of communicating that motion to gross matter so as to heat it and affect it in various ways.
+Maxwell was conflicted on the idea on the nature of the fields, he considered the aether to a mechanical medium in order to carry energy. 
+
+=== Further developments ===
+In 1868 Carl Neumann discussed the idea of the electromagnetic field being an independent energy field.
+In 1887, Heinrich Hertz published his experimental evidence of the existence of electromagnetic waves.
+In 1903, Karl Schwarzschild wrote the Lagrangian density for the electromagnetic field.
+
+== Relativistic field theory ==
+
+=== Special relativity ===
+
+The 1887 Michelson–Morley experiment attempted to prove that electromagnetic radiation were oscillations of a luminiferous aether; however, the result was negative, indicating that the electromagnetic field could exist and travel in vacuum. To explain this phenomenon, Albert Einstein developed his theory of special relativity (1905) which resolved the conflicts between classical mechanics and electromagnetism. Einstein introduced the Lorentz transformation for electromagnetic fields between reference frames.
+
+=== Space-time as a field ===
+
+Einstein developed the Einstein field equations of general relativity in 1915, consistent with special relativity and that could explain gravitation in terms of a field theory of spacetime. This removed the need of a gravitational aether.
+In 1918, Emmy Noether publishes her theorem on the relations between symmetries and conservation laws. Noether's theorem was adapted to general relativity as well as to non-relativistic field theories.
+The geometric aspect of space-time can be used to study Newtonian gravitational field. This was developed by Élie Cartan in 1923 and leads to a classically covariant formulation known as geometrized Newtonian gravitation.
+
+== Unification attempts ==
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+instance: "kb-cron"
+---
+
+Attempts to create a unified field theory based on classical physics are classical unified field theories. During the years between the two World Wars, the idea of unification of gravity with electromagnetism was actively pursued by several mathematicians and physicists like Einstein, Theodor Kaluza, Hermann Weyl, Arthur Eddington, Gustav Mie and Ernst Reichenbacher.
+Early attempts to create such theory were based on incorporation of electromagnetic fields into the geometry of general relativity. In 1918, the case for the first geometrization of the electromagnetic field was proposed in 1918 by Weyl. In this work Weyl coins the term gauge theory. Weyl, in an attempt to generalize the geometrical ideas of general relativity to include electromagnetism, conjectured that Eichinvarianz or invariance under the change of scale (or "gauge") might also be a local symmetry of general relativity.
+In 1919, the idea of a five-dimensional approach was suggested by Kaluza. From that, a theory called Kaluza–Klein theory was developed. It attempts to unify gravitation and electromagnetism, in a five-dimensional space-time.
+There are several ways of extending the representational framework for a unified field theory which have been considered by Einstein and other researchers. These extensions in general are based in two options. The first option is based in relaxing the conditions imposed on the original formulation, and the second is based in introducing other mathematical objects into the theory. An example of the first option is relaxing the restrictions to four-dimensional space-time by considering higher-dimensional representations. That is used in Kaluza–Klein theory. For the second, the most prominent example arises from the concept of the affine connection that was introduced into general relativity mainly through the work of Tullio Levi-Civita and Weyl.
+Further development of quantum field theory changed the focus of searching for unified field theory from classical to quantum description. Because of that, many theoretical physicists gave up looking for a classical unified field theory. Quantum field theory would include unification of two other fundamental interactions of nature, the strong and weak nuclear force which act on the subatomic level.
+
+== Quantum fields ==
+
+Fields become the fundamental object of study in quantum field theory. Mathematically, quantum fields are formalized as operator-valued distributions. Although there is no direct method of measuring the fields themselves, the framework asserts that all particles are "excitations" of these fields. For example: whereas Maxwell's theory of classical electromagnetism describes light as a self-propagating wave in the electromagnetic field, in quantum electrodynamics light is the massless gauge boson particle called the photon. Furthermore, the number of particles in an isolated system need not be conserved; an example of a process for which this is the case is bremsstrahlung. More detailed understanding of the framework is obtained by studying the Lagrangian density of a field theory which encodes the information of its allowed particle interactions.
+
+== See also ==
+History of classical mechanics
+Corpuscularianism
+
+== References ==
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+title: "History of electromagnetic theory"
+chunk: 1/22
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+The history of electromagnetic theory begins with ancient measures to understand atmospheric electricity, in particular lightning. People then had little understanding of electricity, and were unable to explain the phenomena. Scientific understanding and research into the nature of electricity grew throughout the eighteenth and nineteenth centuries through the work of researchers such as André-Marie Ampère, Charles-Augustin de Coulomb, Michael Faraday, Carl Friedrich Gauss and James Clerk Maxwell.
+In the 19th century it had become clear that  electricity and magnetism  were related, and their theories were unified: wherever charges are in motion electric current results, and magnetism is due to electric current. The source for electric field is electric charge, whereas that for magnetic field is electric current (charges in motion).
+
+== Ancient and classical history ==
+The knowledge of static electricity dates back to the earliest civilizations, but for millennia it remained merely an interesting and mystifying phenomenon, without a theory to explain its behavior, and it was often confused with magnetism. The ancients were acquainted with rather curious properties possessed by two minerals, amber (Ancient Greek: ἤλεκτρον, ēlektron) and magnetic iron ore (μαγνῆτις λίθος magnētis lithos, "the Magnesian stone, lodestone"). Amber, when rubbed, attracts lightweight objects, such as feathers; magnetic iron ore has the power of attracting iron.
+
+Based on his find of an Olmec hematite artifact in Central America, the American astronomer John Carlson has suggested that "the Olmec may have discovered and used the geomagnetic lodestone compass earlier than 1000 BC". If true, this "predates the Chinese discovery of the geomagnetic lodestone compass by more than a millennium". Carlson speculates that the Olmecs may have used similar artifacts as a directional device for astrological or geomantic purposes, or to orient their temples, the dwellings of the living or the interments of the dead. The earliest Chinese literature reference to magnetism lies in a 4th-century BC book called The Book of the Devil Valley Master: "When the people of Cheng go out to collect jade, they carry a south-pointer with them so as not to lose their way."
+
+Long before any knowledge of electromagnetism existed, people were aware of the effects of electricity. Lightning and other manifestations of electricity such as St. Elmo's fire were known in ancient times, but it was not understood that these phenomena had a common origin. Ancient Egyptians were aware of shocks when interacting with electric fish (such as the electric catfish) or other animals (such as electric eels). The shocks from animals were apparent to observers since pre-history by a variety of peoples that came into contact with them. Texts from 2750 BC by the ancient Egyptians referred to these fish as "thunderer of the Nile" and saw them as the "protectors" of all the other fish. Another possible approach to the discovery of the identity of lightning and electricity from any other source, is to be attributed to the Arabs, who before the 15th century used the same Arabic word for lightning (barq) and the electric ray.
+Thales of Miletus, writing at around 600 BC, noted that rubbing fur on various substances such as amber would cause them to attract specks of dust and other light objects. Thales wrote on the effect now known as static electricity. The Greeks noted that if they rubbed the amber for long enough they could even get an electric spark to jump.
+The ancient Indian medical text Sushruta Samhita describes using magnetic properties of the lodestone to remove arrows embedded in a person's body.
+These electrostatic phenomena were again reported millennia later by Roman and Arabic naturalists and physicians. Several ancient writers, such as Pliny the Elder and Scribonius Largus, attested to the numbing effect of electric shocks delivered by catfish and electric rays. Pliny in his books writes: "The ancient Tuscans by their learning hold that there are nine gods that send forth lightning and those of eleven sorts." This was in general the early pagan idea of lightning. The ancients held some concept that shocks could travel along conducting objects. Patients with ailments such as gout or headache were directed to touch electric fish in the hope that the powerful jolt might cure them.
+A group of objects found in Iraq in 1938 dated to the early centuries AD (Sassanid Mesopotamia), called the Baghdad Battery, resembles a galvanic cell and is believed by some to have been used for electroplating. The claims are controversial because of supporting evidence and theories for the uses of the artifacts, physical evidence on the objects conducive for electrical functions, and if they were electrical in nature. Despite, or perhaps as a consequence of this uncertainty, discussing the possible ancient technology may engage young students in the science questions.
+Magnetic attraction was once accounted for by Aristotle and Thales as the working of a soul in the stone.
+
+== Middle Ages and the Renaissance ==
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+title: "History of electromagnetic theory"
+chunk: 2/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+The magnetic needle compass was developed in the 11th century and it improved the accuracy of navigation by employing the astronomical concept of true north (Dream Pool Essays, 1088). The Chinese scientist Shen Kuo (1031–1095) was the first person known to write about the magnetic needle compass and by the 12th century Chinese were known to use the lodestone compass for navigation. In Europe, the first description of the compass and its use for navigation are of Alexander Neckam (1187), although the use of compasses was already common. Its development, in European history, was due to Flavio Gioja from Amalfi.
+In the 13th century, Peter Peregrinus, a native of Maricourt in Picardy, conducted experiments on magnetism and wrote the first extant treatise describing the properties of magnets and pivoting compass needles. In 1282, the properties of magnets and dry compasses were discussed by Al-Ashraf Umar II, a Yemeni scholar. The dry compass was invented around 1300 by Italian inventor Flavio Gioja. Magnetism remained elusive to Thomas Aquinas, who in his Summa Theologiae presented it as an example of an "occult"—that is, an unknown—force.
+Archbishop Eustathius of Thessalonica, Greek scholar and writer of the 12th century, records that Woliver, king of the Goths, was able to draw sparks from his body. The same writer states that a certain philosopher was able while dressing to draw sparks from his clothes, a result seemingly akin to that obtained by Robert Symmer in his silk stocking experiments, a careful account of which may be found in the Philosophical Transactions, 1759.
+Italian physician Gerolamo Cardano wrote about electricity in De Subtilitate (1550) distinguishing, perhaps for the first time, between electrical and magnetic forces.
+
+== 17th century ==
+Toward the late 16th century, a physician of Queen Elizabeth's time, William Gilbert, in De Magnete, expanded on Cardano's work and invented the Neo-Latin word electrica from ἤλεκτρον (ēlektron), the Greek word for "amber".
+Gilbert undertook a number of careful electrical experiments, in the course of which he discovered that many substances other than amber, such as sulphur, wax, glass, etc., were capable of manifesting electrical properties. Gilbert also discovered that a heated body lost its electricity and that moisture prevented the electrification of all bodies, due to the now well-known fact that moisture impaired the insulation of such bodies.  He also noticed that electrified substances attracted all other substances indiscriminately, whereas a magnet only attracted iron. The many discoveries of this nature earned for Gilbert the title of founder of the electrical science. By investigating the forces on a light metallic needle, balanced on a point, he extended the list of electric bodies, and found also that many substances, including metals and natural magnets, showed no attractive forces when rubbed. He noticed that dry weather with north or east wind was the most favourable atmospheric condition for exhibiting electric phenomena—an observation liable to misconception until the difference between conductor and insulator was understood.
+
+Gilbert's work was followed up by Robert Boyle (1627–1691), the famous natural philosopher who was once described as "father of Chemistry, and uncle of the Earl of Cork." Boyle was one of the founders of the Royal Society when it met privately in Oxford, and became a member of the council after the Society was incorporated by Charles II in 1663. He left a detailed account of his research under the title of Experiments on the Origin of Electricity. He discovered electrified bodies attracted light substances in a vacuum, indicating the electrical effect did not depend upon the air as a medium. He also added resin, and other substances, to the then known list of electrics.
+In 1663 Otto von Guericke invented a device that is now recognized as an early (possibly the first) electrostatic generator, but he did not recognize it primarily as an electrical device or conduct electrical experiments with it.  By the end of the 17th century, researchers had developed practical means of generating electricity by friction with an electrostatic generator, but the development of electrostatic machines did not begin in earnest until the 18th century, when they became fundamental instruments in the studies about the new science of electricity.
+The first usage of the word electricity is ascribed to Sir Thomas Browne in his 1646 work, Pseudodoxia Epidemica.
+The first appearance of the term electromagnetism was in Magnes, by the Jesuit luminary Athanasius Kircher, in 1641, which carries the provocative chapter-heading: "Elektro-magnetismos i.e. On the Magnetism of amber, or electrical attractions and their causes" (ἠλεκτρο-μαγνητισμός id est sive De Magnetismo electri, seu electricis attractionibus earumque causis).
+
+== 18th century ==
+
+=== Improving the electric machine ===
+
+The electric machine was subsequently improved by Francis Hauksbee, his student Litzendorf, and by Prof. Georg Matthias Bose, about 1750. Litzendorf, researching for Christian August Hausen, substituted a glass ball for the sulphur ball of Guericke. Bose was the first to employ the "prime conductor" in such machines, this consisting of an iron rod held in the hand of a person whose body was insulated by standing on a block of resin. Ingenhousz, during 1746, invented electric machines made of plate glass. Experiments with the electric machine were largely aided by the discovery that a glass plate, coated on both sides with tinfoil, would accumulate electric charge when connected with a source of electromotive force. The electric machine was soon further improved by Andrew Gordon, a Scotsman, Professor at Erfurt, who substituted a glass cylinder in place of a glass globe; and by Giessing of Leipzig who added a "rubber" consisting of a cushion of woollen material. The collector, consisting of a series of metal points, was added to the machine by Benjamin Wilson about 1746, and in 1762, John Canton of England (also the inventor of the first pith-ball electroscope in 1754) improved the efficiency of electric machines by sprinkling an amalgam of tin over the surface of the rubber.
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+title: "History of electromagnetic theory"
+chunk: 11/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+Up to the middle of the 19th century, indeed up to about 1870, electrical science was, it may be said, a sealed book to the majority of electrical workers. Prior to this time a number of handbooks had been published on electricity and magnetism, notably Auguste de La Rive's exhaustive ' Treatise on Electricity,' in 1851 (French) and 1853 (English); August Beer's Einleitung in die Elektrostatik, die Lehre vom Magnetismus und die Elektrodynamik, Wiedemann's ' Galvanismus,' and Reiss' 'Reibungsal-elektricitat.' But these works consisted in the main in details of experiments with electricity and magnetism, and but little with the laws and facts of those phenomena. Henry d'Abria published the results of some researches into the laws of induced currents, but owing to their complexity of the investigation it was not productive of very notable results. Around the mid-19th century, Fleeming Jenkin's work on electricity and magnetism and Clerk Maxwell's ' Treatise on Electricity and Magnetism ' were published.
+These books were departures from the beaten path. As Jenkin states in the preface to his work the science of the schools was so dissimilar from that of the practical electrician that it was quite impossible to give students sufficient, or even approximately sufficient, textbooks. A student he said might have mastered de la Rive's large and valuable treatise and yet feel as if in an unknown country and listening to an unknown tongue in the company of practical men. As another writer has said, with the coming of Jenkin's and Maxwell's books all impediments in the way of electrical students were removed, "the full meaning of Ohm's law becomes clear; electromotive force, difference of potential, resistance, current, capacity, lines of force, magnetization and chemical affinity were measurable, and could be reasoned about, and calculations could be made about them with as much certainty as calculations in dynamics".
+About 1850, Kirchhoff published his laws relating to branched or divided circuits. He also showed mathematically that according to the then prevailing electrodynamic theory, electricity would be propagated along a perfectly conducting wire with the velocity of light. Helmholtz investigated mathematically the effects of induction upon the strength of a current and deduced therefrom equations, which experiment confirmed, showing amongst other important points the retarding effect of self-induction under certain conditions of the circuit.
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+title: "History of electromagnetic theory"
+chunk: 12/22
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+In 1853, Sir William Thomson (later Lord Kelvin) predicted as a result of mathematical calculations the oscillatory nature of the electric discharge of a condenser circuit. To Henry, however, belongs the credit of discerning as a result of his experiments in 1842 the oscillatory nature of the Leyden jar discharge. He wrote: The phenomena require us to admit the existence of a principal discharge in one direction, and then several reflex actions backward and forward, each more feeble than the preceding, until the equilibrium is obtained. These oscillations were subsequently observed by B. W. Feddersen (1857) who using a rotating concave mirror projected an image of the electric spark upon a sensitive plate, thereby obtaining a photograph of the spark which plainly indicated the alternating nature of the discharge. Sir William Thomson was also the discoverer of the electric convection of heat (the "Thomson" effect). He designed for electrical measurements of precision his quadrant and absolute electrometers. The reflecting galvanometer and siphon recorder, as applied to submarine cable signaling, are also due to him.
+About 1876 the American physicist Henry Augustus Rowland of Baltimore demonstrated the important fact that a static charge carried around produces the same magnetic effects as an electric current. The Importance of this discovery consists in that it may afford a plausible theory of magnetism, namely, that magnetism may be the result of directed motion of rows of molecules carrying static charges.
+After Faraday's discovery that electric currents could be developed in a wire by causing it to cut across the lines of force of a magnet, it was to be expected that attempts would be made to construct machines to avail of this fact in the development of voltaic currents. The first machine of this kind was due to Hippolyte Pixii, 1832. It consisted of two bobbins of iron wire, opposite which the poles of a horseshoe magnet were caused to rotate. As this produced in the coils of the wire an alternating current, Pixii arranged a commutating device (commutator) that converted the alternating current of the coils or armature into a direct current in the external circuit. This machine was followed by improved forms of magneto-electric machines due to Edward Samuel Ritchie, Joseph Saxton, Edward M. Clarke 1834, Emil Stohrer 1843, Floris Nollet 1849, Shepperd 1856, Van Maldern, Werner von Siemens, Henry Wilde and others.
+A notable advance in the art of dynamo construction was made by Samuel Alfred Varley in 1866 and by Siemens and Charles Wheatstone, who independently discovered that when a coil of wire, or armature, of the dynamo machine is rotated between the poles (or in the "field") of an electromagnet, a weak current is set up in the coil due to residual magnetism in the iron of the electromagnet, and that if the circuit of the armature be connected with the circuit of the electromagnet, the weak current developed in the armature increases the magnetism in the field. This further increases the magnetic lines of force in which the armature rotates, which still further increases the current in the electromagnet, thereby producing a corresponding increase in the field magnetism, and so on, until the maximum electromotive force which the machine is capable of developing is reached. By means of this principle the dynamo machine develops its own magnetic field, thereby much increasing its efficiency and economical operation. Not by any means, however, was the dynamo electric machine perfected at the time mentioned.
+In 1860 an important improvement had been made by Dr. Antonio Pacinotti of Pisa who devised the first electric machine with a ring armature. This machine was first used as an electric motor, but afterward as a generator of electricity. The discovery of the principle of the reversibility of the dynamo electric machine (variously attributed to Walenn 1860; Pacinotti 1864; Fontaine, Gramme 1873; Deprez 1881, and others) whereby it may be used as an electric motor or as a generator of electricity has been termed one of the greatest discoveries of the 19th century.
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+title: "History of electromagnetic theory"
+chunk: 13/22
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+In 1872 the drum armature was devised by Hefner-Alteneck. This machine in a modified form was subsequently known as the Siemens dynamo. These machines were presently followed by the Schuckert, Gulcher, Fein, Brush, Hochhausen, Edison and the dynamo machines of numerous other inventors. In the early days of dynamo machine construction the machines were mainly arranged as direct current generators, and perhaps the most important application of such machines at that time was in electro-plating, for which purpose machines of low voltage and large current strength were employed.
+Beginning about 1887 alternating current generators came into extensive operation and the commercial development of the transformer, by means of which currents of low voltage and high current strength are transformed to currents of high voltage and low current strength, and vice versa, in time revolutionized the transmission of electric power to long distances. Likewise the introduction of the rotary converter (in connection with the "step-down" transformer) which converts alternating currents into direct currents (and vice versa) has effected large economies in the operation of electric power systems.
+Before the introduction of dynamo electric machines, voltaic, or primary, batteries were extensively used for electro-plating and in telegraphy. There are two distinct types of voltaic cells, namely, the "open" and the "closed", or "constant", type. The open type in brief is that type which operated on closed circuit becomes, after a short time, polarized; that is, gases are liberated in the cell which settle on the negative plate and establish a resistance that reduces the current strength. After a brief interval of open circuit these gases are eliminated or absorbed and the cell is again ready for operation. Closed circuit cells are those in which the gases in the cells are absorbed as quickly as liberated and hence the output of the cell is practically uniform. The Leclanché and Daniell cells, respectively, are familiar examples of the "open" and "closed" type of voltaic cell. Batteries of the Daniell or "gravity" type were employed almost generally in the United States and Canada as the source of electromotive force in telegraphy before the dynamo machine became available.
+In the late 19th century, the term luminiferous aether, meaning light-bearing aether, was a conjectured medium for the propagation of light.  The word aether stems via Latin from the Greek αιθήρ, from a root meaning to kindle, burn, or shine. It signifies the substance which was thought in ancient times to fill the upper regions of space, beyond the clouds.
+
+=== Maxwell ===
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+title: "History of electromagnetic theory"
+chunk: 14/22
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+In 1864 James Clerk Maxwell of Edinburgh announced his electromagnetic theory of light, which was perhaps the greatest single step in the world's knowledge of electricity.  Maxwell had studied and commented on the field of electricity and magnetism as early as 1855/6 when On Faraday's lines of force was read to the Cambridge Philosophical Society. The paper presented a simplified model of Faraday's work, and how the two phenomena were related. He reduced all of the current knowledge into a linked set of differential equations with 20 equations in 20 variables. This work was later published as On Physical Lines of Force in March 1861. In order to determine the force which is acting on any part of the machine we must find its momentum, and then calculate the rate at which this momentum is being changed. This rate of change will give us the force. The method of calculation which it is necessary to employ was first given by Lagrange, and afterwards developed, with some modifications, by Hamilton's equations. It is usually referred to as Hamilton's principle; when the equations in the original form are used they are known as Lagrange's equations. Now Maxwell logically showed how these methods of calculation could be applied to the electro-magnetic field. The energy of a dynamical system is partly kinetic, partly potential. Maxwell supposes that the magnetic energy of the field is kinetic energy, the electric energy potential.
+Around 1862, while lecturing at King's College, Maxwell calculated that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He considered this to be more than just a coincidence, and commented "We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."
+Working on the problem further, Maxwell showed that the equations predict the existence of waves of oscillating electric and magnetic fields that travel through empty space at a speed that could be predicted from simple electrical experiments; using the data available at the time, Maxwell obtained a velocity of 310,740,000 m/s. In his 1864 paper A Dynamical Theory of the Electromagnetic Field, Maxwell wrote, The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.
+As already noted herein Faraday, and before him, Ampère and others, had inklings that the luminiferous ether of space was also the medium for electric action. It was known by calculation and experiment that the velocity of electricity was approximately 186,000 miles per second; that is, equal to the velocity of light, which in itself suggests the idea of a relationship between -electricity and "light." A number of the earlier philosophers or mathematicians, as Maxwell terms them, of the 19th century, held the view that electromagnetic phenomena were explainable by action at a distance. Maxwell, following Faraday, contended that the seat of the phenomena was in the medium. The methods of the mathematicians in arriving at their results were synthetical while Faraday's methods were analytical. Faraday in his mind's eye saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance. Faraday sought the seat of the phenomena in real actions going on in the medium; they were satisfied that they had found it in a power of action at a distance on the electric fluids.
+Both of these methods, as Maxwell points out, had succeeded in explaining the propagation of light as an electromagnetic phenomenon while at the same time the fundamental conceptions of what the quantities concerned are, radically differed. The mathematicians assumed that insulators were barriers to electric currents; that, for instance, in a Leyden jar or electric condenser the electricity was accumulated at one plate and that by some occult action at a distance electricity of an opposite kind was attracted to the other plate.
+Maxwell, looking further than Faraday, reasoned that if light is an electromagnetic phenomenon and is transmissible through dielectrics such as glass, the phenomenon must be in the nature of electromagnetic currents in the dielectrics. He therefore contended that in the charging of a condenser, for instance, the action did not stop at the insulator, but that some "displacement" currents are set up in the insulating medium, which currents continue until the resisting force of the medium equals that of the charging force. In a closed conductor circuit, an electric current is also a displacement of electricity.
+The conductor offers a certain resistance, akin to friction, to the displacement of electricity, and heat is developed in the conductor, proportional to the square of the current (as already stated herein), which current flows as long as the impelling electric force continues. This resistance may be likened to that met with by a ship as it displaces in the water in its progress. The resistance of the dielectric is of a different nature and has been compared to the compression of multitudes of springs, which, under compression, yield with an increasing back pressure, up to a point where the total back pressure equals the initial pressure. When the initial pressure is withdrawn the energy expended in compressing the "springs" is returned to the circuit, concurrently with the return of the springs to their original condition, this producing a reaction in the opposite direction. Consequently, the current due to the displacement of electricity in a conductor may be continuous, while the displacement currents in a dielectric are momentary and, in a circuit or medium which contains but little resistance compared with capacity or inductance reaction, the currents of discharge are of an oscillatory or alternating nature.
+Maxwell extended this view of displacement currents in dielectrics to the ether of free space. Assuming light to be the manifestation of alterations of electric currents in the ether, and vibrating at the rate of light vibrations, these vibrations by induction set up corresponding vibrations in adjoining portions of the ether, and in this way the undulations corresponding to those of light are propagated as an electromagnetic effect in the ether. Maxwell's electromagnetic theory of light obviously involved the existence of electric waves in free space, and his followers set themselves the task of experimentally demonstrating the truth of the theory. By 1871, Maxwell could already reflect on the philosophy of science.
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+title: "History of electromagnetic theory"
+chunk: 15/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+=== End of the 19th century ===
+
+In 1887, the German physicist Heinrich Hertz in a series of experiments proved the actual existence of electromagnetic waves, showing that transverse free space electromagnetic waves can travel over some distance as predicted by Maxwell and Faraday. Hertz published his work in a book titled: Electric waves: being researches on the propagation of electric action with finite velocity through space. The discovery of electromagnetic waves in space led to the development of radio in the closing years of the 19th century.
+The electron as a unit of charge in electrochemistry was posited by G. Johnstone Stoney in 1874, who also coined the term electron in 1894. Plasma was first identified in a Crookes tube, and so described by Sir William Crookes in 1879 (he called it "radiant matter"). The place of electricity in leading up to the discovery of those beautiful phenomena of the Crookes Tube (due to Sir William Crookes), viz., Cathode rays, and later to the discovery of Roentgen or X-rays, must not be overlooked, since without electricity as the excitant of the tube the discovery of the rays might have been postponed indefinitely. It has been noted herein that Dr. William Gilbert was termed the founder of electrical science. This must, however, be regarded as a comparative statement.
+
+Oliver Heaviside was a self-taught scholar who reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis.
+During the late 1890s a number of physicists proposed that electricity, as observed in studies of electrical conduction in conductors, electrolytes, and cathode ray tubes, consisted of discrete units, which were given a variety of names, but the reality of these units had not been confirmed in a compelling way. However, there were also indications that the cathode rays had wavelike properties.
+Faraday, Weber, Helmholtz, Clifford and others had glimpses of this view; and the experimental works of Zeeman, Goldstein, Crookes, J. J. Thomson and others had greatly strengthened this view. Weber predicted that electrical phenomena were due to the existence of electrical atoms, the influence of which on one another depended on their position and relative accelerations and velocities. Helmholtz and others also contended that the existence of electrical atoms followed from Faraday's laws of electrolysis, and Johnstone Stoney, to whom is due the term "electron", showed that each chemical ion of the decomposed electrolyte carries a definite and constant quantity of electricity, and inasmuch as these charged ions are separated on the electrodes as neutral substances there must be an instant, however brief, when the charges must be capable of existing separately as electrical atoms; while in 1887, Clifford wrote: "There is great reason to believe that every material atom carries upon it a small electric current, if it does not wholly consist of this current."
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+---
+title: "History of electromagnetic theory"
+chunk: 16/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+In 1896, J. J. Thomson performed experiments indicating that cathode rays really were particles, found an accurate value for their charge-to-mass ratio e/m, and found that e/m was independent of cathode material. He made good estimates of both the charge e and the mass m, finding that cathode ray particles, which he called "corpuscles", had perhaps one thousandth of the mass of the least massive ion known (hydrogen). He further showed that the negatively charged particles produced by radioactive materials, by heated materials, and by illuminated materials, were universal. The nature of the Crookes tube "cathode ray" matter was identified by Thomson in 1897.
+In the late 19th century, the Michelson–Morley experiment was performed by Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University. It is generally considered to be the evidence against the theory of a luminiferous aether. The experiment has also been referred to as "the kicking-off point for the theoretical aspects of the Second Scientific Revolution." Primarily for this work, Michelson was awarded the Nobel Prize in 1907. Dayton Miller continued with experiments, conducting thousands of measurements and eventually developing the most accurate interferometer in the world at that time. Miller and others, such as Morley, continue observations and experiments dealing with the concepts. A range of proposed aether-dragging theories could explain the null result but these were more complex, and tended to use arbitrary-looking coefficients and physical assumptions.
+By the end of the 19th century electrical engineers had become a distinct profession, separate from physicists and inventors. They created companies that investigated, developed and perfected the techniques of electricity transmission, and gained support from governments all over the world for starting the first worldwide electrical telecommunication network, the telegraph network. Pioneers in this field included Werner von Siemens, founder of Siemens AG in 1847, and John Pender, founder of Cable & Wireless.
+William Stanley made the first public demonstration of a transformer that enabled commercial delivery of  alternating current in 1886. Large two-phase alternating current generators were built by a British electrician, J. E. H. Gordon, in 1882. Lord Kelvin and Sebastian Ferranti also developed early alternators, producing frequencies between 100 and 300 hertz. After 1891, polyphase alternators were introduced to supply currents of multiple differing phases. Later alternators were designed for varying alternating-current frequencies between sixteen and about one hundred hertz, for use with arc lighting, incandescent lighting and electric motors.
+The possibility of obtaining the electric current in large quantities, and economically, by means of dynamo electric machines gave impetus to the development of incandescent and arc lighting. Until these machines had attained a commercial basis voltaic batteries were the only available source of current for electric lighting and power. The cost of these batteries, however, and the difficulties of maintaining them in reliable operation were prohibitory of their use for practical lighting purposes. The date of the employment of arc and incandescent lamps may be set at about 1877.
+Even in 1880, however, but little headway had been made toward the general use of these illuminants; the rapid subsequent growth of this industry is a matter of general knowledge. The employment of storage batteries, which were originally termed secondary batteries or accumulators, began about 1879. Such batteries are now utilized on a large scale as auxiliaries to the dynamo machine in electric power-houses and substations, in electric automobiles and in immense numbers in automobile ignition and starting systems, also in fire alarm telegraphy and other signal systems.
+For the 1893 World's Columbian International Exposition in Chicago, General Electric proposed to power the entire fair with direct current. Westinghouse slightly undercut GE's bid and used the fair to debut their alternating current based system, showing how their system could power poly-phase motors and all the other AC and DC exhibits at the fair.
+
+=== Second Industrial Revolution ===
+
+The Second Industrial Revolution, also known as the Technological Revolution, was a phase of rapid industrialization in the final third of the 19th century and the beginning of the 20th. Along with the expansion of railroads, iron and steel production, widespread use of machinery in manufacturing, greatly increased use of steam power and petroleum, the period saw expansion in the use of electricity and the adaption of electromagnetic theory in developing various technologies.
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+---
+title: "History of electromagnetic theory"
+chunk: 17/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+The 1880s saw the spread of large scale commercial electric power systems, first used for lighting and eventually for electro-motive power and heating. Systems early on used alternating current and direct current. Large centralized power generation became possible when it was recognized that alternating current electric power lines could use transformers  to take advantage of the fact that each doubling of the voltage would allow the same size cable to transmit the same amount of power four times the distance. Transformer were used to raise voltage at the point of generation (a representative number is a generator voltage in the low kilovolt range) to a much higher voltage (tens of thousands to several hundred thousand volts) for primary transmission, followed to several downward transformations, for commercial and residential domestic use. Between 1885 and 1890 poly-phase currents combined with electromagnetic induction and practical AC induction motors were developed.
+The International Electro-Technical Exhibition of 1891 featuring the long-distance transmission of high-power, three-phase electric current. It was held between 16 May and 19 October on the disused site of the three former "Westbahnhöfe" (Western Railway Stations) in Frankfurt am Main. The exhibition featured the first long-distance transmission of high-power, three-phase electric current, which was generated 175 km away at Lauffen am Neckar. As a result of this successful field trial, three-phase current became established for electrical transmission networks throughout the world.
+Much was done in the direction in the improvement of railroad terminal facilities, and it is difficult to find one steam railroad engineer who would have denied that all the important steam railroads of this country were not to be operated electrically. In other directions the progress of events as to the utilization of electric power was expected to be equally rapid. In every part of the world the power of falling water, nature's perpetual motion machine, which has been going to waste since the world began, is now being converted into electricity and transmitted by wire hundreds of miles to points where it is usefully and economically employed.
+
+The first windmill for electricity production was built in Scotland in July 1887 by the Scottish electrical engineer James Blyth. Across the Atlantic, in Cleveland, Ohio a larger and heavily engineered machine was designed and constructed in 1887–88 by Charles F. Brush, this was built by his engineering company at his home and operated from 1886 until 1900. The Brush wind turbine had a rotor 56 feet (17 m) in diameter and was mounted on a 60-foot (18 m) tower. Although large by today's standards, the machine was only rated at 12 kW; it turned relatively slowly since it had 144 blades. The connected dynamo was used either to charge a bank of batteries or to operate up to 100 incandescent light bulbs, three arc lamps, and various motors in Brush's laboratory. The machine fell into disuse after 1900 when electricity became available from Cleveland's central stations, and was abandoned in 1908.
+
+== 20th century ==
+Various units of electricity and magnetism have been adopted and named by representatives of the electrical engineering institutes of the world, which units and names have been confirmed and legalized by the governments of the United States and other countries. Thus the volt, from the Italian Volta, has been adopted as the practical unit of electromotive force, the ohm, from the enunciator of Ohm's law, as the practical unit of resistance; the ampere, after the eminent French scientist of that name, as the practical unit of current strength, the henry as the practical unit of inductance, after Joseph Henry and in recognition of his early and important experimental work in mutual induction.
+Dewar and John Ambrose Fleming predicted that at absolute zero, pure metals would become perfect electromagnetic conductors (though, later, Dewar altered his opinion on the disappearance of resistance believing that there would always be some resistance). Walther Hermann Nernst developed the third law of thermodynamics and stated that absolute zero was unattainable. Carl von Linde and William Hampson, both commercial researchers, nearly at the same time filed for patents on the Joule–Thomson effect. Linde's patent was the climax of 20 years of systematic investigation of established facts, using a regenerative counterflow method. Hampson's design was also of a regenerative method. The combined process became known as the Linde–Hampson liquefaction process. Heike Kamerlingh Onnes purchased a Linde machine for his research. Zygmunt Florenty Wróblewski conducted research into electrical properties at low temperatures, though his research ended early due to his accidental death. Around 1864, Karol Olszewski and Wroblewski predicted the electrical phenomena of dropping resistance levels at ultra-cold temperatures. Olszewski and Wroblewski documented evidence of this in the 1880s. A milestone was achieved on 10 July 1908 when Onnes at the Leiden University in Leiden produced, for the first time, liquified helium and achieved superconductivity.
+In 1900, William Du Bois Duddell develops the Singing Arc and produced melodic sounds, from a low to a high-tone, from this arc lamp.
+
+=== Lorentz and Poincaré ===
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+title: "History of electromagnetic theory"
+chunk: 18/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+Between 1900 and 1910, many scientists like Wilhelm Wien, Max Abraham, Hermann Minkowski, or Gustav Mie believed that all forces of nature are of electromagnetic origin (the so-called "electromagnetic world view"). This was connected with the electron theory developed between 1892 and 1904 by Hendrik Lorentz. Lorentz introduced a strict separation between matter (electrons) and the aether, whereby in his model the ether is completely motionless, and it won't be set in motion in the neighborhood of ponderable matter. Contrary to other electron models before, the electromagnetic field of the ether appears as a mediator between the electrons, and changes in this field can propagate not faster than the speed of light.
+In 1896, three years after submitting his thesis on the Kerr effect, Pieter Zeeman disobeyed the direct orders of his supervisor and used laboratory equipment to measure the splitting of spectral lines by a strong magnetic field. Lorentz theoretically explained the Zeeman effect on the basis of his theory, for which both received the Nobel Prize in Physics in 1902. A fundamental concept of Lorentz's theory in 1895 was the "theorem of corresponding states" for terms of order v/c. This theorem states that a moving observer (relative to the ether) makes the same observations as a resting observer. This theorem was extended for terms of all orders by Lorentz in 1904. Lorentz noticed, that it was necessary to change the space-time variables when changing frames and introduced concepts like physical length contraction (1892) to explain the Michelson–Morley experiment, and the mathematical concept of local time (1895) to explain the aberration of light and the Fizeau experiment. That resulted in the formulation of the so-called Lorentz transformation by Joseph Larmor (1897, 1900) and Lorentz (1899, 1904). As Lorentz later noted (1921, 1928), he considered the time indicated by clocks resting in the aether as "true" time, while local time was seen by him as a heuristic working hypothesis and a mathematical artifice. Therefore, Lorentz's theorem is seen by modern historians as being a mathematical transformation from a "real" system resting in the aether into a "fictitious" system in motion.
+
+Continuing the work of Lorentz, Henri Poincaré between 1895 and 1905 formulated on many occasions the principle of relativity and tried to harmonize it with electrodynamics. He declared simultaneity only a convenient convention which depends on the speed of light, whereby the constancy of the speed of light would be a useful postulate for making the laws of nature as simple as possible. In 1900 he interpreted Lorentz's local time as the result of clock synchronization by light signals, and introduced the electromagnetic momentum by comparing electromagnetic energy to what he called a "fictitious fluid" of mass 
+  
+    
+      
+        m
+        =
+        E
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle m=E/c^{2}}
+  
+. And finally in June and July 1905 he declared the relativity principle a general law of nature, including gravitation. He corrected some mistakes of Lorentz and proved the Lorentz covariance of the electromagnetic equations. Poincaré also suggested that there exist non-electrical forces to stabilize the electron configuration and asserted that gravitation is a non-electrical force as well, contrary to the electromagnetic world view. However, historians pointed out that he still used the notion of an ether and distinguished between "apparent" and "real" time and therefore didn't invent special relativity in its modern understanding.
+
+=== Einstein's Annus Mirabilis ===
+
+In 1905, while he was working in the patent office, Albert Einstein had four papers published in the Annalen der Physik, the leading German physics journal. These are the papers that history has come to call the Annus Mirabilis papers:
+
+His paper on the particulate nature of light put forward the idea that certain experimental results, notably the photoelectric effect, could be simply understood from the postulate that light interacts with matter as discrete "packets" (quanta) of energy, an idea that had been introduced by Max Planck in 1900 as a purely mathematical manipulation, and which seemed to contradict contemporary wave theories of light (Einstein 1905a). This was the only work of Einstein's that he himself called "revolutionary."
+His paper on Brownian motion explained the random movement of very small objects as direct evidence of molecular action, thus supporting the atomic theory. (Einstein 1905b)
+His paper on the electrodynamics of moving bodies introduced the radical theory of special relativity, which showed that the observed independence of the speed of light on the observer's state of motion required fundamental changes to the notion of simultaneity. Consequences of this include the time-space frame of a moving body slowing down and contracting (in the direction of motion) relative to the frame of the observer. This paper also argued that the idea of a luminiferous aether—one of the leading theoretical entities in physics at the time—was superfluous. (Einstein 1905c)
+In his paper on mass–energy equivalence (previously considered to be distinct concepts), Einstein deduced from his equations of special relativity what later became the well-known expression: 
+  
+    
+      
+        E
+        =
+        m
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle E=mc^{2}}
+  
+, suggesting that tiny amounts of mass could be converted into huge amounts of energy. (Einstein 1905d)
+All four papers are today recognized as tremendous achievements—and hence 1905 is known as Einstein's "Wonderful Year". At the time, however, they were not noticed by most physicists as being important, and many of those who did notice them rejected them outright. Some of this work—such as the theory of light quanta—remained controversial for years.
+
+=== Mid-20th century ===
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+title: "History of electromagnetic theory"
+chunk: 19/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+The first formulation of a quantum theory describing radiation and matter interaction is due to Paul Dirac, who, during 1920, was first able to compute the coefficient of spontaneous emission of an atom. Paul Dirac described the quantization of the electromagnetic field as an ensemble of harmonic oscillators with the introduction of the concept of creation and annihilation operators of particles. In the following years, with contributions from Wolfgang Pauli, Eugene Wigner, Pascual Jordan, Werner Heisenberg and an elegant formulation of quantum electrodynamics due to Enrico Fermi, physicists came to believe that, in principle, it would be possible to perform any computation for any physical process involving photons and charged particles. However, further studies by Felix Bloch with Arnold Nordsieck, and Victor Weisskopf,  in 1937 and 1939, revealed that such computations were reliable only at a first order of perturbation theory, a problem already pointed out by Robert Oppenheimer. At higher orders in the series infinities emerged, making such computations meaningless and casting serious doubts on the internal consistency of the theory itself. With no solution for this problem known at the time, it appeared that a fundamental incompatibility existed between special relativity and quantum mechanics.
+In December 1938, the German chemists Otto Hahn and Fritz Strassmann sent a manuscript to Naturwissenschaften reporting they had detected the element barium after bombarding uranium with neutrons; simultaneously, they communicated these results to Lise Meitner. Meitner, and her nephew Otto Robert Frisch, correctly interpreted these results as being nuclear fission. Frisch confirmed this experimentally on 13 January 1939. In 1944, Hahn  received the Nobel Prize in Chemistry for the discovery of nuclear fission. Some historians who have documented the history of the discovery of nuclear fission believe Meitner should have been awarded the Nobel Prize with Hahn.
+Difficulties with the quantum theory increased through the end of 1940. Improvements in microwave technology made it possible to take more precise measurements of the shift of the levels of a hydrogen atom, now known as the Lamb shift and magnetic moment of the electron. These experiments unequivocally exposed discrepancies which the theory was unable to explain. With the invention of bubble chambers and spark chambers in the 1950s, experimental particle physics discovered a large and ever-growing number of particles called hadrons. It seemed that such a large number of particles could not all be fundamental.
+Shortly after the end of the war in 1945, Bell Labs formed a Solid State Physics Group, led by William Shockley and chemist Stanley Morgan; other personnel including John Bardeen and Walter Brattain, physicist Gerald Pearson, chemist Robert Gibney, electronics expert Hilbert Moore and several technicians.  Their assignment was to seek a solid-state alternative to fragile glass vacuum tube amplifiers.  Their first attempts were based on Shockley's ideas about using an external electrical field on a semiconductor to affect its conductivity. These experiments failed every time in all sorts of configurations and materials. The group was at a standstill until Bardeen suggested a theory that invoked surface states that prevented the field from penetrating the semiconductor. The group changed its focus to study these surface states and they met almost daily to discuss the work.  The rapport of the group was excellent, and ideas were freely exchanged.
+As to the problems in the electron experiments, a path to a solution was given by Hans Bethe. In 1947, while he was traveling by train to reach Schenectady from New York, after giving a talk at the conference at Shelter Island on the subject, Bethe completed the first non-relativistic computation of the shift of the lines of the hydrogen atom as measured by Lamb and Retherford. Despite the limitations of the computation, agreement was excellent. The idea was simply to attach infinities to corrections at mass and charge that were actually fixed to a finite value by experiments. In this way, the infinities get absorbed in those constants and yield a finite result in good agreement with experiments. This procedure was named renormalization.
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+title: "History of electromagnetic theory"
+chunk: 20/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+Based on Bethe's intuition and fundamental papers on the subject by Shin'ichirō Tomonaga, Julian Schwinger, Richard Feynman and Freeman Dyson, it was finally possible to get fully covariant formulations that were finite at any order in a perturbation series of quantum electrodynamics. Shin'ichirō Tomonaga, Julian Schwinger and Richard Feynman were jointly awarded with a Nobel Prize in Physics in 1965 for their work in this area. Their contributions, and those of Freeman Dyson, were about covariant and gauge-invariant formulations of quantum electrodynamics that allow computations of observables at any order of perturbation theory. Feynman's mathematical technique, based on his diagrams, initially seemed very different from the field-theoretic, operator-based approach of Schwinger and Tomonaga, but Freeman Dyson later showed that the two approaches were equivalent. Renormalization, the need to attach a physical meaning at certain divergences appearing in the theory through integrals, has subsequently become one of the fundamental aspects of quantum field theory and has come to be seen as a criterion for a theory's general acceptability. Even though renormalization works very well in practice, Feynman was never entirely comfortable with its mathematical validity, even referring to renormalization as a "shell game" and "hocus pocus". QED has served as the model and template for all subsequent quantum field theories. Peter Higgs, Jeffrey Goldstone, and others, Sheldon Glashow, Steven Weinberg and Abdus Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force.
+Robert Noyce credited Kurt Lehovec for the principle of p–n junction isolation caused by the action of a biased p-n junction (the diode) as a key concept behind the integrated circuit. Jack Kilby recorded his initial ideas concerning the integrated circuit in July 1958 and successfully demonstrated the first working integrated circuit on September 12, 1958. In his patent application of February 6, 1959, Kilby described his new device as "a body of semiconductor material ... wherein all the components of the electronic circuit are completely integrated." Kilby won the 2000 Nobel Prize in Physics for his part of the invention of the integrated circuit. Robert Noyce also came up with his own idea of an integrated circuit half a year later than Kilby. Noyce's chip solved many practical problems that Kilby's had not. Noyce's chip, made at Fairchild Semiconductor, was made of silicon, whereas Kilby's chip was made of germanium.
+Philo Farnsworth developed the Farnsworth–Hirsch Fusor, or simply fusor, an apparatus designed by Farnsworth to create nuclear fusion. Unlike most controlled fusion systems, which slowly heat a magnetically confined plasma, the fusor injects high temperature ions directly into a reaction chamber, thereby avoiding a considerable amount of complexity. When the Farnsworth-Hirsch Fusor was first introduced to the fusion research world in the late 1960s, the Fusor was the first device that could clearly demonstrate it was producing fusion reactions at all.  Hopes at the time were high that it could be quickly developed into a practical power source. However, as with other fusion experiments, development into a power source has proven difficult.  Nevertheless, the fusor has since become a practical neutron source and is produced commercially for this role.
+
+=== Parity violation ===
+The mirror image of an electromagnet produces a field with the opposite polarity.  Thus the north and south poles of a magnet have the same symmetry as left and right.  Prior to 1956, it was believed that this symmetry was perfect, and that a technician would be unable to distinguish the north and south poles of a magnet except by reference to left and right.  In that year, T. D. Lee and C. N. Yang predicted the nonconservation of parity in the weak interaction.  To the surprise of many physicists, in 1957 C. S. Wu and collaborators at the U.S. National Bureau of Standards demonstrated that under suitable conditions for polarization of nuclei, the beta decay of cobalt-60 preferentially releases electrons toward the south pole of an external magnetic field, and a somewhat higher number of gamma rays toward the north pole.  As a result, the experimental apparatus does not behave comparably with its mirror image.
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+---
+title: "History of electromagnetic theory"
+chunk: 3/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+=== Electrics and non-electrics ===
+In 1729, Stephen Gray conducted a series of experiments that demonstrated the difference between conductors and non-conductors (insulators), showing amongst other things that a metal wire and even packthread conducted electricity, whereas silk did not. In one of his experiments he sent an electric current through 800 feet of hempen thread which was suspended at intervals by loops of silk thread. When he tried to conduct the same experiment substituting the silk for finely spun brass wire, he found that the electric current was no longer carried throughout the hemp cord, but instead seemed to vanish into the brass wire. From this experiment he classified substances into two categories: "electrics" like glass, resin and silk (what we now call insulators) and "non-electrics" like metal and water (what we now call conductors). "Non-electrics" conducted charges while "electrics" held the charge.
+
+=== Vitreous and resinous ===
+Intrigued by Gray's results, in 1732, C. F. du Fay began to conduct several experiments. In his first experiment, Du Fay concluded that all objects except metals, animals, and liquids could be electrified by rubbing and that metals, animals and liquids could be electrified by means of an electric machine, thus discrediting Gray's "electrics" and "non-electrics" classification of substances.
+In 1733 Du Fay discovered what he believed to be two kinds of frictional electricity; one generated from rubbing glass, the other from rubbing resin. From this, Du Fay theorized that electricity consists of two electrical fluids, "vitreous" and "resinous", that are separated by friction and that neutralize each other when combined. This picture of electricity was also supported by Christian Gottlieb Kratzenstein in his theoretical and experimental works. The two-fluid theory was later proven wrong and replaced with to the concept of positive and negative electrical charges devised by Benjamin Franklin.
+
+=== Leyden jar ===
+
+The Leyden jar, a type of capacitor for electrical energy in large quantities, was invented independently by Ewald Georg von Kleist on 11 October 1744 and by Pieter van Musschenbroek in 1745–1746 at Leiden University (the latter location giving the device its name). William Watson, when experimenting with the Leyden jar, discovered in 1747 that a discharge of static electricity was equivalent to an electric current. Capacitance was first observed by Von Kleist of Leyden in 1754. Von Kleist happened to hold, near his electric machine, a small bottle, in the neck of which there was an iron nail. Touching the iron nail accidentally with his other hand he received a severe electric shock. In much the same way Musschenbroeck assisted by Cunaens received a more severe shock from a somewhat similar glass bottle. Sir William Watson of England greatly improved this device, by covering the bottle, or jar, outside and in with tinfoil. This piece of electrical apparatus will be easily recognized as the well-known Leyden jar, so called by the Abbot Nollet of Paris, after the place of its discovery.
+In 1741, John Ellicott "proposed to measure the strength of electrification by its power to raise a weight in one scale of a balance while the other was held over the electrified body and pulled to it by its attractive power".
+As early as 1746, Jean-Antoine Nollet (1700–1770) had performed experiments on the propagation speed of electricity. By involving 200 Carthusian monks connected from hand to hand by iron wires so as to form a circle of about 1.6 km, he was able to prove that this speed is finite, even though very high. In 1749, Sir William Watson conducted numerous experiments to ascertain the velocity of electricity in a wire. These experiments, although perhaps not so intended, also demonstrated the possibility of transmitting signals to a distance by electricity. In these experiments, the signal appeared to travel the 12,276-foot length of the insulated wire instantaneously. Le Monnier in France had previously made somewhat similar experiments, sending shocks through an iron wire 1,319 feet long.
+About 1750, first experiments in electrotherapy were made. Various experimenters made tests to ascertain the physiological and therapeutical effects of electricity. Typical for this effort was Kratzenstein in Halle who in 1744 wrote a treatise on the subject. Demainbray in Edinburgh examined the effects of electricity upon plants and concluded that the growth of two myrtle trees was quickened by electrification. These myrtles were electrified "during the whole month of October, 1746, and they put forth branches and blossoms sooner than other shrubs of the same kind not electrified." Abbé Ménon in France tried the effects of a continued application of electricity upon men and birds and found that the subjects experimented on lost weight, thus apparently showing that electricity quickened the excretions. The efficacy of electric shocks in cases of paralysis was tested in the county hospital at Shrewsbury, England, with rather poor success.
+
+=== Late 18th century ===
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+title: "History of electromagnetic theory"
+chunk: 21/22
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+category: "reference"
+tags: "science, encyclopedia"
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+instance: "kb-cron"
+---
+
+=== Electroweak theory ===
+The first step towards the Standard Model was Sheldon Glashow's discovery, in 1960, of a way to combine the electromagnetic and weak interactions.  In 1967, Steven Weinberg and Abdus Salam incorporated the Higgs mechanism into Glashow's electroweak theory, giving it its modern form. The Higgs mechanism is believed to give rise to the masses of all the elementary particles in the Standard Model. This includes  the  masses of the W and Z bosons, and the masses of the fermions – i.e. the quarks and leptons. After the neutral weak currents caused by Z boson exchange were discovered at CERN in 1973, the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 Nobel Prize in Physics for discovering it. The W and Z bosons were discovered experimentally in 1981, and their masses were found to be as the Standard Model predicted. The theory of the strong interaction, to which many contributed, acquired its modern form around 1973–74, when experiments confirmed that the hadrons were composed of fractionally charged quarks. With the establishment of quantum chromodynamics in the 1970s finalized a set of fundamental and exchange particles, which allowed for the establishment of a "standard model" based on the mathematics of gauge invariance, which successfully described all forces except for gravity, and which remains generally accepted within the domain to which it is designed to be applied.
+The 'standard model' groups the electroweak interaction theory and quantum chromodynamics into a structure denoted by the gauge group SU(3)×SU(2)×U(1). The formulation of the unification of the electromagnetic and weak interactions in the standard model is due to Abdus Salam, Steven Weinberg and, subsequently, Sheldon Glashow. After the discovery, made at CERN, of the existence of neutral weak currents, mediated by the Z boson foreseen in the standard model, the physicists Salam, Glashow and Weinberg received the 1979 Nobel Prize in Physics for their electroweak theory. Since then, discoveries of the bottom quark (1977), the top quark (1995), tau neutrino (2000) and the Higgs boson (2012) have given credence to the Standard Model.
+
+== 21st century ==
+
+=== Electromagnetic technologies ===
+There are a range of emerging energy technologies. By 2007, solid state micrometer-scale electric double-layer capacitors based on advanced superionic conductors had been for low-voltage electronics such as deep-sub-voltage nanoelectronics and related technologies (the 22 nm technological node of CMOS and beyond). Also, the nanowire battery, a lithium-ion battery, was invented by a team led by Dr. Yi Cui in 2007.
+
+==== Magnetic resonance ====
+Reflecting the fundamental importance and applicability of Magnetic resonance imaging in medicine, Paul Lauterbur of the University of Illinois at Urbana–Champaign and Sir Peter Mansfield of the University of Nottingham were awarded the 2003 Nobel Prize in Physiology or Medicine for their "discoveries concerning magnetic resonance imaging". The Nobel citation acknowledged Lauterbur's insight of using magnetic field gradients to determine spatial localization, a discovery that allowed rapid acquisition of 2D images.
+
+==== Wireless electricity ====
+
+Wireless electricity is a form of wireless energy transfer, the ability to provide electrical energy to remote objects without wires. The term WiTricity was coined in 2005 by Dave Gerding and later used for a project led by Prof. Marin Soljačić in 2007. The MIT researchers successfully demonstrated the ability to power a 60 watt light bulb wirelessly, using two 5-turn copper coils of 60 cm (24 in) diameter, that were 2 m (7 ft) away, at roughly 45% efficiency.  This technology can potentially be used in a large variety of applications, including consumer, industrial, medical and military. Its aim is to reduce the dependence on batteries. Further applications for this technology include transmission of information—it would not interfere with radio waves and thus could be used as a cheap and efficient communication device without requiring a license or a government permit.
+
+=== Unified theories ===
+
+A Grand Unified Theory (GUT) is a model in particle physics in which, at high energy, the electromagnetic force is merged with the other two gauge interactions of the Standard Model, the weak and strong nuclear forces. Many candidates have been proposed, but none is directly supported by experimental evidence. GUTs are often seen as intermediate steps towards a  "Theory of Everything" (TOE), a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and, ideally, has predictive power for the outcome of any experiment that could be carried out in principle. No such theory has yet been accepted by the physics community.
+
+=== Open problems ===
+
+The magnetic monopole in the quantum theory of magnetic charge started with a paper by the physicist Paul A.M. Dirac in 1931. The detection of magnetic monopoles is an open problem in experimental physics. In some theoretical models, magnetic monopoles are unlikely to be observed, because they are too massive to be created in particle accelerators, and also too rare in the Universe to enter a particle detector with much probability.
+After more than twenty years of intensive research, the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of s-wave pairing, d-wave pairings are substantial. One goal of all this research is room-temperature superconductivity.
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+title: "History of electromagnetic theory"
+chunk: 22/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+== See also ==
+Histories
+History of electromagnetic spectrum, History of electrical engineering, History of Maxwell's equations, History of radio, History of optics, History of physics, Physical crystallography before X-rays
+General
+Coulomb's law, Biot–Savart law, Gauss's law, Ampère's circuital law, Gauss's law for magnetism, Faraday's law of induction, Ponderomotive force,  Telluric currents, Terrestrial magnetism, ampere hours, Transverse waves, Longitudinal waves, Plane waves, Refractive index,  torque, Revolutions per minute, Photosphere, Vortex, vortex rings,
+Theory
+permittivity, scalar product, vector product,  tensor, divergent series, linear operator, unit vector, parallelepiped, osculating plane, standard candle
+Technology
+Solenoid, electro-magnets, Nicol prisms, rheostat, voltmeter, gutta-percha covered wire, Electrical conductor, ammeters, Gramme machine, binding posts, Induction motor, Lightning arresters, Technological and industrial history of the United States, Western Electric Company,
+Lists
+Outline of energy development
+Timelines
+Timeline of electromagnetism, Timeline of luminiferous aether
+
+== References ==
+Citations and notes
+
+Attribution
+ This article incorporates text from this source, which is in the public domain: "Electricity, its History and Progress" by William Maver Jr. - article published within The Encyclopedia Americana; a library of universal knowledge, vol. X, pp. 172ff. (1918). New York: Encyclopedia Americana Corp.
+
+== Bibliography ==
+Bakewell, F. C. (1853). Electric science; its history, phenomena, and applications. London: Ingram, Cooke.
+Benjamin, P. (1898). A history of electricity (The intellectual rise in electricity) from antiquity to the days of Benjamin Franklin. New York: J. Wiley & Sons.
+Darrigol, Olivier (2005), "The Genesis of the theory of relativity" (PDF), Séminaire Poincaré, 1: 1–22, Bibcode:2006eins.book....1D, doi:10.1007/3-7643-7436-5_1, ISBN 978-3-7643-7435-8, retrieved 2009-06-21{{citation}}:  CS1 maint: work parameter with ISBN (link)
+Durgin, W. A. (1912). Electricity, its history and development. Chicago: A.C. McClurg.
+Einstein, Albert: "Ether and the Theory of Relativity" (1920), republished in Sidelights on Relativity (Dover, New York, 1922).
+Einstein, Albert, The Investigation of the State of Aether in Magnetic Fields, 1895. (PDF format)
+Einstein, Albert (1905a), "On a Heuristic Viewpoint Concerning the Production and Transformation of Light", Annalen der Physik, 17 (6): 132–148, Bibcode:1905AnP...322..132E, doi:10.1002/andp.19053220607. This annus mirabilis paper on the photoelectric effect was received by Annalen der Physik March 18.
+Einstein, Albert (1905b), "On the Motion—Required by the Molecular Kinetic Theory of Heat—of Small Particles Suspended in a Stationary Liquid" (PDF), Annalen der Physik, 17 (8): 549–560, Bibcode:1905AnP...322..549E, doi:10.1002/andp.19053220806. This annus mirabilis paper on Brownian motion was received May 11.
+Einstein, Albert (1905c), "On the Electrodynamics of Moving Bodies", Annalen der Physik, 17 (10): 891–921, Bibcode:1905AnP...322..891E, doi:10.1002/andp.19053221004. This annus mirabilis paper on special relativity was received June 30.
+Einstein, Albert (1905d), "Does the Inertia of a Body Depend Upon Its Energy Content?", Annalen der Physik, 18 (13): 639–641, Bibcode:1905AnP...323..639E, doi:10.1002/andp.19053231314. This annus mirabilis paper on mass-energy equivalence was received September 27.
+Larmor, Joseph (1911), "Aether" , in Chisholm, Hugh (ed.), Encyclopædia Britannica, vol. 1 (11th ed.), Cambridge University Press, p. 292–297
+The Encyclopedia Americana; a library of universal knowledge; "Electricity, its history and Progress". (1918). New York: Encyclopedia Americana Corp. Page 171
+Galison, Peter (2003), Einstein's Clocks, Poincaré's Maps: Empires of Time, New York: W.W. Norton, ISBN 0-393-32604-7
+Gibson, C. R. (1907). Electricity of to-day, its work & mysteries described in non-technical language. London: Seeley and co., limited
+Heaviside, O. (1894). Electromagnetic theory. London: "The Electrician" Print. and Pub.
+Ireland commissioners of nat. educ., (1861). Electricity, galvanism, magnetism, electro-magnetism, heat, and the steam engine. Oxford University.
+Janssen, Michel; Mecklenburg, Matthew (2007). "From classical to relativistic mechanics: Electromagnetic models of the electron" (PDF). In V. F. Hendricks; et al. (eds.). Interactions: Mathematics, Physics and Philosophy, 1860–1930. Dordrecht: Springer. pp. 65–134. Archived from the original (PDF) on 2017-07-13. Retrieved 2018-04-21.
+Jeans, J. H. (1908). The mathematical theory of electricity and magnetism. Cambridge: University Press.
+Katzir, Shaul (2005), "Poincaré's Relativistic Physics: Its Origins and Nature", Phys. Perspect., 7 (3): 268–292, Bibcode:2005PhP.....7..268K, doi:10.1007/s00016-004-0234-y, S2CID 14751280
+Lord Kelvin (Sir William Thomson), "On Vortex Atoms". Proceedings of the Royal Society of Edinburgh, Vol. VI, 1867, pp. 197–206. (ed., Reprinted in Phil. Mag. Vol. XXXIV, 1867, pp. 15–24.)
+Kolbe, Bruno; Francis ed Legge, Joseph Skellon, tr., "An Introduction to Electricity". Kegan Paul, Trench, Trübner, 1908.
+Lodge, Oliver, "Ether", Encyclopædia Britannica, Thirteenth Edition (1926).
+Lodge, Oliver, "The Ether of Space". ISBN 1-4021-8302-X (paperback) ISBN 1-4021-1766-3 (hardcover)
+Lodge, Oliver, "Ether and Reality". ISBN 0-7661-7865-X
+Lyons, T. A. (1901). A treatise on electromagnetic phenomena, and on the compass and its deviations aboard ship. Mathematical, theoretical, and practical. New York: J. Wiley & Sons.
+Maxwell, James Clerk (1878), "Ether" , in Baynes, T. S. (ed.), Encyclopædia Britannica, vol. 8 (9th ed.), New York: Charles Scribner's Sons, pp. 568–572
+Maxwell, J. C., & Thompson, J. J. (1892). A treatise on electricity and magnetism. Clarendon Press series. Oxford: Clarendon.
+Miller, Arthur I. (1981), Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, ISBN 0-201-04679-2
+Pais, Abraham (1982), Subtle is the Lord: The Science and the Life of Albert Einstein, New York: Oxford University Press, ISBN 0-19-520438-7
+Priestley, J., & Mynde, J. (1775). The history and present state of electricity, with original experiments. London: Printed for C. Bathurst, and T. Lowndes; J. Rivington, and J. Johnson; S. Crowder [and 4 others in London].
+Schaffner, Kenneth F. : Nineteenth-Century Aether Theories, Oxford: Pergamon Press, 1972. (contains several reprints of original papers of famous physicists)
+Slingo, M., Brooker, A., Urbanitzky, A., Perry, J., & Dibner, B. (1895). The cyclopædia of electrical engineering: containing a history of the discovery and application of electricity with its practice and achievements from the earliest period to the present time: the whole being a practical guide to artisans, engineers and students interested in the practice and development of electricity, electric lighting, motors, thermo-piles, the telegraph, the telephone, magnets and every other branch of electrical application. Philadelphia: The Gebbie Pub. Co., Limited.
+Steinmetz, C. P., "Transient Electric Phenomena". Page 38. (ed., contained in: General Electric Company. General Electric review. Schenectady: General Electric Co..)
+A New System of Alternating Current Motors and Transformers, by Nikola Tesla, 1888
+Thompson, S. P. (1891). The electromagnet, and electromagnetic mechanism. London: E. & F.N. Spon.
+Whittaker, E. T., "A History of the Theories of Aether and Electricity, from the Age of Descartes to the Close of the 19th century". Dublin University Press series. London: Longmans, Green and Co.;
+Urbanitzky, A. v., & Wormell, R. (1886). Electricity in the service of man: a popular and practical treatise on the applications of electricity in modern life. London: Cassell &.
+
+== External links ==
+Electrickery, BBC Radio 4 discussion with Simon Schaffer, Patricia Fara & Iwan Morus (In Our Time, Nov. 4, 2004)
+Magnetism, BBC Radio 4 discussion with Stephen Pumphrey, John Heilbron & Lisa Jardine (In Our Time, Sep. 29, 2005)
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+category: "reference"
+tags: "science, encyclopedia"
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+instance: "kb-cron"
+---
+
+Benjamin Franklin promoted his investigations of electricity and theories through the famous, though extremely dangerous, experiment of having his son fly a kite through a storm-threatened sky. A key attached to the kite string sparked and charged a Leyden jar, thus establishing the link between lightning and electricity. Following these experiments, he invented a lightning rod. It is either Franklin (more frequently) or Ebenezer Kinnersley of Philadelphia (less frequently) who is considered to have established the convention of positive and negative electricity.
+Theories regarding the nature of electricity were quite vague at this period, and those prevalent were more or less conflicting. Franklin considered that electricity was an imponderable fluid pervading everything, and which, in its normal condition, was uniformly distributed in all substances. He assumed that the electrical manifestations obtained by rubbing glass were due to the production of an excess of the electric fluid in that substance and that the manifestations produced by rubbing wax were due to a deficit of the fluid. This explanation was opposed by supporters of the "two-fluid" theory like Robert Symmer in 1759. In this theory, the vitreous and resinous electricities were regarded as imponderable fluids, each fluid being composed of mutually repellent particles while the particles of the opposite electricities are mutually attractive. When the two fluids unite as a result of their attraction for one another, their effect upon external objects is neutralized. The act of rubbing a body decomposes the fluids, one of which remains in excess on the body and manifests itself as vitreous or resinous electricity.
+Up to the time of Franklin's historic kite experiment, the identity of the electricity developed by rubbing and by electrostatic machines (frictional electricity) with lightning had not been generally established. Dr. Wall, Abbot Nollet, Hauksbee, Stephen Gray and John Henry Winkler had indeed suggested the resemblance between the phenomena of "electricity" and "lightning", Gray having intimated that they only differed in degree. It was doubtless Franklin, however, who first proposed tests to determine the sameness of the phenomena. In a letter to Peter Comlinson of London, on 19 October 1752, Franklin, referring to his kite experiment, wrote,
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+instance: "kb-cron"
+---
+
+"At this key the phial (Leyden jar) may be charged; and from the electric fire thus obtained spirits may be kindled, and all the other electric experiments be formed which are usually done by the help of a rubbed glass globe or tube, and thereby the sameness of the electric matter with that of lightning be completely demonstrated."
+On 10 May 1742 Thomas-François Dalibard, at Marly (near Paris), using a vertical iron rod 40 feet long, obtained results corresponding to those recorded by Franklin and somewhat prior to the date of Franklin's experiment. Franklin's important demonstration of the sameness of frictional electricity and lightning added zest to the efforts of the many experimenters in this field in the last half of the 18th century, to advance the progress of the science.
+Franklin's observations aided later scientists  such as Michael Faraday, Luigi Galvani, Alessandro Volta, André-Marie Ampère and Georg Simon Ohm, whose collective work provided the basis for modern electrical technology and for whom fundamental units of electrical measurement are named. Others who would advance the field of knowledge included William Watson, Georg Matthias Bose, Smeaton, Louis-Guillaume Le Monnier, Jacques de Romas, Jean Jallabert, Giovanni Battista Beccaria, Tiberius Cavallo, John Canton, Robert Symmer, Abbot Nollet, John Henry Winkler, Benjamin Wilson, Ebenezer Kinnersley, Joseph Priestley, Franz Aepinus, Edward Hussey Délavai, Henry Cavendish, and Charles-Augustin de Coulomb. Descriptions of many of the experiments and discoveries of these early electrical scientists may be found in the scientific publications of the time, notably the Philosophical Transactions, Philosophical Magazine, Cambridge Mathematical Journal, Young's Natural Philosophy, Priestley's History of Electricity, Franklin's Experiments and Observations on Electricity, Cavalli's Treatise on Electricity and De la Rive's Treatise on Electricity.
+Henry Elles was one of the first people to suggest links between electricity and magnetism. In 1757 he claimed that he had written to the Royal Society in 1755 about the links between electricity and magnetism, asserting that "there are some things in the power of magnetism very similar to those of electricity" but he did "not by any means think them the same". In 1760 he similarly claimed that in 1750 he had been the first "to think how the electric fire may be the cause of thunder". Among the more important of the electrical research and experiments during this period were those of Franz Aepinus, a noted German scholar (1724–1802) and Henry Cavendish of London, England.
+Franz Aepinus is credited as the first to conceive of the view of the reciprocal relationship of electricity and magnetism. In his work Tentamen Theoria Electricitatis et Magnetism, published in Saint Petersburg in 1759, he gives the following amplification of Franklin's theory, which in some of its features is measurably in accord with present-day views: "The particles of the electric fluid repel each other, attract and are attracted by the particles of all bodies with a force that decreases in proportion as the distance increases; the electric fluid exists in the pores of bodies; it moves unobstructedly through non-electric (conductors), but moves with difficulty in insulators; the manifestations of electricity are due to the unequal distribution of the fluid in a body, or to the approach of bodies unequally charged with the fluid." Aepinus formulated a corresponding theory of magnetism excepting that, in the case of magnetic phenomena, the fluids only acted on the particles of iron. He also made numerous electrical experiments apparently showing that, in order to manifest electrical effects, tourmaline must be heated to between 37.5 °C and 100 °C. In fact, tourmaline remains unelectrified when its temperature is uniform, but manifests electrical properties when its temperature is rising or falling. Crystals that manifest electrical properties in this way are termed pyroelectric; along with tourmaline, these include sulphate of quinine and quartz.
+Henry Cavendish independently conceived a theory of electricity nearly akin to that of Aepinus. In 1784, he was perhaps the first to utilize an electric spark to produce an explosion of hydrogen and oxygen in the proper proportions that would create pure water. Cavendish also discovered the inductive capacity of dielectrics (insulators), and, as early as 1778, measured the specific inductive capacity for beeswax and other substances by comparison with an air condenser.
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+instance: "kb-cron"
+---
+
+Around 1784 C. A. Coulomb devised the torsion balance, discovering what is now known as Coulomb's law:  the force exerted between two small electrified bodies varies inversely as the square of the distance, not as Aepinus in his theory of electricity had assumed, merely inversely as the distance. According to the theory advanced by Cavendish, "the particles attract and are attracted inversely as some less power of the distance than the cube." A large part of the domain of electricity became virtually annexed by Coulomb's discovery of the law of inverse squares.
+Through the experiments of William Watson and others proving that electricity could be transmitted to a distance, the idea of making practical use of this phenomenon began, around 1753, to engross the minds of inquisitive people. To this end, suggestions as to the employment of electricity in the transmission of intelligence were made. The first of the methods devised for this purpose was probably that of Georges Lesage in 1774. This method consisted of 24 wires, insulated from one another and each having had a pith ball connected to its distant end. Each wire represented a letter of the alphabet. To send a message, a desired wire was charged momentarily with electricity from an electric machine, whereupon the pith ball connected to that wire would fly out. Other methods of telegraphing in which frictional electricity was employed were also tried, some of which are described in the history on the telegraph.
+The era of galvanic or voltaic electricity represented a revolutionary break from the historical focus on frictional electricity. Alessandro Volta discovered that chemical reactions could be used to create positively charged anodes and negatively charged cathodes. When a conductor was attached between these, the difference in the electrical potential (also known as voltage) drove a current between them through the conductor. The potential difference between two points is measured in units of volts in recognition of Volta's work.
+The first mention of voltaic electricity, although not recognized as such at the time, was probably made by Johann Georg Sulzer in 1767, who, upon placing a small disc of zinc under his tongue and a small disc of copper over it, observed a peculiar taste when the respective metals touched at their edges. Sulzer assumed that when the metals came together they were set into vibration, acting upon the nerves of the tongue to produce the effects noticed. In 1790, Prof. Luigi Alyisio Galvani of Bologna, while conducting experiments on "animal electricity", noticed the twitching of a frog's legs in the presence of an electric machine. He observed that a frog's muscle, suspended on an iron balustrade by a copper hook passing through its dorsal column, underwent lively convulsions without any extraneous cause, the electric machine being at this time absent.
+To account for this phenomenon, Galvani assumed that electricity of opposite kinds existed in the nerves and muscles of the frog, the muscles and nerves constituting the charged coatings of a Leyden jar. Galvani published the results of his discoveries, together with his hypothesis, which engrossed the attention of the physicists of that time. The most prominent of these was Volta, professor of physics at Pavia, who contended that the results observed by Galvani were the result of the two metals, copper and iron, acting as electromotors, and that the muscles of the frog played the part of a conductor, completing the circuit. This precipitated a long discussion between the adherents of the conflicting views. One group agreed with Volta that the electric current was the result of an electromotive force of contact at the two metals; the other adopted a modification of Galvani's view and asserted that the current was the result of a chemical affinity between the metals and the acids in the pile. Michael Faraday wrote in the preface to his Experimental Researches, relative to the question of whether metallic contact is productive of a part of the electricity of the voltaic pile: "I see no reason as yet to alter the opinion I have given; ... but the point itself is of such great importance that I intend at the first opportunity renewing the inquiry, and, if I can, rendering the proofs either on the one side or the other, undeniable to all."
+Even Faraday himself, however, did not settle the controversy, and while the views of the advocates on both sides of the question have undergone modifications, as subsequent investigations and discoveries demanded, up to 1918 diversity of opinion on these points continued to crop out. Volta made numerous experiments in support of his theory and ultimately developed the pile or battery, which was the precursor of all subsequent chemical batteries, and possessed the distinguishing merit of being the first means by which a prolonged continuous current of electricity was obtainable. Volta communicated a description of his pile to the Royal Society of London and shortly thereafter Nicholson and Cavendish (1780) produced the decomposition of water by means of the electric current, using Volta's pile as the source of electromotive force.
+
+== 19th century ==
+
+=== Early 19th century ===
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+instance: "kb-cron"
+---
+
+In 1800 Alessandro Volta constructed the first device to produce a large electric current, later known as the electric battery. Napoleon, informed of his works, summoned him in 1801 for a command performance of his experiments. He received many medals and decorations, including the Légion d'honneur.
+Davy in 1806, employing a voltaic pile of approximately 250 cells, or couples, decomposed potash and soda, showing that these substances were respectively the oxides of potassium and sodium, metals which previously had been unknown. These experiments were the beginning of electrochemistry, the investigation of which Faraday took up, and concerning which in 1833 he announced his important law of electrochemical equivalents, viz.: "The same quantity of electricity — that is, the same electric current — decomposes chemically equivalent quantities of all the bodies which it traverses; hence the weights of elements separated in these electrolytes are to each other as their chemical equivalents." Employing a battery of 2,000 elements of a voltaic pile Humphry Davy in 1809 gave the first public demonstration of the electric arc light, using charcoal enclosed in a vacuum.
+Somewhat important to note, it was not until many years after the discovery of the voltaic pile that the sameness of animal and frictional electricity with voltaic electricity was clearly recognized and demonstrated. Thus as late as January 1833 we find Faraday writing in a paper on the electricity of the electric ray. "After an examination of the experiments of Walsh, Ingenhousz, Henry Cavendish, Sir H. Davy, and Dr. Davy, no doubt remains on my mind as to the identity of the electricity of the torpedo with common (frictional) and voltaic electricity; and I presume that so little will remain on the mind of others as to justify my refraining from entering at length into the philosophical proof of that identity. The doubts raised by Sir Humphry Davy have been removed by his brother, Dr. Davy; the results of the latter being the reverse of those of the former. ... The general conclusion which must, I think, be drawn from this collection of facts (a table showing the similarity, of properties of the diversely named electricities) is, that electricity, whatever may be its source, is identical in its nature."
+It is proper to state, however, that prior to Faraday's time the similarity of electricity derived from different sources was more than suspected. Thus, William Hyde Wollaston, wrote in 1801: "This similarity in the means by which both electricity and galvanism (voltaic electricity) appear to be excited in addition to the resemblance that has been traced between their effects shows that they are both essentially the same and confirm an opinion that has already been advanced by others, that all the differences discoverable in the effects of the latter may be owing to its being less intense, but produced in much larger quantity." In the same paper Wollaston describes certain experiments in which he uses very fine wire in a solution of sulphate of copper through which he passed electric currents from an electric machine. This is interesting in connection with the later day use of almost similarly arranged fine wires in electrolytic receivers in wireless, or radio-telegraphy.
+
+In the first half of the 19th century many very important additions were made to the world's knowledge concerning electricity and magnetism. For example, in 1820 Hans Christian Ørsted of Copenhagen discovered the deflecting effect of an electric current traversing a wire upon a suspended magnetic needle.
+This discovery gave a clue to the subsequently proved intimate relationship between electricity and magnetism which was promptly followed up by Ampère who some months later, in September 1820, presented the first elements of his new theory, which he developed in the following years culminating with the publication in his 1827 "Mémoire sur la théorie mathématique des phénomènes électrodynamiques uniquement déduite de l’experience" (Memoir on the Mathematical Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience) announcing his celebrated theory of electrodynamics, relating to the force that one current exerts upon another, by its electro-magnetic effects, namely
+
+Two parallel portions of a circuit attract one another if the currents in them are flowing in the same direction, and repel one another if the currents flow in the opposite direction.
+Two portions of circuits crossing one another obliquely attract one another if both the currents flow either towards or from the point of crossing, and repel one another if one flows to and the other from that point.
+When an element of a circuit exerts a force on another element of a circuit, that force always tends to urge the second one in a direction at right angles to its own direction.
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+---
+title: "History of electromagnetic theory"
+chunk: 8/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+Ampere brought a multitude of phenomena into theory by his investigations of the mechanical forces between conductors supporting currents and magnets. James Clerk Maxwell, in his "A Treatise on Electricity and Magnetism", named Ampere “the Newton of electricity”.
+The German physicist Seebeck discovered in 1821 that when heat is applied to the junction of two metals that had been soldered together an electric current is set up. This is termed thermoelectricity. Seebeck's device consists of a strip of copper bent at each end and soldered to a plate of bismuth. A magnetic needle is placed parallel with the copper strip. When the heat of a lamp is applied to the junction of the copper and bismuth an electric current is set up which deflects the needle.
+Around this time, Siméon Denis Poisson attacked the difficult problem of induced magnetization, and his results, though differently expressed, are still the theory, as a most important first approximation. It was in the application of mathematics to physics that his services to science were performed. Perhaps the most original, and certainly the most permanent in their influence, were his memoirs on the theory of electricity and magnetism, which virtually created a new branch of mathematical physics.
+George Green wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism in 1828. The essay introduced several important concepts, among them a theorem similar to the modern Green's theorem, the idea of potential functions as currently used in physics, and the concept of what are now called Green's functions. George Green was the first person to create a mathematical theory of electricity and magnetism and his theory formed the foundation for the work of other scientists such as James Clerk Maxwell, William Thomson, and others.
+Peltier in 1834 discovered an effect opposite to thermoelectricity, namely, that when a current is passed through a couple of dissimilar metals the temperature is lowered or raised at the junction of the metals, depending on the direction of the current. This is termed the Peltier effect. The variations of temperature are found to be proportional to the strength of the current and not to the square of the strength of the current as in the case of heat due to the ordinary resistance of a conductor. This second law is the I2R law, discovered experimentally in 1841 by the English physicist Joule. In other words, this important law is that the heat generated in any part of an electric circuit is directly proportional to the product of the resistance R of this part of the circuit and to the square of the strength of current I flowing in the circuit.
+In 1822 Johann Schweigger devised the first galvanometer. This instrument was subsequently much improved by Wilhelm Weber (1833). In 1825 William Sturgeon of Woolwich, England, invented the horseshoe and straight bar electromagnet, receiving therefor the silver medal of the Society of Arts. In 1837 Carl Friedrich Gauss and Weber (both noted workers of this period) jointly invented a reflecting galvanometer for telegraph purposes. This was the forerunner of the Thomson reflecting and other exceedingly sensitive galvanometers once used in submarine signaling and still widely employed in electrical measurements. Arago in 1824 made the important discovery that when a copper disc is rotated in its own plane, and if a magnetic needle be freely suspended on a pivot over the disc, the needle will rotate with the disc. If on the other hand the needle is fixed it will tend to retard the motion of the disc. This effect was termed Arago's rotations.
+
+Futile attempts were made by Charles Babbage, Peter Barlow, John Herschel and others to explain this phenomenon. The true explanation was reserved for Faraday, namely, that electric currents are induced in the copper disc by the cutting of the magnetic lines of force of the needle, which currents in turn react on the needle. Georg Simon Ohm did his work on resistance in the years 1825 and 1826, and published his results in 1827 as the book Die galvanische Kette, mathematisch bearbeitet.
+He drew considerable inspiration from Fourier's work on heat conduction in the theoretical explanation of his work.  For experiments, he initially used voltaic piles, but later used a thermocouple as this provided a more stable voltage source in terms of internal resistance and constant potential difference.  He used a galvanometer to measure current, and knew that the voltage between the thermocouple terminals was proportional to the junction temperature.  He then added test wires of varying length, diameter, and material to complete the circuit.  He found that his data could be modeled through a simple equation with variable composed of the reading from a galvanometer, the length of the test conductor, thermocouple junction temperature, and a constant of the entire setup. From this, Ohm determined his law of proportionality and published his results. In 1827, he announced the now famous law that bears his name, that is:
+
+Ohm brought into order a host of puzzling facts connecting electromotive force and electric current in conductors, which all previous electricians had only succeeded in loosely binding together qualitatively under some rather vague statements. Ohm found that the results could be summed up in such a simple law and by Ohm's discovery a large part of the domain of electricity became annexed to theory.
+
+=== Faraday and Henry ===
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+title: "History of electromagnetic theory"
+chunk: 9/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+The discovery of electromagnetic induction was made almost simultaneously, although independently, by Michael Faraday, who was first to make the discovery in 1831, and Joseph Henry in 1832. Henry's discovery of self-induction and his work on spiral conductors using a copper coil were made public in 1835, just before those of Faraday.
+In 1831 began the epoch-making researches of Michael Faraday, the famous pupil and successor of Humphry Davy at the head of the Royal Institution, London, relating to electric and electromagnetic induction. The remarkable researches of Faraday, the prince of experimentalists, on electrostatics and electrodynamics and the induction of currents. These were rather long in being brought from the crude experimental state to a compact system, expressing the real essence. Faraday was not a competent mathematician, but had he been one, he would have been greatly assisted in his researches, have saved himself much useless speculation, and would have anticipated much later work. He would, for instance, knowing Ampere's theory, by his own results have readily been led to Neumann's theory, and the connected work of Helmholtz and Thomson. Faraday's studies and researches extended from 1831 to 1855 and a detailed description of his experiments, deductions and speculations are to be found in his compiled papers, entitled Experimental Researches in Electricity.' Faraday was by profession a chemist. He was not in the remotest degree a mathematician in the ordinary sense — indeed it is a question if in all his writings there is a single mathematical formula.
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+title: "History of electromagnetic theory"
+chunk: 10/22
+source: "https://en.wikipedia.org/wiki/History_of_electromagnetic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:28:58.553199+00:00"
+instance: "kb-cron"
+---
+
+The experiment which led Faraday to the discovery of electromagnetic induction was made as follows: He constructed what is now and was then termed an induction coil, the primary and secondary wires of which were wound on a wooden bobbin, side by side, and insulated from one another. In the circuit of the primary wire he placed a battery of approximately 100 cells. In the secondary wire he inserted a galvanometer. On making his first test he observed no results, the galvanometer remaining quiescent, but on increasing the length of the wires he noticed a deflection of the galvanometer in the secondary wire when the circuit of the primary wire was made and broken. This was the first observed instance of the development of electromotive force by electromagnetic induction.
+He also discovered that induced currents are established in a second closed circuit when the current strength is varied in the first wire, and that the direction of the current in the secondary circuit is opposite to that in the first circuit. Also that a current is induced in a secondary circuit when another circuit carrying a current is moved to and from the first circuit, and that the approach or withdrawal of a magnet to or from a closed circuit induces momentary currents in the latter. In short, within the space of a few months Faraday discovered by experiment virtually all the laws and facts now known concerning electro-magnetic induction and magneto-electric induction. Upon these discoveries, with scarcely an exception, depends the operation of the telephone, the dynamo machine, and incidental to the dynamo electric machine practically all the gigantic electrical industries of the world, including electric lighting, electric traction, the operation of electric motors for power purposes, and electro-plating, electrotyping, etc.
+In his investigations of the peculiar manner in which iron filings arrange themselves on a cardboard or glass in proximity to the poles of a magnet, Faraday conceived the idea of magnetic "lines of force" extending from pole to pole of the magnet and along which the filings tend to place themselves. On the discovery being made that magnetic effects accompany the passage of an electric current in a wire, it was also assumed that similar magnetic lines of force whirled around the wire. For convenience and to account for induced electricity it was then assumed that when these lines of force are "cut" by a wire in passing across them or when the lines of force in rising and falling cut the wire, a current of electricity is developed, or to be more exact, an electromotive force is developed in the wire that sets up a current in a closed circuit. Faraday advanced what has been termed the molecular theory of electricity which assumes that electricity is the manifestation of a peculiar condition of the molecule of the body rubbed or the ether surrounding the body. Faraday also, by experiment, discovered paramagnetism and diamagnetism, namely, that all solids and liquids are either attracted or repelled by a magnet. For example, iron, nickel, cobalt, manganese, chromium, etc., are paramagnetic (attracted by magnetism), whilst other substances, such as bismuth, phosphorus, antimony, zinc, etc., are repelled by magnetism or are diamagnetic.
+Brugans of Leyden in 1778 and Le Baillif and Becquerel in 1827 had previously discovered diamagnetism in the case of bismuth and antimony. Faraday also rediscovered specific inductive capacity in 1837, the results of the experiments by Cavendish not having been published at that time. He also predicted the retardation of signals on long submarine cables due to the inductive effect of the insulation of the cable, in other words, the static capacity of the cable. In 1816 telegraph pioneer Francis Ronalds had also observed signal retardation on his buried telegraph lines, attributing it to induction.
+The 25 years immediately following Faraday's discoveries of electromagnetic induction were fruitful in the promulgation of laws and facts relating to induced currents and to magnetism. In 1834 Heinrich Lenz and Moritz von Jacobi independently demonstrated the now familiar fact that the currents induced in a coil are proportional to the number of turns in the coil. Lenz also announced at that time his important law that, in all cases of electromagnetic induction the induced currents have such a direction that their reaction tends to stop the motion that produces them, a law that was perhaps deducible from Faraday's explanation of Arago's rotations.
+The induction coil was first designed by Nicholas Callan in 1836. In 1845 Joseph Henry, the American physicist, published an account of his valuable and interesting experiments with induced currents of a high order, showing that currents could be induced from the secondary of an induction coil to the primary of a second coil, thence to its secondary wire, and so on to the primary of a third coil, etc. Heinrich Daniel Ruhmkorff further developed the induction coil, the Ruhmkorff coil was patented in 1851, and he utilized long windings of copper wire to achieve a spark of approximately 2 inches (50 mm) in length. In 1857, after examining a greatly improved version made by an American inventor, Edward Samuel Ritchie, Ruhmkorff improved his design (as did other engineers), using glass insulation and other innovations to allow the production of sparks more than 300 millimetres (12 in) long.
+
+=== Middle 19th century ===
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+---
+title: "History of fluid mechanics"
+chunk: 1/7
+source: "https://en.wikipedia.org/wiki/History_of_fluid_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:18.315710+00:00"
+instance: "kb-cron"
+---
+
+The history of fluid mechanics is a fundamental strand of the history of physics and engineering. The study of the movement of fluids (liquids and gases) and the forces that act upon them dates back to pre-history. The field has undergone a continuous evolution, driven by human dependence on water, meteorological conditions, and internal biological processes.
+The success of early civilizations, can be attributed to developments in the understanding of water dynamics, allowing for the construction of canals and aqueducts for water distribution and farm irrigation, as well as maritime transport. Due to its conceptual complexity, most discoveries in this field relied almost entirely on experiments, at least until the development of advanced understanding of differential equations and computational methods. Significant theoretical contributions were made by notables figures like Archimedes, Johann Bernoulli and his son Daniel Bernoulli, Leonhard Euler, Claude-Louis Navier and George Stokes, who developed the fundamental equations to describe fluid mechanics. Advancements in experimentation and computational methods have further propelled the field, leading to practical applications in more specialized industries ranging from aerospace to environmental engineering. Fluid mechanics has also been important for the study of astronomical bodies and the dynamics of galaxies.
+
+== Antiquity ==
+
+=== Pre-history ===
+A pragmatic, if not scientific, knowledge of fluid flow was exhibited by ancient civilizations, such as in the design of arrows, spears, boats, and particularly hydraulic engineering projects for flood protection, irrigation, drainage, and water supply.  The earliest human civilizations began near the shores of rivers, and consequently coincided with the dawn of hydrology, hydraulics, and hydraulic engineering.
+
+=== Buoyancy ===
+Observations of specific gravity and buoyancy were recorded by ancient Chinese philosophers. In the 4th century BCE Mencius describes the weight of the gold is equivalent to the feathers. In 3rd century CE, Cao Chong describes the story of weighing  the elephant by observing displacement of the boats loaded with different weights.
+
+The fundamental principles of hydrostatics and dynamics were given by Archimedes in his work On Floating Bodies, around 250 BC.  In it, Archimedes develops the law of buoyancy, also known as Archimedes' principle.  This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.  Archimedes maintained that each particle of a fluid mass, when in equilibrium, is equally pressed in every direction; and he inquired into the conditions according to which a solid body floating in a fluid should assume and preserve a position of equilibrium.
+
+=== Greco-Roman engineering ===
+In the Greek school at Alexandria, which flourished under the auspices of the Ptolemies, attempts were made at the construction of hydraulic machinery, and about 120 BC the fountain of compression, the siphon, and the forcing-pump were invented by Ctesibius and Hero. The siphon is a simple instrument; but the forcing-pump is a complicated invention, which could scarcely have been expected in the infancy of hydraulics. It was probably suggested to Ctesibius by the Egyptian wheel or Noria, which was common at that time, and which was a kind of chain pump, consisting of a number of earthen pots carried round by a wheel. In some of these machines the pots have a valve in the bottom which enables them to descend without much resistance, and diminishes greatly the load upon the wheel; and, if we suppose that this valve was introduced so early as the time of Ctesibius, it is not difficult to perceive how such a machine might have led to the invention of the forcing-pump.
+Notwithstanding these inventions of the Alexandrian school, its attention does not seem to have been directed to the motion of fluids; and the first attempt to investigate this subject was made by Sextus Julius Frontinus, inspector of the public fountains at Rome in the reigns of Nerva and Trajan. In his work De aquaeductibus urbis Romae commentarius, he considers the methods which were at that time employed for ascertaining the quantity of water discharged from ajutages (tubes), and the mode of distributing the waters of an aqueduct or a fountain. He remarked that the flow of water from an orifice depends not only on the magnitude of the orifice itself, but also on the height of the water in the reservoir; and that a pipe employed to carry off a portion of water from an aqueduct should, as circumstances required, have a position more or less inclined to the original direction of the current. But as he was unacquainted with the law of the velocities of running water as depending upon the depth of the orifice, the want of precision which appears in his results is not surprising.
+
+== Middle Ages ==
+
+=== Islamicate physicists ===
+
+Islamicate scientists, particularly Abu Rayhan Biruni (973–1048) and later Al-Khazini (fl. 1115–1130), were the first to apply experimental scientific methods to fluid mechanics, especially in the field of fluid statics, such as for determining specific weights.  They applied the mathematical theories of ratios and infinitesimal techniques, and introduced algebraic and fine calculation techniques into the field of fluid statics. Al-Khazini, in The Book of the Balance of Wisdom (1121), invented a hydrostatic balance.
+During his experiments on fluid mechanics, Al-Biruni invented the conical measure.
+
+=== Islamicate engineers ===
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+title: "History of fluid mechanics"
+chunk: 2/7
+source: "https://en.wikipedia.org/wiki/History_of_fluid_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:18.315710+00:00"
+instance: "kb-cron"
+---
+
+In the 9th century, Banū Mūsā brothers' Book of Ingenious Devices described a number of early automatic controls in fluid mechanics. Two-step level controls for fluids, an early form of discontinuous variable structure controls, was developed by the Banu Musa brothers. They also described an early feedback controller for fluids. According to Donald Routledge Hill, the Banu Musa brothers were "masters in the exploitation of small variations" in hydrostatic pressures and in using conical valves as "in-line" components in flow systems, "the first known use of conical valves as automatic controllers". They also described the use of other valves, including a plug valve, float valve and tap. The Banu Musa also developed an early fail-safe system where "one can withdraw small quantities of liquid repeatedly, but if one withdraws a large quantity, no further extractions are possible". The double-concentric siphon and the funnel with bent end for pouring in different liquids, neither of which appear in any earlier Greek works, were also original inventions by the Banu Musa brothers. Some of the other mechanisms they described include a float chamber and an early differential pressure.
+In 1206, Al-Jazari's Book of Knowledge of Ingenious Mechanical Devices described many hydraulic machines. Of particular importance were his water-raising pumps. The first known use of a crankshaft in a chain pump was in one of al-Jazari's saqiya machines. The concept of minimizing intermittent working is also first implied in one of al-Jazari's saqiya chain pumps, which was for the purpose of maximising the efficiency of the saqiya chain pump. Al-Jazari also invented a twin-cylinder reciprocating piston suction pump, which included the first suction pipes, suction pumping, double-action pumping, and made early uses of valves and a crankshaft-connecting rod mechanism. This pump is remarkable for three reasons: the first known use of a true suction pipe (which sucks fluids into a partial vacuum) in a pump, the first application of the double-acting principle, and the conversion of rotary to reciprocating motion, via the crankshaft-connecting rod mechanism.
+
+== Sixteenth century ==
+During the Renaissance, Leonardo da Vinci was well known for his experimental skills. His notes provide precise depictions of various phenomena, including vessels, jets, hydraulic jumps, eddy formation, tides, as well as designs for both low drag (streamlined) and high drag (parachute) configurations. Da Vinci is also credited for formulating the conservation of mass in one-dimensional steady flow.
+In 1586, the Flemish engineer and mathematician Simon Stevin published De Beghinselen des Waterwichts (Principles on the Weight of Water), a study of hydrostatics that, among other things, extensively discussed the hydrostatic paradox.
+
+== Seventeenth century ==
+
+=== Castelli and Torricelli ===
+Benedetto Castelli, and Evangelista Torricelli, two of the disciples of Galileo Galilei, applied the discoveries of their master to the science of hydrodynamics. In 1628 Castelli published a small work, Della misura dell' acque correnti, in which he satisfactorily explained several phenomena in the motion of fluids in rivers and canals; but he committed a great paralogism in supposing the velocity of the water proportional to the depth of the orifice below the surface of the vessel. Torricelli, observing that in a jet where the water rushed through a small ajutage it rose to nearly the same height with the reservoir from which it was supplied, imagined that it ought to move with the same velocity as if it had fallen through that height by the force of gravity, and hence he deduced the proposition that the velocities of liquids are as the square root of the head, apart from the resistance of the air and the friction of the orifice. Torricelli's law was published in 1643, at the end of his treatise De motu gravium projectorum, and it was confirmed by the experiments of Raffaello Magiotti on the quantities of water discharged from different ajutages under different pressures (1648).
+
+=== Blaise Pascal ===
+In the hands of Blaise Pascal hydrostatics assumed the dignity of a science, and in a treatise on the equilibrium of liquids (Sur l'équilibre des liqueurs), found among his manuscripts after his death and published in 1663, the laws of the equilibrium of liquids were demonstrated in the most simple manner, and amply confirmed by experiments.
+
+=== Mariotte and Guglielmini ===
+The theorem of Torricelli was employed by many succeeding writers, but particularly by Edme Mariotte (1620–1684), whose Traité du mouvement des eaux, published after his death in the year 1686, is founded on a great variety of well-conducted experiments on the motion of fluids, performed at Versailles and Chantilly. In the discussion of some points he committed considerable mistakes. Others he treated very superficially, and in none of his experiments apparently did he attend to the diminution of efflux arising from the contraction of the liquid vein, when the orifice is merely a perforation in a thin plate; but he appears to have been the first who attempted to ascribe the discrepancy between theory and experiment to the retardation of the water's velocity through friction. His contemporary Domenico Guglielmini (1655–1710), who was inspector of the rivers and canals at Bologna, had ascribed this diminution of velocity in rivers to transverse motions arising from inequalities in their bottom. But as Mariotte observed similar obstructions even in glass pipes where no transverse currents could exist, the cause assigned by Guglielmini seemed destitute of foundation. The French philosopher, therefore, regarded these obstructions as the effects of friction. He supposed that the filaments of water which graze along the sides of the pipe lose a portion of their velocity; that the contiguous filaments, having on this account a greater velocity, rub upon the former, and suffer a diminution of their celerity; and that the other filaments are affected with similar retardations proportional to their distance from the axis of the pipe. In this way the medium velocity of the current may be diminished, and consequently the quantity of water discharged in a given time must, from the effects of friction, be considerably less than that which is computed from theory.
+
+== Eighteenth century ==
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+title: "History of fluid mechanics"
+chunk: 3/7
+source: "https://en.wikipedia.org/wiki/History_of_fluid_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:18.315710+00:00"
+instance: "kb-cron"
+---
+
+=== Studies by Isaac Newton ===
+
+==== Friction and viscosity ====
+The effects of friction and viscosity in diminishing the velocity of running water were noticed in the Principia of Sir Isaac Newton, who threw much light upon several branches of hydromechanics. At a time when the Cartesian system of vortices universally prevailed, he found it necessary to investigate that hypothesis, and in the course of his investigations he showed that the velocity of any stratum of the vortex is an arithmetical mean between the velocities of the strata which enclose it; and from this it evidently follows that the velocity of a filament of water moving in a pipe is an arithmetical mean between the velocities of the filaments which surround it. Taking advantage of these results,  French engineer Henri Pitot afterwards showed that the retardations arising from friction are inversely as the diameters of the pipes in which the fluid moves.
+
+==== Orifices ====
+The attention of Newton was also directed to the discharge of water from orifices in the bottom of vessels. He supposed a cylindrical vessel full of water to be perforated in its bottom with a small hole by which the water escaped, and the vessel to be supplied with water in such a manner that it always remained full at the same height. He then supposed this cylindrical column of water to be divided into two parts – the first, which he called the "cataract", being an hyperboloid generated by the revolution of an hyperbola of the fifth degree around the axis of the cylinder which should pass through the orifice, and the second the remainder of the water in the cylindrical vessel. He considered the horizontal strata of this hyperboloid as always in motion, while the remainder of the water was in a state of rest, and imagined that there was a kind of cataract in the middle of the fluid.
+When the results of this theory were compared with the quantity of water actually discharged, Newton concluded that the velocity with which the water issued from the orifice was equal to that which a falling body would receive by descending through half the height of water in the reservoir. This conclusion, however, is absolutely irreconcilable with the known fact that jets of water rise nearly to the same height as their reservoirs, and Newton seems to have been aware of this objection. Accordingly, in the second edition of his Principia, which appeared in 1713, he reconsidered his theory. He had discovered a contraction in the vein of fluid (vena contracta) which issued from the orifice, and found that, at the distance of about a diameter of the aperture, the section of the vein was contracted in the subduplicate ratio of two to one. He regarded, therefore, the section of the contracted vein as the true orifice from which the discharge of water ought to be deduced, and the velocity of the effluent water as due to the whole height of water in the reservoir; and by this means his theory became more conformable to the results of experience, though still open to serious objections.
+
+==== Waves ====
+Newton was also the first to investigate the difficult subject of the motion of waves.
+
+=== Bernoulli's principle ===
+
+In 1738 Daniel Bernoulli published his book Hydrodynamica. His theory of the motion of fluids, the germ of which was first published in his memoir entitled Theoria nova de motu aquarum per canales quocunque fluentes, communicated to the academy of St Petersburg as early as 1726, was founded on two suppositions, which appeared to him conformable to experience. He supposed that the surface of the fluid, contained in a vessel which is emptying itself by an orifice, remains always horizontal; and, if the fluid mass is conceived to be divided into an infinite number of horizontal strata of the same bulk, that these strata remain contiguous to each other, and that all their points descend vertically, with velocities inversely proportional to their breadth, or to the horizontal sections of the reservoir. In order to determine the motion of each stratum, he employed the principle of the conservatio virium vivarum, and obtained very elegant solutions. But in the absence of a general demonstration of that principle, his results did not command the confidence which they would otherwise have deserved, and it became desirable to have a theory more certain, and depending solely on the fundamental laws of mechanics. Colin Maclaurin and John Bernoulli, who were of this opinion, resolved the problem by more direct methods, the one in his Fluxions, published in 1742, and the other in his Hydraulica nunc primum detecta, et demonstrata directe ex fundamentis pure mechanicis, which forms the fourth volume of his works. The method employed by Maclaurin has been thought not sufficiently rigorous; and that of John Bernoulli is, in the opinion of Joseph-Louis Lagrange, defective in clearness and precision.
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+---
+title: "History of fluid mechanics"
+chunk: 4/7
+source: "https://en.wikipedia.org/wiki/History_of_fluid_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:18.315710+00:00"
+instance: "kb-cron"
+---
+
+=== Jean le Rond d'Alembert ===
+The theory of Daniel Bernoulli was opposed also by Jean le Rond d'Alembert. When generalizing the theory of pendulums of Jacob Bernoulli he discovered a principle of dynamics so simple and general that it reduced the laws of the motions of bodies to that of their equilibrium. He applied this principle to the motion of fluids, and gave a specimen of its application at the end of his Dynamics in 1743. It was more fully developed in his Traité des fluides, published in 1744, in which he gave simple and elegant solutions of problems relating to the equilibrium and motion of fluids. He made use of the same suppositions as Daniel Bernoulli, though his calculus was established in a very different manner. He considered, at every instant, the actual motion of a stratum as composed of a motion which it had in the preceding instant and of a motion which it had lost; and the laws of equilibrium between the motions lost furnished him with equations representing the motion of the fluid. It remained a desideratum to express by equations the motion of a particle of the fluid in any assigned direction. These equations were found by d'Alembert from two principles – that a rectangular canal, taken in a mass of fluid in equilibrium, is itself in equilibrium, and that a portion of the fluid, in passing from one place to another, preserves the same volume when the fluid is incompressible, or dilates itself according to a given law when the fluid is elastic. His ingenious method, published in 1752, in his Essai sur la résistance des fluides, was brought to perfection in his Opuscules mathématiques, and was adopted by Leonhard Euler.
+
+=== Ideal fluid equations ===
+
+The resolution of the questions concerning the motion of fluids was effected by means of Leonhard Euler's equations of fluid dynamics for ideal fluids. Differential equations were first applied to the motion of water by d'Alembert, and enabled both him and Euler to represent the theory of fluids in formulae restricted by no particular hypothesis.
+
+=== Early works on fluid resistance ===
+One of the most successful labourers in the science of hydrodynamics at this period was Pierre-Louis-Georges du Buat. Following in the steps of the Abbé Charles Bossut (Nouvelles Experiences sur la résistance des fluides, 1777), he published, in 1786, a revised edition of his Principes d'hydraulique, which contains a satisfactory theory of the motion of fluids, founded solely upon experiments. Dubuat considered that if water were a perfect fluid, and the channels in which it flowed infinitely smooth, its motion would be continually accelerated, like that of bodies descending in an inclined plane. But as the motion of rivers is not continually accelerated, and soon arrives at a state of uniformity, it is evident that the viscosity of the water, and the friction of the channel in which it descends, must equal the accelerating force. Dubuat, therefore, assumed it as a proposition of fundamental importance that, when water flows in any channel or bed, the accelerating force which obliges it to move is equal to the sum of all the resistances which it meets with, whether they arise from its own viscosity or from the friction of its bed. This principle was employed by him in the first edition of his work, which appeared in 1779. The theory contained in that edition was founded on the experiments of others, but he soon saw that a theory so new, and leading to results so different from the ordinary theory, should be founded on new experiments more direct than the former, and he was employed in the performance of these from 1780 to 1783. The experiments of Bossut were made only on pipes of a moderate declivity, but Dubuat used declivities of every kind, and made his experiments upon channels of various sizes.
+
+== Nineteenth century ==
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+title: "History of fluid mechanics"
+chunk: 5/7
+source: "https://en.wikipedia.org/wiki/History_of_fluid_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:18.315710+00:00"
+instance: "kb-cron"
+---
+
+=== Navier–Stokes equations and viscous flow ===
+In 1808, the French Academie des Sciences posed a prize for whoever could explain Ernst Chladni's experiment of vibrating plates. In 1820, Claude-Louis Navier proposed a Lagrangian approach of the problem. Although he did not win the prize, Navier continued his work in elasticity and in 1821, he derived results which were valid for more general elastic bodies. He then began work on generalizing these equations to hydrodynamics.
+The first derivations of the Navier-Stokes equation appeared in two memoirs by Navier as a result of this work, Sur les lois des mouvements des fluides, en ayant égard à l'adhésion des molecules in 1822, and Sur Les Lois du Mouvement des Fluides in 1823. Previous to these publications, most equations of fluid flow had been formulated in terms of perfect, frictionless fluids. However, in his memoir, Navier introduced friction into the equations of motion of fluids. As a result, Navier is credited with developing the equation of motion for viscous flows.
+Navier's original proof was not widely influential, and was re-derived again by Augustin-Louis Cauchy in 1823, by Siméon Denis Poisson in 1829, by Adhémar Barré de Saint-Venant in 1837, and by George Stokes in 1845, with methodological differences, such as which molecular assumptions to use.
+Stokes' 1845 proof, published after Navier's death, was particularly influential because he extended Navier's equations to address different behaviors of fluids under boundary conditions. He explicitly addressed the behavior of incompressible fluids, which are fluids that do not change volume under pressure. He also addressed creeping flow (also called 'Stokes flow'), where very slow velocities allow for the equations to simplify and result in analytical solutions. These simplified equations are now called the Stokes equations. Stokes also rederived the Hagen–Poiseuille equation, that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe, discovered previously by Jean Léonard Marie Poiseuille and independently by Gotthilf Hagen in 1838.
+The final result of these physicists' work was the Navier–Stokes equations, a set of partial differential equations that describe how the velocity, pressure, temperature, and density of a moving fluid are related.
+In honor of Stokes' many contributions to fluid mechanics, the unit for kinematic viscosity is called a stoke in his honor.
+
+=== Reynolds number and turbulence ===
+The concept of a number to quantify turbulence was introduced by Stokes in 1851, and its use was popularized by Osborne Reynolds in 1883. Arnold Sommerfeld later christened this number the Reynolds number.
+
+=== Vortex dynamics ===
+
+In 1858 Hermann von Helmholtz published his seminal paper "Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen," in Journal für die reine und angewandte Mathematik, vol. 55, pp. 25–55. So important was the paper that a few years later P. G. Tait published an English translation, "On integrals of the hydrodynamical equations which express vortex motion", in Philosophical Magazine, vol. 33, pp. 485–512 (1867). In his paper Helmholtz established his three "laws of vortex motion" in much the same way one finds them in any advanced textbook of fluid mechanics today. This work established the significance of vorticity to fluid mechanics and science in general.
+For the next century or so vortex dynamics matured as a subfield of fluid mechanics, always commanding at least a major chapter in treatises on the subject. Thus, Horace Lamb's well known Hydrodynamics (6th ed., 1932) devotes a full chapter to vorticity and vortex dynamics as does G. K. Batchelor's Introduction to Fluid Dynamics (1967). In due course entire treatises were devoted to vortex motion. Henri Poincaré's Théorie des Tourbillons (1893), Henri Villat's Leçons sur la Théorie des Tourbillons (1930), Clifford Truesdell's The Kinematics of Vorticity (1954), and Philip Saffman's Vortex Dynamics (1992) may be mentioned. Early on individual sessions at scientific conferences were devoted to vortices, vortex motion, vortex dynamics and vortex flows. Later, entire meetings were devoted to the subject.
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+---
+title: "History of fluid mechanics"
+chunk: 6/7
+source: "https://en.wikipedia.org/wiki/History_of_fluid_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:18.315710+00:00"
+instance: "kb-cron"
+---
+
+=== 19th century hydraulics ===
+The theory of running water was greatly advanced by the researches of Gaspard Riche de Prony (1755–1839). From a collection of the best experiments by previous workers he selected eighty-two (fifty-one on the velocity of water in conduit pipes, and thirty-one on its velocity in open canals); and, discussing these on physical and mechanical principles, he succeeded in drawing up general formulae, which afforded a simple expression for the velocity of running water.
+J. A. Eytelwein of Berlin, who published in 1801 a valuable compendium of hydraulics entitled Handbuch der Mechanik und der Hydraulik, investigated the subject of the discharge of water by compound pipes, the motions of jets and their impulses against plane and oblique surfaces; and he showed theoretically that a water-wheel will have its maximum effect when its circumference moves with half the velocity of the stream.
+Jean Nicolas Pierre Hachette in 1816–1817 published memoirs containing the results of experiments on the spouting of fluids and the discharge of vessels. His object was to measure the contracted part of a fluid vein, to examine the phenomena attendant on additional tubes, and to investigate the form of the fluid vein and the results obtained when different forms of orifices are employed. Extensive experiments on the discharge of water from orifices (Expériences hydrauliques, Paris, 1832) were conducted under the direction of the French government by J. V. Poncelet (1788–1867) and J. A. Lesbros (1790–1860).
+Pierre Prosper Boileau (1811–1891) discussed their results and added experiments of his own (Traité de la mesure des eaux courantes, Paris, 1854). K. R. Bornemann re-examined all these results with great care, and gave formulae expressing the variation of the coefficients of discharge in different conditions (Civil Ingénieur, 1880). Julius Weisbach (1806–1871) also made many experimental investigations on the discharge of fluids.
+The experiments of J. B. Francis (Lowell Hydraulic Experiments, Boston, Mass., 1855) led him to propose variations in the accepted formulae for the discharge over weirs, and a generation later a very complete investigation of this subject was carried out by Henri-Émile Bazin. An elaborate inquiry on the flow of water in pipes and channels was conducted by Henry G. P. Darcy (1803–1858) and continued by Bazin, at the expense of the French government (Recherches hydrauliques, Paris, 1866).
+German engineers have also devoted special attention to the measurement of the flow in rivers; the Beiträge zur Hydrographie des Königreiches Böhmen (Prague, 1872–1875) of Andreas Rudolf Harlacher contained valuable measurements of this kind, together with a comparison of the experimental results with the formulae of flow that had been proposed up to the date of its publication, and important data were yielded by the gaugings of the Mississippi made for the United States government by Andrew Atkinson Humphreys and Henry Larcom Abbot, by Robert Gordon's gaugings of the Irrawaddy River, and by Allen J. C. Cunningham's experiments on the Ganges canal. The friction of water, investigated for slow speeds by Charles-Augustin de Coulomb, was measured for higher speeds by William Froude (1810–1879), whose work is of great value in the theory of ship resistance (Brit. Assoc. Report., 1869), and stream line motion was studied by Reynolds and by Henry Selby Hele-Shaw.
+
+== Twentieth century ==
+
+=== Boundary layer ===
+In 1904, German scientist Ludwig Prandtl pioneered boundary layer theory. He pointed out that fluids with small viscosity can be divided into a thin viscous layer, known as the boundary layer, near solid surfaces and interfaces, and an outer layer where Bernoulli's principle and Euler equations apply.
+
+=== Developments in vorticity and turbulence ===
+From 1894-1910, vortex dynamics achieved more attention and development as a result of the concurrently developing field of aerodynamics. The Kutta-Joucowski theorem, for example, developed from 1902-1906, is a fundamental result in aerodynamics that was proved by considering the fluid flow in the presence of the airfoil as the superposition of a translational flow and a rotating flow. The rotating flow is solved using vortex dynamics by considering it as being induced by a line vortex. Much of the wing-flow problem in aerodynamics was solved in a similar fashion, by taking advantage of vortex dynamics.
+As high-speed flight necessitated further developments, the problem of turbulence began to gain increasing relevance in the mid-twentieth century. A detailed theory of turbulence was published in 1941 by Andrey Kolmogorov. Turbulent flow describes unpredictable or chaotic changes in pressure and flow velocity.  In turbulent flow, unsteady vortices interact with each other and increase drag and friction as a result.
+Vorticity and vortex lines have been used to understand how turbulent fluids behave. In the twentieth century, the discovery of turbulent coherent structures allowed for the development of theories of vortex dynamics in turbulence. These turbulent coherent structures are regions of concentrated vorticity that are organized and persist for a long time. In modern fluid mechanics the role of vortex dynamics in explaining flow phenomena is firmly established. Well known vortices have acquired names and are regularly depicted in the popular media: hurricanes, tornadoes, waterspouts, aircraft trailing vortices (e.g., wingtip vortices), drainhole vortices (including the bathtub vortex), smoke rings, underwater bubble air rings, cavitation vortices behind ship propellers, and so on. In the technical literature a number of vortices that arise under special conditions also have names: the Kármán vortex street wake behind a bluff body, Taylor vortices between rotating cylinders, Görtler vortices in flow along a curved wall, etc.
+The behavior of turbulent flow remains an unsolved problem in fluid mechanics. Methods to address turbulence include direct numerical simulation and large eddy simulation.
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+---
+title: "History of fluid mechanics"
+chunk: 7/7
+source: "https://en.wikipedia.org/wiki/History_of_fluid_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:18.315710+00:00"
+instance: "kb-cron"
+---
+
+=== Microfluidics ===
+Beginning in the 1950s, advances in semiconductor device fabrication enabled the creation of engraving micro-patterns, sparking interest in miniaturizing sensors, and integrating them with microcomputers to develop portable platforms for scientific research. Stephen C. Terry from Standford University miniaturized gas chromatograph on a silicon wafer in the 1979, considered one of the first lab-on-a-chip. Building on this, Swiss chemist Andreas Manz introduced in 1990 the concept of the miniaturized total analysis system (μTAS), capable of performing complete analyses on a microfluidic chip.  The 1990s saw rapid progress through soft lithography techniques pioneered by George M. Whitesides, which enabled inexpensive devices fabricated in polymers such as polydimethylsiloxane (PDMS). By the end of the decade, microfluidics was firmly established with applications in capillary electrophoresis, genetic testing, droplet-based microfluidics, polymerase chain reaction (PCR) tests and other technologies of the 21st century.
+
+== Twenty-first century ==
+
+=== Millennium Prize Problem ===
+
+In 2000, the Clay Mathematics Institute put forth the Millennium Prize Problems, which are seven unsolved mathematical problems which are deemed to be the most difficult and illusive. One of which is the fluid mechanics problem of Navier–Stokes existence and smoothness, which deals with the mathematical properties of the Navier-Stokes equations. The statement of the problem, as proposed by Charles Fefferman, goes as follows: Prove or give a counter-example of the following statement:
+In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.The prize sparked interest in the problem. In 2016, mathematician Terrence Tao published "Finite time blowup for an averaged three-dimensional Navier–Stokes equation", where he invents an "averaged" version of the equations and shows that it exhibits breakdown. He suggests a program for constructing a blowup solution to the true Navier-Stokes equations. In September 2025, Google DeepMind announced it had used machine learning techniques to uncover "the first systematic discovery of new families of unstable singularities" in the equations of fluid flow.
+
+== See also ==
+Timeline of fluid and continuum mechanics
+
+== Further reading ==
+J. D. Anderson Jr. (1997).  A History of Aerodynamics (Cambridge University Press).  ISBN 0-521-45435-2
+J. D. Anderson Jr. (1998).  Some Reflections on the History of Fluid Dynamics, in The Handbook of Fluid Dynamics (ed. by R.W. Johnson, CRC Press) Ch. 2.
+D. Bloor (2012).  The Enigma of the Aerofoil: Rival Theories in Aerodynamics, 1909-1930 (University of Chicago Press).
+J. S. Calero (2008).  The Genesis of Fluid Mechanics, 1640–1780 (Springer).  ISBN 978-1-4020-6414-2
+A. F. Chalmers (2017). One Hundred Years of Pressure: Hydrostatics from Stevin to Newton (Springer).
+O. Darrigol  (2005).  Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl (Oxford University Press).  ISBN 0-19-856843-6
+P. A. Davidson, Y. Kaneda, K. Moffatt, and K. R. Sreenivasan (eds, 2011).  A Voyage Through Turbulence (Cambridge University Press).  ISBN 978-0-521-19868-4
+M. Eckert (2006).  The Dawn of Fluid Dynamics: A Discipline Between Science and Technology (Wiley-VCH).  ISBN 978-3-527-40513-8
+G. Garbrecht (ed., 1987).  Hydraulics and Hydraulic Research: A Historical Review (A.A. Balkema).  ISBN 90-6191-621-6
+M. J. Lighthill (1995).  Fluid mechanics, in Twentieth Century Physics ed. by L.M. Brown, A. Pais, and B. Pippard (IOP/AIP), Vol. 2, pp. 795–912.
+C. Maffioli (1994). Out of Galileo: The Science of Waters, 1628-1718 (Erasmus).
+H. Rouse and S. Ince (1957).  History of Hydraulics (Iowa Institute of Hydraulic Research, State University of Iowa).
+G. A. Tokaty (1994).  A History and Philosophy of Fluid Mechanics (Dover).  ISBN 0-486-68103-3
+
+== References ==
+
+Rashed, Roshdi; Morelon, Régis, eds. (1996). Encyclopedia of the History of Arabic Science.
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+---
+title: "History of general relativity"
+chunk: 1/5
+source: "https://en.wikipedia.org/wiki/History_of_general_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:09.244516+00:00"
+instance: "kb-cron"
+---
+
+General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.
+Before the advent of general relativity, Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses, even though Newton himself did not regard the theory as the final word on the nature of gravity. Within a century of Newton's formulation, careful astronomical observation revealed unexplainable differences between the theory and the observations.  Under Newton's model, gravity was the result of an attractive force between massive objects. Although even Newton was bothered by the unknown nature of that force, the basic framework was extremely successful at describing motion.
+However, experiments and observations show that Einstein's description accounts for several effects that are unexplained by Newton's law, such as minute anomalies in the orbits of Mercury and other planets. General relativity also predicts novel effects of gravity, such as gravitational waves, gravitational lensing and an effect of gravity on time known as gravitational time dilation. Many of these predictions have been confirmed by experiment or observation, while others are the subject of ongoing research.
+General relativity has developed into an essential tool in modern astrophysics. It provides the foundation for the current understanding of black holes, regions of space where gravitational attraction is so strong that not even light can escape. Their strong gravity is thought to be responsible for the intense radiation emitted by certain types of astronomical objects (such as active galactic nuclei or microquasars). General relativity is also part of the framework of the standard Big Bang model of cosmology.
+
+== Creation of general relativity ==
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+---
+title: "History of general relativity"
+chunk: 2/5
+source: "https://en.wikipedia.org/wiki/History_of_general_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:09.244516+00:00"
+instance: "kb-cron"
+---
+
+=== Early investigations ===
+The first relativistic theory of gravity was proposed by Henri Poincaré in 1905. He published a Lorentz invariant theory on four-dimensional spacetime, where gravity is transmitted by gravitational waves that travel at the speed of light.
+As Einstein later said, the reason for the development of general relativity was the preference of inertial motion within special relativity, while a theory which from the outset prefers no particular state of motion appeared more satisfactory to him. So, while still working at the patent office in 1907, Einstein had what he would call his "happiest thought". He realized that the principle of relativity could be extended to gravitational fields.
+Consequently, in 1907 he wrote an article, published in 1908, on acceleration under special relativity.
+In that article, he argued that free fall is really inertial motion, and that for a freefalling observer the rules of special relativity must apply. This argument is called the equivalence principle. In the same article, Einstein also predicted the phenomenon of gravitational time dilation.
+In 1911, Einstein published another article expanding on the 1907 article.
+There, he considered the case of a uniformly accelerated box not in a gravitational field, and noted that it would be indistinguishable from a box sitting still in an unchanging gravitational field. He used special relativity to show that clocks at the top of a box accelerating upward would run faster than clocks at the bottom. He concluded that the rate at which time passes depends on the position in a gravitational field, and that the difference in rate is proportional to the gravitational potential to a first approximation.
+The article also predicted the deflection of light by massive bodies, such as Jupiter or the Sun. Although the approximation was crude, it allowed him to calculate that the deflection is nonzero. Einstein urged astronomers to attempt direct observation of light deflection of fixed stars near the Sun during solar eclipses when they would be visible. German astronomer Erwin Finlay-Freundlich publicized Einstein's challenge to scientists around the world.
+In October 1911, Freundlich contacted astronomer Charles D. Perrine in Berlin to inquire as to the suitability of examining existing solar eclipse photographs to prove Einstein's prediction of light deflection. Perrine, the director of the Argentine National Observatory at Cordoba, had participated in four solar eclipse expeditions while at the Lick Observatory, in 1900, 1901, 1905, and 1908. "...he had become, in the opinion of the director of the Lick Observatory, W. W. Campbell, an observer without peer in the field of solar eclipses." He did not believe existing eclipse photos would be useful in proving Einstein's claim. In 1912 Freundlich asked if Perrine would include observation of light deflection as part of his program for the solar eclipse of October 10, 1912, in Brazil. W. W. Campbell, director of the Lick Observatory, loaned Perrine a long-focus, narrow-field camera lense, called an intramercurial lense. Perrine and the Cordoba team were the only eclipse expedition to construct specialized equipment dedicated to observing light deflection. However, all the expeditions experienced heavy rain which prevented any observations. Nevertheless, Perrine was the first astronomer to make a dedicated attempt to observe light deflection to test Einstein's prediction.
+Two years later, the three observatory directors, Perrine, Freundlich, and Campbell included light deflection in their expeditions to the Russian Empire for the solar eclipse of August 21, 1914. However, due to clouds and the outbreak of World War I, no results were possible. However, Perrine was able to take the first photographs in an attempt to verify Einstein's prediction of light deflection. A light cloud cover prevented determining accurate star positions.
+In hindsight, the occluding weather and lack of results in 1912 and 1914 favored Einstein. If clear photographs and measurable results had been possible, Einstein's 1911 prediction might have been proven wrong. The amount of deflection that he calculated in 1911 was too small (0.83 seconds of arc) by a factor of two because the approximation he used does not work well for things moving at near the speed of light. When Einstein completed the full theory of general relativity in 1915, he rectified this error and predicted the correct amount of light deflection caused by the Sun (1.75 seconds of arc). Eddington and Dyson in 1919 and W. W. Campbell in 1922 were able to compare their results to Einstein's corrected prediction.
+Another of Einstein's notable thought experiments about the nature of the gravitational field is that of a rotating disk (a variant of the Ehrenfest paradox). He imagined an observer performing experiments on a rotating turntable. He noted that such an observer would find the ratio of the circumference of a circle to its radius greater than 
+  
+    
+      
+        2
+        π
+      
+    
+    {\displaystyle 2\pi }
+  
+ expected from Euclidean geometry. The reason is that the radius of a circle would be measured with an uncontracted ruler, but, according to special relativity, the circumference would seem to be longer because the ruler would be contracted. Since Einstein believed that the laws of physics were local, described by local fields, he concluded from this that spacetime could be locally curved. This led him to study Riemannian geometry, and to formulate general relativity in this language.
+
+=== Developing general relativity ===
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+---
+title: "History of general relativity"
+chunk: 3/5
+source: "https://en.wikipedia.org/wiki/History_of_general_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:09.244516+00:00"
+instance: "kb-cron"
+---
+
+In 1912, Einstein returned to Switzerland to accept a professorship at his alma mater, ETH Zurich. Once back in Zurich, he immediately visited his old ETH classmate Marcel Grossmann, now a professor of mathematics, who introduced him to Riemannian geometry and, more generally, to differential geometry. On the recommendation of Italian mathematician Tullio Levi-Civita, Einstein began exploring the usefulness of general covariance (essentially the use of tensors) for his gravitational theory. For a while, Einstein thought that there were problems with the approach, but he later returned to it and, by late 1915, had published his general theory of relativity in the form in which it is used today. This theory explains gravitation as the distortion of the structure of spacetime by matter, affecting the inertial motion of other matter.
+During World War I, the work of Central Powers scientists was available only to Central Powers academics, for national security reasons. Some of Einstein's work did reach the United Kingdom and the United States through the efforts of the Austrian Paul Ehrenfest and physicists in the Netherlands, especially 1902 Nobel Prize-winner Hendrik Lorentz and Willem de Sitter of Leiden University. After the war, Einstein maintained his relationship with Leiden University, accepting a contract as an Extraordinary Professor; for ten years, from 1920 to 1930, he travelled to the Netherlands regularly to lecture.
+In 1917, several astronomers accepted Einstein's 1911 challenge from Prague. The Mount Wilson Observatory in California, United States, published a solar spectroscopic analysis that showed no gravitational redshift. In 1918, the Lick Observatory, also in California, announced that it too had disproved Einstein's prediction, although its findings were not published.
+However, in May 1919, a team led by the British astronomer Arthur Stanley Eddington claimed to have confirmed Einstein's prediction of gravitational deflection of starlight by the sun while photographing a solar eclipse with dual expeditions in Sobral, northern Brazil, and Príncipe, a west African island. Nobel laureate Max Born praised general relativity as the "greatest feat of human thinking about nature"; fellow laureate Paul Dirac was quoted saying it was "probably the greatest scientific discovery ever made".
+There have been claims that scrutiny of the specific photographs taken on the Eddington expedition showed the experimental uncertainty to be comparable to the magnitude of the effect Eddington claimed to have demonstrated, and that a 1962 British expedition concluded that the method was inherently unreliable. The deflection of light during a solar eclipse was confirmed by later, more accurate observations. Some resented the newcomer's fame, notably some nationalistic German physicists, who later started the Deutsche Physik (German Physics) movement.
+
+=== General covariance and the hole argument ===
+By 1912, Einstein was actively seeking a theory in which gravitation was explained as a geometric phenomenon. At the urging of Tullio Levi-Civita, Einstein began by exploring the use of general covariance (which is essentially the use of curvature tensors) to create a gravitational theory.  However, in 1913 Einstein abandoned that approach, arguing that it is inconsistent based on the "hole argument".  In 1914 and much of 1915, Einstein was trying to create field equations based on another approach.  When that approach was proven to be inconsistent, Einstein revisited the concept of general covariance and discovered that the hole argument was flawed.
+
+=== The development of the Einstein field equations ===
+
+When Einstein realized that general covariance was tenable, he quickly completed the development of the field equations that are named after him. However, he made a now-famous mistake. The field equations he published in October 1915 were
+
+  
+    
+      
+        
+          R
+          
+            μ
+            ν
+          
+        
+        =
+        κ
+        
+          T
+          
+            μ
+            ν
+          
+        
+        
+      
+    
+    {\displaystyle R_{\mu \nu }=\kappa T_{\mu \nu }\,}
+  
+
+where 
+  
+    
+      
+        
+          R
+          
+            μ
+            ν
+          
+        
+      
+    
+    {\displaystyle R_{\mu \nu }}
+  
+ is the Ricci tensor, 
+  
+    
+      
+        
+          T
+          
+            μ
+            ν
+          
+        
+      
+    
+    {\displaystyle T_{\mu \nu }}
+  
+ the energy–momentum tensor and 
+  
+    
+      
+        κ
+      
+    
+    {\displaystyle \kappa }
+  
+ is Einstein gravitational constant. This predicted the non-Newtonian perihelion precession of Mercury, and so had Einstein very excited.  However, it was soon realized that they were inconsistent with the local conservation of energy–momentum unless the universe had a constant density of mass–energy–momentum.  In other words, air, rock and even a vacuum should all have the same density.  This inconsistency with observation sent Einstein back to the drawing board and, on 25 November 1915, Einstein presented the updated Einstein field equations to the Prussian Academy of Sciences:
+
+  
+    
+      
+        
+          R
+          
+            μ
+            ν
+          
+        
+        −
+        
+          
+            
+              1
+              2
+            
+          
+        
+        R
+        
+          g
+          
+            μ
+            ν
+          
+        
+        =
+        κ
+        
+          T
+          
+            μ
+            ν
+          
+        
+      
+    
+    {\displaystyle R_{\mu \nu }-{\tfrac {1}{2}}Rg_{\mu \nu }=\kappa T_{\mu \nu }}
+  
+,
+where 
+  
+    
+      
+        R
+      
+    
+    {\displaystyle R}
+  
+ is the Ricci scalar and 
+  
+    
+      
+        
+          g
+          
+            μ
+            ν
+          
+        
+      
+    
+    {\displaystyle g_{\mu \nu }}
+  
+ the metric tensor. With the publication of the field equations, the issue became one of solving them for various cases and interpreting the solutions.  This and experimental verification have dominated general relativity research ever since.
+
+=== Einstein and Hilbert ===
+
+In the last year of Einstein's work on general relativity he met with and corresponded with the German mathematician David Hilbert. Hilbert had been working on a unified field theory based on the ideas of Gustav Mie; he derived the theory of general relativity from an elegant variational principle almost simultaneously with Einstein's discovery of the theory. The timing of the correspondence and publications has led to a number of in depth historical analyses.
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+---
+title: "History of general relativity"
+chunk: 4/5
+source: "https://en.wikipedia.org/wiki/History_of_general_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:09.244516+00:00"
+instance: "kb-cron"
+---
+
+=== Sir Arthur Eddington ===
+In the early years after Einstein's theory was published, Sir Arthur Eddington lent his considerable prestige in the British scientific establishment in an effort to champion the work of this German scientist.  Because the theory was so complex and abstruse (even today it is popularly considered the pinnacle of scientific thinking; in the early years it was even more so), it was rumored that only three people in the world understood it.  There was an illuminating, though probably apocryphal, anecdote about this.  As related by Ludwik Silberstein, during one of Eddington's lectures he asked "Professor Eddington, you must be one of three persons in the world who understands  general relativity."  Eddington paused, unable to answer. Silberstein continued "Don't be modest, Eddington!" Finally, Eddington replied "On the contrary, I'm trying to think who the third person is."
+
+== Solutions ==
+
+=== The Schwarzschild solution ===
+Since the field equations are non-linear, Einstein assumed that they were unsolvable.  However, Karl Schwarzschild discovered in 1915 and published in 1916 an exact solution for the case of a spherically symmetric spacetime surrounding a massive object in spherical coordinates. This is now known as the Schwarzschild solution. Since then, many other exact solutions have been found.
+
+=== The expanding universe and the cosmological constant ===
+
+In 1922, Alexander Friedmann found a solution in which the universe may expand or contract, and later Georges Lemaître derived a solution for an expanding universe.  However, Einstein believed that the universe was static, and since a static cosmology was not supported by the general relativistic field equations, he added a cosmological constant 
+  
+    
+      
+        Λ
+      
+    
+    {\displaystyle \Lambda }
+  
+ to the field equations, which became:
+
+  
+    
+      
+        
+          R
+          
+            μ
+            ν
+          
+        
+        −
+        
+          
+            
+              1
+              2
+            
+          
+        
+        R
+        
+          g
+          
+            μ
+            ν
+          
+        
+        +
+        Λ
+        
+          g
+          
+            μ
+            ν
+          
+        
+        =
+        κ
+        
+          T
+          
+            μ
+            ν
+          
+        
+      
+    
+    {\displaystyle R_{\mu \nu }-{\tfrac {1}{2}}Rg_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }}
+  
+.
+This permitted the creation of steady-state solutions, but they were unstable: the slightest perturbation of a static state would result in the universe expanding or contracting. In 1929, Edwin Hubble found evidence for the universe expanding. This resulted in Einstein dropping the cosmological constant, referring to it as "the biggest blunder in my career". At the time, it was an ad hoc hypothesis to add in the cosmological constant, as it was only intended to justify one result (a static universe).
+
+=== More exact solutions ===
+Progress in solving the field equations and understanding the solutions has been ongoing.  The solution for a spherically symmetric charged object was discovered by Reissner and later rediscovered by Nordström, and is called the Reissner–Nordström solution.  The black hole aspect of the Schwarzschild solution was very controversial, and Einstein did not believe that singularities could be real.  However, in 1957 (two years after Einstein's death), Martin Kruskal published a proof that black holes are called for by the Schwarzschild solution.  Additionally, the solution for a rotating massive object was obtained by Roy Kerr in the 1960s and is called the Kerr solution.  The Kerr–Newman solution for a rotating, charged massive object was published a few years later.
+
+== Testing the theory ==
+
+The first piece of evidence in support of general relativity came from its correct prediction of the anomalous rate of precession of Mercury's orbit. Subsequently, Arthur Stanley Eddington's 1919 expedition confirmed Einstein's prediction of the deflection of light by the Sun during the total solar eclipse of 29 May 1919, which helped to cement the status of general relativity as a viable theory. Since then, many observations have shown agreement with the predictions of general relativity. These include studies of binary pulsars, observations of radio signals passing the limb of the Sun, and even the global positioning system.
+
+The theory predicts gravitational waves, which are ripples in the curvature of spacetime that propagate as waves, travelling outward from the source. The first observation of gravitational waves, which came from the merger of two black holes, was made on 14 September 2015 by the Advanced LIGO team, corroborating another prediction of the theory 100 years after it was published.
+The first image of a black hole, the supermassive one at the center of galaxy Messier 87, was published by the Event Horizon Telescope Collaboration on 10 April 2019.
+
+== Alternative theories ==
+
+There have been various attempts to find modifications to general relativity. The most famous of these are the Brans–Dicke theory (also known as scalar–tensor theory), and Rosen's bimetric theory. Both of these theories proposed changes to the field equations of general relativity, and both suffer from these changes permitting the presence of bipolar gravitational radiation. As a result, Rosen's original theory has been refuted by observations of binary pulsars. As for Brans–Dicke (which has a tunable parameter ω such that ω = ∞ is the same as general relativity), the amount by which it can differ from general relativity has been severely constrained by these observations. Many other alternatives to general relativity have also been ruled out by analyses of the neutron-star merger GW170817.
+In addition, general relativity is inconsistent with quantum mechanics, the physical theory that describes the wave–particle duality of matter, and quantum mechanics does not currently describe gravitational attraction at relevant (microscopic) scales. There is a great deal of speculation in the physics community as to the modifications that might be needed to both general relativity and quantum mechanics in order to unite them consistently. The speculative theory that unites general relativity and quantum mechanics is usually called quantum gravity, prominent examples of which include string theory and loop quantum gravity.
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+---
+title: "History of general relativity"
+chunk: 5/5
+source: "https://en.wikipedia.org/wiki/History_of_general_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:09.244516+00:00"
+instance: "kb-cron"
+---
+
+== Golden age ==
+Kip Thorne identifies the "golden age of black hole research" as the period roughly from 1960 to 1975, during which the study of general relativity, which had previously been regarded as something of a curiosity, entered the mainstream of theoretical physics. During this period, many of the concepts and terms which continue to inspire the imaginations of gravitation researchers and the general public were introduced, including black holes and gravitational singularities.  At the same time, in a closely related development, the study of physical cosmology entered the mainstream and the Big Bang became well established.
+Fulvio Melia refers frequently to the "golden age of relativity" in his book Cracking the Einstein Code. Andrzej Trautman hosted a relativity conference in Warsaw in 1962 to which Melia refers:
+
+General relativity moved very successfully from that meeting in Warsaw, hot on the heels of the Pound–Rebka experiment, and entered its golden age of discovery that lasted into the mid-1970s.
+Roy Kerr, protagonist of the book, contributed an Afterword, saying of the book: "It is a remarkable piece of writing capturing beautifully the period we now refer to as the golden age of relativity."
+
+== See also ==
+
+List of contributors to general relativity
+Golden age of cosmology
+Golden age of physics
+Mach's principle
+Timeline of gravitational physics and relativity
+W. K. Clifford#Premonition of relativity
+
+== References ==
+
+=== Bibliography ===
+
+== External links ==
+ Works related to The Foundation of the Generalised Theory of Relativity at Wikisource
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+---
+title: "History of gravitational theory"
+chunk: 1/8
+source: "https://en.wikipedia.org/wiki/History_of_gravitational_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:19.613655+00:00"
+instance: "kb-cron"
+---
+
+In physics, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation since ancient times. The first extant sources discussing such theories are found in ancient Greek philosophy. This work was furthered through the Middle Ages by Indian, Islamic, and European scientists, before gaining great strides during the Renaissance and Scientific Revolution—culminating in the formulation of Newton's law of gravity. This was superseded by Albert Einstein's theory of relativity in the early 20th century.
+Greek philosopher Aristotle (fl. 4th century BC) found that objects immersed in a medium tend to fall at speeds proportional to their weight. Vitruvius (fl. 1st century BC) understood that objects fall based on their specific gravity. In the 6th century AD, Byzantine Alexandrian scholar John Philoponus modified the Aristotelian concept of gravity with the theory of impetus. In the 7th century, Indian astronomer Brahmagupta spoke of gravity as an attractive force. In the 14th century, European philosophers Jean Buridan and Albert of Saxony—who were influenced by Islamic scholars Ibn Sina and Abu'l-Barakat respectively—developed the theory of impetus and linked it to the acceleration and mass of objects. Albert also developed a law of proportion regarding the relationship between the speed of an object in free fall and the time elapsed.
+Italians of the 16th century found that objects in free fall tend to accelerate equally. In 1632, Galileo Galilei put forth the basic principle of relativity. The existence of the gravitational constant was explored by various researchers from the mid-17th century, helping Isaac Newton formulate his law of universal gravitation. Newton's classical mechanics were superseded in the early 20th century, when Einstein developed the special and general theories of relativity. An elemental force carrier of gravity is hypothesized in quantum gravity approaches such as string theory, in a potentially unified theory of everything.
+
+== Antiquity ==
+
+=== Classical antiquity ===
+
+==== Heraclitus, Anaxagoras, Empedocles and Leucippus ====
+
+The pre-Socratic Greek philosopher Heraclitus (c. 535 – c. 475 BC) of the Ionian School used the word logos ('word') to describe a kind of law which keeps the cosmos in harmony, moving all objects, including the stars, winds, and waves. Anaxagoras (c. 500 – c. 428 BC), another Ionian philosopher, introduced the concept of nous ('cosmic mind') as an ordering force.
+In the cosmogony of the Greek philosopher Empedocles (c. 494 – c. 434/443 BC), there were two opposing fundamental cosmic forces of "attraction" and "repulsion", which Empedocles personified as "Love" and "Strife" (Philotes and Neikos).
+The ancient atomist Leucippus (5th century BC) proposed the cosmos was created when a large group of atoms came together and swirled as a vortex. The smaller atoms became the celestial bodies of the cosmos. The larger atoms in the center came together as a membrane from which the Earth was formed.
+
+==== Aristotle ====
+
+In the 4th century BC, Greek philosopher Aristotle taught that there is no effect or motion without a cause. The cause of the downward natural motion of heavy bodies, such as the classical elements of earth and water, was related to their nature (gravity), which caused them to move downward toward the center of the (geocentric) universe. For this reason Aristotle supported a spherical Earth, since "every portion of earth has weight until it reaches the centre, and the jostling of parts greater and smaller would bring about not a waved surface, but rather compression and convergence of part and part until the centre is reached". On the other hand, light bodies such as the element fire and air, were moved by their nature (levity) upward toward the celestial sphere of the Moon (see sublunary sphere). Astronomical objects near the fixed stars are composed of aether, whose natural motion is circular. Beyond them is the prime mover, the final cause of all motion in the cosmos. In his Physics, Aristotle correctly asserted that objects immersed in a medium tend to fall at speeds proportional to their weight and inversely proportional to the density of the medium.
+
+==== Strato of Lampsacus, Epicurus and Aristarchus of Samos ====
+Greek philosopher Strato of Lampsacus (c. 335 – c. 269 BC) rejected the Aristotelian belief of "natural places" in exchange for a mechanical view in which objects do not gain weight as they fall, instead arguing that the greater impact was due to an increase in speed.
+Epicurus (c. 341 – 270 BC) viewed weight as an inherent property of atoms which influences their movement. These atoms move downward in constant free fall within an infinite vacuum without friction at equal speed, regardless of their mass. On the other hand, upward motion is due to atomic collisions. Epicureans deviated from older atomist theories like that of Democritus (c. 460 – c. 370 BC) by proposing the idea that atoms may randomly deviate from their expected course.
+Greek astronomer Aristarchus of Samos (c. 310 – c. 230 BC) theorized Earth's rotation around its own axis, as well as Earth's orbit around the Sun in a heliocentric cosmology. Seleucus of Seleucia (c. 190 – c. 150 BC) supported his cosmology and also described gravitational effects of the Moon on the tidal range.
+
+==== Archimedes ====
+The 3rd-century BC Greek physicist Archimedes (c. 287 – c. 212 BC) discovered the centre of mass of a triangle. He also postulated that if the centres of gravity of two equal weights was not the same, it would be located in the middle of the line that joins them, a result he used to prove the law of the lever and to extend his equilibrium analysis to floating bodies. In On Floating Bodies, Archimedes claimed that for any object submerged in a fluid there is an equivalent upward buoyant force to the weight of the fluid displaced by the object's volume. The fluids described by Archimedes are not self-gravitating, since he assumes that "any fluid at rest is the surface of a sphere whose centre is the same as that of the Earth".
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+---
+title: "History of gravitational theory"
+chunk: 2/8
+source: "https://en.wikipedia.org/wiki/History_of_gravitational_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:19.613655+00:00"
+instance: "kb-cron"
+---
+
+==== Hipparchus of Nicaea, Lucretius and Vitruvius ====
+Greek astronomer Hipparchus of Nicaea (c. 190 – c. 120 BC) also rejected Aristotelian physics and followed Strato in adopting some form of theory of impetus to explain motion. The poem De rerum natura by Lucretius (c. 99 – c. 55 BC) asserts that more massive bodies fall faster in a medium because the latter resists less, but in a vacuum fall with equal speed.  Roman engineer and architect Vitruvius (c. 85 – c. 15 BC) contends in his De architectura that gravity is not dependent on a substance's weight but rather on its 'nature' (cf. specific gravity):
+
+If the quicksilver is poured into a vessel, and a stone weighing one hundred pounds is laid upon it, the stone swims on the surface, and cannot depress the liquid, nor break through, nor separate it. If we remove the hundred pound weight, and put on a scruple of gold, it will not swim, but will sink to the bottom of its own accord. Hence, it is undeniable that the gravity of a substance depends not on the amount of its weight, but on its nature. (translated from the original Latin by W. Newton)
+
+==== Plutarch, Pliny the Elder, and Claudius Ptolemy ====
+
+Greek philosopher Plutarch (c. 46 – c. 120 AD) attested the existence of Roman astronomers who rejected Aristotelian physics, "even contemplating theories of inertia and universal gravitation". In his work De facie in orbe lunae, he suggested that gravitational attraction was not unique to the Earth, but applied to other bodies such as the Sun and the Moon, which were held to attract the parts of which they are made. His conception of gravity as a tendency of parts to unite with their whole coincides with Nicolaus Copernicus’s account of gravity. He also proposed a thought experiment in which a heavy object falling through a tunnel in the Earth might either stop at the center or overshoot and oscillate, anticipating the medieval theory of impetus.
+The gravitational effects of the Moon on the tides were noticed by Pliny the Elder (23–79 AD) in his Naturalis Historia and Claudius Ptolemy (c. 100 – c. 170 AD) in his Tetrabiblos.
+
+=== Byzantine era ===
+
+==== John Philoponus ====
+In the 6th century AD, the Byzantine Alexandrian scholar John Philoponus proposed the theory of impetus, which modifies Aristotle's theory that "continuation of motion depends on continued action of a force" by incorporating a causative force which diminishes over time. In his commentary on Aristotle's Physics that "if one lets fall simultaneously from the same height two bodies differing greatly in weight, one will find that the ratio of the times of their motion does not correspond to the ratios of their weights, but the difference in time is a very small one".
+
+== Indian subcontinent ==
+
+=== Brahmagupta ===
+
+Brahmagupta (c. 598 – c. 668 AD) was the first Indian scholar to describe gravity as an attractive force:
+
+The earth on all its sides is the same; all people on the earth stand upright, and all heavy things fall down to the earth by a law of nature, for it is the nature of the earth to attract and to keep things, as it is the nature of water to flow ... If a thing wants to go deeper down than the earth, let it try. The earth is the only low thing, and seeds always return to it, in whatever direction you may throw them away, and never rise upwards from the earth.
+
+=== Bhāskara II ===
+Bhāskara II (c. 1114 – c. 1185), another Indian mathematician and astronomer, describes gravity as an inherent attractive property of Earth in the section "Golādhyāyah" ("On Spherics") of his treatise Siddhānta Shiromani:
+
+The property of attraction is inherent in the Earth. By this property the Earth attracts any unsupported heavy thing towards it: The thing appears to be falling but it is in a state of being drawn to Earth. ... It is manifest from this that ... people situated at distances of a fourth part of the circumference [of earth] from us or in the opposite hemisphere, cannot by any means fall downwards [in space].
+
+== Islamic world ==
+
+=== Abu Ma'shar ===
+Ancient Greeks like Posidonius had associated the tides in the sea with to be influenced by moonlight. Around 850, Abu Ma'shar al-Balkhi recorded the tides and the moon position and noticed high-tides when the Moon was below the horizon. Abu Ma'shar considered an alternative explanation where the Moon and the sea had to share some astrological virtue that attracted each other. This work was translated into Latin and became one of the two main theories for tides for European scholars.
+
+=== Ibn Sina ===
+
+In the 11th century, Persian polymath Ibn Sina (Avicenna) agreed with Philoponus' theory that "the moved object acquires an inclination from the mover" as an explanation for projectile motion. Ibn Sina then published his own theory of impetus in The Book of Healing (c. 1020). Unlike Philoponus, who believed that it was a temporary virtue that would decline even in a vacuum, Ibn Sina viewed it as a persistent, requiring external forces such as air resistance to dissipate it. Ibn Sina made distinction between force and inclination (mayl), and argued that an object gained inclination when the object is in opposition to its natural motion. He concluded that continuation of motion is attributed to the inclination that is transferred to the object, and that object will be in motion until the inclination is spent. The Iraqi polymath Ibn al-Haytham describes gravity as a force in which heavier body moves towards the centre of the earth. He also describes the force of gravity will only move towards the direction of the centre of the earth not in different directions.
+
+=== Al-Biruni ===
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+---
+title: "History of gravitational theory"
+chunk: 3/8
+source: "https://en.wikipedia.org/wiki/History_of_gravitational_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:19.613655+00:00"
+instance: "kb-cron"
+---
+
+Another 11th-century Persian polymath, Al-Biruni, proposed that heavenly bodies have mass, weight, and gravity, just like the Earth. He criticized both Aristotle and Ibn Sina for holding the view that only the Earth has these properties. The 12th-century scholar Al-Khazini suggested that the gravity an object contains varies depending on its distance from the centre of the universe (referring to the centre of the Earth). Al-Biruni and Al-Khazini studied the theory of the centre of gravity, and generalized and applied it to three-dimensional bodies. Fine experimental methods were also developed for determining the specific gravity or specific weight of objects, based the theory of balances and weighing.
+
+=== Abu'l-Barakāt al-Baghdādī ===
+In the 12th century, Ibn Malka al-Baghdadi adopted and modified Ibn Sina's theory on projectile motion. In his Kitab al-Mu'tabar, Abu'l-Barakat stated that the mover imparts a violent inclination (mayl qasri) on the moved and that this diminishes as the moving object distances itself from the mover. According to Shlomo Pines, al-Baghdādī's theory of motion was "the oldest negation of Aristotle's fundamental dynamic law [namely, that a constant force produces a uniform motion], [and is thus an] anticipation in a vague fashion of the fundamental law of classical mechanics [namely, that a force applied continuously produces acceleration]."
+
+== European Renaissance ==
+
+=== 14th century ===
+
+==== Jean Buridan, the Oxford Calculators, Albert of Saxony ====
+In the 14th century, both the French philosopher Jean Buridan and the Oxford Calculators (the Merton School) of the Merton College of Oxford rejected the Aristotelian concept of gravity. They attributed the motion of objects to an impetus (akin to momentum), which varies according to velocity and mass; Buridan was influenced in this by Ibn Sina's Book of Healing. Buridan and the philosopher Albert of Saxony (c. 1320 – c. 1390) adopted Abu'l-Barakat's theory that the acceleration of a falling body is a result of its increasing impetus. Influenced by Buridan, Albert developed a law of proportion regarding the relationship between the speed of an object in free fall and the time elapsed. He also theorized that mountains and valleys are caused by erosion—displacing the Earth's centre of gravity.
+
+==== Uniform and difform motion ====
+The roots of Domingo de Soto's expression uniform difform motion [uniformly accelerated motion] lies in the Oxford Calculators terms "uniform" and "difform" motion: "uniform motion" was used differently then than it would be by later writers, and might have referred both to constant speed and to motion in which all parts of a body are moving at equal speed. The Calculators did not illustrate the different types of motion with real-world examples. John of Holland at the University of Prague, illustrated uniform motion with what would later be called uniform velocity, but also with a falling stone (all parts moving at the same speed), and with a sphere in uniform rotation. He did, however, make distinctions between different kinds of "uniform" motion. Difform motion was exemplified by walking at increasing speed.
+
+==== Mean speed theorem ====
+
+Also in the 14th century, the Merton School developed the mean speed theorem; a uniformly accelerated body starting from rest travels the same distance as a body with uniform speed whose speed is half the final velocity of the accelerated body. The mean speed theorem was proved by Nicole Oresme (c. 1323 – 1382) and would be influential in later gravitational equations. Written as a modern equation:
+
+  
+    
+      
+         
+        s
+        =
+        
+          
+            1
+            2
+          
+        
+        
+          v
+          
+            f
+          
+        
+        t
+      
+    
+    {\displaystyle \ s={\frac {1}{2}}v_{f}t}
+  
+
+However, since small time intervals could not be measured, the relationship between time and distance was not so evident as the equation suggests. More generally; equations, which were not widely used until after Galileo's time, imply a clarity that was not there.
+
+=== 15th–16th centuries ===
+
+==== Leonardo da Vinci ====
+
+Leonardo da Vinci (1452–1519) made drawings recording the acceleration of falling objects. He wrote that the "mother and origin of gravity" is energy. He describes two pairs of physical powers which stem from a metaphysical origin and have an effect on everything: abundance of force and motion, and gravity and resistance. He associates gravity with the 'cold' classical elements, water and earth, and calls its energy infinite. In Codex Arundel, Leonardo recorded that if a water-pouring vase moves transversally (sideways), simulating the trajectory of a vertically falling object, it produces a right triangle with equal leg length, composed of falling material that forms the hypotenuse and the vase trajectory forming one of the legs. On the hypotenuse, Leonardo noted the equivalence of the two orthogonal motions, one effected by gravity and the other proposed by the experimenter.
+
+==== Nicolaus Copernicus, Petrus Apianus ====
+
+By 1514, Nicolaus Copernicus had written an outline of his heliocentric model, in which he stated that Earth's centre is the centre of both its rotation and the orbit of the Moon. In 1533, German humanist Petrus Apianus described the exertion of gravity:
+
+Since it is apparent that in the descent [along the arc] there is more impediment acquired, it is clear that gravity is diminished on this account. But because this comes about by reason of the position of heavy bodies, let it be called a positional gravity [i.e. gravitas secundum situm]
+
+==== Francesco Beato and Luca Ghini ====
+By 1544, according to Benedetto Varchi, the experiments of at least two Italians, Francesco Beato, a Dominican philosopher at Pisa, and Luca Ghini, a physician and botanist from Bologna, had dispelled the Aristotelian claim that objects fall at speeds proportional to their weight.
+
+==== Domingo de Soto ====
+
+In 1551, Domingo de Soto theorized that objects in free fall accelerate uniformly in his book Physicorum Aristotelis quaestiones. This idea was subsequently explored in more detail by Galileo Galilei, who derived his kinematics from the 14th-century Merton College and Jean Buridan, and possibly De Soto as well.
+
+== Scientific Revolution ==
+
+=== Simon Stevin ===
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_gravitational_theory-3.md b/data/en.wikipedia.org/wiki/History_of_gravitational_theory-3.md
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--- /dev/null
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@@ -0,0 +1,42 @@
+---
+title: "History of gravitational theory"
+chunk: 4/8
+source: "https://en.wikipedia.org/wiki/History_of_gravitational_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:19.613655+00:00"
+instance: "kb-cron"
+---
+
+In 1585, Flemish polymath Simon Stevin performed a demonstration for Jan Cornets de Groot, a local politician in the Dutch city of Delft. Stevin dropped two lead balls from the Nieuwe Kerk in that city. From the sound of the impacts, Stevin deduced that the balls had fallen at the same speed. The result was published in 1586.
+
+Let us take (as ... Jan Cornets de Groot ... and I have done) two balls of lead, the one ten times larger and heavier than the other, and drop them together from a height of 30 feet on to a board or something on which they give a perceptible sound. Then it will be found that the lighter will not be ten times longer on its way than the heavier, but that they fall together on to the board so simultaneously that their two sounds seem to be one and the same. ... Therefore Aristotle ... is wrong.
+
+=== Galileo Galilei ===
+
+Galileo successfully applied mathematics to the acceleration of falling objects, correctly hypothesizing in a 1604 letter to Paolo Sarpi that the distance of a falling object is proportional to the square of the time elapsed.
+
+I have arrived at a proposition, ... namely, that spaces traversed in natural motion are in the squared proportion of the times.
+Written with modern symbols: s ∝ t2
+The result was published in Two New Sciences in 1638. In the same book, Galileo suggested that the slight variance of speed of falling objects of different mass was due to air resistance, and that objects would fall completely uniformly in a vacuum. The relation of the distance of objects in free fall to the square of the time taken was confirmed by Italian Jesuits Grimaldi and Riccioli between 1640 and 1650. They also made a calculation of the gravity of Earth by recording the oscillations of a pendulum.
+
+=== Johannes Kepler ===
+
+In his Astronomia nova (1609), Johannes Kepler proposed an attractive force of limited radius between any "kindred" bodies:
+
+Gravity is a mutual corporeal disposition among kindred bodies to unite or join together; thus the earth attracts a stone much more than the stone seeks the earth. (The magnetic faculty is another example of this sort).... If two stones were set near one another in some place in the world outside the sphere of influence of a third kindred body, these stones, like two magnetic bodies, would come together in an intermediate place, each approaching the other by a space proportional to the bulk [moles] of the other....
+Kepler claimed that if the Earth and Moon were not held apart by some force they would come together. He recognized that mechanical forces cause action, resulting in a more modern view of planetary motion, in his view a celestial machine. On the other hand Kepler viewed the force of the Sun on the planets as magnetic and acting tangential to their orbits and he assumed with Aristotle that inertia meant objects tend to come to rest.
+
+=== Giovanni Borelli ===
+In 1666, Giovanni Alfonso Borelli avoided the key problems that limited Kepler. By Borelli's time the concept of inertia had its modern meaning as the tendency of objects to remain in uniform motion and he viewed the Sun as just another heavenly body. Borelli developed the idea of mechanical equilibrium, a balance between inertia and gravity. Newton cited Borelli's influence on his theory.
+
+=== Evangelista Torricelli ===
+A disciple of Galileo, Evangelista Torricelli reiterated Aristotle's model involving a gravitational centre, adding his view that a system can only be in equilibrium when the common centre itself is unable to fall.
+The relation of the distance of objects in free fall to the square of the time taken was confirmed by Francesco Maria Grimaldi and Giovanni Battista Riccioli between 1640 and 1650. They also made a calculation of the gravity of Earth constant by recording the oscillations of a pendulum.
+
+=== Mechanical explanations ===
+
+In 1644, René Descartes proposed that no empty space can exist and that a continuum of matter causes every motion to be curvilinear. Thus, centrifugal force thrusts relatively light matter away from the central vortices of celestial bodies, lowering density locally and thereby creating centripetal pressure. Using aspects of this theory, between 1669 and 1690, Christiaan Huygens designed a mathematical vortex model. In one of his proofs, he shows that the distance elapsed by an object dropped from a spinning wheel will increase proportionally to the square of the wheel's rotation time. In 1671, Robert Hooke speculated that gravitation is the result of bodies emitting waves in the aether. Nicolas Fatio de Duillier (1690) and Georges-Louis Le Sage (1748) proposed a corpuscular model using some sort of screening or shadowing mechanism. In 1784, Le Sage posited that gravity could be a result of the collision of atoms, and in the early 19th century, he expanded Daniel Bernoulli's theory of corpuscular pressure to the universe as a whole. A similar model was later created by Hendrik Lorentz (1853–1928), who used electromagnetic radiation instead of corpuscles.
+English mathematician Isaac Newton used Descartes' argument that curvilinear motion constrains inertia, and in 1675, argued that aether streams attract all bodies to one another. Newton (1717) and Leonhard Euler (1760) proposed a model in which the aether loses density near mass, leading to a net force acting on bodies. Further mechanical explanations of gravitation (including Le Sage's theory) were created between 1650 and 1900 to explain Newton's theory, but mechanistic models eventually fell out of favor because most of them lead to an unacceptable amount of drag (air resistance), which was not observed. Others violate the energy conservation law and are incompatible with modern thermodynamics.
+
+=== 'Weight' before Newton ===
\ No newline at end of file
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_gravitational_theory-4.md
@@ -0,0 +1,312 @@
+---
+title: "History of gravitational theory"
+chunk: 5/8
+source: "https://en.wikipedia.org/wiki/History_of_gravitational_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:19.613655+00:00"
+instance: "kb-cron"
+---
+
+Before Newton, 'weight' had the double meaning 'amount' and 'heaviness'.What we now know as mass was until the time of Newton called "weight." ... A goldsmith believed that an ounce of gold was a quantity of gold. ... But the ancients believed that a beam balance also measured "heaviness" which they recognized through their muscular senses. ... Mass and its associated downward force were believed to be the same thing.
+Kepler formed a [distinct] concept of mass ("amount of matter" (copia materiae), but called it "weight" as did everyone at that time.
+
+=== Mass as distinct from weight ===
+
+In 1686, Newton gave the concept of mass its name. In the first paragraph of Principia, Newton defined quantity of matter as "density and bulk conjunctly", and mass as quantity of matter.The quantity of matter is the measure of the same, arising from its density and bulk conjunctly. ... It is this quantity that I mean hereafter everywhere under the name of body or mass. And the same is known by the weight of each body; for it is proportional to the weight.
+
+=== Newton's law of universal gravitation ===
+
+In 1679, Robert Hooke wrote to Isaac Newton of his hypothesis concerning orbital motion as a combination of tangential inertial motion and a central force. He also asked for the precise trajectory implied an inverse-square force. Newton was almost certainly influenced by this correspondence to do his subsequent work on gravitation, although he denied that Hooke had told him of the inverse-square force. In January 1684 Hooke told Edmond Halley and Christopher Wren that he had proven the inverse-square law of planetary motion but he refused to produce his proof.  That summer, Halley visited Newton and asked if Newton knew what trajectory an inverse square force would produce. Newton said an ellipse and by November 1684 he sent Halley De motu corporum in gyrum ('On the motion of bodies in an orbit'), in which he mathematically derives Kepler's laws of planetary motion. In 1687, with Halley's support Newton published Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), which hypothesizes the inverse-square law of universal gravitation. In his own words:I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centres about which they revolve; and thereby compared the force requisite to keep the moon in her orb with the force of gravity at the surface of the earth; and found them to answer pretty nearly.
+Although Hooke was unable develop a mathematical theory of gravity and work out the consequences, he claimed that the inverse square law portion was his "notion".
+Newton's original formula was:
+
+  
+    
+      
+        
+          
+            F
+            o
+            r
+            c
+            e
+            
+            o
+            f
+            
+            g
+            r
+            a
+            v
+            i
+            t
+            y
+          
+        
+        ∝
+        
+          
+            
+              m
+              a
+              s
+              s
+              
+              o
+              f
+              
+              o
+              b
+              j
+              e
+              c
+              t
+              
+              1
+              
+              ×
+              
+              m
+              a
+              s
+              s
+              
+              o
+              f
+              
+              o
+              b
+              j
+              e
+              c
+              t
+              
+              2
+            
+            
+              d
+              i
+              s
+              t
+              a
+              n
+              c
+              e
+              
+              f
+              r
+              o
+              m
+              
+              c
+              e
+              n
+              t
+              e
+              r
+              
+                s
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\rm {Force\,of\,gravity}}\propto {\frac {\rm {mass\,of\,object\,1\,\times \,mass\,of\,object\,2}}{\rm {distance\,from\,centers^{2}}}}}
+  
+
+where the symbol 
+  
+    
+      
+        ∝
+      
+    
+    {\displaystyle \propto }
+  
+ means "is proportional to". To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them – the gravitational constant. Newton would need an accurate measure of this constant to prove his inverse-square law. Reasonably accurate measurements were not available in until the Cavendish experiment by Henry Cavendish in 1797.
+In Newton's theory (rewritten using more modern mathematics) the density of mass 
+  
+    
+      
+        ρ
+        
+      
+    
+    {\displaystyle \rho \,}
+  
+ generates a scalar field, the gravitational potential 
+  
+    
+      
+        φ
+        
+      
+    
+    {\displaystyle \varphi \,}
+  
+ in joules per kilogram, by
+
+  
+    
+      
+        
+          
+            
+              
+                ∂
+                
+                  2
+                
+              
+              φ
+            
+            
+              ∂
+              
+                x
+                
+                  j
+                
+              
+              
+              ∂
+              
+                x
+                
+                  j
+                
+              
+            
+          
+        
+        =
+        4
+        π
+        G
+        ρ
+        
+        .
+      
+    
+    {\displaystyle {\partial ^{2}\varphi  \over \partial x^{j}\,\partial x^{j}}=4\pi G\rho \,.}
+  
+
+Using the Nabla operator 
+  
+    
+      
+        ∇
+      
+    
+    {\displaystyle \nabla }
+  
+ for the gradient and divergence (partial derivatives), this can be conveniently written as:
+
+  
+    
+      
+        
+          ∇
+          
+            2
+          
+        
+        φ
+        =
+        4
+        π
+        G
+        ρ
+        
+        .
+      
+    
+    {\displaystyle \nabla ^{2}\varphi =4\pi G\rho \,.}
+  
+
+This scalar field governs the motion of a free-falling particle by:
+
+  
+    
+      
+        
+          
+            
+              
+                d
+                
+                  2
+                
+              
+              
+                x
+                
+                  j
+                
+              
+            
+            
+              d
+              
+                t
+                
+                  2
+                
+              
+            
+          
+        
+        =
+        −
+        
+          
+            
+              ∂
+              φ
+            
+            
+              ∂
+              
+                x
+                
+                  j
+                
+              
+              
+            
+          
+        
+        .
+      
+    
+    {\displaystyle {d^{2}x^{j} \over dt^{2}}=-{\partial \varphi  \over \partial x^{j}\,}.}
+  
+
+At distance r from an isolated mass M, the scalar field is
+
+  
+    
+      
+        φ
+        =
+        −
+        
+          
+            
+              G
+              M
+            
+            r
+          
+        
+        
+        .
+      
+    
+    {\displaystyle \varphi =-{\frac {GM}{r}}\,.}
+  
\ No newline at end of file
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--- /dev/null
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@@ -0,0 +1,23 @@
+---
+title: "History of gravitational theory"
+chunk: 6/8
+source: "https://en.wikipedia.org/wiki/History_of_gravitational_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:19.613655+00:00"
+instance: "kb-cron"
+---
+
+The Principia sold out quickly, inspiring Newton to publish a second edition in 1713.
+However the theory of gravity itself was not accepted quickly.
+The theory of gravity faced two barriers. First scientists like Gottfried Wilhelm Leibniz complained that it relied on action at a distance, that the mechanism of gravity was "invisible, intangible, and not mechanical". The French philosopher Voltaire countered these concerns, ultimately writing his own book to explain aspects of it to French readers in 1738, which helped to popularize Newton's theory.
+Second, detailed comparisons with astronomical data were not initially favorable. Among the most conspicuous issue was the so-called great inequality of Jupiter and Saturn. Comparisons of ancient astronomical observations to those of the early 1700s implied that the orbit of Saturn was increasing in diameter while that of Jupiter was decreasing. Ultimately this meant Saturn would exit the Solar System and Jupiter would collide with other planets or the Sun. The problem was tackled first by Leonhard Euler in 1748, then Joseph-Louis Lagrange in 1763, by Pierre-Simon Laplace in 1773. Each effort improved the mathematical treatment until the issue was resolved by Laplace in 1784 approximately 100 years after Newton's first publication on gravity. Laplace showed that the changes were periodic but with immensely long periods beyond any existing measurements.
+Successes such the solution to the great inequality of Jupiter and Saturn mystery accumulated. In 1755, Prussian philosopher Immanuel Kant published a cosmological manuscript based on Newtonian principles, in which he develops an early version of the nebular hypothesis. Edmond Halley proposed that similar looking objects appearing every 76 years was in fact a single comet. The appearance of the comet in 1759, now named after him, within a month of predictions based on Newton's gravity greatly improved scientific opinion of the theory. Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted by the actions of the other planets. Calculations by John Couch Adams and Urbain Le Verrier both predicted the general position of the planet. In 1846, Le Verrier sent his position to Johann Gottfried Galle, asking him to verify it. The same night, Galle spotted Neptune near the position Le Verrier had predicted.
+Not every comparison was successful. By the end of the 19th century, Le Verrier showed that the orbit of Mercury could not be accounted for entirely under Newtonian gravity, and all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) were fruitless. Even so, Newton's theory is thought to be exceptionally accurate in the limit of weak gravitational fields and low speeds.
+At the end of the 19th century, many tried to combine Newton's force law with the established laws of electrodynamics (like those of Wilhelm Eduard Weber, Carl Friedrich Gauss, and Bernhard Riemann) to explain the anomalous perihelion precession of Mercury. In 1890, Maurice Lévy succeeded in doing so by combining the laws of Weber and Riemann, whereby the speed of gravity is equal to the speed of light. In another attempt, Paul Gerber (1898) succeeded in deriving the correct formula for the perihelion shift (which was identical to the formula later used by Albert Einstein). These hypotheses were rejected because of the outdated laws they were based on, being superseded by those of James Clerk Maxwell.
+
+== Modern era ==
+
+In 1900, Hendrik Lorentz tried to explain gravity on the basis of his ether theory and Maxwell's equations. He assumed, like Ottaviano Fabrizio Mossotti and Johann Karl Friedrich Zöllner, that the attraction of opposite charged particles is stronger than the repulsion of equal charged particles. The resulting net force is exactly what is known as universal gravitation, in which the speed of gravity is that of light. Lorentz calculated that the value for the perihelion advance of Mercury was much too low.
+In the late 19th century, Lord Kelvin pondered the possibility of a theory of everything. He proposed that every body pulsates, which might be an explanation of gravitation and electric charges. His ideas were largely mechanistic and required the existence of the aether, which the Michelson–Morley experiment failed to detect in 1887. This, combined with Mach's principle, led to gravitational models which feature action at a distance.
+Albert Einstein developed his revolutionary theory of relativity in papers published in 1905 and 1915; these account for the perihelion precession of Mercury. In 1914, Gunnar Nordström attempted to unify gravity and electromagnetism in his theory of five-dimensional gravitation. General relativity was proven in 1919, when Arthur Eddington observed gravitational lensing around a solar eclipse, matching Einstein's equations. This resulted in Einstein's theory superseding Newtonian physics. Thereafter, German mathematician Theodor Kaluza promoted the idea of general relativity with a fifth dimension, which in 1921 Swedish physicist Oskar Klein gave a physical interpretation of in a prototypical string theory, a possible model of quantum gravity and potential theory of everything.
\ No newline at end of file
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@@ -0,0 +1,556 @@
+---
+title: "History of gravitational theory"
+chunk: 7/8
+source: "https://en.wikipedia.org/wiki/History_of_gravitational_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:19.613655+00:00"
+instance: "kb-cron"
+---
+
+Einstein's field equations include a cosmological constant to account for the alleged staticity of the universe. However, Edwin Hubble observed in 1929 that the universe appears to be expanding. By the 1930s, Paul Dirac developed the hypothesis that gravitation should slowly and steadily decrease over the course of the history of the universe. Alan Guth and Alexei Starobinsky proposed in 1980 that cosmic inflation in the very early universe could have been driven by a negative pressure field, a concept later coined 'dark energy'—found in 2013 to have composed around 68.3% of the early universe.
+In 1922, Jacobus Kapteyn proposed the existence of dark matter, an unseen force that moves stars in galaxies at higher velocities than gravity alone accounts for. It was found in 2013 to have comprised 26.8% of the early universe. Along with dark energy, dark matter is an outlier in Einstein's relativity, and an explanation for its apparent effects is a requirement for a successful theory of everything.
+In 1957, Hermann Bondi proposed that negative gravitational mass (combined with negative inertial mass) would comply with the strong equivalence principle of general relativity and Newton's laws of motion. Bondi's proof yielded singularity-free solutions for the relativity equations.
+Early theories of gravity attempted to explain planetary orbits (Newton) and more complicated orbits (e.g. Lagrange). Then came unsuccessful attempts to combine gravity and either wave or corpuscular theories of gravity. The whole landscape of physics was changed with the discovery of Lorentz transformations, and this led to attempts to reconcile it with gravity. At the same time, experimental physicists started testing the foundations of gravity and relativity—Lorentz invariance, the gravitational deflection of light, the Eötvös experiment. These considerations led to and past the development of general relativity.
+
+=== Einstein (1905–1912) ===
+In 1905, Albert Einstein published a series of papers in which he established the special theory of relativity and the fact that mass and energy are equivalent. In 1907, in what he described as "the happiest thought of my life", Einstein realized that someone who is in free fall experiences no gravitational field. In other words, gravitation is exactly equivalent to acceleration.
+Einstein's two-part publication in 1912 (and before in 1908) is really only important for historical reasons. By then he knew of the gravitational redshift and the deflection of light. He had realized that Lorentz transformations are not generally applicable, but retained them. The theory states that the speed of light is constant in free space but varies in the presence of matter. The theory was only expected to hold when the source of the gravitational field is stationary. It includes the principle of least action:
+
+  
+    
+      
+        δ
+        ∫
+        d
+        τ
+        =
+        0
+        
+      
+    
+    {\displaystyle \delta \int d\tau =0\,}
+  
+
+  
+    
+      
+        
+          
+            d
+            τ
+          
+          
+            2
+          
+        
+        =
+        −
+        
+          η
+          
+            μ
+            ν
+          
+        
+        
+        d
+        
+          x
+          
+            μ
+          
+        
+        
+        d
+        
+          x
+          
+            ν
+          
+        
+        
+      
+    
+    {\displaystyle {d\tau }^{2}=-\eta _{\mu \nu }\,dx^{\mu }\,dx^{\nu }\,}
+  
+
+where 
+  
+    
+      
+        
+          η
+          
+            μ
+            ν
+          
+        
+        
+      
+    
+    {\displaystyle \eta _{\mu \nu }\,}
+  
+ is the Minkowski metric, and there is a summation from 1 to 4 over indices 
+  
+    
+      
+        μ
+        
+      
+    
+    {\displaystyle \mu \,}
+  
+ and 
+  
+    
+      
+        ν
+        
+      
+    
+    {\displaystyle \nu \,}
+  
+.
+Einstein and Grossmann includes Riemannian geometry and tensor calculus.
+
+  
+    
+      
+        δ
+        ∫
+        d
+        τ
+        =
+        0
+        
+      
+    
+    {\displaystyle \delta \int d\tau =0\,}
+  
+
+  
+    
+      
+        
+          
+            d
+            τ
+          
+          
+            2
+          
+        
+        =
+        −
+        
+          g
+          
+            μ
+            ν
+          
+        
+        
+        d
+        
+          x
+          
+            μ
+          
+        
+        
+        d
+        
+          x
+          
+            ν
+          
+        
+        
+      
+    
+    {\displaystyle {d\tau }^{2}=-g_{\mu \nu }\,dx^{\mu }\,dx^{\nu }\,}
+  
+
+The equations of electrodynamics exactly match those of general relativity. The equation
+
+  
+    
+      
+        
+          T
+          
+            μ
+            ν
+          
+        
+        =
+        ρ
+        
+          
+            
+              d
+              
+                x
+                
+                  μ
+                
+              
+            
+            
+              d
+              τ
+            
+          
+        
+        
+          
+            
+              d
+              
+                x
+                
+                  ν
+                
+              
+            
+            
+              d
+              τ
+            
+          
+        
+        
+      
+    
+    {\displaystyle T^{\mu \nu }=\rho {dx^{\mu } \over d\tau }{dx^{\nu } \over d\tau }\,}
+  
+
+is not in general relativity. It expresses the stress–energy tensor as a function of the matter density.
+
+=== Lorentz-invariant models (1905–1910) ===
+Based on the principle of relativity, Henri Poincaré (1905, 1906), Hermann Minkowski (1908), and Arnold Sommerfeld (1910) tried to modify Newton's theory and to establish a Lorentz invariant gravitational law, in which the speed of gravity is that of light. As in Lorentz's model, the value for the perihelion advance of Mercury was much too low.
+
+=== Abraham (1912) ===
+Meanwhile, Max Abraham developed an alternative model of gravity in which the speed of light depends on the gravitational field strength and so is variable almost everywhere. Abraham's 1914 review of gravitation models is said to be excellent, but his own model was poor.
+
+=== Nordström (1912) ===
+The first approach of Nordström (1912) was to retain the Minkowski metric and a constant value of 
+  
+    
+      
+        c
+        
+      
+    
+    {\displaystyle c\,}
+  
+ but to let mass depend on the gravitational field strength 
+  
+    
+      
+        φ
+        
+      
+    
+    {\displaystyle \varphi \,}
+  
+. Allowing this field strength to satisfy
+
+  
+    
+      
+        ◻
+        φ
+        =
+        ρ
+        
+      
+    
+    {\displaystyle \Box \varphi =\rho \,}
+  
+
+where 
+  
+    
+      
+        ρ
+        
+      
+    
+    {\displaystyle \rho \,}
+  
+ is rest mass energy and 
+  
+    
+      
+        ◻
+        
+      
+    
+    {\displaystyle \Box \,}
+  
+ is the d'Alembertian,
+
+  
+    
+      
+        m
+        =
+        
+          m
+          
+            0
+          
+        
+        exp
+        ⁡
+        
+          (
+          
+            
+              φ
+              
+                c
+                
+                  2
+                
+              
+            
+          
+          )
+        
+        
+      
+    
+    {\displaystyle m=m_{0}\exp \left({\frac {\varphi }{c^{2}}}\right)\,}
+  
+
+where 
+  
+    
+      
+        
+          m
+          
+            0
+          
+        
+      
+    
+    {\displaystyle m_{0}}
+  
+ is the mass when gravitational potential vanishes and,
+
+  
+    
+      
+        −
+        
+          
+            
+              ∂
+              φ
+            
+            
+              ∂
+              
+                x
+                
+                  μ
+                
+              
+            
+          
+        
+        =
+        
+          
+            
+              
+                u
+                ˙
+              
+            
+          
+          
+            μ
+          
+        
+        +
+        
+          
+            
+              u
+              
+                μ
+              
+            
+            
+              
+                c
+                
+                  2
+                
+              
+              
+                
+                  
+                    φ
+                    ˙
+                  
+                
+              
+            
+          
+        
+        
+      
+    
+    {\displaystyle -{\partial \varphi  \over \partial x^{\mu }}={\dot {u}}_{\mu }+{u_{\mu } \over c^{2}{\dot {\varphi }}}\,}
+  
+
+where 
+  
+    
+      
+        u
+        
+      
+    
+    {\displaystyle u\,}
+  
+ is the four-velocity and the dot is a differential with respect to time.
+The second approach of Nordström (1913) is remembered as the first logically consistent relativistic field theory of gravitation ever formulated. (notation from Pais not Nordström):
+
+  
+    
+      
+        δ
+        ∫
+        ψ
+        
+        d
+        τ
+        =
+        0
+        
+      
+    
+    {\displaystyle \delta \int \psi \,d\tau =0\,}
+  
+
+  
+    
+      
+        
+          
+            d
+            τ
+          
+          
+            2
+          
+        
+        =
+        −
+        
+          η
+          
+            μ
+            ν
+          
+        
+        
+        d
+        
+          x
+          
+            μ
+          
+        
+        
+        d
+        
+          x
+          
+            ν
+          
+        
+        
+      
+    
+    {\displaystyle {d\tau }^{2}=-\eta _{\mu \nu }\,dx^{\mu }\,dx^{\nu }\,}
+  
+
+where 
+  
+    
+      
+        ψ
+        
+      
+    
+    {\displaystyle \psi \,}
+  
+ is a scalar field,
+
+  
+    
+      
+        −
+        
+          
+            
+              ∂
+              
+                T
+                
+                  μ
+                  ν
+                
+              
+            
+            
+              ∂
+              
+                x
+                
+                  ν
+                
+              
+            
+          
+        
+        =
+        T
+        
+          
+            1
+            ψ
+          
+        
+        
+          
+            
+              ∂
+              ψ
+            
+            
+              ∂
+              
+                x
+                
+                  μ
+                
+              
+            
+          
+        
+        
+      
+    
+    {\displaystyle -{\partial T^{\mu \nu } \over \partial x^{\nu }}=T{1 \over \psi }{\partial \psi  \over \partial x_{\mu }}\,}
+  
+
+This theory is Lorentz invariant, satisfies the conservation laws, correctly reduces to the Newtonian limit and satisfies the weak equivalence principle.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_gravitational_theory-7.md b/data/en.wikipedia.org/wiki/History_of_gravitational_theory-7.md
new file mode 100644
index 000000000..47e544527
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_gravitational_theory-7.md
@@ -0,0 +1,158 @@
+---
+title: "History of gravitational theory"
+chunk: 8/8
+source: "https://en.wikipedia.org/wiki/History_of_gravitational_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:19.613655+00:00"
+instance: "kb-cron"
+---
+
+=== Einstein and Fokker (1914) ===
+This theory is Einstein's first treatment of gravitation in which general covariance is strictly obeyed. Writing:
+
+  
+    
+      
+        δ
+        ∫
+        d
+        s
+        =
+        0
+        
+      
+    
+    {\displaystyle \delta \int ds=0\,}
+  
+
+  
+    
+      
+        
+          
+            d
+            s
+          
+          
+            2
+          
+        
+        =
+        
+          g
+          
+            μ
+            ν
+          
+        
+        
+        d
+        
+          x
+          
+            μ
+          
+        
+        
+        d
+        
+          x
+          
+            ν
+          
+        
+        
+      
+    
+    {\displaystyle {ds}^{2}=g_{\mu \nu }\,dx^{\mu }\,dx^{\nu }\,}
+  
+
+  
+    
+      
+        
+          g
+          
+            μ
+            ν
+          
+        
+        =
+        
+          ψ
+          
+            2
+          
+        
+        
+          η
+          
+            μ
+            ν
+          
+        
+        
+      
+    
+    {\displaystyle g_{\mu \nu }=\psi ^{2}\eta _{\mu \nu }\,}
+  
+
+they relate Einstein–Grossmann to Nordström. They also state:
+
+  
+    
+      
+        T
+        
+        ∝
+        
+        R
+        
+        .
+      
+    
+    {\displaystyle T\,\propto \,R\,.}
+  
+
+That is, the trace of the stress energy tensor is proportional to the curvature of space.
+Between 1911 and 1915, Einstein developed the idea that gravitation is equivalent to acceleration, initially stated as the equivalence principle, into his general theory of relativity, which fuses the three dimensions of space and the one dimension of time into the four-dimensional fabric of spacetime. However, it does not unify gravity with quanta—individual particles of energy, which Einstein himself had postulated the existence of in 1905.
+
+=== General relativity ===
+
+In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of to a force. The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion. The issue that this creates is that free-falling objects can accelerate with respect to each other. To deal with this difficulty, Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. More specifically, Einstein and David Hilbert discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime. These field equations are a set of 10 simultaneous, non-linear, differential equations. The solutions of the field equations are the components of the metric tensor of spacetime, which describes its geometry. The geodesic paths of spacetime are calculated from the metric tensor.
+Notable solutions of the Einstein field equations include:
+
+The Schwarzschild solution, which describes spacetime surrounding a spherically symmetrical non-rotating uncharged massive object. For objects with radii smaller than the Schwarzschild radius, this solution generates a black hole with a central singularity.
+The Reissner–Nordström solution, in which the central object has an electrical charge. For charges with a geometrized length less than the geometrized length of the mass of the object, this solution produces black holes with an event horizon surrounding a Cauchy horizon.
+The Kerr solution for rotating massive objects. This solution also produces black holes with multiple horizons.
+The cosmological Robertson–Walker solution (from 1922 and 1924), which  predicts the expansion of the universe.
+General relativity has enjoyed much success because its predictions (not called for by older theories of gravity) have been regularly confirmed. For example:
+
+General relativity accounts for the anomalous perihelion precession of Mercury.
+Gravitational lensing was first confirmed in 1919, and has more recently been strongly confirmed through the use of a quasar which passes behind the Sun as seen from the Earth.
+The expansion of the universe (predicted by the Robertson–Walker metric) was confirmed by Edwin Hubble in 1929.
+The prediction that time runs slower at lower potentials has been confirmed by the Pound–Rebka experiment, the Hafele–Keating experiment, and the GPS.
+The time delay of light passing close to a massive object was first identified by Irwin Shapiro in 1964 in interplanetary spacecraft signals.
+Gravitational radiation has been indirectly confirmed through studies of binary pulsars such as PSR 1913+16.
+In 2015, the LIGO experiments directly detected gravitational radiation from two colliding black holes, making this the first direct observation of both gravitational waves and black holes.
+It is believed that neutron star mergers (since detected in 2017) and black hole formation may also create detectable amounts of gravitational radiation.
+
+=== Quantum gravity ===
+
+Several decades after the discovery of general relativity, it was realized that it cannot be the complete theory of gravity because it is incompatible with quantum mechanics. Later it was understood that it is possible to describe gravity in the framework of quantum field theory like the other fundamental forces. In this framework, the attractive force of gravity arises due to exchange of virtual gravitons, in the same way as the electromagnetic force arises from exchange of virtual photons. This reproduces general relativity in the classical limit, but only at the linearized level and postulating that the conditions for the applicability of Ehrenfest theorem holds, which is not always the case. Moreover, this approach fails at short distances of the order of the Planck length.
+
+== See also ==
+Anti-gravity
+History of physics
+
+== Notes ==
+
+== References ==
+
+=== Citations ===
+
+=== Sources ===
+Gillispie, Charles Coulston (1960). The Edge of Objectivity: An Essay in the History of Scientific Ideas. Princeton University Press. ISBN 0-691-02350-6. {{cite book}}: ISBN / Date incompatibility (help)
+Wallace, W. A. (2004a). "The enigma of Domingo de Soto: Uniformiter difformis and falling bodies in late medieval physics". In Wallace, W. A. (ed.). Domingo de Soto and the early Galileo: Essays on intellectual history. Routledge. (Reprinted from "The enigma of Domingo de Soto: Uniformiter difformis and falling bodies in late medieval physics". (1968). Isis, 59(4), 384–401).
+Wallace, W. A. (2004b). "Domingo de Soto and the Iberian roots of Galileo's science". In Wallace, W. A. (ed.). Domingo de Soto and the early Galileo: Essays on intellectual history. Routledge. (Reprinted from White, K. (Ed.). (1997). Hispanic philosophy in the age of discovery. Studies in Philosophy and the History of Philosophy 29. Catholic University of America Press).
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_loop_quantum_gravity-0.md b/data/en.wikipedia.org/wiki/History_of_loop_quantum_gravity-0.md
new file mode 100644
index 000000000..1d5222ee6
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_loop_quantum_gravity-0.md
@@ -0,0 +1,32 @@
+---
+title: "History of loop quantum gravity"
+chunk: 1/2
+source: "https://en.wikipedia.org/wiki/History_of_loop_quantum_gravity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:35.490943+00:00"
+instance: "kb-cron"
+---
+
+The history of loop quantum gravity spans more than three decades of intense research.
+
+== History ==
+
+=== Classical theories of gravitation ===
+General relativity is the theory of gravitation published by Albert Einstein in 1915. According to it, the force of gravity is a manifestation of the local geometry of spacetime. Mathematically, the theory is modelled after Bernhard Riemann's metric geometry, but the Lorentz group of spacetime symmetries (an essential ingredient of Einstein's own theory of special relativity) replaces the group of rotational symmetries of space. (Later, loop quantum gravity inherited this geometric interpretation of gravity, and posits that a quantum theory of gravity is fundamentally a quantum theory of spacetime.)
+In the 1920s, the French mathematician Élie Cartan formulated Einstein's theory in the language of bundles and connections, a generalization of Riemannian geometry to which Cartan made important contributions. The so-called Einstein–Cartan theory of gravity not only reformulated but also generalized general relativity, and allowed spacetimes with torsion as well as curvature. In Cartan's geometry of bundles, the concept of parallel transport is more fundamental than that of distance, the centerpiece of Riemannian geometry. A similar conceptual shift occurs between the invariant interval of Einstein's general relativity and the parallel transport of Einstein–Cartan theory.
+
+=== Spin networks ===
+In 1971, physicist Roger Penrose explored the idea of space arising from a quantum combinatorial structure. His investigations resulted in the development of spin networks. Because this was a quantum theory of the rotational group and not the Lorentz group, Penrose went on to develop twistors.
+
+=== Loop quantum gravity ===
+In 1982, Amitabha Sen tried to formulate a Hamiltonian formulation of general relativity based on spinorial variables, where these variables are the left and right spinorial component equivalents of Einstein–Cartan connection of general relativity. Particularly, Sen discovered a new way to write down the two constraints of the ADM Hamiltonian formulation of general relativity in terms of these spinorial connections. In his form, the constraints are simply conditions that the spinorial Weyl curvature is trace free and symmetric. He also discovered the presence of new constraints which he suggested to be interpreted as the equivalent of Gauss constraint of Yang–Mills field theories. But Sen's work fell short of giving a full clear systematic theory and particularly failed to clearly discuss the conjugate momenta to the spinorial variables, its physical interpretation, and its relation to the metric (in his work he indicated this as some lambda variable).
+In 1986–87, physicist Abhay Ashtekar completed the project which Amitabha Sen began. He clearly identified the fundamental conjugate variables of spinorial gravity: The configuration variable is as a spinoral connection (a rule for parallel transport; technically, a connection) and the conjugate momentum variable is a coordinate frame (called a vierbein) at each point. So these variable became what we know as Ashtekar variables, a particular flavor of Einstein–Cartan theory with a complex connection. General relativity theory expressed in this way, made possible to pursue quantization of it using well-known techniques from quantum gauge field theory.
+The quantization of gravity in the Ashtekar formulation was based on Wilson loops, a technique developed by Kenneth G. Wilson in 1974 to study the strong-interaction regime of quantum chromodynamics (QCD). It is interesting in this connection that Wilson loops were known to be ill-behaved in the case of standard quantum field theory on (flat) Minkowski space, and so did not provide a nonperturbative quantization of QCD. However, because the Ashtekar formulation was background-independent, it was possible to use Wilson loops as the basis for nonperturbative quantization of gravity.
+Due to efforts by Sen and Ashtekar, a setting in which the Wheeler–DeWitt equation was written in terms of a well-defined Hamiltonian operator on a well-defined Hilbert space was obtained. This led to the construction of the first known exact solution, the so-called Chern–Simons form or Kodama state. The physical interpretation of this state remains obscure.
+In 1988–90, Carlo Rovelli and Lee Smolin obtained an explicit basis of states of quantum geometry, which turned out to be labeled by Penrose's spin networks. In this context, spin networks arose as a generalization of Wilson loops necessary to deal with mutually intersecting loops. Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial. Loop quantum gravity (LQG) thus became related to topological quantum field theory and group representation theory.
+In 1994, Rovelli and Smolin showed that the quantum operators of the theory associated to area and volume have a discrete spectrum. Work on the semi-classical limit, the continuum limit, and dynamics was intense after this, but progress was slower.
+On the semi-classical limit front, the goal is to obtain and study analogues of the harmonic oscillator coherent states (candidates are known as weave states).
+
+=== Hamiltonian dynamics ===
+LQG was initially formulated as a quantization of the Hamiltonian ADM formalism, according to which the Einstein equations are a collection of constraints (Gauss, Diffeomorphism and Hamiltonian). The kinematics are encoded in the Gauss and Diffeomorphism constraints, whose solution is the space spanned by the spin network basis. The problem is to define the Hamiltonian constraint as a self-adjoint operator on the kinematical state space. The most promising work in this direction is Thomas Thiemann's Phoenix Project.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_loop_quantum_gravity-1.md b/data/en.wikipedia.org/wiki/History_of_loop_quantum_gravity-1.md
new file mode 100644
index 000000000..f04e92ef8
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_loop_quantum_gravity-1.md
@@ -0,0 +1,46 @@
+---
+title: "History of loop quantum gravity"
+chunk: 2/2
+source: "https://en.wikipedia.org/wiki/History_of_loop_quantum_gravity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:35.490943+00:00"
+instance: "kb-cron"
+---
+
+=== Covariant dynamics ===
+Much of the recent work in LQG has been done in the covariant formulation of the theory, called "spin foam theory." The present version of the covariant dynamics is due to the convergent work of different groups, but it is commonly named after a paper by Jonathan Engle, Roberto Pereira and Carlo Rovelli in 2007–08. Heuristically, it would be expected that evolution between spin network states might be described by discrete combinatorial operations on the spin networks, which would then trace a two-dimensional skeleton of spacetime. This approach is related to state-sum models of statistical mechanics and topological quantum field theory such as the Turaeev–Viro model of 3D quantum gravity, and also to the Regge calculus approach to calculate the Feynman path integral of general relativity by discretizing spacetime.
+
+== See also ==
+History of string theory
+
+== References ==
+
+== Further reading ==
+Topical reviews
+Carlo Rovelli, "Loop Quantum Gravity," Living Reviews in Relativity 1, (1998), 1, online article, 2001 version.
+Thomas Thiemann, "Lectures on Loop Quantum Gravity," e-print available as gr-qc/0210094
+Abhay Ashtekar and Jerzy Lewandowski, "Background Independent Quantum Gravity: A Status Report," e-print available as gr-qc/0404018
+Carlo Rovelli and Marcus Gaul, "Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance," e-print available as gr-qc/9910079.
+Lee Smolin, "The Case for Background Independence," e-print available as hep-th/0507235.
+Popular books
+Julian Barbour, The End of Time: The Next Revolution in Our Understanding of the Universe (1999).
+Lee Smolin, Three Roads to Quantum Gravity (2001).
+Carlo Rovelli, Che cos'è il tempo? Che cos'è lo spazio?, Di Renzo Editore, Roma, 2004. French translation: Qu'est ce que le temps? Qu'est ce que l'espace?, Bernard Gilson ed, Brussel, 2006. English translation: What is Time? What is space?, Di Renzo Editore, Roma, 2006.
+Magazine articles
+Lee Smolin, "Atoms in Space and Time", Scientific American, January 2004.
+Easier introductory, expository or critical works
+Abhay Ashtekar, "Gravity and the Quantum," e-print available as gr-qc/0410054.
+John C. Baez and Javier P. Muniain, Gauge Fields, Knots and Quantum Gravity, World Scientific (1994).
+Carlo Rovelli, "A Dialog on Quantum Gravity," e-print available as hep-th/0310077.
+More advanced introductory/expository works
+Carlo Rovelli, Quantum Gravity, Cambridge University Press (2004); draft available online.
+Thomas Thiemann, "Introduction to Modern Canonical Quantum General Relativity," e-print available as gr-qc/0110034.
+Abhay Ashtekar, New Perspectives in Canonical Gravity, Bibliopolis (1988).
+Abhay Ashtekar, Lectures on Non-Perturbative Canonical Gravity, World Scientific (1991).
+Rodolfo Gambini and Jorge Pullin, Loops, Knots, Gauge Theories and Quantum Gravity, Cambridge University Press (1996).
+Hermann Nicolai, Kasper Peeters, Marija Zamaklar, "Loop Quantum Gravity: An Outside View," e-print available as hep-th/0501114.
+"Loop and Spin Foam Quantum Gravity: A Brief Guide for beginners" arXiv:hep-th/0601129 H. Nicolai and K. Peeters.
+Edward Witten, "Quantum Background Independence In String Theory," e-print available as hep-th/9306122.
+Conference proceedings
+John C. Baez (ed.), Knots and Quantum Gravity (1993).
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_materials_science-0.md b/data/en.wikipedia.org/wiki/History_of_materials_science-0.md
index 3e0bfbfeb..776906897 100644
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+date_saved: "2026-05-05T16:29:39.536188+00:00"
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diff --git a/data/en.wikipedia.org/wiki/History_of_materials_science-1.md b/data/en.wikipedia.org/wiki/History_of_materials_science-1.md
index 3c031e07f..d1551424d 100644
--- a/data/en.wikipedia.org/wiki/History_of_materials_science-1.md
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 category: "reference"
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-date_saved: "2026-05-05T16:16:07.324542+00:00"
+date_saved: "2026-05-05T16:29:39.536188+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/History_of_materials_science-2.md b/data/en.wikipedia.org/wiki/History_of_materials_science-2.md
index ab26fd4a3..1593faaa1 100644
--- a/data/en.wikipedia.org/wiki/History_of_materials_science-2.md
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+date_saved: "2026-05-05T16:29:39.536188+00:00"
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diff --git a/data/en.wikipedia.org/wiki/History_of_materials_science-3.md b/data/en.wikipedia.org/wiki/History_of_materials_science-3.md
index ab5d2a067..60264d22a 100644
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-date_saved: "2026-05-05T16:16:07.324542+00:00"
+date_saved: "2026-05-05T16:29:39.536188+00:00"
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diff --git a/data/en.wikipedia.org/wiki/History_of_nuclear_fusion-0.md b/data/en.wikipedia.org/wiki/History_of_nuclear_fusion-0.md
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+---
+title: "History of nuclear fusion"
+chunk: 1/6
+source: "https://en.wikipedia.org/wiki/History_of_nuclear_fusion"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:53.709188+00:00"
+instance: "kb-cron"
+---
+
+The history of nuclear fusion began early in the 20th century as an inquiry into how stars powered themselves and expanded to incorporate a broad inquiry into the nature of matter and energy, as potential applications expanded to include warfare, energy production and rocket propulsion.
+
+== Early research ==
+
+In 1920, the British physicist, Francis William Aston, discovered that the mass of four hydrogen atoms is greater than the mass of one helium atom (He-4), which implied that energy can be released by combining hydrogen atoms to form helium. This provided the first hints of a mechanism by which stars could produce energy. Throughout the 1920s, Arthur Stanley Eddington became a major proponent of the proton–proton chain reaction (PP reaction) as the primary system running the Sun. Quantum tunneling was discovered by Friedrich Hund in 1929, and shortly afterwards Robert Atkinson and Fritz Houtermans used the measured masses of light elements to show that large amounts of energy could be released by fusing small nuclei.
+Henry Norris Russell observed that the relationship in the Hertzsprung–Russell diagram suggested that a star's heat came from a hot core rather than from the entire star. Eddington used this to calculate that the temperature of the core would have to be about 40 million K. This became a matter of debate, because the value is much higher than astronomical observations that suggested about one-third to one-half that value. George Gamow introduced the mathematical basis for quantum tunnelling in 1928. In 1929, Robert d'Escourt Atkinson and Fritz Houtermans provided the first estimates of the stellar fusion rate. They showed that fusion can occur at lower energies than previously believed, backing Eddington's calculations.
+Nuclear experiments began using a particle accelerator built by John Cockcroft and Ernest Walton at Ernest Rutherford's Cavendish Laboratory at the University of Cambridge. In 1932, Walton produced the first man-made fission by using protons from the accelerator to split lithium into alpha particles. The accelerator was then used to fire deuterons at various targets. Working with Rutherford and others, Mark Oliphant discovered the nuclei of helium-3 (helions) and tritium (tritons), the first case of human-caused fusion.
+Neutrons from fusion were first detected in 1933. The experiment involved the acceleration of protons towards a target at energies of up to 600,000 electron volts. In August 1938, Arthur J. Ruhlig published an article in the Physical Review, in which he recorded observations on deuterium-tritium fusion. Although not well known or much cited, the paper inspired the Manhattan Project to investigate the process.
+A theory verified by Hans Bethe in 1939 showed that beta decay and quantum tunneling in the Sun's core might convert one of the protons into a neutron and thereby produce deuterium rather than a diproton. The deuterium would then fuse through other reactions to further increase the energy output. For this work, Bethe won the 1967 Nobel Prize in Physics.
+In 1938, Peter Thonemann developed a detailed plan for a pinch device, but was told to do other work for his thesis.
+The first patent related to a fusion reactor was registered in 1946 by the United Kingdom Atomic Energy Authority. The inventors were Sir George Paget Thomson and Moses Blackman. This was the first detailed examination of the Z-pinch concept. Starting in 1947, two UK teams carried out experiments based on this concept.
+
+== 1950s ==
+
+The first successful man-made fusion device was the boosted fission weapon tested in 1951 in the Greenhouse Item test. The first true fusion weapon was 1952's Ivy Mike, and the first practical example was 1954's Castle Bravo. In these devices, the energy released by a fission explosion compresses and heats the fuel, starting a fusion reaction. Fusion releases neutrons. These neutrons hit the surrounding fission fuel, causing the atoms to split apart much faster than normal fission processes. This increased the effectiveness of bombs: normal fission weapons blow themselves apart before all their fuel is used; fusion/fission weapons do not waste their fuel.
+
+=== Stellarator ===
+In 1949 expatriate German Ronald Richter proposed the Huemul Project in Argentina, announcing positive results in 1951. These turned out to be fake, but prompted others' interest. Lyman Spitzer began considering ways to solve problems involved in confining a hot plasma, and, unaware of the Z-pinch efforts, he created the stellarator. Spitzer applied to the US Atomic Energy Commission for funding to build a test device.
+During this period, James L. Tuck, who had worked with the UK teams on Z-pinch, had been introducing the stellarator concept to his coworkers at LANL. When he heard of Spitzer's pitch, he applied to build a pinch machine of his own, the Perhapsatron.
+Spitzer's idea won funding and he began work under Project Matterhorn. His work led to the creation of Princeton Plasma Physics Laboratory (PPPL). Tuck returned to LANL and arranged local funding to build his machine. By this time it was clear that the pinch machines were afflicted by instability, stalling progress. In 1953, Tuck and others suggested solutions that led to a second series of pinch machines, such as the ZETA and Sceptre devices.
+Spitzer's first machine, 'A' worked, but his next one, 'B', suffered from instabilities and plasma leakage.
+In 1954 AEC chair Lewis Strauss foresaw electricity as "too cheap to meter". Strauss was likely referring to fusion power, part of the secret Project Sherwood—but his statement was interpreted as referring to fission. The AEC had issued more realistic testimony regarding fission to Congress months before, projecting that "costs can be brought down... [to]... about the same as the cost of electricity from conventional sources..."
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+---
+title: "History of nuclear fusion"
+chunk: 2/6
+source: "https://en.wikipedia.org/wiki/History_of_nuclear_fusion"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:53.709188+00:00"
+instance: "kb-cron"
+---
+
+=== Edward Teller ===
+In 1951 Edward Teller and Stanislaw Ulam at Los Alamos National Laboratory (LANL) developed the Teller-Ulam design for a thermonuclear weapon, allowing for the development of multi-megaton yield fusion bombs. Fusion work in the UK was classified after the Klaus Fuchs affair.
+In the mid-1950s the theoretical tools used to calculate the performance of fusion machines were not predicting their actual behavior. Machines invariably leaked plasma at rates far higher than predicted. In 1954, Edward Teller gathered fusion researchers at the Princeton Gun Club. He pointed out the problems and suggested that any system that confined plasma within concave fields was doomed due to what became known as interchange instability. Attendees remember him saying in effect that the fields were like rubber bands, and they would attempt to snap back to a straight configuration whenever the power was increased, ejecting the plasma. He suggested that the only way to predictably confine plasma would be to use convex fields: a "cusp" configuration.:118
+When the meeting concluded, most researchers turned out papers explaining why Teller's concerns did not apply to their devices. Pinch machines did not use magnetic fields in this way, while the mirror and stellarator claques proposed various solutions. This was soon followed by Martin David Kruskal and Martin Schwarzschild's paper discussing pinch machines, however, which demonstrated those devices' instabilities were inherent.:118
+
+=== ZETA ===
+The largest "classic" pinch device was the ZETA, which started operation in the UK in 1957. Its name is a take-off on small experimental fission reactors that often had "zero energy" in their name, such as ZEEP.
+In early 1958, John Cockcroft announced that fusion had been achieved in the ZETA, an announcement that made headlines around the world. He dismissed US physicists' concerns. US experiments soon produced similar neutrons, although temperature measurements suggested these could not be from fusion. The ZETA neutrons were later demonstrated to be from different versions of the instability processes that had plagued earlier machines. Cockcroft was forced to retract his fusion claims, tainting the entire field for years. ZETA ended in 1968.
+
+=== Scylla ===
+The first experiment to achieve controlled thermonuclear fusion was accomplished using Scylla I at LANL in 1958. Scylla I was a θ-pinch machine, with a cylinder full of deuterium. Electric current shot down the sides of the cylinder. The current made magnetic fields that pinched the plasma, raising temperatures to 15 million degrees Celsius, for long enough that atoms fused and produced neutrons. The Sherwood program sponsored a series of Scylla machines at Los Alamos. The program began with 5 researchers and $100,000 in US funding in January 1952. By 1965, a total of $21 million had been spent. The θ-pinch approach was abandoned after calculations showed it could not scale up to produce a reactor.
+
+=== Tokamak ===
+In 1950–1951 in the Soviet Union, Igor Tamm and Andrei Sakharov first discussed a tokamak-like approach. Experimental research on those designs began in 1956 at the Moscow Kurchatov Institute by a group of Soviet scientists led by Lev Artsimovich. The tokamak essentially combined a low-power pinch device with a low-power stellarator. The notion was to combine the fields in such a way that the particles orbited within the reactor a particular number of times, today known as the "safety factor". The combination of these fields dramatically improved confinement times and densities, resulting in huge improvements over existing devices.
+
+=== Other ===
+
+In 1951, the United States completed the Greenhouse Item test of the first boosted fission weapon. A deuterium–tritium gas was used to enhance the fission yield. This became the first instance of artificial thermonuclear fusion, and the first weaponization of fusion. In 1952 Ivy Mike, part of Operation Ivy, became the first detonation of a hydrogen bomb, yielding 10.4 megatons of TNT using liquid deuterium. Cousins and Ware built a toroidal pinch device in England and demonstrated that the plasma in pinch devices is inherently unstable. In 1953 The Soviet Union tested its RDS-6S test, (codenamed "Joe 4" in the US) demonstrated a fission/fusion/fission ("Layercake") design that yielded 600 kilotons. Igor Kurchatov spoke at Harwell on pinch devices, revealing that the USSR was working on fusion.
+Seeking to generate electricity, Japan, France and Sweden all start fusion research programs
+In 1955, John D. Lawson (scientist) creates what is now known as the Lawson criterion which is a criterion for a fusion reactor to produce more energy than is lost to the environment due to problems like Bremsstrahlung radiation.
+In 1956 the Soviet Union began publishing articles on plasma physics, leading the US and UK to follow over the next several years.
+The Sceptre III z-pinch plasma column remained stable for 300 to 400 microseconds, a dramatic improvement on previous efforts. The team calculated that the plasma had an electrical resistivity around 100 times that of copper, and was able to carry 200 kA of current for 500 microseconds.
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+---
+title: "History of nuclear fusion"
+chunk: 3/6
+source: "https://en.wikipedia.org/wiki/History_of_nuclear_fusion"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:53.709188+00:00"
+instance: "kb-cron"
+---
+
+== 1960s ==
+In 1960 John Nuckolls published the concept of inertial confinement fusion (ICF). The laser, introduced the same year, turned out to be a suitable "driver".
+In 1961 the Soviet Union tested its 50 megaton Tsar Bomba, the most powerful thermonuclear weapon ever.
+Spitzer published a key plasma physics text at Princeton in 1963. He took the ideal gas laws and adapted them to an ionized plasma, developing many of the fundamental equations used to model a plasma.
+Laser fusion was suggested in 1962 by scientists at LLNL. Initially, lasers had little power. Laser fusion (inertial confinement fusion) research began as early as 1965.
+At the 1964 World's Fair, the public was given its first fusion demonstration. The device was a Theta-pinch from General Electric. This was similar to the Scylla machine developed earlier at Los Alamos.
+By the mid-1960s progress had stalled across the world. All of the major designs were losing plasma at unsustainable rates. The 12-beam "4 pi laser" attempt at inertial confinement fusion developed at LLNL targeted a gas-filled target chamber of about 20 centimeters in diameter.
+The magnetic mirror was first published in 1967 by Richard F. Post and many others at LLNL. The mirror consisted of two large magnets arranged so they had strong fields within them, and a weaker, but connected, field between them. Plasma introduced in the area between the two magnets would "bounce back" from the stronger fields in the middle.
+A.D. Sakharov's group constructed the first tokamaks. The most successful were the T-3 and its larger version T-4. T-4 was tested in 1968 in Novosibirsk, producing the first quasistationary fusion reaction.:90 When this was announced, the international community was skeptical. A British team was invited to see T-3, and confirmed the Soviet claims. A burst of activity followed as many planned devices were abandoned and tokamaks were introduced in their place—the C model stellarator, then under construction after many redesigns, was quickly converted to the Symmetrical Tokamak.
+In his work with vacuum tubes, Philo Farnsworth observed that electric charge accumulated in the tube. In 1962, Farnsworth patented a design using a positive inner cage to concentrate plasma and fuse protons. During this time, Robert L. Hirsch joined Farnsworth Television labs and began work on what became the Farnsworth-Hirsch Fusor. This effect became known as the Multipactor effect. Hirsch patented the design in 1966 and published it in 1967.
+Plasma temperatures of approximately 40 million degrees Celsius and 109 deuteron-deuteron fusion reactions per discharge were achieved at LANL with Scylla IV.
+In 1968 the Soviets announced results from the T-3 tokamak, claiming temperatures an order of magnitude higher than any other device. A UK team, nicknamed "The Culham Five", confirmed the results. The results led many other teams, including the Princeton group, which converted their stellarator to a tokamak.
+
+== 1970s ==
+
+Princeton's conversion of the Model C stellarator to a tokamak produced results matching the Soviets. With an apparent solution to the magnetic bottle problem in-hand, plans begin for a larger machine to test scaling and methods to heat the plasma.
+In 1972, John Nuckolls outlined the idea of fusion ignition, a fusion chain reaction. Hot helium made during fusion reheats the fuel and starts more reactions. Nuckolls's paper started a major development effort. LLNL built laser systems including Argus, Cyclops, Janus, the neodymium-doped glass (Nd:glass) laser Long Path, Shiva laser, and the 10 beam Nova in 1984. Nova would ultimately produce 120 kilojoules of infrared light during a nanosecond pulse.
+The UK built the Central Laser Facility in 1976.
+The "advanced tokamak" concept emerged, which included non-circular plasma, internal diverters and limiters, superconducting magnets, and operation in the so-called "H-mode" island of increased stability. Two other designs became prominent; the compact tokamak sited the magnets on the inside of the vacuum chamber, and the spherical tokamak with as small a cross section as possible.
+In 1974 J.B. Taylor re-visited ZETA and noticed that after an experimental run ended, the plasma entered a short period of stability. This led to the reversed field pinch concept. On May 1, 1974, the KMS fusion company (founded by Kip Siegel) achieved the world's first laser induced fusion in a deuterium-tritium pellet.
+
+The Princeton Large Torus (PLT), the follow-on to the Symmetrical Tokamak, surpassed the best Soviet machines and set temperature records that were above what was needed for a commercial reactor. Soon after it received funding with the target of breakeven.
+In the mid-1970s, Project PACER, carried out at LANL explored the possibility of exploding small hydrogen bombs (fusion bombs) inside an underground cavity.:25 As an energy source, the system was the only system that could work using the technology of the time. It required a large, continuous supply of nuclear bombs, however, with questionable economics.
+In 1976, the two beam Argus laser became operational at LLNL. In 1977, the 20 beam Shiva laser there was completed, capable of delivering 10.2 kilojoules of infrared energy on target. At a price of $25 million and a size approaching that of a football field, Shiva was the first megalaser.
+At a 1977 workshop at the Claremont Hotel in Berkeley Dr. C. Martin Stickley, then Director of the Energy Research and Development Agency 's Office of Inertial Fusion, claimed that "no showstoppers" lay on the road to fusion energy.
+The DOE selected a Princeton design Tokamak Fusion Test Reactor (TFTR) and the challenge of running on deuterium-tritium fuel.
+The 20 beam Shiva laser at LLNL became capable of delivering 10.2 kilojoules of infrared energy on target. Costing $25 million and nearly covering a football field, Shiva was the first "megalaser" at LLNL.
+
+== 1980s ==
+  
+
+In the German/US HIBALL study, Garching used the high repetition rate of the RF driver to serve four reactor chambers using liquid lithium inside the chamber cavity. In 1982 high-confinement mode (H-mode) was discovered in ASDEX. 
\ No newline at end of file
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+---
+title: "History of nuclear fusion"
+chunk: 4/6
+source: "https://en.wikipedia.org/wiki/History_of_nuclear_fusion"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:53.709188+00:00"
+instance: "kb-cron"
+---
+
+=== Magnetic mirror ===
+The US funded a magnetic mirror program in the late 1970s and early 1980s. This program resulted in a series of magnetic mirror devices including: 2X,:273 Baseball I, Baseball II, the Tandem Mirror Experiment and upgrade, the Mirror Fusion Test Facility, and MFTF-B. These machines were built and tested at LLNL from the late 1960s to the mid-1980s. The final machine, MFTF cost 372 million dollars and was, at that time, the most expensive project in LLNL history. It opened on February 21, 1986, and immediately closed, allegedly to balance the federal budget.
+
+=== Laser ===
+Laser fusion progress: in 1983, the NOVETTE laser was completed. The following December, the ten-beam NOVA laser was finished. Five years later, NOVA produced 120 kilojoules of infrared light during a nanosecond pulse.
+Research focused on either fast delivery or beam smoothness. Both focused on increasing energy uniformity. One early problem was that the light in the infrared wavelength lost energy before hitting the fuel. Breakthroughs were made at LLE at University of Rochester. Rochester scientists used frequency-tripling crystals to transform infrared laser beams into ultraviolet beams.
+
+==== Chirped-pulse amplification laser technique ====
+In 1985, Donna Strickland and Gérard Mourou invented a method to amplify ultra-short laser pulses by frequency "chirping" them before amplification. This approach rearranges the frequency content of a picosecond or shorter pulse by group-velocity dispersion (GVD), creating a pulse stretched in time by a factor of 1,000 or more, and reducing peak intensity by the same factor. This much less intense, longer duration, pulse can then be safely amplified to an intensity approaching the practical limit of the laser (such as the optical damage threshold). After amplification the pulse is recompressed to near-original duration, using an optical system having the opposite sign of group-velocity dispersion. This recompression in time of 1,000 or more means a jump in intensity of the same factor, producing a pulse orders of magnitude more intense than could have been produced by direct laser amplification. Chirp pulsed amplification rapidly became a transformative contribution for research in high-intensity laser-matter interaction physics, using laser systems like ELI Beamlines, Omega EP, and many others worldwide, as well as for the ‘fast ignition’ concept of laser fusion in which fuel compression and fuel heating become partially separated processes.
+LANL constructed a series of laser facilities. They included Gemini (a two beam system), Helios (eight beams), Antares (24 beams) and Aurora (96 beams). The program ended in the early nineties with a cost on the order of one billion dollars.
+In 1987, Akira Hasegawa noticed that in a dipolar magnetic field, fluctuations tended to compress the plasma without energy loss. This effect was noticed in data taken by Voyager 2, when it encountered Uranus. This observation became the basis for a fusion approach known as the levitated dipole.
+In tokamaks, the Tore Supra was under construction from 1983 to 1988 in Cadarache, France. Its superconducting magnets permitted it to generate a strong permanent toroidal magnetic field. First plasma came in 1988.
+In 1983, JET achieved first plasma. In 1985, the Japanese tokamak, JT-60 produced its first plasmas. In 1988, the T-15 a Soviet tokamak was completed, the first to use (helium-cooled) superconducting magnets.
+In 1998, the T-15 Soviet tokamak with superconducting helium-cooled coils was completed.
+
+=== Spherical tokamak ===
+In 1984, Martin Peng proposed an alternate arrangement of magnet coils that would greatly reduce the aspect ratio while avoiding the erosion issues of the compact tokamak: a spherical tokamak. Instead of wiring each magnet coil separately, he proposed using a single large conductor in the center, and wiring the magnets as half-rings off of this conductor. What was once a series of individual rings passing through the hole in the center of the reactor was reduced to a single post, allowing for aspect ratios as low as 1.2.:B247:225 The ST concept appeared to represent an enormous advance in tokamak design. The proposal came during a period when US fusion research budgets were dramatically smaller. ORNL was provided with funds to develop a suitable central column built out of a high-strength copper alloy called "Glidcop". However, they were unable to secure funding to build a demonstration machine.
+Failing at ORNL, Peng began a worldwide effort to interest other teams in the concept and get a test machine built. One approach would be to convert a spheromak.:225 Peng's advocacy caught the interest of Derek Robinson, of the United Kingdom Atomic Energy Authority. Robinson gathered a team and secured on the order of 100,000 pounds to build an experimental machine, the Small Tight Aspect Ratio Tokamak, or START. Parts of the machine were recycled from earlier projects, while others were loaned from other labs, including a 40 keV neutral beam injector from ORNL. Construction began in 1990 and operation started in January 1991.:11 It achieved a record beta (plasma pressure compared to magnetic field pressure) of 40% using a neutral beam injector
+
+=== ITER ===
+The International Thermonuclear Experimental Reactor (ITER) coalition forms, involving EURATOM, Japan, the Soviet Union and United States and kicks off the conceptual design process.
+
+== 1990s ==
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+---
+title: "History of nuclear fusion"
+chunk: 5/6
+source: "https://en.wikipedia.org/wiki/History_of_nuclear_fusion"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:53.709188+00:00"
+instance: "kb-cron"
+---
+
+In 1991 JET's Preliminary Tritium Experiment achieved the world's first controlled release of fusion power.
+In 1992, Physics Today published Robert McCory's outline of the current state of ICF, advocating for a national ignition facility. This was followed by a review article from John Lindl in 1995, making the same point. During this time various ICF subsystems were developed, including target manufacturing, cryogenic handling systems, new laser designs (notably the NIKE laser at NRL) and improved diagnostics including time of flight analyzers and Thomson scattering. This work was done at the NOVA laser system, General Atomics, Laser Mégajoule and the GEKKO XII system in Japan. Through this work and lobbying by groups like the fusion power associates and John Sethian at NRL, Congress authorized funding for the NIF project in the late nineties.
+In 1992 the United States and the former republics of the Soviet Union stopped testing nuclear weapons.
+In 1993 TFTR at PPPL experimented with 50% deuterium, 50% tritium, eventually reaching 10 megawatts.
+In the early nineties, theory and experimental work regarding fusors and polywells was published. In response, Todd Rider at MIT developed general models of these devices, arguing that all plasma systems at thermodynamic equilibrium were fundamentally limited. In 1995, William Nevins published a criticism arguing that the particles inside fusors and polywells would acquire angular momentum, causing the dense core to degrade.
+In 1995, the University of Wisconsin–Madison built a large fusor, known as HOMER. Dr George H. Miley at Illinois built a small fusor that produced neutrons using deuterium and discovered the "star mode" of fusor operation. At this time in Europe, an IEC device was developed as a commercial neutron source by Daimler-Chrysler and NSD Fusion.
+The next year, Tore Supra reached a record plasma duration of two minutes with a current of almost 1 M amperes driven non-inductively by 2.3 MW of lower hybrid frequency waves (i.e. 280 MJ of injected and extracted energy), enabled by actively cooled plasma-facing components.
+The upgraded Z-machine opened to the public in August 1998. The key attributes were its 18 million ampere current and a discharge time of less than 100 nanoseconds. This generated a magnetic pulse inside a large oil tank, which struck a liner (an array of tungsten wires). Firing the Z-machine became a way to test high energy, high temperature (2 billion degrees) conditions. In 1996.
+In 1997, JET reached 16.1 MW (65% of heat to plasma), sustaining over 10 MW for over 0.5 sec. As of 2020 this remained the record output level. Four megawatts of alpha particle self-heating was achieved.
+ITER was officially announced as part of a seven-party consortium (six countries and the EU). ITER was designed to produce ten times more fusion power than the input power. ITER was sited in Cadarache. The US withdrew from the project in 1999.
+JT-60 produced a reversed shear plasma with the equivalent fusion amplification factor 
+  
+    
+      
+        
+          Q
+          
+            e
+            q
+          
+        
+      
+    
+    {\displaystyle Q_{eq}}
+  
+ of 1.25 - as of 2021 this remained the world record.
+In the late nineties, a team at Columbia University and MIT developed the levitated dipole, a fusion device that consisted of a superconducting electromagnet, floating in a saucer shaped vacuum chamber. Plasma swirled around this donut and fused along the center axis.
+In 1999 MAST replaced START.
+
+== 2000s ==
+
+"Fast ignition" appeared in the late nineties, as part of a push by LLE to build the Omega EP system, which finished in 2008. Fast ignition showed dramatic power savings and moved ICF into the race for energy production. The HiPER experimental facility became dedicated to fast ignition.
+In 2001 the United States, China and Republic of Korea joined ITER while Canada withdrew.
+In April 2005, a UCLA team announced a way of producing fusion using a machine that "fits on a lab bench", using lithium tantalate to generate enough voltage to fuse deuterium. The process did not generate net power.
+The next year, China's EAST test reactor was completed. This was the first tokamak to use superconducting magnets to generate both toroidal and poloidal fields.
+In the early 2000s, LANL researchers claimed that an oscillating plasma could reach local thermodynamic equilibrium. This prompted the POPS and Penning trap designs.
+In 2005 NIF fired its first bundle of eight beams, achieving the most powerful laser pulse to date - 152.8 kJ (infrared).
+MIT researchers became interested in fusors for space propulsion, using fusors with multiple inner cages. Greg Piefer founded Phoenix Nuclear Labs and developed the fusor into a neutron source for medical isotope production. Robert Bussard began speaking openly about the polywell in 2006.
+In March 2009, NIF became operational.
+In the early 2000s privately backed fusion companies launched to develop commercial fusion power. Tri Alpha Energy, founded in 1998, began by exploring a field-reversed configuration approach. In 2002, Canadian company General Fusion began proof-of-concept experiments based on a hybrid magneto-inertial approach called Magnetized Target Fusion. Investors included Jeff Bezos (General Fusion) and Paul Allen (Tri Alpha Energy). Toward the end of the decade, Tokamak Energy started exploring spherical tokamak devices using reconnection.
+
+== 2010s ==
+
+Private and public research accelerated in the 2010s.
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+---
+title: "History of nuclear fusion"
+chunk: 6/6
+source: "https://en.wikipedia.org/wiki/History_of_nuclear_fusion"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:53.709188+00:00"
+instance: "kb-cron"
+---
+
+=== Private projects ===
+In 2017, General Fusion developed its plasma injector technology and Tri Alpha Energy constructed and operated its C-2U device. In August 2014, Phoenix Nuclear Labs announced the sale of a high-yield neutron generator that could sustain 5×1011 deuterium fusion reactions per second over a 24-hour period.
+In October 2014, Lockheed Martin's Skunk Works announced the development of a high beta fusion reactor, the Compact Fusion Reactor.
+In January 2015, the polywell was presented at Microsoft Research. TAE Technologies announced that its Norman reactor had achieved plasma.
+ST40 generated "first plasma".
+In 2018, Eni announced a $50 million investment in Commonwealth Fusion Systems, to attempt to commercialize ARC technology using a test reactor (SPARC) in collaboration with MIT. The reactor planned to employ yttrium barium copper oxide (YBCO) high-temperature superconducting magnet technology. Commonwealth Fusion Systems in 2021 tested successfully a 20 T magnet making it the strongest high-temperature superconducting magnet in the world. Following the 20 T magnet CFS raised $1.8 billion from private investors.
+General Fusion began developing a 70% scale demo system. In 2018, TAE Technologies' reactor reached nearly 20 M°C.
+
+=== Government and academic projects ===
+In 2010, NIF researchers conducted a series of "tuning" shots to determine the optimal target design and laser parameters for high-energy ignition experiments with fusion fuel. Net fuel energy gain was achieved in September 2013.
+In April 2014, LLNL ended the Laser Inertial Fusion Energy (LIFE) program and directed their efforts towards NIF.
+A 2012 paper demonstrated that a dense plasma focus had achieved temperatures of 1.8 billion degrees Celsius, sufficient for boron fusion, and that fusion reactions were occurring primarily within the contained plasmoid, necessary for net power.
+In August 2014, MIT announced a tokamak it named the ARC fusion reactor, using rare-earth barium-copper oxide (REBCO) superconducting tapes to construct high-magnetic field coils that it claimed produced comparable magnetic field strength in a smaller configuration than other designs.
+In October 2015, researchers at the Max Planck Institute of Plasma Physics completed building the largest stellarator to date, the Wendelstein 7-X. In December they produced the first helium plasma, and in February 2016 produced hydrogen plasma. 
+In 2014 EAST achieved a record confinement time of 30 seconds for plasma in the high-confinement mode (H-mode), thanks to improved heat dispersal. This was an order of magnitude improvement vs other reactors. In 2017 the reactor achieved a stable 101.2-second steady-state high confinement plasma, setting a world record in long-pulse H-mode operation.
+In 2018 MIT scientists formulated a theoretical means to remove the excess heat from compact nuclear fusion reactors via larger and longer divertors.
+In 2019 the United Kingdom announced a planned £200-million (US$248-million) investment to produce a design for a fusion facility named the Spherical Tokamak for Energy Production (STEP), by the early 2040s.
+
+== 2020s ==
+
+In December 2020, the Chinese experimental nuclear fusion reactor HL-2M achieved its first plasma discharge. In May 2021, Experimental Advanced Superconducting Tokamak (EAST) announced a new world record for superheated plasma, sustaining a temperature of 120 M°C for 101 seconds and a peak of 160 M°C for 20 seconds. In December 2021 EAST set a new world record for high temperature (70 M°C) plasma of 1,056 seconds.
+In 2020, Chevron Corporation announced an investment in start-up Zap Energy, co-founded by British entrepreneur and investor, Benj Conway, together with physicists Brian Nelson and Uri Shumlak from University of Washington. In 2021 the company raised $27.5 million in Series B funding led by Addition.
+In 2021, the US DOE launched the INFUSE program, a public-private knowledge sharing initiative involving a PPPL, MIT Plasma Science and Fusion Center and Commonwealth Fusion Systems partnership, together with partnerships with TAE Technologies, Princeton Fusion Systems, and Tokamak Energy. In 2021, DOE's Fusion Energy Sciences Advisory Committee approved a strategic plan to guide fusion energy and plasma physics research that included a working power plant by 2040, similar to Canadian, Chinese, and U.K. efforts.
+In January 2021, SuperOx announced the commercialization of a new superconducting wire, with more than 700 A/mm2 current capability.
+TAE Technologies announced that its Norman device had sustained a temperature of about 60 million degrees C for 30 milliseconds, 8 and 10 times higher, respectively, than the company's previous devices. The duration was claimed to be limited by the power supply rather than the device.
+In August 2021, the National Ignition Facility recorded a record-breaking 1.3 megajoules of energy created from fusion which is the first example of the Lawson criterion being surpassed in a laboratory.
+In February 2022, JET sustained 11 MW and a Q value of 0.33 for over 5 seconds, outputting 59.7 megajoules, using a mix of deuterium and tritium for fuel. In March 2022 it was announced that Tokamak Energy achieved a record plasma temperature of 100 million kelvins, inside a commercial compact tokamak.
+In October 2022, the Korea Superconducting Tokamak Advanced Research (KSTAR) reached a record plasma duration of 45 seconds, sustaining the high-temperature fusion plasma over the 100 million degrees Celsus based on the integrated real-time RMP control for ELM-less H-mode, i.e. fast ions regulated enhancement (FIRE) mode, machine learning algorithm, and 3D field optimization via an edge-localized RMP.
+In December 2022, the NIF achieved the first scientific breakeven controlled fusion experiment, with an energy gain of 1.5.
+In February 2024, the KSTAR tokamak set a new record (shot #34705) for the longest duration (102 seconds) of a magnetically confined plasma. The plasma was operated in the H-mode, with much better control of the error field than was possible previously. KSTAR also set a record (shot #34445) for the longest steady-state duration at a temperature of 100 million degrees Celsius (48 seconds, ELM-LESS FIRE mode).
+
+== See also ==
+Timeline of nuclear fusion
+Fusion power § History
+Timeline of nuclear weapons development
+Timeline of nuclear power
+
+== References ==
+
+=== Citations ===
+
+=== Bibliography ===
+Cockburn, Stewart; Ellyard, David (1981). Oliphant, the life and times of Sir Mark Oliphant. Adelaide: Axiom Books. ISBN 0-9594164-0-4. OCLC 8666832.
+Dean, Stephen O. (2013). "The Ultimate Energy Source?". Search for the Ultimate Energy Source. Green Energy and Technology. New York, NY: Springer New York. pp. 233–238. doi:10.1007/978-1-4614-6037-4_15. ISBN 978-1-4614-6036-7. Retrieved 2021-06-14.
+
+== External links ==
+"Science Museum, London - Famous Fusion Experiments". 2003-12-16. Archived from the original on 2003-12-16. Retrieved 2022-11-06.
+Burkart, Werner (2005-09-21). "Status report on fusion research". Nuclear Fusion. 45 (10A). doi:10.1088/0029-5515/45/10a/e01. ISSN 0029-5515. S2CID 250865675.
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+source: "https://en.wikipedia.org/wiki/History_of_optics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:57.544716+00:00"
+instance: "kb-cron"
+---
+
+Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, followed by theories on light and vision developed by ancient Greek philosophers, and the development of geometrical optics in the Greco-Roman world. The word optics is derived from the Greek term τα ὀπτικά meaning 'appearance, look'. Optics was significantly reformed by the developments in the medieval Islamic world, such as the beginnings of physical and physiological optics, and then significantly advanced in early modern Europe, where diffractive optics began. These earlier studies on optics are now known as "classical optics". The term "modern optics" refers to areas of optical research that largely developed in the 20th century, such as wave optics and quantum optics.
+
+== Early history ==
+In the fifth century BCE, Empedocles postulated that everything was composed of four elements; fire, air, earth and water. He believed that Aphrodite made the human eye out of the four elements and that she lit the fire in the eye which shone out from the eye making sight possible. If this were true, then one could see during the night just as well as during the day, so Empedocles postulated an interaction between rays from the eyes and rays from a source such as the sun. He stated that light has a finite speed.
+In the 4th century BC Chinese text, credited to the philosopher Mozi, it is described how light passing through a pinhole creates an inverted image in a "collecting-point" or "treasure house".
+In his Optics Greek mathematician Euclid observed that "things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal". In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Pappus believed these results to be important in astronomy and included Euclid's Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Ptolemy.
+In 55 BC, Lucretius, a Roman atomist, wrote:
+
+For from whatsoever distances fires can throw us their light and breathe their warm heat upon our limbs, they lose nothing of the body of their flames because of the interspaces, their fire is no whit shrunken to the sight.
+In his Catoptrica, Hero of Alexandria showed by a geometrical method that the actual path taken by a ray of light reflected from a plane mirror is shorter than any other reflected path that might be drawn between the source and point of observation.
+The Indian Buddhists, such as Dignāga in the 5th century and Dharmakirti in the 7th century, developed a type of atomism which defined the atoms which make up the world as momentary flashes of light or energy. They viewed light as being an atomic entity equivalent to energy, though they also viewed all matter as being composed of these light/energy particles.
+
+=== Geometrical optics ===
+
+The early writers discussed here treated vision more as a geometrical than as a physical, physiological, or psychological problem. The first known author of a treatise on geometrical optics was the geometer Euclid (c. 325 BC–265 BC). Euclid began his study of optics as he began his study of geometry, with a set of self-evident axioms.
+
+Lines (or visual rays) can be drawn in a straight line to the object.
+Those lines falling upon an object form a cone.
+Those things upon which the lines fall are seen.
+Those things seen under a larger angle appear larger.
+Those things seen by a higher ray, appear higher.
+Right and left rays appear right and left.
+Things seen within several angles appear clearer.
+Euclid did not define the physical nature of these visual rays but, using the principles of geometry, he discussed the effects of perspective and the rounding of things seen at a distance.
+Where Euclid had limited his analysis to simple direct vision, Hero of Alexandria (c. AD 10–70) extended the principles of geometrical optics to consider problems of reflection (catoptrics).  Unlike Euclid, Hero occasionally commented on the physical nature of visual rays, indicating that they proceeded at great speed from the eye to the object seen and were reflected from smooth surfaces but could become trapped in the porosities of unpolished surfaces. This has come to be known as emission theory.
+Hero demonstrated the equality of the angle of incidence and reflection on the grounds that this is the shortest path from the object to the observer.  On this basis, he was able to define the fixed relation between an object and its image in a plane mirror.  Specifically, the image appears to be as far behind the mirror as the object really is in front of the mirror.
+Like Hero, Claudius Ptolemy in his second-century Optics considered the visual rays as proceeding from the eye to the object seen, but, unlike Hero, considered that the visual rays were not discrete lines, but formed a continuous cone.
+Optics documents Ptolemy's studies of reflection and refraction.  He measured the angles of refraction between air, water, and glass, but his published results indicate that he adjusted his measurements to fit his (incorrect) assumption that the angle of refraction is proportional to the angle of incidence.
+
+== In the Islamic world ==
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+
+Al-Kindi (c. 801–873) was one of the earliest important optical writers in the Islamic world.  In a work known in the west as De radiis stellarum, al-Kindi developed a theory "that everything in the world ... emits rays in every direction, which fill the whole world."   This theory of the active power of rays had an influence on later scholars such as Ibn al-Haytham, Robert Grosseteste and Roger Bacon.
+Ibn Sahl, a mathematician active in Baghdad during the 980s, is the first Islamic scholar known to have compiled a commentary on Ptolemy's Optics. His treatise Fī al-'āla al-muḥriqa "On the burning instruments" was reconstructed from fragmentary manuscripts by Rashed (1993). The work is concerned with how curved mirrors and lenses bend and focus light. Ibn Sahl also describes a law of refraction mathematically equivalent to Snell's law. He used his law of refraction to compute the shapes of lenses and mirrors that focus light at a single point on the axis.
+
+Ibn al-Haytham (known in as Alhacen or Alhazen in Western Europe), writing in the 1010s, received both Ibn Sahl's treatise and a partial Arabic translation of Ptolemy's Optics. He produced a comprehensive and systematic analysis of Greek optical theories.  Ibn al-Haytham's key achievement was twofold: first, to insist, against the opinion of Ptolemy, that vision occurred because of rays entering the eye; the second was to define the physical nature of the rays discussed by earlier geometrical optical writers, considering them as the forms of light and color.  
+He then analyzed these physical rays according to the principles of geometrical optics.  He wrote many books on optics, most significantly the Book of Optics (Kitab al Manazir in Arabic), translated into Latin as the De aspectibus or Perspectiva, which disseminated his ideas to Western Europe and had great influence on the later developments of optics. Ibn al-Haytham was called "the father of modern optics".
+Avicenna (980–1037) agreed with Alhazen that the speed of light is finite, as he "observed that if the perception of light is due to the emission of some sort of particles by a luminous source, the speed of light must be finite." Abū Rayhān al-Bīrūnī (973-1048) also agreed that light has a finite speed, and stated that the speed of light is much faster than the speed of sound.
+Abu 'Abd Allah Muhammad ibn Ma'udh, who lived in Al-Andalus during the second half of the 11th century, wrote a work on optics later translated into Latin as Liber de crepisculis, which was mistakenly attributed to Alhazen. This was a "short work containing an estimation of the angle of depression of the sun at the beginning of the morning twilight and at the end of the evening twilight, and an attempt to calculate on the basis of this and other data the height of the atmospheric moisture responsible for the refraction of the sun's rays." Through his experiments, he obtained the value of 18°, which comes close to the modern value.
+In the late 13th and early 14th centuries, Qutb al-Din al-Shirazi (1236–1311) and his student Kamāl al-Dīn al-Fārisī (1260–1320) continued the work of Ibn al-Haytham, and they were among the first to give the correct explanations for the rainbow phenomenon. Al-Fārisī published his findings in his Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).
+
+== In medieval Europe ==
+The English bishop Robert Grosseteste (c. 1175–1253) wrote on a wide range of scientific topics at the time of the origin of the medieval university and the recovery of the works of Aristotle.  Grosseteste reflected a period of transition between the Platonism of early medieval learning and the new Aristotelianism, hence he tended to apply mathematics and the Platonic metaphor of light in many of his writings.  He has been credited with discussing light from four different perspectives: an epistemology of light, a metaphysics or cosmogony of light, an etiology or physics of light, and a theology of light.
+Setting aside the issues of epistemology and theology, Grosseteste's cosmogony of light describes the origin of the universe in what may loosely be described as a medieval "big bang" theory.  Both his biblical commentary, the Hexaemeron (1230 x 35), and his scientific On Light (1235 x 40), took their inspiration from Genesis 1:3, "God said, let there be light", and described the subsequent process of creation as a natural physical process arising from the generative power of an expanding (and contracting) sphere of light.
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+instance: "kb-cron"
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+
+His more general consideration of light as a primary agent of physical causation appears in his On Lines, Angles, and Figures where he asserts that "a natural agent propagates its power from itself to the recipient" and in On the Nature of Places where he notes that "every natural action is varied in strength and weakness through variation of lines, angles and figures."
+The English Franciscan, Roger Bacon (c. 1214–1294) was strongly influenced by Grosseteste's writings on the importance of light.  In his optical writings (the Perspectiva, the De multiplicatione specierum, and the De speculis comburentibus) he cited a wide range of recently translated optical and philosophical works, including those of Alhacen, Aristotle, Avicenna, Averroes, Euclid, al-Kindi, Ptolemy, Tideus, and Constantine the African.  Although he was not a slavish imitator, he drew his mathematical analysis of light and vision from the writings of the Arabic writer, Alhacen.  But he added to this the Neoplatonic concept, perhaps drawn from Grosseteste, that every object radiates a power (species) by which it acts upon nearby objects suited to receive those species.  Note that Bacon's optical use of the term species differs significantly from the genus/species categories found in Aristotelian philosophy.
+Several later works, including the influential A Moral Treatise on the Eye (Latin: Tractatus Moralis de Oculo) by Peter of Limoges (1240–1306), helped popularize and spread the ideas found in Bacon's writings.
+Another English Franciscan, John Pecham (died 1292) built on the work of Bacon, Grosseteste, and a diverse range of earlier writers to produce what became the most widely used textbook on optics of the Middle Ages, the Perspectiva communis.  His book centered on the question of vision, on how we see, rather than on the nature of light and color.  Pecham followed the model set forth by Alhacen, but interpreted Alhacen's ideas in the manner of Roger Bacon.
+Like his predecessors, Witelo (born circa 1230, died between 1280 and 1314) drew on the extensive body of optical works recently translated from Greek and Arabic to produce a massive presentation of the subject entitled the Perspectiva.  His theory of vision follows Alhacen and he does not consider Bacon's concept of species, although passages in his work demonstrate that he was influenced by Bacon's ideas.  Judging from the number of surviving manuscripts, his work was not as influential as those of Pecham and Bacon, yet his importance, and that of Pecham, grew with the invention of printing.
+Theodoric of Freiberg (ca. 1250–ca. 1310) was among the first in Europe to provide the correct scientific explanation for the rainbow phenomenon, as well as Qutb al-Din al-Shirazi (1236–1311) and his student Kamāl al-Dīn al-Fārisī (1260–1320) mentioned above.
+
+== Renaissance and early modern period ==
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+
+Johannes Kepler (1571–1630) picked up the investigation of the laws of optics from his lunar essay of 1600. Both lunar and solar eclipses presented unexplained phenomena, such as unexpected shadow sizes, the red color of a total lunar eclipse, and the reportedly unusual light surrounding a total solar eclipse. Related issues of atmospheric refraction applied to all astronomical observations. Through most of 1603, Kepler paused his other work to focus on optical theory; the resulting manuscript, presented to the emperor on January 1, 1604, was published as Astronomiae Pars Optica (The Optical Part of Astronomy). In it, Kepler described the inverse-square law governing the intensity of light, reflection by flat and curved mirrors, and principles of pinhole cameras, as well as the astronomical implications of optics such as parallax and the apparent sizes of heavenly bodies.  Astronomiae Pars Optica is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent).
+Willebrord Snellius (1580–1626) found the mathematical law of refraction, now known as Snell's law, in 1621. Subsequently, René Descartes (1596–1650) showed, by using geometric construction and the law of refraction (also known as Descartes' law), that the angular radius of a rainbow is 42° (i.e. the angle subtended at the eye by the edge of the rainbow and the rainbow's centre is 42°). He also independently discovered the law of refraction, and his essay on optics was the first published mention of this law.
+Christiaan Huygens (1629–1695) wrote several works in the area of optics. These included the Opera reliqua (also known as Christiani Hugenii Zuilichemii, dum viveret Zelhemii toparchae, opuscula posthuma) and the Traité de la lumière.
+Isaac Newton (1643–1727) investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light. He also showed that the coloured light does not change its properties by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This is known as Newton's theory of colour. From this work he concluded that any refracting telescope would suffer from the dispersion of light into colours. He went on to invent a reflecting telescope (today known as a Newtonian telescope), which showed that using a mirror to form an image bypassed the problem. In 1671 the Royal Society asked for a demonstration of his reflecting telescope. Their interest encouraged him to publish his notes On Colour, which he later expanded into his Opticks. He argued that light is composed of particles or corpuscles and were refracted by accelerating toward the denser medium, but he had to associate them with waves to explain the diffraction of light (Opticks Bk. II, Props. XII-L). Later physicists instead favoured a purely wavelike explanation of light to account for diffraction.
+In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. In 1704, Newton published Opticks, in which he expounded his corpuscular theory of light. He considered light to be made up of extremely subtle corpuscles, that ordinary matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation "Are not gross Bodies and Light convertible into one another, ...and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?" Newton was also the first to describe the use of prisms as beam expanders and multiple-prism arrays, which would later become integral to the development of early tunable lasers.
+
+=== Diffractive optics ===
+
+The effects of diffraction of light were carefully observed and characterized by Francesco Maria Grimaldi, who also coined the term diffraction, from the Latin diffringere, 'to break into pieces', referring to light breaking up into different directions. The results of Grimaldi's observations were published posthumously in 1665. Isaac Newton studied these effects and attributed them to inflexion of light rays. James Gregory (1638–1675) observed the diffraction patterns caused by a bird feather, which was effectively the first diffraction grating. In 1803 Thomas Young demonstrated interference of water waves in a ripple tank and described diffraction effects from two closely spaced slits illuminated by sunlight. He deduced that light must propagate as waves. Augustin-Jean Fresnel provided an influential mathematical formulation of diffraction, published in 1815 and 1818, and thereby gave great support to the wave theory of light that had been advanced by Christiaan Huygens and reinvigorated by Young, against Newton's particle theory.
+
+== Lenses and lensmaking ==
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+category: "reference"
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+instance: "kb-cron"
+---
+
+Although disputed, archeological evidence has been suggested of the use of lenses in ancient times over a period of several millennia. It has been proposed that glass eye covers in hieroglyphs from the Old Kingdom of Egypt (c. 2686–2181 BCE) were functional simple glass meniscus lenses. The so-called Nimrud lens, a rock crystal artifact dated to the 7th century BCE, might have been used as a magnifying glass, although it could have simply been a decoration.
+The earliest written record of magnification dates back to the 1st century CE, when Seneca the Younger, a tutor of Emperor Nero, wrote: "Letters, however small and indistinct, are seen enlarged and more clearly through a globe or glass filled with water." Emperor Nero is also said to have watched the gladiatorial games using an emerald as a corrective lens.
+Ibn al-Haytham (Alhacen) wrote about the effects of pinhole, concave lenses, and magnifying glasses in his 11th century Book of Optics (1021 CE). The English friar Roger Bacon, during the 1260s or 1270s,
+wrote works on optics, partly based on the works of Arab writers, that described the function of corrective lenses for vision and burning glasses. These volumes were outlines for a larger publication that was never produced, so his ideas never saw mass dissemination.
+Between the 11th and 13th centuries, so-called "reading stones" were invented. Often used by monks to assist in illuminating manuscripts, these were primitive plano-convex lenses, initially made by cutting a glass sphere in half. As the stones were experimented with, it was slowly understood that shallower lenses magnified more effectively. Around 1286, possibly in Pisa, Italy, the first pair of eyeglasses was made, although it is unclear who the inventor was.
+The earliest known working telescopes were the refracting telescopes that appeared in the Netherlands in 1608. Their inventor is unknown: Hans Lippershey applied for the first patent that year followed by a patent application by Jacob Metius of Alkmaar two weeks later (neither was granted since examples of the device seemed to be numerous at the time). Galileo greatly improved upon these designs the following year. Isaac Newton is credited with constructing the first functional reflecting telescope in 1668,  his Newtonian reflector.
+The earliest known examples of compound microscopes, which combine an objective lens near the specimen with an eyepiece to view a real image, appeared in Europe around 1620. The design is very similar to the telescope and, like that device, its inventor is unknown. Again claims revolve around the spectacle making centers in the Netherlands including claims it was invented in 1590 by Zacharias Janssen and/or his father, Hans Martens, claims it was invented by rival spectacle maker, Hans Lippershey, and claims it was invented by expatriate Cornelis Drebbel who was noted to have a version in London in 1619.
+Galileo Galilei (also sometimes cited as a compound microscope inventor) seems to have found after 1609 that he could close focus his telescope to view small objects and, after seeing a compound microscope built by Drebbel exhibited in Rome in 1624, built his own improved version. The name microscope was coined by Giovanni Faber, who gave that name to Galileo Galilei's compound microscope in 1625.
+
+== Quantum optics ==
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+title: "History of optics"
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+category: "reference"
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+date_saved: "2026-05-05T16:29:57.544716+00:00"
+instance: "kb-cron"
+---
+
+Light is made up of particles called photons and hence inherently is quantized.  Quantum optics is the study of the nature and effects of light as quantized photons. The first indication that light might be quantized came from Max Planck in 1899 when he correctly modelled blackbody radiation by assuming that the exchange of energy between light and matter only occurred in discrete amounts he called quanta. It was unknown whether the source of this discreteness was the matter or the light. In 1905, Albert Einstein published the theory of the photoelectric effect. It appeared that the only possible explanation for the effect was the quantization of light itself. Later, Niels Bohr showed that atoms could only emit discrete amounts of energy. The understanding of the interaction between light and matter following from these developments not only formed the basis of quantum optics but also were crucial for the development of quantum mechanics as a whole. However, the subfields of quantum mechanics dealing with matter-light interaction were principally regarded as research into matter rather than into light and hence, one rather spoke of atom physics and quantum electronics.
+This changed with the invention of the maser in 1953 and the laser in 1960. Laser science—research into principles, design and application of these devices—became an important field, and the quantum mechanics underlying the laser's principles was studied now with more emphasis on the properties of light, and the name quantum optics became customary.
+As laser science needed good theoretical foundations, and also because research into these soon proved very fruitful, interest in quantum optics rose. Following the work of Dirac in quantum field theory, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light (see degree of coherence). This led to the introduction of the coherent state as a quantum description of laser light and the realization that some states of light could not be described with classical waves. In 1977, Kimble et al. demonstrated the first source of light which required a quantum description: a single atom that emitted one photon at a time.  Another quantum state of light with certain advantages over any classical state, squeezed light, was soon proposed. At the same time, development of short and ultrashort laser pulses—created by Q-switching and mode-locking techniques—opened the way to the study of unimaginably fast ("ultrafast") processes. Applications for solid state research (e.g. Raman spectroscopy) were found, and mechanical forces of light on matter were studied. The latter led to levitating and positioning clouds of atoms or even small biological samples in an optical trap or optical tweezers by laser beam. This, along with Doppler cooling was the crucial technology needed to achieve the celebrated Bose–Einstein condensation.
+Other remarkable results are the demonstration of quantum entanglement, quantum teleportation, and (recently, in 1995) quantum logic gates. The latter are of much interest in quantum information theory, a subject which partly emerged from quantum optics, partly from theoretical computer science.
+Today's fields of interest among quantum optics researchers include parametric down-conversion, parametric oscillation, even shorter (attosecond) light pulses, use of quantum optics for quantum information, manipulation of single atoms and Bose–Einstein condensates, their application, and how to manipulate them (a sub-field often called atom optics).
+
+== See also ==
+Giambattista della Porta
+List of astronomical instrument makers
+
+== Notes ==
+
+=== Works cited ===
+Elliott, Robert Stratman (1966). Electromagnetics. McGraw-Hill.
+Wade, Nicholas J.; Finger, Stanley (2001), "The eye as an optical instrument: from camera obscura to Helmholtz's perspective", Perception, 30 (10): 1157–77, doi:10.1068/p3210, PMID 11721819, S2CID 8185797
+
+== Further reading ==
+Howard, Ian P.; Wade, Nicholas J. (1996), "Ptolemy's contributions to the geometry of binocular vision", Perception, 25 (10): 1189–201, doi:10.1068/p251189, PMID 9027922, S2CID 34431898.
+Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, vol. 2, Routledge, ISBN 0-415-12410-7, OCLC 34731151.
+Wade, Nicholas J. (1998), A Natural History of Vision, Cambridge, Massachusetts: MIT Press, ISBN 0-262-23194-8, OCLC 37246567.
+
+== External links ==
+
+History of Optics (audio mp3) by Simon Schaffer, Professor in History and Philosophy of Science at the University of Cambridge, Jim Bennett, Director of the Museum of the History of Science at the University of Oxford and Emily Winterburn, Curator of Astronomy at the National Maritime Museum (recorded by the BBC).
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+instance: "kb-cron"
+---
+
+In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major advances in the theory were made in the 1940s and 1950s, leading to the introduction of renormalized quantum electrodynamics (QED). The field theory behind QED was so accurate and successful in predictions that efforts were made to apply the same basic concepts for the other forces of nature. Beginning in 1954, the parallel was found by way of gauge theory, leading by the late 1970s, to quantum field models of strong nuclear force and weak nuclear force, united in the modern Standard Model of particle physics.
+Efforts to describe gravity using the same techniques have, to date, failed. The study of quantum field theory is still flourishing, as are applications of its methods to many physical problems. It remains one of the most vital areas of theoretical physics today, providing a common language to  several different branches of physics.
+
+== Early developments ==
+Quantum field theory originated in the 1920s from the problem of creating a quantum mechanical theory of the electromagnetic field. In particular, de Broglie in 1924 introduced the idea of a wave description of elementary systems in the following way: "we proceed in this work from the assumption of the existence of a certain periodic phenomenon of a yet to be determined character, which is to be attributed to each and every isolated energy parcel".
+In 1925, Werner Heisenberg, Max Born, and Pascual Jordan constructed just such a theory by expressing the field's internal degrees of freedom as an infinite set of harmonic oscillators, and by then utilizing the canonical quantization procedure to these oscillators; their paper was published in 1926. This theory assumed that no electric charges or currents were present and today would be called a free field theory.
+The first reasonably complete theory of quantum electrodynamics, which included both the electromagnetic field and electrically charged matter as quantum mechanical objects, was created by Paul Dirac in 1927. This quantum field theory could be used to model important processes such as the emission of a photon by an electron dropping into a quantum state of lower energy, a process in which the number of particles changes—one atom in the initial state becomes an atom plus a photon in the final state. It is now understood that the ability to describe such processes is one of the most important features of quantum field theory.
+The final crucial step was Enrico Fermi's theory of β-decay (1934). It was shown that the non-conservation of fermion species is a consequence of second quantization. Creation and annihilation of fermions came to the fore, and it was shown that quantum field theory describes particle decays. Fermi's  breakthrough was somewhat foreshadowed in the  abstract studies of Soviet physicists, Viktor Ambartsumian and Dmitri Ivanenko, in particular the Ambarzumian–Ivanenko hypothesis of creation of massive particles (1930). The idea was that not only the quanta of the electromagnetic field, photons, but also other particles might emerge and disappear as a result of their interaction with other particles.
+
+== Incorporating special relativity ==
+It was evident from the beginning that a proper quantum treatment of the electromagnetic field had to somehow incorporate Einstein's relativity theory, which had grown out of the study of classical electromagnetism. This need to put together relativity and quantum mechanics was the second major motivation in the development of quantum field theory.
+Pascual Jordan and Wolfgang Pauli showed in 1928 that quantum fields could be made to behave in the way predicted by special relativity during coordinate transformations. Specifically, they showed that the field commutators were Lorentz invariant. Quantum field theory received a further boost from the discovery of the Dirac equation, which was originally formulated and interpreted as a single-particle equation analogous to the Schrödinger equation. Unlike the Schrödinger equation, the Dirac equation satisfies both Lorentz invariance, i.e. the requirements of special relativity, and the rules of quantum mechanics. The Dirac equation took into account the spin-1/2 value of the electron and its magnetic moment, and also provided accurate predictions for the spectra of hydrogen.
+The attempt to interpret the Dirac equation as a single-particle equation did not last long, however, and it eventually became apparent that some of its undesirable properties, such as states of negative energy, could be explained by reformulating and reinterpreting the Dirac equation as a true field equation. The quantized "Dirac field" or "electron field" was introduced, with the "solutions of negative energy" pointing to the existence of antiparticles. This work was performed first by Dirac himself with the invention of hole theory in 1930 and by Wendell Furry, Robert Oppenheimer, Vladimir Fock and others. 
+Erwin Schrödinger, during the same period that he discovered his equation in 1926, also independently found the relativistic generalization of it known as the Klein–Gordon equation but dismissed it since, without spin, it predicted impossible properties for the hydrogen spectrum. Refer also to the work of Oskar Klein and Walter Gordon. All relativistic wave equations that describe spin-zero particles are said to be of the Klein–Gordon type.
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+---
+
+== Uncertainty, again ==
+A subtle and careful analysis in 1933 by Niels Bohr and Léon Rosenfeld showed that there is a fundamental limitation on the ability to simultaneously measure the electric and magnetic field strengths that enter into the description of charges in interaction with radiation, imposed by the uncertainty principle, which must apply to all canonically conjugate quantities. This limitation is crucial for the successful formulation and interpretation of a quantum field theory of photons and electrons (quantum electrodynamics), and indeed, any perturbative quantum field theory. The analysis of Bohr and Rosenfeld explains fluctuations in the values of the electromagnetic field that differ from the classically "allowed" values distant from the sources of the field.
+Their analysis was crucial to showing that the limitations and physical implications of the uncertainty principle apply to all dynamical systems, whether fields or material particles. Their analysis also convinced most physicists that any notion of returning to a fundamental description of nature based on classical field theory, such as what Einstein aimed at with his numerous and failed attempts at a classical unified field theory, was simply out of the question. Fields had to be quantized.
+
+== Second quantization ==
+The third thread in the development of quantum field theory was the need to handle the statistics of many-particle systems consistently and with ease. In 1927, Pascual Jordan tried to extend the canonical quantization of fields to the many-body wave functions of identical particles using a formalism which is known as statistical transformation theory; this procedure is now sometimes called second quantization. Dirac is also credited with the invention, as he introduced the key ideas in a 1927 paper.
+In 1928, Jordan and Eugene Wigner found that the quantum field describing electrons, or other fermions, had to be expanded using anti-commuting creation and annihilation operators due to the Pauli exclusion principle (see Jordan–Wigner transformation). This thread of development was incorporated into many-body theory and strongly influenced condensed matter physics and nuclear physics.
+
+== The problem of infinities ==
+
+Despite its early successes quantum field theory was plagued by several serious theoretical difficulties. Basic physical quantities, such as the self-energy of the electron, the energy shift of electron states due to the presence of the electromagnetic field, gave infinite, divergent contributions—a nonsensical result—when computed using the perturbative techniques available in the 1930s and most of the 1940s. 
+The electron self-energy problem was already a serious issue in the classical electromagnetic field theory, where the attempt to attribute to the electron a finite size or extent (the classical electron-radius) led immediately to the question of what non-electromagnetic stresses would need to be invoked, which would presumably hold the electron together against the Coulomb repulsion of its finite-sized "parts". The situation was dire, and had certain features that reminded many of the "Rayleigh–Jeans catastrophe". 
+What made the situation in the 1940s so desperate and gloomy, however, was the fact that the correct ingredients (the second-quantized Maxwell–Dirac field equations) for the theoretical description of interacting photons and electrons were well in place, and no major conceptual change was needed analogous to that which was necessitated by a finite and physically sensible account of the radiative behavior of hot objects, as provided by the Planck radiation law.
+
+== Renormalization procedures ==
+Improvements in microwave technology made it possible to take more precise measurements of the shift of the levels of a hydrogen atom, now known as the Lamb shift and magnetic moment of the electron. These experiments exposed discrepancies which the theory was unable to explain.
+A first indication of a possible way out was given by Hans Bethe in 1947, after attending the Shelter Island Conference.  While he was traveling by train from the conference to Schenectady he made the first non-relativistic computation of the shift of the lines of the hydrogen atom as measured by Lamb and Retherford. Despite the limitations of the computation, agreement was excellent. The idea was simply to attach infinities to corrections of mass and charge that were actually fixed to a finite value by experiments. In this way, the infinities get absorbed in those constants and yield a finite result in good agreement with experiments. This procedure was named renormalization.
+This "divergence problem" was solved in the case of quantum electrodynamics through the procedure known as renormalization in 1947–49 by Hans Kramers, Hans Bethe, Julian Schwinger, Richard Feynman, and Shin'ichiro Tomonaga; the procedure was systematized by Freeman Dyson in 1949. Great progress was made after realizing that all infinities in quantum electrodynamics are related to two effects: the self-energy of the electron/positron, and vacuum polarization.
+Renormalization requires paying very careful attention to just what is meant by, for example, the very concepts "charge" and "mass" as they occur in the pure, non-interacting field-equations. The "vacuum" is itself polarizable and, hence, populated by virtual particle (on shell and off shell) pairs, and, hence, is a seething and busy dynamical system in its own right. This was a critical step in identifying the source of "infinities" and "divergences". The "bare mass" and the "bare charge" of a particle, the values that appear in the free-field equations (non-interacting case), are abstractions that are simply not realized in experiment (in interaction). What we measure, and hence, what we must take account of with our equations, and what the solutions must account for, are the "renormalized mass" and the "renormalized charge" of a particle. That is to say, the "shifted" or "dressed" values these quantities must have when due systematic care is taken to include all deviations from their "bare values" is dictated by the very nature of quantum fields themselves.
+
+== Quantum electrodynamics ==
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+
+The first approach that bore fruit is known as the "interaction representation" (see the article Interaction picture), a Lorentz-covariant and gauge-invariant generalization of time-dependent perturbation theory used in ordinary quantum mechanics, and developed by Tomonaga and Schwinger, generalizing earlier efforts of Dirac, Fock and Boris Podolsky. Tomonaga and Schwinger invented a relativistically covariant scheme for representing field commutators and field operators intermediate between the two main representations of a quantum system, the Schrödinger and the Heisenberg representations. Within this scheme, field commutators at separated points can be evaluated in terms of "bare" field creation and annihilation operators. This allows for keeping track of the time-evolution of both the "bare" and "renormalized", or perturbed, values of the Hamiltonian and expresses everything in terms of the coupled, gauge invariant "bare" field-equations. Schwinger gave the most elegant formulation of this approach. The next development was due to Richard Feynman, with his rules for assigning a graph to the terms in the scattering matrix (see S-matrix and Feynman diagrams). These directly corresponded (through the Schwinger–Dyson equation) to the measurable physical processes (cross sections, probability amplitudes, decay widths and lifetimes of excited states) one needs to be able to calculate. This revolutionized how quantum field theory calculations are carried out in practice.
+Two classic text-books from the 1960s, James D. Bjorken, Sidney David Drell, Relativistic Quantum Mechanics (1964) and J. J. Sakurai, Advanced Quantum Mechanics (1967), thoroughly developed the Feynman graph expansion techniques using physically intuitive and practical methods following from the correspondence principle, without worrying about the technicalities involved in deriving the Feynman rules from the superstructure of quantum field theory itself. Although both Feynman's heuristic and pictorial style of dealing with the infinities, as well as the formal methods of Tomonaga and Schwinger, worked extremely well, and gave spectacularly accurate answers, the true analytical nature of the question of "renormalizability", that is, whether ANY theory formulated as a "quantum field theory" would give finite answers, was not worked-out until much later, when the urgency of trying to formulate finite theories for the strong and electro-weak (and gravitational) interactions demanded its solution.
+Renormalization in the case of QED was largely fortuitous due to the smallness of the coupling constant, the fact that the coupling has no dimensions involving mass, the so-called fine-structure constant, and also the zero-mass of the gauge boson involved, the photon, rendered the small-distance/high-energy behavior of QED manageable. Also, electromagnetic processes are very "clean" in the sense that they are not badly suppressed/damped and/or hidden by the other gauge interactions. By 1965 James D. Bjorken and Sidney David Drell observed: "Quantum electrodynamics (QED) has achieved a status of peaceful coexistence with its divergences ...".
+The unification of the electromagnetic force with the weak force encountered initial difficulties due to the lack of accelerator energies high enough to reveal processes beyond the Fermi interaction range. Additionally, a satisfactory theoretical understanding of hadron substructure had to be developed, culminating in the quark model.
+Thanks to the somewhat brute-force, ad hoc and heuristic early methods of Feynman, and the  abstract methods of Tomonaga and Schwinger, elegantly synthesized by Freeman Dyson, from the period of early renormalization, the modern theory of quantum electrodynamics (QED) has established itself. It is still the most accurate physical theory known, the prototype of a successful quantum field theory. Quantum electrodynamics is an example of what is known as an abelian gauge theory. It relies on the symmetry group U(1) and has one massless gauge field, the U(1) gauge symmetry, dictating the form of the interactions involving the electromagnetic field, with the photon being the gauge boson.
+
+== Yang-Mills theory ==
+
+In the 1950s Yang and Mills, following the previous lead of Hermann Weyl, explored the impact of symmetries and invariances on field theory. All field theories, including QED, were generalized to a class of quantum field theories known as gauge theories. That symmetries dictate, limit and necessitate the form of interaction between particles is the essence of the "gauge theory revolution". Yang and Mills formulated the first explicit example of a non-abelian gauge theory, Yang–Mills theory, with an attempted explanation of the strong interactions in mind. The strong interactions were then (incorrectly) understood in the mid-1950s, to be mediated by the pi-mesons, the particles predicted by Hideki Yukawa in 1935, based on his profound reflections concerning the reciprocal connection between the mass of any force-mediating particle and the range of the force it mediates. This was allowed by the uncertainty principle. In the absence of dynamical information, Murray Gell-Mann pioneered the extraction of physical predictions from sheer non-abelian symmetry considerations, and introduced non-abelian Lie groups to current algebra and so the gauge theories that came to supersede it.
+The 1960s and 1970s saw the formulation of a gauge theory now known as the Standard Model of particle physics, which systematically describes the elementary particles and the interactions between them. The strong interactions are described by quantum chromodynamics (QCD), based on "color" SU(3).  The weak interactions  require the additional feature of spontaneous symmetry breaking, elucidated by Yoichiro Nambu and the adjunct Higgs mechanism, considered next.
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+
+== Electroweak unification ==
+The electroweak interaction part of the Standard Model was formulated by Sheldon Glashow, Abdus Salam, and John Clive Ward in 1959, with their discovery of the SU(2)xU(1) group structure of the theory. In 1967, Steven Weinberg invoked the Higgs mechanism for the generation of the W and Z masses (the intermediate vector bosons responsible for the weak interactions and neutral-currents) and keeping the mass of the photon zero. The Goldstone and Higgs idea for generating mass in gauge theories was sparked in the late 1950s and early 1960s when a number of theoreticians (including Yoichiro Nambu, Steven Weinberg, Jeffrey Goldstone, François Englert, Robert Brout, G. S. Guralnik, C. R. Hagen, Tom Kibble and Philip Warren Anderson) noticed a possibly useful analogy to the (spontaneous) breaking of the U(1) symmetry of electromagnetism in the formation of the BCS ground-state of a superconductor. The gauge boson involved in this situation, the photon, behaves as though it has acquired a finite mass.
+There is a further possibility that the physical vacuum (ground-state) does not respect the symmetries implied by the "unbroken" electroweak Lagrangian from which one arrives at the field equations (see the article Electroweak interaction for more details). The electroweak theory of Weinberg and Salam was shown to be renormalizable (finite) and hence consistent by Gerardus 't Hooft and Martinus Veltman. The Glashow–Weinberg–Salam theory (GWS theory), in certain applications, gives an accuracy on a par with quantum electrodynamics.
+
+== Quantum chromodynamics ==
+In the case of the strong interactions, progress concerning their short-distance/high-energy behavior was much slower and more frustrating. For strong interactions with the electro-weak fields, there were difficult issues regarding the strength of coupling, the mass generation of the force carriers as well as their non-linear, self interactions. Although there has been theoretical progress toward a grand unified quantum field theory incorporating the electro-magnetic force, the weak force and the strong force, empirical verification is still pending. Superunification, incorporating the gravitational force, is still very speculative, and is under intensive investigation by many of the best minds in contemporary theoretical physics. Gravitation is a tensor field description of a spin-2 gauge-boson, the "graviton", and is further discussed in the articles on general relativity and quantum gravity.
+
+== Quantum gravity ==
+From the point of view of the techniques of (four-dimensional) quantum field theory, and as the numerous efforts to formulate a consistent quantum gravity theory attests, gravitational quantization has been the reigning champion for bad behavior.
+There are technical problems underlain by the fact that the Newtonian constant of gravitation has dimensions involving inverse powers of mass, and, as a simple consequence, it is plagued by perturbatively badly behaved non-linear self-interactions. Gravity is itself a source of gravity, analogously to gauge theories (whose couplings, are, by contrast, dimensionless) leading to uncontrollable divergences at increasing orders of perturbation theory.
+Moreover, gravity couples to all energy equally strongly, as per the equivalence principle, so this makes the notion of ever really "switching-off", "cutting-off" or separating, the gravitational interaction from other interactions ambiguous, since, with gravitation, we are dealing with the very structure of space-time itself.
+
+Moreover, it has not been established that a theory of quantum gravity is necessary (see Quantum field theory in curved spacetime).
+
+== Contemporary framework of renormalization ==
+
+Parallel breakthroughs in the understanding of phase transitions in condensed matter physics led to novel insights based on the renormalization group. They involved the work of Leo Kadanoff (1966) and Kenneth Geddes Wilson–Michael Fisher (1972)—extending the work of Ernst Stueckelberg–André Petermann (1953) and Murray Gell-Mann–Francis Low (1954)—which led to the seminal reformulation of quantum field theory by Kenneth Geddes Wilson in 1975. This reformulation provided insights into the evolution of effective field theories with scale, which classified all field theories, renormalizable or not.  The remarkable conclusion is that, in general, most observables are "irrelevant", i.e., the macroscopic physics is dominated by only a few observables in most systems.
+During the same period, Leo Kadanoff (1969) introduced an operator algebra formalism for the two-dimensional Ising model, a widely studied mathematical model of ferromagnetism in statistical physics. This development suggested that quantum field theory describes its scaling limit. Later, there developed the idea that a finite number of generating operators could represent all the correlation functions of the Ising model. The existence of a much stronger symmetry for the scaling limit of two-dimensional critical systems was suggested by Alexander Belavin, Alexander Markovich Polyakov and Alexander Zamolodchikov in 1984, which eventually led to the development of conformal field theory, a special case of quantum field theory, which is presently utilized in different areas of particle physics and condensed matter physics.
+The renormalization group spans a set of ideas and methods to monitor changes of the behavior of the theory with scale, providing a deep physical understanding  which sparked what has been called the "grand synthesis" of theoretical physics, uniting the quantum field theoretical techniques used in particle physics and condensed matter physics into a single powerful theoretical framework.
+The gauge field theory of the strong interactions, quantum chromodynamics, relies crucially on this renormalization group for its distinguishing characteristic features, asymptotic freedom and color confinement.
+
+== See also ==
+History of quantum mechanics
+History of string theory
+QED vacuum
+
+== References ==
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+
+== Further reading ==
+Pais, Abraham; Inward Bound – Of Matter & Forces in the Physical World, Oxford University Press (1986) ISBN 0-19-851997-4. Written by a former Einstein assistant at Princeton, this is a beautiful detailed history of modern fundamental physics, from 1895 (discovery of X-rays) to 1983 (discovery of vectors bosons at CERN).
+Weinberg, Steven; The Quantum Theory of Fields - Foundations (vol. I), Cambridge University Press (1995) ISBN 0-521-55001-7 The first chapter (pp. 1–40) of Weinberg's monumental treatise gives a brief history of Q.F.T., p. 608.
+Weinberg, Steven; The Quantum Theory of Fields - Modern Applications (vol. II), Cambridge University Press:Cambridge, U.K. (1996) ISBN 0-521-55001-7, pp. 489.
+Weinberg, Steven; The Quantum Theory of Fields – Supersymmetry (vol. III), Cambridge University Press:Cambridge, U.K. (2000) ISBN 0-521-55002-5, pp. 419.
+Schweber, Silvan S.; QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga, Princeton University Press (1994) ISBN 0-691-03327-7
+Ynduráin, Francisco José; Quantum Chromodynamics: An Introduction to the Theory of Quarks and Gluons, Springer Verlag, New York, 1983. ISBN 0-387-11752-0
+Miller, Arthur I.; Early Quantum Electrodynamics : A Sourcebook, Cambridge University Press (1995) ISBN 0-521-56891-9
+Schwinger, Julian; Selected Papers on Quantum Electrodynamics, Dover Publications, Inc. (1958) ISBN 0-486-60444-6
+O'Raifeartaigh, Lochlainn; The Dawning of Gauge Theory, Princeton University Press (May 5, 1997) ISBN 0-691-02977-6
+Cao, Tian Yu; Conceptual Developments of 20th Century Field Theories, Cambridge University Press (1997) ISBN 0-521-63420-2
+Darrigol, Olivier; La genèse du concept de champ quantique, Annales de Physique (France) 9 (1984) pp. 433–501. Text in French, adapted from the author's Ph.D. thesis.
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diff --git a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-2.md b/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-2.md
index 389b474c5..d6e51341c 100644
--- a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-2.md
+++ b/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-2.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-3.md b/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-3.md
index ceb2ebb80..cb9c4cc00 100644
--- a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-3.md
+++ b/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-3.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-4.md b/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-4.md
index 2baa1c33f..d9ccfc18e 100644
--- a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-4.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-5.md b/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-5.md
index 521228943..ba38a747e 100644
--- a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-5.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-6.md b/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-6.md
index e3f2dfdbf..fe1d474b0 100644
--- a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-6.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-7.md b/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-7.md
index 81c6b4866..d40b34999 100644
--- a/data/en.wikipedia.org/wiki/History_of_quantum_mechanics-7.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-0.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-0.md
index 3d1877448..718fea401 100644
--- a/data/en.wikipedia.org/wiki/History_of_radiation_protection-0.md
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 instance: "kb-cron"
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-1.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-1.md
index 30ea8fde4..5c6a911d9 100644
--- a/data/en.wikipedia.org/wiki/History_of_radiation_protection-1.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-10.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-10.md
index 6054374f7..0a1f025b1 100644
--- a/data/en.wikipedia.org/wiki/History_of_radiation_protection-10.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-11.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-11.md
index 7eb279c00..ec1549941 100644
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index ef1f8cffa..db64c497f 100644
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 instance: "kb-cron"
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-13.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-13.md
index b9dfbe4ce..62c32bf60 100644
--- a/data/en.wikipedia.org/wiki/History_of_radiation_protection-13.md
+++ b/data/en.wikipedia.org/wiki/History_of_radiation_protection-13.md
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index 88438ea24..a545372f3 100644
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index c43135518..84c3d0c9e 100644
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-16.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-16.md
index f07afa9c7..8e20e0c50 100644
--- a/data/en.wikipedia.org/wiki/History_of_radiation_protection-16.md
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index 8eb3d2a97..4baddb29e 100644
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index cdc2b1520..fd3b1cbaa 100644
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index b8ed66552..6ec523317 100644
--- a/data/en.wikipedia.org/wiki/History_of_radiation_protection-19.md
+++ b/data/en.wikipedia.org/wiki/History_of_radiation_protection-19.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-2.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-2.md
index a9371f3a8..d5ad90d0e 100644
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index 1175155c2..bc961ea54 100644
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+++ b/data/en.wikipedia.org/wiki/History_of_radiation_protection-20.md
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index 0774cf2f0..d3eb9f3c7 100644
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index b519b9f33..11a489c89 100644
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+++ b/data/en.wikipedia.org/wiki/History_of_radiation_protection-22.md
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index 59036d607..d8d62ce2b 100644
--- a/data/en.wikipedia.org/wiki/History_of_radiation_protection-23.md
+++ b/data/en.wikipedia.org/wiki/History_of_radiation_protection-23.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-24.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-24.md
index d2746d8ed..53bca7f90 100644
--- a/data/en.wikipedia.org/wiki/History_of_radiation_protection-24.md
+++ b/data/en.wikipedia.org/wiki/History_of_radiation_protection-24.md
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 instance: "kb-cron"
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-25.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-25.md
index 978c1e2e6..36141b785 100644
--- a/data/en.wikipedia.org/wiki/History_of_radiation_protection-25.md
+++ b/data/en.wikipedia.org/wiki/History_of_radiation_protection-25.md
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-26.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-26.md
index 0dde4db0d..d11d7b4d4 100644
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-27.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-27.md
index 5b29a9cf6..5f4ac0bc9 100644
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-3.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-3.md
index 4ba15f859..4479e7c35 100644
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-4.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-4.md
index 41f0b85b2..bbc005ab7 100644
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diff --git a/data/en.wikipedia.org/wiki/History_of_radiation_protection-5.md b/data/en.wikipedia.org/wiki/History_of_radiation_protection-5.md
index b360d1e0c..b76f5dd12 100644
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index 3c706b810..0f6ef6e70 100644
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index fd4d13b74..77bbdd41a 100644
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+---
+title: "History of special relativity"
+chunk: 1/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein and subsequent work of Max Planck, Hermann Minkowski and others.
+
+== Introduction ==
+Although Isaac Newton based his physics on absolute time and space, he also adhered to the principle of relativity of Galileo Galilei restating it precisely for mechanical systems. This can be stated: as far as the laws of mechanics are concerned, all observers in inertial motion are equally privileged, and no preferred state of motion can be attributed to any particular inertial observer. However, electromagnetic theory and electrodynamics, developed during the 19th century, did not obey Galileo's relativity.  The wave theory of electromagnetism or light viewed as a disturbance of a "light medium" or luminiferous aether was widely accepted. The theory reached its most developed form in the work of James Clerk Maxwell.  Maxwell thought all optical and electrical phenomena propagate through an aether, making his equations valid only for systems at rest with respect to that aether. The concept of this aether was widely discussed and subjected to many unsuccessful efforts experimentally determine motion relative to the aether.
+The failure of any experiment to detect motion through the aether led Hendrik Lorentz, starting in 1892, to develop a theory of electrodynamics based on an immobile luminiferous aether (about whose material constitution Lorentz did not speculate), physical length contraction, and a "local time" in which Maxwell's equations retain their form in all inertial frames of reference. Working with Lorentz's aether theory, Henri Poincaré, having earlier proposed the "relativity principle" as a general law of nature (including electrodynamics and gravitation), used this principle in 1905 to correct Lorentz's preliminary transformation formulas, resulting in an exact set of equations that are now called the Lorentz transformations.
+A little later in the same year Albert Einstein published his original paper on special relativity. He independently derived and radically reinterpreted the Lorentz transformations by changing the fundamental definitions of space and time intervals, while abandoning the absolute simultaneity of Galilean kinematics, avoiding the need for any reference to a luminiferous aether in classical electrodynamics. Before Einstein's paper Galilean relativity applied to particle mechanics and Lorentzian relativity to electrodynamics; afterwards both systems used Lorentz transformations. In subsequent work Hermann Minkowski, introduced a 4-dimensional geometric "spacetime" model,  Arnold Sommerfeld developed the electromagnetic tensor, and Max Planck applied the concept of special relativity to relativistic Lagrangian mechanics.
+The special theory of relativity gave invariant laws of physics in inertial frames of reference, but the meaning of these frames was unclear until Einstein's later development of his equivalence principle and general theory of relativity.  In comparing to the general theory, Einstein specifically called his earlier work "special theory of relativity" (German: Spezielle Relativitätstheorie) in two short papers published in November 1915 and in a long review article published in 1916,  saying he meant a restriction to frames in uniform motion, and was featured in the title of Einstein's popular book Relativity: The Special and the General Theory first published in 1916.
+
+== Aether and electrodynamics of moving bodies ==
+
+=== Aether models and Maxwell's equations ===
+Following the work of Thomas Young (1804) and Augustin-Jean Fresnel (1816), it was believed that light propagates as a transverse wave within an elastic medium called luminiferous aether. However, a distinction was made between optical and electrodynamical phenomena so it was necessary to create specific aether models for all phenomena. Attempts to unify those models or to create a complete mechanical description of them did not succeed, but after considerable work by many scientists, including Michael Faraday and Lord Kelvin, James Clerk Maxwell (1864) developed an accurate theory of electromagnetism by deriving a set of equations in electricity, magnetism and inductance, named Maxwell's equations. He first proposed that light was in fact undulations (electromagnetic radiation) in the same aetherial medium that is the cause of electric and magnetic phenomena. However, Maxwell's theory was unsatisfactory regarding the optics of moving bodies, and while he was able to present a complete mathematical model, he was not able to provide a coherent mechanical description of the aether.
+After Heinrich Hertz in 1887 demonstrated the existence of electromagnetic waves, Maxwell's theory was widely accepted. In addition, Oliver Heaviside and Hertz further developed the theory and introduced modernized versions of Maxwell's equations. The "Maxwell–Hertz" or "Heaviside–Hertz" equations subsequently formed an important basis for the further development of electrodynamics, and Heaviside's notation is still used today. Other important contributions to Maxwell's theory were made by George FitzGerald, Joseph John Thomson, John Henry Poynting, Hendrik Lorentz, and Joseph Larmor.
+
+=== Search for the aether ===
+Regarding the relative motion and the mutual influence of matter and aether, there were two theories, neither entirely satisfactory. One was developed by Fresnel (and subsequently Lorentz). This model (stationary aether theory) supposed that light propagates as a transverse wave and aether is partially dragged with a certain coefficient by matter. Based on this assumption, Fresnel was able to explain the aberration of light and many optical phenomena.
+The other hypothesis was proposed by George Gabriel Stokes, who stated in 1845 that the aether was fully dragged by matter (later this view was also shared by Hertz). In this model the aether might be (by analogy with pine pitch) rigid for fast objects and fluid for slower objects. Thus the Earth could move through it fairly freely, but it would be rigid enough to transport light. Fresnel's theory was preferred because his dragging coefficient was confirmed by the Fizeau experiment in 1851, which measured the speed of light in moving liquids.
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+title: "History of special relativity"
+chunk: 2/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+ Albert A. Michelson (1881) tried to measure the relative motion of the Earth and aether (the "aether-wind"), as it was expected in Fresnel's theory, by using an interferometer. He could not determine any relative motion, so he interpreted the result as a confirmation of the thesis of Stokes. However, Lorentz (1886) showed Michelson's calculations were wrong and that he had overestimated the accuracy of the measurement. This, together with the large margin of error, made the result of Michelson's experiment inconclusive. In addition, Lorentz showed that Stokes' completely dragged aether led to contradictory consequences, and therefore he supported an aether theory similar to Fresnel's. To check Fresnel's theory again, Michelson and Edward W. Morley (1886) performed a repetition of the Fizeau experiment. Fresnel's dragging coefficient was confirmed very exactly on that occasion, and Michelson was now of the opinion that Fresnel's stationary aether theory was correct. To clarify the situation, Michelson and Morley (1887) repeated Michelson's 1881 experiment, and they substantially increased the accuracy of the measurement. However, this now famous Michelson–Morley experiment again yielded a negative result: no motion of the apparatus through the aether was detected (although the Earth's velocity differs by 60 km/s in the northern winter compared to the summer). So the physicists were confronted with two seemingly contradictory experiments: the 1886 experiment as an apparent confirmation of Fresnel's stationary aether, and the 1887 experiment as an apparent confirmation of Stokes' completely dragged aether.
+A possible solution to the problem was shown by Woldemar Voigt (1887), who investigated the Doppler effect for waves propagating in an incompressible elastic medium and deduced transformation relations that left the wave equation in free space unchanged, and explained the negative result of the Michelson–Morley experiment. The Voigt transformations include the Lorentz factor 
+  
+    
+      
+        
+          
+            1
+            
+              1
+              −
+              
+                
+                  v
+                  
+                    2
+                  
+                
+              
+              
+                /
+              
+              
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\textstyle {\frac {1}{\sqrt {1-{v^{2}}/{c^{2}}}}}}
+  
+ for the y- and z-coordinates, and a new time variable 
+  
+    
+      
+        
+          t
+          ′
+        
+        =
+        t
+        −
+        
+          
+            
+              v
+              x
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\textstyle t'=t-{\frac {vx}{c^{2}}}}
+  
+ which later was called "local time". However, Voigt's work was completely ignored by his contemporaries.
+FitzGerald (1889) offered another explanation of the negative result of the Michelson–Morley experiment. Contrary to Voigt, he speculated that the intermolecular forces are possibly of electrical origin so that material bodies would contract in the line of motion (length contraction). This was in connection with the work of Heaviside (1887), who determined that the electrostatic fields in motion were deformed (Heaviside Ellipsoid), which leads to physically undetermined conditions at the speed of light. However, FitzGerald's idea remained widely unknown and was not discussed before Oliver Lodge published a summary of the idea in 1892. Also Lorentz (1892b) proposed length contraction independently from FitzGerald in order to explain the Michelson–Morley experiment. For plausibility reasons, Lorentz referred to the analogy of the contraction of electrostatic fields. However, even Lorentz admitted that that was not a necessary reason and length contraction consequently remained an ad hoc hypothesis.
+
+=== Lorentz's theory of electrons ===
+
+Lorentz (1892a) set the foundations of Lorentz aether theory, by assuming the existence of electrons which he separated from the aether, and by replacing the "Maxwell–Hertz" equations by the "Maxwell–Lorentz" equations. In his model, the aether is completely motionless and, contrary to Fresnel's theory, also is not partially dragged by matter. An important consequence of this notion was that the velocity of light is totally independent of the velocity of the source. Lorentz gave no statements about the mechanical nature of the aether and the electromagnetic processes, but, rather, tried to explain the mechanical processes by electromagnetic ones and therefore created an abstract electromagnetic æther. In the framework of his theory, Lorentz calculated, like Heaviside, the contraction of the electrostatic fields. Lorentz (1895) also introduced what he called the "Theorem of Corresponding States" for terms of first order in 
+  
+    
+      
+        
+          
+            v
+            c
+          
+        
+      
+    
+    {\textstyle {\frac {v}{c}}}
+  
+. This theorem states that a moving observer (relative to the aether) in his "fictitious" field makes the same observations as a resting observer in his "real" field. An important part of it was local time 
+  
+    
+      
+        
+          t
+          ′
+        
+        =
+        t
+        −
+        
+          
+            
+              v
+              x
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\textstyle t'=t-{\frac {vx}{c^{2}}}}
+  
+, which paved the way to the Lorentz transformation and which he introduced independently of Voigt. With the help of this concept, Lorentz could explain the aberration of light, the Doppler effect and the Fizeau experiment as well. However, Lorentz's local time was only an auxiliary mathematical tool to simplify the transformation from one system into another – it was Poincaré in 1900 who recognized that "local time" is actually indicated by moving clocks. Lorentz also recognized that his theory violated the principle of action and reaction, since the aether acts on matter, but matter cannot act on the immobile aether.
+A very similar model was created by Joseph Larmor (1897, 1900). Larmor was the first to put Lorentz's 1895 transformation into a form algebraically equivalent to the modern Lorentz transformations, however, he stated that his transformations preserved the form of Maxwell's equations only to second order of 
+  
+    
+      
+        
+          
+            v
+            c
+          
+        
+      
+    
+    {\textstyle {\frac {v}{c}}}
+  
+. Lorentz later noted that these transformations did in fact preserve the form of Maxwell's equations to all orders of 
+  
+    
+      
+        
+          
+            v
+            c
+          
+        
+      
+    
+    {\textstyle {\frac {v}{c}}}
+  
+. Larmor noticed on that occasion that length contraction was derivable from the model; furthermore, he calculated some manner of time dilation for electron orbits. Larmor specified his considerations in 1900 and 1904. Independently of Larmor, Lorentz (1899) extended his transformation for second-order terms and noted a (mathematical) time dilation effect as well.
+Other physicists besides Lorentz and Larmor also tried to develop a consistent model of electrodynamics. For example, Emil Cohn (1900, 1901) created an alternative electrodynamics in which he, as one of the first, discarded the existence of the aether (at least in the previous form) and would use, like Ernst Mach, the fixed stars as a reference frame instead. Due to inconsistencies within his theory, like different light speeds in different directions, it was superseded by Lorentz's and Einstein's.
+
+=== Electromagnetic mass ===
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+---
+title: "History of special relativity"
+chunk: 11/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+==== Non-euclidean formulations without imaginary time coordinate ====
+Minkowski in his earlier works in 1907 and 1908 followed Poincaré in representing space and time together in complex form 
+  
+    
+      
+        (
+        x
+        ,
+        y
+        ,
+        z
+        ,
+        i
+        c
+        t
+        )
+      
+    
+    {\textstyle (x,y,z,ict)}
+  
+ emphasizing the formal similarity with Euclidean space. He noted that spacetime is in a certain sense a four-dimensional non-Euclidean manifold. Sommerfeld (1910) used Minkowski's complex representation to combine non-collinear velocities by spherical geometry and so derive Einstein's addition formula. Subsequent writers, principally Varićak, dispensed with the imaginary time coordinate, and wrote in explicitly non-Euclidean (Lobachevskian) form reformulating relativity using the concept of rapidity previously introduced by Alfred Robb (1911); Edwin Bidwell Wilson and Gilbert N. Lewis (1912) introduced a vector notation for spacetime; Émile Borel (1913) showed how parallel transport in non-Euclidean space provides the kinematic basis of Thomas precession twelve years before its experimental discovery by Thomas; Felix Klein (1910) and Ludwik Silberstein (1914) employed such methods as well. One historian argues that the non-Euclidean style had little to show "in the way of creative power of discovery", but it offered notational advantages in some cases, particularly in the law of velocity addition. So in the years before World War I, the acceptance of the non-Euclidean style was approximately equal to that of the initial spacetime formalism, and it continued to be employed in relativity textbooks of the 20th century.
+
+==== Time dilation and twin paradox ====
+
+Einstein (1907a) proposed a method for detecting the transverse Doppler effect as a direct consequence of time dilation. And in fact, that effect was measured in 1938 by Herbert E. Ives and G. R. Stilwell (Ives–Stilwell experiment). And Lewis and Tolman (1909) described the reciprocity of time dilation by using two light clocks A and B, traveling with a certain relative velocity to each other. The clocks consist of two plane mirrors parallel to one another and to the line of motion. Between the mirrors a light signal is bouncing, and for the observer resting in the same reference frame as A, the period of clock A is the distance between the mirrors divided by the speed of light. But if the observer looks at clock B, he sees that within that clock the signal traces out a longer, angled path, thus clock B is slower than A. However, for the observer moving alongside B the situation is completely in reverse: Clock B is faster and A is slower. Lorentz (1910–1912) discussed the reciprocity of time dilation and analyzed a clock "paradox", which apparently occurs as a consequence of the reciprocity of time dilation. Lorentz showed that there is no paradox if one considers that in one system only one clock is used, while in the other system two clocks are necessary, and the relativity of simultaneity is fully taken into account.
+
+ A similar situation was created by Paul Langevin in 1911 with what was later called the "twin paradox", where he replaced the clocks by persons (Langevin never used the word "twins" but his description contained all other features of the paradox). Langevin solved the paradox by alluding to the fact that one twin accelerates and changes direction, so Langevin could show that the symmetry is broken and the accelerated twin is younger. However, Langevin himself interpreted this as a hint as to the existence of an aether. Although Langevin's explanation is still accepted by some, his conclusions regarding the aether were not generally accepted. Laue (1913) pointed out that any acceleration can be made arbitrarily small in relation to the inertial motion of the twin, and that the real explanation is that one twin is at rest in two different inertial frames during his journey, while the other twin is at rest in a single inertial frame. Laue was also the first to analyze the situation based on Minkowski's spacetime model for special relativity – showing how the world lines of inertially moving bodies maximize the proper time elapsed between two events.
+
+==== Acceleration ====
+Einstein (1908) tried – as a preliminary in the framework of special relativity – also to include accelerated frames within the relativity principle. In the course of this attempt he recognized that for any single moment of acceleration of a body one can define an inertial reference frame in which the accelerated body is temporarily at rest. It follows that in accelerated frames defined in this way, the application of the constancy of the speed of light to define simultaneity is restricted to small localities. However, the equivalence principle that was used by Einstein in the course of that investigation, which expresses the equality of inertial and gravitational mass and the equivalence of accelerated frames and homogeneous gravitational fields, transcended the limits of special relativity and resulted in the formulation of general relativity.
+Nearly simultaneously with Einstein, Minkowski (1908) considered the special case of uniform accelerations within the framework of his spacetime formalism. He recognized that the worldline of such an accelerated body corresponds to a hyperbola. This notion was further developed by Born (1909) and Sommerfeld (1910), with Born introducing the expression "hyperbolic motion". He noted that uniform acceleration can be used as an approximation for any form of acceleration within special relativity. In addition, Harry Bateman and Ebenezer Cunningham (1910) showed that Maxwell's equations are invariant under a much wider group of transformation than the Lorentz group, namely the spherical wave transformations, being a form of conformal transformations. Under those transformations the equations preserve their form for some types of accelerated motions. A general covariant formulation of electrodynamics in Minkowski space was eventually given by Friedrich Kottler (1912), whereby his formulation is also valid for general relativity. Concerning the further development of the description of accelerated motion in special relativity, the works by Langevin and others for rotating frames (Born coordinates), and by Wolfgang Rindler and others for uniform accelerated frames (Rindler coordinates) must be mentioned.
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+---
+title: "History of special relativity"
+chunk: 12/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+==== Rigid bodies and Ehrenfest paradox ====
+Einstein (1907b) discussed the question of whether, in rigid bodies, as well as in all other cases, the velocity of information can exceed the speed of light, and explained that information could be transmitted under these circumstances into the past, thus causality would be violated. Since this contravenes radically against every experience, superluminal velocities are thought impossible. He added that a dynamics of the rigid body must be created in the framework of SR. Eventually, Max Born (1909) in the course of his above-mentioned work concerning accelerated motion, tried to include the concept of rigid bodies into SR. However, Paul Ehrenfest (1909) showed that Born's concept leads to the so-called Ehrenfest paradox, in which, due to length contraction, the circumference of a rotating disk is shortened while the radius stays the same. This question was also considered by Gustav Herglotz (1910), Fritz Noether (1910), and von Laue (1911). It was recognized by Laue that the classic concept is not applicable in SR since a "rigid" body possesses infinitely many degrees of freedom. Yet, while Born's definition was not applicable on rigid bodies, it was very useful in describing rigid motions of bodies. In connection to the Ehrenfest paradox, it was also discussed (by Vladimir Varićak and others) whether length contraction is "real" or "apparent", and whether there is a difference between the dynamic contraction of Lorentz and the kinematic contraction of Einstein. However, it was rather a dispute over words because, as Einstein said, the kinematic length contraction is "apparent" for a co-moving observer, but for an observer at rest it is "real" and the consequences are measurable.
+
+==== Acceptance of special relativity ====
+Planck, in 1909, compared the implications of the modern relativity principle — he particularly referred to the relativity of time – with the revolution by the Copernican system. Poincaré made a similar analogy in 1905. An important factor in the adoption of special relativity by physicists was its development by Poincaré and Minkowski into a spacetime theory. Consequently, by about 1911, most theoretical physicists accepted special relativity. In 1912 Wilhelm Wien recommended both Lorentz (for the mathematical framework) and Einstein (for reducing it to a simple principle) for the Nobel Prize in Physics – although it was decided by the Nobel committee not to award the prize for special relativity. Only a minority of theoretical physicists such as Abraham, Lorentz, Poincaré, or Langevin still believed in the existence of an aether. Einstein later (1918–1920) qualified his position by arguing that one can speak about a relativistic aether, but the "idea of motion" cannot be applied to it. Lorentz and Poincaré had always argued that motion through the aether was undetectable. Einstein used the expression "special theory of relativity" in 1915, to distinguish it from general relativity.
+
+=== Relativistic theories ===
+
+==== Gravitation ====
+The first attempt to formulate a relativistic theory of gravitation was undertaken by Poincaré (1905). He tried to modify Newton's law of gravitation so that it assumes a Lorentz-covariant form. He noted that there were many possibilities for a relativistic law, and he discussed two of them. It was shown by Poincaré that the argument of Pierre-Simon Laplace, who argued that the speed of gravity is many times faster than the speed of light, is not valid within a relativistic theory. That is, in a relativistic theory of gravitation, planetary orbits are stable even when the speed of gravity is equal to that of light. Similar models to that of Poincaré were discussed by Minkowski (1907b) and Sommerfeld (1910). However, it was shown by Abraham (1912) that those models belong to the class of "vector theories" of gravitation. The fundamental defect of those theories is that they implicitly contain a negative value for the gravitational energy in the vicinity of matter, which would violate the energy principle. As an alternative, Abraham (1912) and Gustav Mie (1913) proposed different "scalar theories" of gravitation. While Mie never formulated his theory in a consistent way, Abraham completely gave up the concept of Lorentz-covariance (even locally), and therefore it was irreconcilable with relativity.
+In addition, all of those models violated the equivalence principle, and Einstein argued that it is impossible to formulate a theory which is both Lorentz-covariant and satisfies the equivalence principle. However, Gunnar Nordström (1912, 1913) was able to create a model which fulfilled both conditions. This was achieved by making both the gravitational and the inertial mass dependent on the gravitational potential. Nordström's theory of gravitation was remarkable because it was shown by Einstein and Adriaan Fokker (1914), that in this model gravitation can be completely described in terms of spacetime curvature. Although Nordström's theory is without contradiction, from Einstein's point of view a fundamental problem persisted: It does not fulfill the important condition of general covariance, as in this theory preferred frames of reference can still be formulated. So contrary to those "scalar theories", Einstein (1911–1915) developed a "tensor theory" (general relativity), which fulfills both the equivalence principle and general covariance. As a consequence, the notion of a complete "special relativistic" theory of gravitation had to be given up, as in general relativity the constancy of light speed (and Lorentz covariance) is only locally valid. The decision between those models was brought about by Einstein, when he was able to exactly derive the perihelion precession of Mercury, while the other theories gave erroneous results. In addition, only Einstein's theory gave the correct value for the deflection of light near the Sun.
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+---
+title: "History of special relativity"
+chunk: 13/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+==== Quantum field theory ====
+The need to put together relativity and quantum mechanics was one of the major motivations in the development of quantum field theory. Pascual Jordan and Wolfgang Pauli showed in 1928 that quantum fields could be made to be relativistic, and Paul Dirac produced the Dirac equation for electrons, and in so doing predicted the existence of antimatter.
+Many other domains have since been reformulated with relativistic treatments, including relativistic thermodynamics, relativistic statistical mechanics, relativistic hydrodynamics, relativistic quantum chemistry, and relativistic heat conduction. 
+
+=== Experimental evidence ===
+
+Important early experiments confirming special relativity as mentioned above were the Fizeau experiment, the Michelson–Morley experiment, the Kaufmann–Bucherer–Neumann experiments, the Trouton–Noble experiment, the experiments of Rayleigh and Brace, and the Trouton–Rankine experiment.
+In the 1920s, a series of Michelson–Morley type experiments were conducted, confirming relativity to even higher precision than the original experiment. Another type of interferometer experiment was the Kennedy–Thorndike experiment in 1932, by which the independence of the speed of light from the velocity of the apparatus was confirmed. Time dilation was directly measured in the Ives–Stilwell experiment in 1938 and by measuring the decay rates of moving particles in 1940. All of those experiments have been repeated several times with increased precision. In addition, that the speed of light is unreachable for massive bodies was measured in many tests of relativistic energy and momentum. Therefore, knowledge of those relativistic effects is required in the construction of particle accelerators.
+In 1962 J. G. Fox pointed out that all previous experimental tests of the constancy of the speed of light were conducted using light which had passed through stationary material: glass, air, or the incomplete vacuum of deep space.  As a result, all were thus subject to the effects of the extinction theorem.  This implied that the light being measured would have had a velocity different from that of the original source.  He concluded that there was likely as yet no acceptable proof of the second postulate of special relativity.  This surprising gap in the experimental record was quickly closed in the ensuing years, by experiments by Fox, and by Alvager et al., which used gamma rays sourced from high energy mesons.  The high energy levels of the measured photons, along with very careful accounting for extinction effects, eliminated any significant doubt from their results.
+Many other tests of special relativity have been conducted, testing possible violations of Lorentz invariance in certain variations of quantum gravity. However, no sign of anisotropy of the speed of light has been found even at the 10−17 level, and some experiments even ruled out Lorentz violations at the 10−40 level, see Modern searches for Lorentz violation.
+
+=== Priority ===
+Some claim that Poincaré and Lorentz, not Einstein, are the true discoverers of special relativity. For more see the article on relativity priority dispute.
+
+=== Criticisms ===
+
+Early criticisms of the theory of special relativity for various reasons – such as lack of empirical evidence, internal inconsistencies, rejection of mathematical physics per se, or philosophical reasons – have been turned back by many successful experimental confirmations and uses of the theory. The theory is now considered one of the fundamental laws of nature.
+
+== See also ==
+
+Timeline of special relativity and the speed of light
+Einstein's thought experiments
+History of Lorentz transformations
+Tests of special relativity
+
+== References ==
+
+=== Primary sources ===
+
+=== Notes and secondary sources ===
+
+== External links ==
+
+O'Connor, John J.; Robertson, Edmund F., "Special relativity", MacTutor History of Mathematics Archive, University of St Andrews
+Mathpages: Corresponding States, The End of My Latin, Who Invented Relativity?, Poincaré Contemplates Copernicus
+Berger, Andy "All in Einstein's Head" June 2016, Discover magazine,  explanations of Einstein's thought experiments
\ No newline at end of file
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+---
+title: "History of special relativity"
+chunk: 3/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+During his development of Maxwell's theory, J. J. Thomson (1881) recognized that charged bodies are harder to set in motion than uncharged bodies. Electrostatic fields behave as if they add an "electromagnetic mass" to the mechanical mass of the bodies. This is to say, according to Thomson, electromagnetic energy corresponds to a certain mass. This was interpreted as some form of self-inductance of the electromagnetic field. He also noticed that the mass of a body in motion is increased by a constant quantity. Thomson's work was continued and perfected by FitzGerald, Heaviside (1888), and George Frederick Charles Searle (1896, 1897). For the electromagnetic mass they gave — in modern notation — the formula 
+  
+    
+      
+        m
+        =
+        
+          
+            4
+            3
+          
+        
+        
+          
+            E
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\textstyle m={\frac {4}{3}}{\frac {E}{c^{2}}}}
+  
+, where m is the electromagnetic mass and E is the electromagnetic energy. Heaviside and Searle also recognized that the increase of the mass of a body is not constant and varies with its velocity. Consequently, Searle noted the impossibility of superluminal velocities, because infinite energy would be needed to exceed the speed of light. Also for Lorentz (1899), the integration of the speed-dependence of masses recognized by Thomson was especially important. He noticed that the mass not only varied due to speed, but is also dependent on the direction, and he introduced what Abraham later called "longitudinal" and "transverse" mass. (The transverse mass corresponds to what later was called relativistic mass.)
+Wilhelm Wien (1900) assumed (following the works of Thomson, Heaviside, and Searle) that the entire mass is of electromagnetic origin, which was formulated in the context that all forces of nature are electromagnetic ones (the "electromagnetic worldview"). Wien stated that, if it is assumed that gravitation is an electromagnetic effect too, then there has to be a proportionality between electromagnetic energy, inertial mass and gravitational mass. In the same paper Henri Poincaré (1900b) found another way of combining the concepts of mass and energy. He recognized that electromagnetic energy behaves like a fictitious fluid with mass density of 
+  
+    
+      
+        m
+        =
+        
+          
+            E
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\textstyle m={\frac {E}{c^{2}}}}
+  
+ (or 
+  
+    
+      
+        E
+        =
+        m
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\textstyle E=mc^{2}}
+  
+) and defined a fictitious electromagnetic momentum as well. However, he arrived at a radiation paradox which was fully explained by Einstein in 1905.
+Walter Kaufmann (1901–1903) was the first to confirm the velocity dependence of electromagnetic mass by analyzing the ratio 
+  
+    
+      
+        
+          
+            e
+            m
+          
+        
+      
+    
+    {\textstyle {\frac {e}{m}}}
+  
+ (where e is the charge and m the mass) of cathode rays. He found that the value of 
+  
+    
+      
+        
+          
+            e
+            m
+          
+        
+      
+    
+    {\textstyle {\frac {e}{m}}}
+  
+ decreased with the speed, showing that, assuming the charge constant, the mass of the electron increased with the speed. He also believed that those experiments confirmed the assumption of Wien, that there is no "real" mechanical mass, but only the "apparent" electromagnetic mass, or in other words, the mass of all bodies is of electromagnetic origin.
+Max Abraham (1902–1904), who was a supporter of the electromagnetic worldview, quickly offered an explanation for Kaufmann's experiments by deriving expressions for the electromagnetic mass. Together with this concept, Abraham introduced (like Poincaré in 1900) the notion of "electromagnetic momentum" which is proportional to 
+  
+    
+      
+        
+          
+            E
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\textstyle {\frac {E}{c^{2}}}}
+  
+. But unlike the fictitious quantities introduced by Poincaré, he considered it as a real, physical entity. Abraham also noted (like Lorentz in 1899) that this mass also depends on the direction and coined the names "longitudinal" and "transverse" mass. In contrast to Lorentz, he did not incorporate the contraction hypothesis into his theory, and therefore his mass terms differed from those of Lorentz.
+Based on the preceding work on electromagnetic mass, Friedrich Hasenöhrl suggested that part of the mass of a body (which he called apparent mass) can be thought of as radiation bouncing around a cavity. The "apparent mass" of radiation depends on the temperature (because every heated body emits radiation) and is proportional to its energy. Hasenöhrl stated that this energy–apparent-mass relation only holds as long as the body radiates, that is, if the temperature of a body is greater than 0 K. At first he gave the expression 
+  
+    
+      
+        m
+        =
+        
+          
+            8
+            3
+          
+        
+        
+          
+            E
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\textstyle m={\frac {8}{3}}{\frac {E}{c^{2}}}}
+  
+ for the apparent mass; however, Abraham and Hasenöhrl himself in 1905 changed the result to 
+  
+    
+      
+        m
+        =
+        
+          
+            4
+            3
+          
+        
+        
+          
+            E
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\textstyle m={\frac {4}{3}}{\frac {E}{c^{2}}}}
+  
+, the same value as for the electromagnetic mass for a body at rest.
\ No newline at end of file
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+---
+title: "History of special relativity"
+chunk: 4/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+=== Absolute space and time ===
+Some scientists and philosophers of science were critical of Newton's definitions of absolute space and time. Ernst Mach (1883) argued that absolute time and space are essentially metaphysical concepts and thus scientifically meaningless, and suggested that only relative motion between material bodies is a useful concept in physics. Mach argued that even effects that according to Newton depend on accelerated motion with respect to absolute space, such as rotation, could be described purely with reference to material bodies, and that the inertial effects cited by Newton in support of absolute space might instead be related purely to acceleration with respect to the fixed stars. Carl Neumann (1870) introduced a "Body alpha", which represents some sort of rigid and fixed body for defining inertial motion. Based on the definition of Neumann, Heinrich Streintz (1883) argued that in a coordinate system where gyroscopes do not measure any signs of rotation, inertial motion is related to a "fundamental body" and a "fundamental coordinate system". Eventually, Ludwig Lange (1885) was the first to coin the expression inertial frame of reference and "inertial time scale" as operational replacements for absolute space and time; he defined "inertial frame" as "a reference frame in which a mass point thrown from the same point in three different (non-coplanar) directions follows rectilinear paths each time it is thrown". In 1902, Henri Poincaré published a collection of essays titled Science and Hypothesis, which included: detailed philosophical discussions on the relativity of space and time; the conventionality of distant simultaneity; the conjecture that a violation of the relativity principle can never be detected; the possible non-existence of the aether, together with some arguments supporting the aether; and many remarks on non-Euclidean vs. Euclidean geometry.
+There were also some attempts to use time as a fourth dimension. This was done as early as 1754 by Jean le Rond d'Alembert in the Encyclopédie, and by some authors in the 19th century like H. G. Wells in his novel The Time Machine (1895). In 1901 a philosophical model was developed by Menyhért Palágyi, in which space and time were only two sides of some sort of "spacetime". He used time as an imaginary fourth dimension, which he gave the form it (where 
+  
+    
+      
+        i
+        =
+        
+          
+            −
+            1
+          
+        
+      
+    
+    {\textstyle i={\sqrt {-1}}}
+  
+ the imaginary unit). However, Palágyi's time coordinate is not connected to the speed of light. He also rejected any connection with the existing constructions of n-dimensional spaces and non-Euclidean geometry, so his philosophical model bears only slight resemblance to spacetime physics, as it was later developed by Minkowski.
+
+=== Light constancy and the principle of relative motion ===
+
+In the second half of the 19th century, there were many attempts to develop a worldwide clock network synchronized by electrical signals. For that endeavor, the finite propagation speed of light had to be considered, because synchronization signals could travel no faster than the speed of light. 
+In his paper "The Measure of Time" (1898), Henri Poincaré described some important consequences of this process and explained that astronomers, in determining the speed of light, simply assumed that light has a constant speed and that this speed is the same in all directions. Without this postulate, it would be impossible to infer the speed of light from astronomical observations, as Ole Rømer did based on observations of the moons of Jupiter. 
+
+Poincaré also noted that the propagation speed of light can be (and in practice often is) used to define simultaneity between spatially separate events:The simultaneity of two events, or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible. In other words, all these rules, all these definitions are only the fruit of an unconscious opportunism.
+In some other papers (1895, 1900b), Poincaré argued that experiments like that of Michelson and Morley show the impossibility of detecting the absolute motion of matter, that is, the relative motion of matter in relation to the aether. He called this the "principle of relative motion". In the same year, he interpreted Lorentz's local time as the result of a synchronization procedure based on light signals. He assumed that two observers who are moving in the aether synchronize their clocks by optical signals. Since they believe themselves to be at rest, they consider only the transmission time of the signals and then cross-reference their observations to examine whether their clocks are synchronous. From the point of view of an observer at rest in the aether, the clocks are not synchronous and indicate the local time 
+  
+    
+      
+        
+          t
+          ′
+        
+        =
+        t
+        −
+        
+          
+            
+              v
+              x
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\textstyle t'=t-{\frac {vx}{c^{2}}}}
+  
+, but the moving observers fail to recognize this because they are unaware of their movement. So, contrary to Lorentz, Poincaré-defined local time can be measured and indicated by clocks. Therefore, in his recommendation of Lorentz for the Nobel Prize in 1902, Poincaré argued that Lorentz had convincingly explained the negative outcome of the aether drift experiments by inventing the "diminished" or "local" time, that is, a time coordinate in which two events at different places could appear as simultaneous, although they are not simultaneous in reality.
+Like Poincaré, Alfred Bucherer (1903) believed in the validity of the relativity principle within the domain of electrodynamics, but contrary to Poincaré, Bucherer even assumed that this implies the nonexistence of the aether. However, the theory that he created later in 1906 was incorrect and not self-consistent, and the Lorentz transformation was absent within his theory as well.
\ No newline at end of file
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+---
+title: "History of special relativity"
+chunk: 5/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+=== Lorentz's 1904 model ===
+ 
+In his paper Electromagnetic phenomena in a system moving with any velocity smaller than that of light, Lorentz (1904) was following the suggestion of Poincaré and attempted to create a formulation of electrodynamics which explains the failure of all known aether drift experiments, and thus the validity of the relativity principle. He tried to prove the applicability of the Lorentz transformation for all orders, although he did not succeed completely. Like Wien and Abraham, he argued that there exists only electromagnetic mass, not mechanical mass, and derived the correct expression for longitudinal and transverse mass, which were in agreement with Kaufmann's experiments (even though those experiments were not precise enough to distinguish between the theories of Lorentz and Abraham). And using the electromagnetic momentum, he could explain the negative result of the Trouton–Noble experiment, in which a charged parallel-plate capacitor moving through the aether should orient itself perpendicular to the motion. Also the experiments of Rayleigh and Brace could be explained. Another important step was the postulate that the Lorentz transformation has to be valid for non-electrical forces as well.
+At the same time, when Lorentz worked out his theory, Wien (1903) recognized an important consequence of the velocity dependence of mass. He argued that superluminal velocities were impossible, because that would require an infinite amount of energy — the same was already noted by Thomson (1893) and Searle (1897). And in June 1904, after he had read Lorentz's 1904 paper, he noticed the same in relation to length contraction, because at superluminal velocities the factor 
+  
+    
+      
+        
+          
+            1
+            −
+            
+              
+                v
+                
+                  2
+                
+              
+            
+            
+              /
+            
+            
+              
+                c
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\textstyle {\sqrt {1-{v^{2}}/{c^{2}}}}}
+  
+ becomes imaginary.
+Lorentz's theory was criticized by Abraham, who demonstrated that on one side the theory obeys the relativity principle, and on the other side the electromagnetic origin of all forces is assumed. Abraham showed that both assumptions were incompatible, because in Lorentz's theory of the contracted electrons, non-electric forces were needed in order to guarantee the stability of matter. However, in Abraham's theory of the rigid electron, no such forces were needed. Thus the question arose whether the Electromagnetic conception of the world (compatible with Abraham's theory) or the Relativity Principle (compatible with Lorentz's Theory) was correct.
+In a September 1904 lecture in St. Louis named The Principles of Mathematical Physics, Poincaré drew some consequences from Lorentz's theory and defined (in modification of Galileo's Relativity Principle and Lorentz's Theorem of Corresponding States) the following principle: "The Principle of Relativity, according to which the laws of physical phenomena must be the same for a stationary observer as for one carried along in a uniform motion of translation, so that we have no means, and can have none, of determining whether or not we are being carried along in such a motion." He also specified his clock synchronization method and explained the possibility of a "new method" or "new mechanics", in which no velocity can surpass that of light for all observers. However, he critically noted that the relativity principle, Newton's action and reaction, the conservation of mass, and the conservation of energy are not fully established and are even threatened by some experiments.
+Also Emil Cohn (1904) continued to develop his alternative model (as described above), and while comparing his theory with that of Lorentz, he discovered some important physical interpretations of the Lorentz transformations. He illustrated (like Joseph Larmor in the same year) this transformation by using rods and clocks: If they are at rest in the aether, they indicate the true length and time, and if they are moving, they indicate contracted and dilated values. Like Poincaré, Cohn defined local time as the time that is based on the assumption of isotropic propagation of light. Contrary to Lorentz and Poincaré, it was noticed by Cohn that within Lorentz's theory the separation of "real" and "apparent" coordinates is artificial, because no experiment can distinguish between them. Yet according to Cohn's own theory, the Lorentz transformed quantities would only be valid for optical phenomena, while mechanical clocks would indicate the "real" time.
\ No newline at end of file
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+---
+title: "History of special relativity"
+chunk: 6/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+=== Poincaré's dynamics of the electron ===
+ 
+On June 5, 1905, Henri Poincaré submitted the summary of a work which closed the existing gaps of Lorentz's work. (This short paper contained the results of a more complete work which would be published later, in January 1906.) He showed that Lorentz's equations of electrodynamics were not fully Lorentz-covariant. So he pointed out the group characteristics of the transformation, and he corrected Lorentz's formulas for the transformations of charge density and current density (which implicitly contained the relativistic velocity-addition formula, which he elaborated in May in a letter to Lorentz). Poincaré used for the first time the term "Lorentz transformation", and he gave the transformations their symmetrical form used to this day. He introduced a non-electrical binding force (the so-called "Poincaré stresses") to ensure the stability of the electrons and to explain length contraction. He also sketched a Lorentz-invariant model of gravitation (including gravitational waves) by extending the validity of Lorentz-invariance to non-electrical forces.
+Eventually Poincaré (independently of Einstein) finished a substantially extended work of his June paper (the so-called "Palermo paper", received July 23, printed December 14, published January 1906 ). He spoke literally of "the postulate of relativity". He showed that the transformations are a consequence of the principle of least action and developed the properties of the Poincaré stresses.  He demonstrated in more detail the group characteristics of the transformation, which he called the Lorentz group, and he showed that the combination 
+  
+    
+      
+        
+          x
+          
+            2
+          
+        
+        +
+        
+          y
+          
+            2
+          
+        
+        +
+        
+          z
+          
+            2
+          
+        
+        −
+        
+          c
+          
+            2
+          
+        
+        
+          t
+          
+            2
+          
+        
+      
+    
+    {\textstyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}}
+  
+ is invariant. While elaborating his gravitational theory, he said the Lorentz transformation is merely a rotation in four-dimensional space about the origin, by introducing 
+  
+    
+      
+        c
+        t
+        
+          
+            −
+            1
+          
+        
+      
+    
+    {\textstyle ct{\sqrt {-1}}}
+  
+ as a fourth imaginary coordinate (contrary to Palágyi, he included the speed of light), and he already used four-vectors. He wrote that the discovery of magneto-cathode rays by Paul Ulrich Villard (1904) seemed to threaten the entire theory of Lorentz, but this problem was quickly solved. However, although in his philosophical writings Poincaré rejected the ideas of absolute space and time, in his physical papers he continued to refer to an (undetectable) aether. He also continued (1900b, 1904, 1906, 1908b) to describe coordinates and phenomena as local/apparent (for moving observers) and true/real (for observers at rest in the aether). So, with a few exceptions, most historians of science argue that Poincaré did not invent what is now called special relativity, although it is admitted that Poincaré anticipated much of Einstein's methods and terminology.
+
+== Special relativity ==
+
+=== Einstein 1905 ===
+
+==== Electrodynamics of moving bodies ====
+
+On September 26, 1905 (received June 30), Albert Einstein published his annus mirabilis paper on what is now called special relativity. Einstein's paper includes a fundamental description of the kinematics of the rigid body, and it did not require an absolutely stationary space, such as the aether. Einstein identified two fundamental principles, the principle of relativity and the principle of the constancy of light (light principle), which served as the axiomatic basis of his theory. To better understand Einstein's step, a summary of the situation before 1905, as it was described above, shall be given (it must be remarked that Einstein was familiar with the 1895 theory of Lorentz, and Science and Hypothesis by Poincaré, but possibly not their papers of 1904–1905):
+
+with the following consequences for the speed of light and the theories known at that time:
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+---
+title: "History of special relativity"
+chunk: 7/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+The speed of light is not composed of the speed of light in vacuum and the velocity of a preferred frame of reference, by b. This contradicts the theory of the (nearly) stationary aether.
+The speed of light is not composed of the speed of light in vacuum and the velocity of the light source, by a and c. This contradicts the emission theory.
+The speed of light is not composed of the speed of light in vacuum and the velocity of an aether that would be dragged within or in the vicinity of matter, by a, c, and d. This contradicts the hypothesis of the complete aether drag.
+The speed of light in moving media is not composed of the speed of light when the medium is at rest and the velocity of the medium, but is determined by Fresnel's dragging coefficient, by c.
+In order to make the principle of relativity as required by Poincaré an exact law of nature in the immobile aether theory of Lorentz, the introduction of a variety of ad hoc hypotheses was required, such as the contraction hypothesis, local time, the Poincaré stresses, and so on. This method was criticized by many scholars, since the assumption of a conspiracy of effects which completely prevent the discovery of the aether drift is considered to be very improbable, and it would violate Occam's razor as well. Einstein is considered the first who completely dispensed with such auxiliary hypotheses and drew the direct conclusions from the facts stated above: that the relativity principle is correct and the directly observed speed of light is the same in all inertial reference frames. Based on his axiomatic approach, Einstein was able to derive all results obtained by his predecessors – and in addition the formulas for the relativistic Doppler effect and relativistic aberration – in a few pages, while prior to 1905 his competitors had devoted years of long, complicated work to arrive at the same mathematical formalism. Before 1905 Lorentz and Poincaré had adopted these same principles, as necessary to achieve their final results, but did not recognize that they were also sufficient in the sense that there was no immediate logical need to assume the existence of a stationary aether in order to arrive at the Lorentz transformations. As Lorentz later said, "Einstein simply postulates what we have deduced". Another reason for Einstein's early rejection of the aether in any form (which he later partially retracted) may have been related to his work on quantum physics. Einstein discovered that light can also be described (at least heuristically) as a kind of particle, so the aether as the medium for electromagnetic "waves" (which was highly important for Lorentz and Poincaré) no longer fitted into his conceptual scheme.
+Einstein's paper contains no direct references to other papers. However, many historians of science like Holton, Miller, Stachel, have tried to find out possible influences on Einstein. He stated that his thinking was influenced by the empiricist philosophers David Hume and Ernst Mach. Regarding the Relativity Principle, the moving magnet and conductor problem (possibly after reading a book of August Föppl) and the various negative aether drift experiments were important for him to accept that principle — but he denied any significant influence of the most important experiment: the Michelson–Morley experiment. Other likely influences include Poincaré's Science and Hypothesis, where Poincaré presented the Principle of Relativity (which, as has been reported by Einstein's friend Maurice Solovine, was closely studied and discussed by Einstein and his friends over a period of years before the publication of Einstein's 1905 paper), and the writings of Max Abraham, from whom he borrowed the terms "Maxwell–Hertz equations" and "longitudinal and transverse mass".
+Regarding his views on Electrodynamics and the Principle of the Constancy of Light, Einstein stated that Lorentz's theory of 1895 (or the Maxwell–Lorentz electrodynamics) and also the Fizeau experiment had considerable influence on his thinking. He said in 1909 and 1912 that he borrowed that principle from Lorentz's stationary aether (which implies validity of Maxwell's equations and the constancy of light in the aether frame), but he recognized that this principle together with the principle of relativity makes any reference to an aether unnecessary (at least as to the description of electrodynamics in inertial frames). As he wrote in 1907 and in later papers, the apparent contradiction between those principles can be resolved if it is admitted that Lorentz's local time is not an auxiliary quantity, but can simply be defined as time and is connected with signal velocity. Before Einstein, Poincaré also developed a similar physical interpretation of local time and noticed the connection with signal velocity, but contrary to Einstein he continued to argue that clocks at rest in the stationary aether show the true time, while clocks in inertial motion relative to the aether show only the apparent time. Eventually, near the end of his life in 1953 Einstein described the advantages of his theory over that of Lorentz as follows (although Poincaré had already stated in 1905 that Lorentz invariance is an exact condition for any physical theory):
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+---
+title: "History of special relativity"
+chunk: 8/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+There is no doubt, that the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905. Lorentz had already recognized that the transformations named after him are essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further. Concerning myself, I knew only Lorentz's important work of 1895 […] but not Lorentz's later work, nor the consecutive investigations by Poincaré. In this sense my work of 1905 was independent. […]  The new feature of it was the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell's equations and was concerned with the nature of space and time in general. A further new result was that the "Lorentz invariance" is a general condition for any physical theory. This was for me of particular importance because I had already previously found that Maxwell's theory did not account for the micro-structure of radiation and could therefore have no general validity.
+
+==== Mass–energy equivalence ====
+
+Already in §10 of his paper on electrodynamics, Einstein used the formula
+
+  
+    
+      
+        
+          E
+          
+            kin
+          
+        
+        =
+        m
+        
+          c
+          
+            2
+          
+        
+        
+          (
+          
+            
+              
+                1
+                
+                  1
+                  −
+                  
+                    
+                      
+                        v
+                        
+                          2
+                        
+                      
+                      
+                        c
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+            
+            −
+            1
+          
+          )
+        
+      
+    
+    {\displaystyle E_{\text{kin}}=mc^{2}\left({\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}-1\right)}
+  
+
+for the kinetic energy of an electron. In elaboration of this he published a paper (received September 27, November 1905), in which Einstein showed that when a material body lost energy (either radiation or heat) of amount E, its mass decreased by the amount 
+  
+    
+      
+        
+          
+            E
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\textstyle {\frac {E}{c^{2}}}}
+  
+. This led to the famous mass–energy equivalence formula: 
+  
+    
+      
+        E
+        =
+        m
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\textstyle E=mc^{2}}
+  
+. Einstein considered the equivalency equation to be of paramount importance because it showed that a massive particle possesses an energy, the "rest energy", distinct from its classical kinetic and potential energies. As it was shown above, many authors before Einstein arrived at similar formulas (including a factor of ⁠4/3⁠) for the relation of mass to energy. However, their work was focused on electromagnetic energy which (as we know today) only represents a small part of the entire energy within matter. So it was Einstein who was the first to ascribe this relation to all forms of energy, and to understand the connection of mass–energy equivalence with the relativity principle.
+
+=== Early reception ===
+
+==== First assessments ====
+Walter Kaufmann (1905, 1906) was probably the first who referred to Einstein's work. He compared the theories of Lorentz and Einstein and, although he said Einstein's method is to be preferred, he argued that both theories are observationally equivalent. Therefore, he spoke of the relativity principle as the "Lorentz–Einsteinian" basic assumption. Shortly afterwards, Max Planck (1906a) was the first who publicly defended the theory and interested his students, Max von Laue and Kurd von Mosengeil, in this formulation. He described Einstein's theory as a "generalization" of Lorentz's theory and, to this "Lorentz–Einstein Theory", he gave the name "relative theory"; while Alfred Bucherer changed Planck's nomenclature into the now common "theory of relativity" ("Einsteinsche Relativitätstheorie"). On the other hand, Einstein himself and many others continued to refer simply to the new method as the "relativity principle". And in an important overview article on the relativity principle (1908a), Einstein described SR as a "union of Lorentz's theory and the relativity principle", including the fundamental assumption that Lorentz's local time can be described as real time. (Yet, Poincaré's contributions were rarely mentioned in the first years after 1905.) All of those expressions, (Lorentz–Einstein theory, relativity principle, relativity theory) were used by different physicists alternately in the next years.
+Following Planck, other German physicists quickly became interested in relativity, including Arnold Sommerfeld, Wilhelm Wien, Max Born, Paul Ehrenfest, and Alfred Bucherer. von Laue, who learned about the theory from Planck, published the first definitive monograph on relativity  in 1911. By 1911, Sommerfeld altered his plan to speak about relativity at the Solvay Congress because the theory was already considered well established.
+
+==== Kaufmann–Bucherer-Neumann experiments ====
+Kaufmann–Bucherer–Neumann experiments  
+Kaufmann (1903) presented results of his experiments on the charge-to-mass ratio of beta rays from a radium source, showing the dependence of the velocity on mass. He announced that these results confirmed Abraham's theory. However, Lorentz (1904a) reanalyzed results from Kaufmann (1903) against his theory and based on the data in tables concluded (p. 828) that the agreement with his theory "is seen to come out no less satisfactory than" with Abraham's theory. A recent reanalysis of the data from Kaufmann (1903) confirms that Lorentz's theory (1904a) does agree substantially better than Abraham's theory when applied to data from Kaufmann (1903). Kaufmann (1905, 1906) presented further results, this time with electrons from cathode rays. They represented, in his opinion, a clear refutation of the relativity principle and the Lorentz-Einstein-Theory, and a confirmation of Abraham's theory. For some years Kaufmann's experiments represented a weighty objection against the relativity principle, although it was criticized by Planck and Adolf Bestelmeyer (1906). Other physicists working with beta rays from radium, like Alfred Bucherer (1908) and Günther Neumann (1914), following on Bucherer's work and improving on his methods, also examined the velocity-dependence of mass and this time it was thought that the "Lorentz-Einstein theory" and the relativity principle were confirmed, and Abraham's theory disproved. A distinction needs to be made between work with beta ray electrons and cathode ray electrons since beta rays from radium have substantially larger velocities than cathode-ray electrons and so relativistic effects are substantially easier to detect with beta rays. Kaufmann's experiments with electrons from cathode rays only showed a qualitative mass increase of moving electrons, but they were not precise enough to distinguish between the models of Lorentz-Einstein and Abraham. It was not until 1940 that experiments with electrons from cathode rays were repeated with sufficient accuracy for confirming the Lorentz-Einstein formula. However, this problem occurred only with this kind of experiment. The investigations of the fine structure of the hydrogen lines already in 1917 provided a clear confirmation of the Lorentz-Einstein formula and the refutation of Abraham's theory.
\ No newline at end of file
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+---
+title: "History of special relativity"
+chunk: 9/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+==== Relativistic momentum and mass ====
+
+Planck (1906a) defined the relativistic momentum and gave the correct values for the longitudinal and transverse mass by correcting a slight mistake of the expression given by Einstein in 1905. Planck's expressions were in principle equivalent to those used by Lorentz in 1899. Based on the work of Planck, the concept of relativistic mass was developed by Gilbert Newton Lewis and Richard C. Tolman (1908, 1909) by defining mass as the ratio of momentum to velocity. So the older definition of longitudinal and transverse mass, in which mass was defined as the ratio of force to acceleration, became superfluous. Finally, Tolman (1912) interpreted relativistic mass simply as the mass of the body. However, many modern textbooks on relativity do not use the concept of relativistic mass anymore, and mass in special relativity is considered as an invariant quantity.
+
+==== Mass and energy ====
+Einstein (1906) showed that the inertia of energy (mass–energy equivalence) is a necessary and sufficient condition for the conservation of the center of mass theorem. On that occasion, he noted that the formal mathematical content of Poincaré's paper on the center of mass (1900b) and his own paper were mainly the same, although the physical interpretation was different in light of relativity.
+Kurd von Mosengeil (1906) by extending Hasenöhrl's calculation of black-body radiation in a cavity, derived the same expression for the additional mass of a body due to electromagnetic radiation as Hasenöhrl. Hasenöhrl's idea was that the mass of a body included a contribution from the electromagnetic field; he imagined a body as a cavity containing light. His relationship between mass and energy, like all other pre-Einstein ones, contained incorrect numerical prefactors (see Electromagnetic mass). Eventually Planck (1907) derived the mass–energy equivalence in general within the framework of special relativity, including the binding forces within matter. He acknowledged the priority of Einstein's 1905 work on 
+  
+    
+      
+        E
+        =
+        m
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle E=mc^{2}}
+  
+, but Planck judged his own approach as more general than Einstein's.
+
+==== Experiments by Fizeau and Sagnac ====
+As was explained above, already in 1895 Lorentz succeeded in deriving Fresnel's dragging coefficient (to first order of 
+  
+    
+      
+        
+          
+            v
+            c
+          
+        
+      
+    
+    {\textstyle {\frac {v}{c}}}
+  
+ and the Fizeau experiment by using the electromagnetic theory and the concept of local time. After first attempts by Jakob Laub (1907) to create a relativistic "optics of moving bodies", it was Max von Laue (1907) who derived the coefficient for terms of all orders by using the colinear case of the relativistic velocity addition law. In addition, Laue's calculation was much simpler than the complicated methods used by Lorentz.
+In 1911 von Laue also discussed a situation where on a platform a beam of light is split and the two beams are made to follow the same trajectory in opposite directions. On return to the point of entry the light is allowed to exit the platform in such a way that an interference pattern is obtained. Laue calculated a displacement of the interference pattern if the platform is in rotation –  because the speed of light is independent of the velocity of the source, so one beam has covered less distance than the other beam. An experiment of this kind was performed by Georges Sagnac in 1913, who actually measured a displacement of the interference pattern (Sagnac effect). While Sagnac himself concluded that his theory confirmed the theory of an aether at rest, Laue's earlier calculation showed that it is compatible with special relativity as well because, in both theories, the speed of light is independent of the velocity of the source. This effect can be understood as the electromagnetic counterpart of the mechanics of rotation, for example in analogy to a Foucault pendulum. Already in 1909–1911, Franz Harress (1912) performed an experiment which can be considered as a synthesis of the experiments of Fizeau and Sagnac. He tried to measure the dragging coefficient within glass. Contrary to Fizeau he used a rotating device so he found the same effect as Sagnac. While Harress himself misunderstood the meaning of the result, it was shown by von Laue that the theoretical explanation of Harress' experiment is in accordance with the Sagnac effect. Eventually, the Michelson–Gale–Pearson experiment (1925, a variation of the Sagnac experiment) indicated the angular velocity of the Earth itself in accordance with special relativity and a resting aether.
+
+==== Relativity of simultaneity ====
+The first derivations of relativity of simultaneity by synchronization with light signals were also simplified. Daniel Frost Comstock (1910) placed an observer in the middle between two clocks A and B. From this observer a signal is sent to both clocks, and in the frame in which A and B are at rest, they synchronously start to run. But from the perspective of a system in which A and B are moving, clock B is first set in motion, and then comes clock A – so the clocks are not synchronized. Also Einstein (1917) created a model with an observer in the middle between A and B. However, in his description two signals are sent from A and B to an observer aboard a moving train. From the perspective of the frame in which A and B are at rest, the signals are sent at the same time and the observer "is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."
+
+=== Spacetime physics ===
+
+==== Minkowski's spacetime ====
\ No newline at end of file
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+---
+title: "History of special relativity"
+chunk: 10/13
+source: "https://en.wikipedia.org/wiki/History_of_special_relativity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:25.411676+00:00"
+instance: "kb-cron"
+---
+
+Poincaré's attempt of a four-dimensional reformulation of the new mechanics was not continued by himself, so it was Hermann Minkowski (1907), who worked out the consequences of that notion (other contributions were made by Roberto Marcolongo (1906) and Richard Hargreaves (1908)). This was based on the work of many mathematicians of the 19th century like Arthur Cayley, Felix Klein, or William Kingdon Clifford, who contributed to group theory, invariant theory and projective geometry, formulating concepts such as the Cayley–Klein metric or the hyperboloid model in which the interval 
+  
+    
+      
+        
+          x
+          
+            1
+          
+          
+            2
+          
+        
+        +
+        
+          x
+          
+            2
+          
+          
+            2
+          
+        
+        +
+        
+          x
+          
+            3
+          
+          
+            2
+          
+        
+        −
+        
+          x
+          
+            4
+          
+          
+            2
+          
+        
+      
+    
+    {\textstyle x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-x_{4}^{2}}
+  
+ and its invariance was defined in terms of hyperbolic geometry. Using similar methods, Minkowski succeeded in formulating a geometrical interpretation of the Lorentz transformation. He completed, for example, the concept of four vectors; he created the Minkowski diagram for the depiction of spacetime; he was the first to use expressions like world line, proper time, Lorentz invariance and covariance, and so on; and most notably he presented a four-dimensional formulation of electrodynamics. Similar to Poincaré he tried to formulate a Lorentz-invariant law of gravity, but that work was subsequently superseded by Einstein's elaborations on gravitation.
+In 1907 Minkowski named four predecessors who contributed to the formulation of the relativity principle: Lorentz, Einstein, Poincaré and Planck. And in his famous lecture "Space and Time" (1908) he mentioned Voigt, Lorentz and Einstein. Minkowski himself considered Einstein's theory as a generalization of Lorentz's and credited Einstein for completely stating the relativity of time, but he criticized his predecessors for not fully developing the relativity of space. However, modern historians of science argue that Minkowski's claim for priority was unjustified, because Minkowski (like Wien or Abraham) adhered to the electromagnetic world picture and apparently did not fully understand the difference between Lorentz's electron theory and Einstein's kinematics. In 1908, Einstein and Laub rejected the four-dimensional electrodynamics of Minkowski as overly complicated "learned superfluousness" and published a "more elementary", non-four-dimensional derivation of the basic equations for moving bodies. But it was Minkowski's geometric model that showed that the special relativity is a complete and internally self-consistent theory, that added the Lorentz invariant proper time interval (which accounts for the actual readings shown by moving clocks), and that served as a basis for further development of relativity. Eventually, Einstein (1912) recognized the importance of Minkowski's geometric spacetime model and used it as the basis for his work on the foundations of general relativity.
+Today special relativity is seen as an application of linear algebra, but at the time special relativity was being developed the field of linear algebra was still in its infancy. There were no textbooks on linear algebra as modern vector space and transformation theory, and the matrix notation of Arthur Cayley (that unifies the subject) had not yet come into widespread use. Cayley's matrix calculus notation was used by Minkowski (1908) in formulating relativistic electrodynamics, even though it was later replaced by Sommerfeld using vector notation. According to a recent source the Lorentz transformations are equivalent to hyperbolic rotations. However Varićak (1910) had shown that the standard Lorentz transformation is a translation in hyperbolic space.
+
+==== Vector notation and closed systems ====
+Minkowski's spacetime formalism was quickly accepted and further developed. For example, Arnold Sommerfeld (1910) replaced Minkowski's matrix notation by an elegant vector notation and coined the terms "four vector" and "six vector". He also introduced a trigonometric formulation of the relativistic velocity addition rule, which according to Sommerfeld, removes much of the strangeness of that concept. Other important contributions were made by Laue (1911, 1913), who used the spacetime formalism to create a relativistic theory of deformable bodies and an elementary particle theory. He extended Minkowski's expressions for electromagnetic processes to all possible forces and thereby clarified the concept of mass–energy equivalence. Laue also showed that non-electrical forces are needed to ensure the proper Lorentz transformation properties, and for the stability of matter – he could show that the "Poincaré stresses" (as mentioned above) are a natural consequence of relativity theory so that the electron can be a closed system.
+
+==== Lorentz transformation without second postulate ====
+There were some attempts to derive the Lorentz transformation without the postulate of the constancy of the speed of light. Vladimir Ignatowski (1910) for example used for this purpose the principle of relativity, the homogeneity and isotropy of space, and the requirement of reciprocity. Philipp Frank and Hermann Rothe (1911) argued that this derivation is incomplete and needs additional assumptions. Their own calculation was based on the assumptions: that the Lorentz transformation forms a homogeneous linear group; that when changing frames, only the sign of the relative speed changes; and that length contraction solely depends on the relative speed. However, according to Pauli and Miller such models were insufficient to identify the invariant speed in their transformation with the speed of light — for example, Ignatowski was forced to seek recourse in electrodynamics to include the speed of light. So Pauli and others argued that both postulates are needed to derive the Lorentz transformation. However, until today, others continued the attempts to derive special relativity without the light postulate.
\ No newline at end of file
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diff --git a/data/en.wikipedia.org/wiki/History_of_spectroscopy-2.md b/data/en.wikipedia.org/wiki/History_of_spectroscopy-2.md
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+date_saved: "2026-05-05T16:29:22.444346+00:00"
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diff --git a/data/en.wikipedia.org/wiki/History_of_string_theory-0.md b/data/en.wikipedia.org/wiki/History_of_string_theory-0.md
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+---
+title: "History of string theory"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/History_of_string_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:23.791663+00:00"
+instance: "kb-cron"
+---
+
+The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum gravity, particle and condensed matter physics, cosmology, and pure mathematics.
+
+== 1943–1959: S-matrix theory ==
+String theory represents an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 following John Archibald Wheeler's 1937 introduction of the S-matrix. Many prominent theorists picked up and advocated S-matrix theory, starting in the late 1950s and throughout the 1960s. The field became marginalized and discarded in the mid-1970s and disappeared in the 1980s. Physicists neglected it because some of its mathematical methods were alien, and because quantum chromodynamics supplanted it as an experimentally better-qualified approach to the strong interactions.
+The theory presented a radical rethinking of the foundations of physical laws. By the 1940s it had become clear that the proton and the neutron were not pointlike particles like the electron. Their magnetic moment differed greatly from that of a pointlike spin-½ charged particle, too much to attribute the difference to a small perturbation. Their interactions were so strong that they scattered like a small sphere, not like a point. Heisenberg proposed that the strongly interacting particles were in fact extended objects, and because there are difficulties of principle with extended relativistic particles, he proposed that the notion of a space-time point broke down at nuclear scales.
+Without space and time, it becomes difficult to formulate a physical theory. Heisenberg proposed a solution to this problem: focusing on the observable quantities—those things measurable by experiments. An experiment only sees a microscopic quantity if it can be transferred by a series of events to the classical devices that surround the experimental chamber. The objects that fly to infinity are stable particles, in quantum superpositions of different momentum states.
+Heisenberg proposed that even when space and time are unreliable, the notion of momentum state, which is defined far away from the experimental chamber, still works. The physical quantity he proposed as fundamental is the quantum mechanical amplitude for a group of incoming particles to turn into a group of outgoing particles, and he did not admit that there were any steps in between.
+The S-matrix is the quantity that describes how a collection of incoming particles turn into outgoing ones. Heisenberg proposed to study the S-matrix directly, without any assumptions about space-time structure. But when transitions from the far-past to the far-future occur in one step with no intermediate steps, it becomes difficult to calculate anything. In quantum field theory, the intermediate steps are the fluctuations of fields or equivalently the fluctuations of virtual particles. In this proposed S-matrix theory, there are no local quantities at all.
+Heisenberg proposed to use unitarity to determine the S-matrix. In all conceivable situations, the sum of the squares of the amplitudes must equal 1. This property can determine the amplitude in a quantum field theory order by order in a perturbation series once the basic interactions are given, and in many quantum field theories the amplitudes grow too fast at high energies to make a unitary S-matrix. But without extra assumptions on the high-energy behavior, unitarity is not enough to determine the scattering, and the proposal was ignored for many years.
+Heisenberg's proposal was revived in 1956 when Murray Gell-Mann recognized that dispersion relations—like those discovered by Hendrik Kramers and Ralph Kronig in the 1920s (see Kramers–Kronig relations)—allow the formulation of a notion of causality, a notion that events in the future would not influence events in the past, even when the microscopic notion of past and future are not clearly defined. He also recognized that these relations might be useful in computing observables for the case of strong interaction physics. The dispersion relations were analytic properties of the S-matrix, and they imposed more stringent conditions than those that follow from unitarity alone. This development in S-matrix theory stemmed from Murray Gell-Mann and Marvin Leonard Goldberger's (1954) discovery of crossing symmetry, another condition that the S-matrix had to fulfil.
+Prominent advocates of the new "dispersion relations" approach included Stanley Mandelstam and Geoffrey Chew, both at UC Berkeley at the time. Mandelstam discovered the double dispersion relations, a new and powerful analytic form, in 1958, and believed that it would provide the key to progress in the intractable strong interactions.
+
+== 1959–1968: Regge theory and bootstrap models ==
+
+By the late 1950s, many strongly interacting particles of ever higher spins had been discovered, and it became clear that they were not all fundamental. While Japanese physicist Shoichi Sakata proposed that the particles could be understood as bound states of just three of them (the proton, the neutron and the Lambda; see Sakata model), Geoffrey Chew believed that none of these particles are fundamental (for details, see Bootstrap model). Sakata's approach was reworked in the 1960s into the quark model by Murray Gell-Mann and George Zweig by making the charges of the hypothetical constituents fractional and rejecting the idea that they were observed particles. At the time, Chew's approach was considered more mainstream because it did not introduce fractional charge values and because it focused on experimentally measurable S-matrix elements, not on hypothetical pointlike constituents.
\ No newline at end of file
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+---
+title: "History of string theory"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/History_of_string_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:23.791663+00:00"
+instance: "kb-cron"
+---
+
+In 1959, Tullio Regge, a young theorist in Italy, discovered that bound states in quantum mechanics can be organized into families known as Regge trajectories, each family having distinctive angular momenta. This idea was generalized to relativistic quantum mechanics by Stanley Mandelstam, Vladimir Gribov and Marcel Froissart, using a mathematical method (the Sommerfeld–Watson representation) discovered decades earlier by Arnold Sommerfeld and Kenneth M. Watson: the result was dubbed the Froissart–Gribov formula.
+In 1961, Geoffrey Chew and Steven Frautschi recognized that mesons had straight line Regge trajectories (in their scheme, spin is plotted against mass squared on a so-called Chew–Frautschi plot), which implied that the scattering of these particles would have very strange behavior—it should fall off exponentially quickly at large angles. With this realization, theorists hoped to construct a theory of composite particles on Regge trajectories, whose scattering amplitudes had the asymptotic form demanded by Regge theory.
+In 1967, a notable step forward in the bootstrap approach was the principle of DHS duality introduced by Richard Dolen, David Horn, and Christoph Schmid in 1967, at Caltech (the original term for it was "average duality" or "finite energy sum rule (FESR) duality"). The three researchers noticed that Regge pole exchange (at high energy) and resonance (at low energy) descriptions offer multiple representations/approximations of one and the same physically observable process.
+
+== 1968–1974: Dual resonance model ==
+The first model in which hadronic particles essentially follow the Regge trajectories was the dual resonance model that was constructed by Gabriele Veneziano in 1968, who noted that the Euler beta function could be used to describe 4-particle scattering amplitude data for such particles. The Veneziano scattering amplitude (or Veneziano model) was quickly generalized to an N-particle amplitude by Ziro Koba and Holger Bech Nielsen (their approach was dubbed the Koba–Nielsen formalism), and to what are now recognized as closed strings by Miguel Virasoro and Joel A. Shapiro (their approach was dubbed the Shapiro–Virasoro model).
+In 1969, the Chan–Paton rules (proposed by Jack E. Paton and Hong-Mo Chan) enabled isospin factors to be added to the Veneziano model.
+In 1969–70, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind presented a physical interpretation of the Veneziano amplitude by representing nuclear forces as vibrating, one-dimensional strings. However, this string-based description of the strong force made many predictions that directly contradicted experimental findings.
+In 1971, Pierre Ramond and, independently, John H. Schwarz and André Neveu attempted to implement fermions into the dual model. This led to the concept of "spinning strings", and pointed the way to a method for removing the problematic tachyon (see RNS formalism).
+Dual resonance models for strong interactions were a relatively popular subject of study between 1968 and 1973. The scientific community lost interest in string theory as a theory of strong interactions in 1973 when quantum chromodynamics became the main focus of theoretical research (mainly due to the theoretical appeal of its asymptotic freedom).
+
+== 1974–1984: Bosonic string theory and superstring theory ==
+In 1974, John H. Schwarz and Joël Scherk, and independently Tamiaki Yoneya, studied the boson-like patterns of string vibration and found that their properties exactly matched those of the graviton, the gravitational force's hypothetical messenger particle. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. This led to the development of bosonic string theory.
+String theory is formulated in terms of the Polyakov action, which describes how strings move through space and time. Like springs, the strings tend to contract to minimize their potential energy, but conservation of energy prevents them from disappearing, and instead they oscillate. By applying the ideas of quantum mechanics to strings it is possible to deduce the different vibrational modes of strings, and that each vibrational state appears to be a different particle. The mass of each particle, and the fashion with which it can interact, are determined by the way the string vibrates—in essence, by the "note" the string "sounds." The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory.
+Early models included both open strings, which have two distinct endpoints, and closed strings, where the endpoints are joined to make a complete loop.  The two types of string behave in slightly different ways, yielding two spectra.  Not all modern string theories use both types; some incorporate only the closed variety.
+The earliest string model has several problems: it has a critical dimension D = 26, a feature that was originally discovered by Claud Lovelace in 1971; the theory has a fundamental instability, the presence of tachyons (see tachyon condensation); additionally, the spectrum of particles contains only bosons, particles like the photon that obey particular rules of behavior.  While bosons are a critical ingredient of the Universe, they are not its only constituents.  Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry (in the West) in 1971, a mathematical transformation between bosons and fermions. String theories that include fermionic vibrations are now known as superstring theories.
+In 1977, the GSO projection (named after Ferdinando Gliozzi, Joël Scherk, and David I. Olive) led to a family of tachyon-free unitary free string theories, the first consistent superstring theories (see below).
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+---
+title: "History of string theory"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/History_of_string_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:23.791663+00:00"
+instance: "kb-cron"
+---
+
+== 1984–1994: First superstring revolution ==
+The first superstring revolution is a period of important discoveries that began in 1984. It was realized that string theory was capable of describing all elementary particles as well as the interactions between them. Hundreds of physicists started to work on string theory as the most promising idea to unify physical theories. The revolution was started by a discovery of anomaly cancellation in type I string theory via the Green–Schwarz mechanism (named after Michael Green and John H. Schwarz) in 1984. The ground-breaking discovery of the heterotic string was made by David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm in 1985. It was also realized by Philip Candelas, Gary Horowitz, Andrew Strominger, and Edward Witten in 1985 that to obtain 
+  
+    
+      
+        N
+        =
+        1
+      
+    
+    {\displaystyle N=1}
+  
+ supersymmetry, the six small extra dimensions (the D = 10 critical dimension of superstring theory had been originally discovered by John H. Schwarz in 1972) need to be compactified on a Calabi–Yau manifold. (In string theory, compactification is a generalization of Kaluza–Klein theory, which was first proposed in the 1920s.)
+By 1985, five separate superstring theories had been described: type I, type II (IIA and IIB), and heterotic (SO(32) and E8×E8).
+Discover magazine in the November 1986 issue (vol. 7, #11) featured a cover story written by Gary Taubes, "Everything's Now Tied to Strings", which explained string theory for a popular audience.
+In 1987, Eric Bergshoeff, Ergin Sezgin and Paul Townsend showed that there are no superstrings in eleven dimensions (the largest number of dimensions consistent with a single graviton in supergravity theories), but supermembranes.
+
+== 1994–2003: Second superstring revolution ==
+In the early 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of an 11-dimensional theory that became known as M-theory (for details, see Introduction to M-theory). These discoveries sparked the second superstring revolution that took place approximately between 1994 and 1995.
+The different versions of superstring theory were unified, as long hoped, by new equivalences. These are known as S-duality, T-duality, U-duality, mirror symmetry, and conifold transitions. The different theories of strings were also related to M-theory.
+In 1995, Joseph Polchinski discovered that the theory requires the inclusion of higher-dimensional objects, called D-branes: these are the sources of electric and magnetic Ramond–Ramond fields that are required by string duality. D-branes added additional rich mathematical structure to the theory, and opened possibilities for constructing realistic cosmological models in the theory (for details, see Brane cosmology).
+In 1997–98, Juan Maldacena conjectured a relationship between type IIB string theory and N = 4 supersymmetric Yang–Mills theory, a gauge theory. This conjecture, called the AdS/CFT correspondence, has generated a great deal of interest in high energy physics. It is a realization of the holographic principle, which has far-reaching implications: the AdS/CFT correspondence has helped elucidate the mysteries of black holes suggested by Stephen Hawking's work and is believed to provide a resolution of the black hole information paradox.
+
+== 2003–present ==
+
+In 2003, Michael R. Douglas's discovery of the string theory landscape, which suggests that string theory has a large number of inequivalent false vacua, led to much discussion of what string theory might eventually be expected to predict, and how cosmology can be incorporated into the theory.
+A possible mechanism of string theory vacuum stabilization (the KKLT mechanism) was proposed in 2003 by Shamit Kachru, Renata Kallosh, Andrei Linde, and Sandip Trivedi.
+Much of the present-day research is focused on characterizing the "swampland" of theories incompatible with quantum gravity. The Ryu–Takayanagi conjecture introduced many concepts from quantum information into string theory.
+
+== See also ==
+History of quantum field theory
+History of loop quantum gravity
+Strings (conference)
+
+== Notes ==
+
+== References ==
+Rickles, Dean (2014). A Brief History of String Theory: From Dual Models to M-Theory. Springer. ISBN 978-3-642-45128-7.
+
+== Further reading ==
+Paul Frampton (1974). Dual Resonance Models. Frontiers in Physics, W. A. Benjamin. ISBN 978-0-8053-2581-2.
+Joel A. Shapiro (2007). "Reminiscence on the Birth of String Theory". arXiv:0711.3448 [hep-th].
+John H. Schwarz (2012). "The Early History of String Theory and Supersymmetry". arXiv:1201.0981 [physics.hist-ph].
+Andrea Cappelli; Elena Castellani; Filippo Colomo; Paolo Di Vecchia (2012). The Birth of String Theory. Cambridge University Press. ISBN 978-0-521-19790-8.
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+---
+title: "History of subatomic physics"
+chunk: 1/4
+source: "https://en.wikipedia.org/wiki/History_of_subatomic_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:31.842332+00:00"
+instance: "kb-cron"
+---
+
+The idea that matter consists of smaller particles and that there exists a limited number of sorts of primary, smallest particles in nature has existed in natural philosophy at least since the 6th century BC. Such ideas gained physical credibility beginning in the 19th century, but the concept of "elementary particle" underwent some changes in its meaning: notably, modern physics no longer deems elementary particles indestructible. Even elementary particles can decay or collide destructively; they can cease to exist and create (other) particles in result.
+Increasingly small particles have been discovered and researched: they include molecules, which are constructed of atoms, that in turn consist of subatomic particles, namely atomic nuclei and electrons. Many more types of subatomic particles have been found. Most such particles (but not electrons) were eventually found to be composed of even smaller particles such as quarks. Particle physics studies these smallest particles; nuclear physics studies atomic nuclei and their (immediate) constituents: protons and neutrons.
+
+== Early development ==
+
+The idea that all matter is composed of elementary particles dates to as far as the 6th century BCE. The Jains in ancient India were the earliest to advocate the particular nature of material objects between 9th and 5th century BCE. According to Jain leaders like Parshvanatha and Mahavira, the ajiva (non living part of universe) consists of matter or pudgala, of definite or indefinite shape which is made up tiny uncountable and invisible particles called permanu. Permanu occupies space-point and each permanu has definite colour, smell, taste and texture. Infinite varieties of permanu unite and form pudgala. The philosophical doctrine of atomism and the nature of elementary particles were also studied by ancient Greek philosophers such as Leucippus, Democritus, and Epicurus; ancient Indian philosophers such as Kanada, Dignāga, and Dharmakirti; Muslim scientists such as Ibn al-Haytham, Ibn Sina, and Mohammad al-Ghazali; and in early modern Europe by physicists such as Pierre Gassendi, Robert Boyle, and Isaac Newton. The particle theory of light was also proposed by Ibn al-Haytham, Ibn Sina, Gassendi, and Newton.
+Those early ideas were founded through abstract, philosophical reasoning rather than experimentation and empirical observation and represented only one line of thought among many. In contrast, certain ideas of Gottfried Wilhelm Leibniz (see Monadology) contradict to almost everything known in modern physics.
+In the 19th century, John Dalton, through his work on stoichiometry, concluded that each chemical element was composed of a single, unique type of particle. Dalton and his contemporaries believed those were the fundamental particles of nature and thus named them atoms, after the Greek word atomos, meaning "indivisible" or "uncut".
+However, near the end of 19th century, physicists discovered that Dalton's atoms are not, in fact, the fundamental particles of nature, but conglomerates of even smaller particles.
+
+== From atoms to nucleons ==
+
+=== Electromagnetic theory ===
+
+Throughout the 1800s scientists explored many phenomena of electricity and magnetism, culminating in an accurate theory by James Clerk Maxwell. This theory was a continuous field model developed around the ideas of luminiferous aether. When no experiment could produce evidence of such an ether, and in view of the growing evidence supporting the atomic model, Hendrik Antoon Lorentz developed a theory of electromagnetism based on "ions" that reproduced Maxwell's model.
+
+=== Discovery of the electron ===
+The electron was discovered between 1879 and 1897 in works of William Crookes, Arthur Schuster, J. J. Thomson, and other physicists; its charge was carefully measured by Robert Andrews Millikan and Harvey Fletcher in their oil drop experiment of 1909. Physicists theorized that negatively charged electrons are constituent part of "atoms", along with some (yet unknown) positively charged substance, and it was later confirmed. Electron became the first elementary, truly fundamental particle discovered.
+
+=== Radioactivity ===
+Studies of the "radioactivity", that soon revealed the phenomenon of radioactive decay, provided another argument against considering chemical elements as fundamental nature's elements. Despite these discoveries, the term atom stuck to Dalton's (chemical) atoms and now denotes the smallest particle of a chemical element, not something really indivisible.
+
+=== Researching particles' interaction ===
+
+Early 20th-century physicists knew only two fundamental forces: electromagnetism and gravitation, where the latter could not explain the structure of atoms. So, it was obvious to assume that unknown positively charged substance attracts electrons by Coulomb force.
+
+In 1909 Ernest Rutherford and Thomas Royds demonstrated that an alpha particle combines with two electrons and forms a helium atom. In modern terms, alpha particles are doubly ionized helium (more precisely, 4He) atoms. Speculation about the structure of atoms was severely constrained by Rutherford's 1907 gold foil experiment, showing that the atom is mainly empty space, with almost all its mass concentrated in a tiny atomic nucleus.
+
+=== Inside the atom ===
+
+By 1914, experiments by Ernest Rutherford, Henry Moseley, James Franck and Gustav Hertz had largely established the structure of an atom as a dense nucleus of positive charge surrounded by lower-mass electrons.
+These discoveries shed a light to the nature of radioactive decay and other forms of transmutation of elements, as well as of elements themselves. It appeared that atomic number is nothing else than (positive) electric charge of the atomic nucleus of a particular atom. Chemical transformations, governed by electromagnetic interactions, do not change nuclei – that's why elements are chemically indestructible. But when the nucleus change its charge and/or mass (by emitting or capturing a particle), the atom can become the one of another element. Special relativity explained how the mass defect is related to the energy produced or consumed in reactions. The branch of physics that studies transformations and the structure of nuclei is now called nuclear physics, contrasted to atomic physics that studies the structure and properties of atoms ignoring most nuclear aspects. The development in the nascent quantum physics, such as Bohr model, led to the understanding of chemistry in terms of the arrangement of electrons in the mostly empty volume of atoms.
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+---
+title: "History of subatomic physics"
+chunk: 2/4
+source: "https://en.wikipedia.org/wiki/History_of_subatomic_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:31.842332+00:00"
+instance: "kb-cron"
+---
+
+In 1918, Rutherford confirmed that the hydrogen nucleus was a particle with a positive charge, which he named the proton. By then, Frederick Soddy's researches of radioactive elements, and experiments of J. J. Thomson and F.W. Aston conclusively demonstrated existence of isotopes, whose nuclei have different masses in spite of identical atomic numbers. It prompted Rutherford to conjecture that all nuclei other than hydrogen contain chargeless particles, which he named the neutron.
+Evidences that atomic nuclei consist of some smaller particles (now called nucleons) grew; it became obvious that, while protons repulse each other electrostatically, nucleons attract each other by some new force (nuclear force). It culminated in proofs of nuclear fission in 1939 by Lise Meitner (based on experiments by Otto Hahn), and nuclear fusion by Hans Bethe in that same year. Those discoveries gave rise to an active industry of generating one atom from another, even rendering possible (although it will probably never be profitable) the transmutation of lead into gold; and, those same discoveries also led to the development of nuclear weapons.
+
+== Revelations of quantum mechanics ==
+
+Further understanding of atomic and nuclear structures became impossible without improving the knowledge about the essence of particles. Experiments and improved theories (such as Erwin Schrödinger's "electron waves") gradually revealed that there is no fundamental difference between particles and waves. For example, electromagnetic waves were reformulated in terms of particles called photons. It also revealed that physical objects do not change their parameters, such as total energy, position and momentum, as continuous functions of time, as it was thought of in classical physics: see atomic electron transition for example.
+Another crucial discovery was identical particles or, more generally, quantum particle statistics. It was established that all electrons are identical: although two or more electrons can exist simultaneously that have different parameters, but they do not keep separate, distinguishable histories. This also applies to protons, neutrons, and (with certain differences) to photons as well. It suggested that there is a limited number of sorts of smallest particles in the universe.
+The spin–statistics theorem established that any particle in our spacetime may be either a boson (that means its statistics is Bose–Einstein) or a fermion (that means its statistics is Fermi–Dirac). It was later found that all fundamental bosons transmit forces, like the photon that transmits light. Some of non-fundamental bosons (namely, mesons) also may transmit forces (see below), although non-fundamental ones. Fermions are particles "like electrons and nucleons" and generally comprise the matter. Note that any subatomic or atomic particle composed of even total number of fermions (such as protons, neutrons, and electrons) is a boson, so a boson is not necessarily a force transmitter and perfectly can be an ordinary material particle.
+The spin is the quantity that distinguishes bosons and fermions. Practically it appears as an intrinsic angular momentum of a particle, that is unrelated to its motion but is linked with some other features like a magnetic dipole. Theoretically it is explained from different types representations of symmetry groups, namely tensor representations (including vectors and scalars) for bosons with their integer (in ħ) spins, and spinor representations for fermions with their half-integer spins.
+Improved understanding of the world of particles prompted physicists to make bold predictions, such as Dirac's positron in 1928 (founded on the Dirac Sea model) and Pauli's neutrino in 1930 (founded on conservation of energy and angular momentum in beta decay). Both were later confirmed.
+This culminated in the formulation of ideas of a quantum field theory. The first (and the only mathematically complete) of these theories, quantum electrodynamics, allowed to explain thoroughly the structure of atoms, including the Periodic Table and atomic spectra. Ideas of quantum mechanics and quantum field theory were applied to nuclear physics too. For example, α decay was explained  as a quantum tunneling through nuclear potential, nucleons' fermionic statistics explained the nucleon pairing, and Hideki Yukawa proposed certain virtual particles (now knows as π-mesons) as an explanation of the nuclear force.
+
+== From nuclides to nuclear engineering ==
+
+Development of nuclear models (such as the liquid-drop model and nuclear shell model) made prediction of properties of nuclides possible. No existing model of nucleon–nucleon interaction can analytically compute something more complex than 4He based on principles of quantum mechanics, though (note that complete computation of electron shells in atoms is also impossible as yet).
+The most developed branch of nuclear physics in 1940s was studies related to nuclear fission due to its military significance. The main focus of fission-related problems is interaction of atomic nuclei with neutrons: a process that occurs in a fission bomb and a nuclear fission reactor. It gradually drifted away from the rest of subatomic physics and virtually became the nuclear engineering. The first synthesised transuranium elements were also obtained in this context, through neutron capture and subsequent β− decay.
+The elements beyond fermium cannot be produced in this way. To make a nuclide with more than 100 protons per nucleus one has to use an inventory and methods of particle physics (see details below), namely to accelerate and collide atomic nuclei. Production of progressively heavier synthetic elements continued into 21st century as a branch of nuclear physics, but only for scientific purposes.
+The third important stream in nuclear physics are researches related to nuclear fusion. This is related to thermonuclear weapons (and conceived peaceful thermonuclear energy), as well as to astrophysical researches, such as stellar nucleosynthesis and Big Bang nucleosynthesis.
+
+== High energy physics ==
+
+=== Strange particles and the weak interaction ===
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+---
+title: "History of subatomic physics"
+chunk: 3/4
+source: "https://en.wikipedia.org/wiki/History_of_subatomic_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:31.842332+00:00"
+instance: "kb-cron"
+---
+
+In the 1950s, with development of particle accelerators and studies of cosmic rays, inelastic scattering experiments on protons (and other atomic nuclei) with energies about hundreds of MeVs became affordable. They created some short-lived resonance "particles", but also hyperons and K-mesons with unusually long lifetime. The cause of the latter was found in a new quasi-conserved quantity, named strangeness, that is conserved in all circumstances except for the weak interaction. The strangeness of heavy particles and the μ-lepton were first two signs of what is now known as the second generation of fundamental particles.
+The weak interaction revealed soon yet another mystery. In 1957 Chien-Shiung Wu proved that it does not conserve parity. In other words, the mirror symmetry was disproved as a fundamental symmetry law.
+Throughout the 1950s and 1960s, improvements in particle accelerators and particle detectors led to a bewildering variety of particles found in high-energy experiments. The term elementary particle came to refer to dozens of particles, most of them unstable. It prompted Wolfgang Pauli's remark: "Had I foreseen this, I would have gone into botany". The entire collection was nicknamed the "particle zoo". It became evident that some smaller constituents, yet invisible, form mesons and baryons that counted most of then-known particles.
+
+=== Deeper constituents of matter ===
+
+The interaction of these particles by scattering and decay provided a key to new fundamental quantum theories. Murray Gell-Mann and Yuval Ne'eman brought some order to mesons and baryons, the most numerous classes of particles, by classifying them according to certain qualities. It began with what Gell-Mann referred to as the "Eightfold Way", but proceeding into several different "octets" and "decuplets" which could predict new particles, most famously the Ω−, which was detected at Brookhaven National Laboratory in 1964, and which gave rise to the quark model of hadron composition.  While the quark model at first seemed inadequate to describe strong nuclear forces, allowing the temporary rise of competing theories such as the S-matrix theory, the establishment of quantum chromodynamics in the 1970s finalized a set of fundamental and exchange particles (Kragh 1999). It postulated the fundamental strong interaction, experienced by quarks and mediated by gluons. These particles were proposed as a building material for hadrons (see hadronization). This theory is unusual because individual (free) quarks cannot be observed (see color confinement), unlike the situation with composite atoms where electrons and nuclei can be isolated by transferring ionization energy to the atom.
+Then, the old, broad denotation of the term elementary particle was deprecated and a replacement term subatomic particle covered all the "zoo", with its hyponym "hadron" referring to composite particles directly explained by the quark model. The designation of an "elementary" (or "fundamental") particle was reserved for leptons, quarks, their antiparticles, and quanta of fundamental interactions (see below) only.
+
+=== Quarks, leptons, and four fundamental forces ===
+
+Because the quantum field theory (see above) postulates no difference between particles and interactions, classification of elementary particles allowed also to classify interactions and fields.
+Now a large number of particles and (non-fundamental) interactions is explained as combinations of a (relatively) small number of fundamental substances, thought to be fundamental interactions (incarnated in fundamental bosons), quarks (including antiparticles), and leptons (including antiparticles). As the theory distinguished several fundamental interactions, it became possible to see which elementary particles participate in which interaction. Namely:
+
+All particles participate in gravitation.
+All charged elementary particles participate in electromagnetic interaction.
+As a consequence, neutron participates in it with its magnetic dipole in spite of zero electric charge. This is because it is composed of charged quarks whose charges sum to zero.
+All fermions participate in the weak interaction.
+Quarks participate in the strong interaction, along gluons (its own quanta), but not leptons nor any fundamental bosons other than gluons.
+The next step was a reduction in number of fundamental interactions, envisaged by early 20th century physicists as the "united field theory". The first successful modern unified theory was the electroweak theory, developed by Abdus Salam, Steven Weinberg and, subsequently, Sheldon Glashow. This development culminated in the completion of the theory called the Standard Model in the 1970s, that included also the strong interaction, thus covering three fundamental forces. After the discovery, made at CERN, of the existence of neutral weak currents, mediated by the Z boson foreseen in the standard model, the physicists Salam, Glashow and Weinberg received the 1979 Nobel Prize in Physics for their electroweak theory.
+The discovery of the weak gauge bosons (quanta of the weak interaction) through the 1980s, and the verification of their properties through the 1990s is considered to be an age of consolidation in particle physics.
+While accelerators have confirmed most aspects of the Standard Model by detecting expected particle interactions at various collision energies, no theory reconciling general relativity with the Standard Model has yet been found, although supersymmetry and string theory were believed by many theorists to be a promising avenue forward. The Large Hadron Collider, however, which began operating in 2008, has failed to find any evidence whatsoever that is supportive of supersymmetry and string theory, and appears unlikely to do so, meaning "the current situation in fundamental theory is one of a serious lack of any new ideas at all." This state of affairs should not be viewed as a crisis in physics, but rather, as David Gross has said, "the kind of acceptable scientific confusion that discovery eventually transcends."
+Gravitation, the fourth fundamental interaction, is not yet integrated into particle physics in a consistent way.
+
+=== Higgs boson ===
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+---
+title: "History of subatomic physics"
+chunk: 4/4
+source: "https://en.wikipedia.org/wiki/History_of_subatomic_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:31.842332+00:00"
+instance: "kb-cron"
+---
+
+As of 2011, the Higgs boson, the quantum of a field that is thought to provide particles with rest masses, remained the only particle of the Standard Model to be verified.
+On July 4, 2012, physicists working at CERN's Large Hadron Collider announced that they had discovered a new subatomic particle greatly resembling the Higgs boson, a potential key to an understanding of why elementary particles have masses and indeed to the existence of diversity and life in the universe. Rolf-Dieter Heuer, the director general of CERN, said that it was too soon to know for sure whether it is an entirely new massive particle – one of the heaviest subatomic particles yet – or, indeed, the elusive particle predicted by the Standard Model, the theory that has ruled physics for the last half-century. It is unknown if this particle is an impostor, a single particle or even the first of many particles yet to be discovered. The latter possibilities are particularly exciting to physicists since they could point the way to new deeper ideas, beyond the Standard Model, about the nature of reality. For now, some physicists are calling it a "Higgslike" particle. Joe Incandela, of the University of California, Santa Barbara, said, "It's something that may, in the end, be one of the biggest observations of any new phenomena in our field in the last 30 or 40 years, going way back to the discovery of quarks, for example." The groups operating the large detectors in the collider said that the likelihood that their signal was a result of a chance fluctuation was less than one chance in 3.5 million, so-called "five sigma," which is the gold standard in physics for a discovery. Michael Turner, a cosmologist at the University of Chicago and the chairman of the physics center board, said
+
+This is a big moment for particle physics and a crossroads — will this be the high water mark or will it be the first of many discoveries that point us toward solving the really big questions that we have posed?
+Confirmation of the Higgs boson or something very much like it would constitute a rendezvous with destiny for a generation of physicists who have believed the boson existed for half a century without ever seeing it. Further, it affirms a grand view of a universe ruled by simple and elegant and symmetrical laws, but in which everything interesting in it being a result of flaws or breaks in that symmetry. According to the Standard Model, the Higgs boson is the only visible and particular manifestation of an invisible force field that permeates space and imbues elementary particles that would otherwise be massless with mass. Without this Higgs field, or something like it, physicists say all the elementary forms of matter would zoom around at the speed of light; there would be neither atoms nor life. The Higgs boson achieved a notoriety rare for abstract physics. To the eternal dismay of his colleagues, Leon Lederman, the former director of Fermilab, called it the "God particle" in his book of the same name, later quipping that he had wanted to call it "the goddamn particle". Professor Incandela also stated,
+
+This boson is a very profound thing we have found. We're reaching into the fabric of the universe at a level we've never done before. We've kind of completed one particle's story [...] We're on the frontier now, on the edge of a new exploration. This could be the only part of the story that's left, or we could open a whole new realm of discovery.
+Dr. Peter Higgs was one of six physicists, working in three independent groups, who in 1964 invented the notion of the cosmic molasses, or Higgs field. The others were Tom Kibble of Imperial College, London; Carl Hagen of the University of Rochester; Gerald Guralnik of Brown University; and François Englert and Robert Brout, both of Université Libre de Bruxelles. One implication of their theory was that this Higgs field would produce its own quantum particle if hit hard enough by the right amount of energy. The particle would be fragile and fall apart within a millionth of a second in a dozen different ways depending upon its own mass. Unfortunately, the theory did not predict the particle mass making it difficult to find. The particle eluded researchers at a succession of particle accelerators.
+Further experiments continued and in March 2013 it was tentatively confirmed that the newly discovered particle was a Higgs Boson.
+Although they have never been seen, Higgs-like fields play an important role in theories of the universe and in string theory. Under certain conditions, according to the strange accounting of Einsteinian physics, they can become suffused with energy that exerts an antigravitational force. Such fields have been proposed as the source of an enormous burst of expansion, known as inflation, early in the universe and, possibly, as the secret of the dark energy that now seems to be speeding up the expansion of the universe.
+
+== Notes ==
+
+== References ==
+Kragh, Helge (1999), Quantum Generations: A History of Physics in the Twentieth Century, Princeton: Princeton University Press.
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+---
+title: "History of superconductivity"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/History_of_superconductivity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:33.041097+00:00"
+instance: "kb-cron"
+---
+
+Superconductivity is the phenomenon of certain materials exhibiting zero electrical resistance and the expulsion of magnetic fields below a characteristic temperature. The history of superconductivity began with Dutch physicist Heike Kamerlingh Onnes's discovery of superconductivity in mercury in 1911. Since then, many other superconducting materials have been discovered and the theory of superconductivity has been developed. These subjects remain active areas of study in the field of condensed matter physics.
+The study of superconductivity has a fascinating history, with several breakthroughs having dramatically accelerated publication and patenting activity in this field, as shown in the figure on the right and described in details below. Throughout its 100+ year history the number of non-patent publications per year about superconductivity has been a factor of 10 larger than the number of patent families, which is characteristic of a technology, that has not achieved a substantial commercial success (see Technological applications of superconductivity).
+
+== Exploring ultra-cold phenomena (to 1908) ==
+
+James Dewar initiated research into electrical resistance at low temperatures. Dewar and John Ambrose Fleming predicted that at absolute zero, pure metals would become perfect electromagnetic conductors (though, later, Dewar altered his opinion on the disappearance of resistance, believing that there would always be some resistance). Walther Hermann Nernst developed the third law of thermodynamics and stated that absolute zero was unattainable. Carl von Linde and William Hampson, both commercial researchers, nearly at the same time filed for patents on the Joule–Thomson effect for the liquefaction of gases. Linde's patent was the climax of 20 years of systematic investigation of established facts, using a regenerative counterflow method. Hampson's designs was also of a regenerative method. The combined process became known as the Hampson–Linde liquefaction process.
+Onnes purchased a Linde machine for his research. On March 21, 1900, Nikola Tesla was granted a patent for the means for increasing the intensity of electrical oscillations by lowering the temperature, which was caused by lowered resistance. Within this patent it describes the increased intensity and duration of electric oscillations of a low temperature resonating circuit. It is believed that Tesla had intended that Linde's machine would be used to attain the cooling agents.
+A milestone was achieved on July 10, 1908, when Heike Kamerlingh Onnes at Leiden University in the Netherlands produced, for the first time, liquified helium, which has a boiling point of 4.2 K (−269 °C) at atmospheric pressure.
+
+== Sudden and fundamental disappearance ==
+Heike Kamerlingh Onnes and Jacob Clay reinvestigated Dewar's earlier experiments on the reduction of resistance at low temperatures. Onnes began the investigations with platinum and gold, replacing these later with mercury (a more readily refinable material). Onnes's research into the resistivity of solid mercury at cryogenic temperatures was accomplished by using liquid helium as a refrigerant. On April 8, 1911, 16:00 hours Onnes noted "Kwik nagenoeg nul", which translates as "[Resistance of] mercury almost zero." At the temperature of 4.19 K, he observed that the resistivity abruptly disappeared (the measuring device Onnes was using did not indicate any resistance). Onnes disclosed his research in 1911, in a paper titled "On the Sudden Rate at Which the Resistance of Mercury Disappears." Onnes stated in that paper that the "specific resistance" became thousands of times less in amount relative to the best conductor at ordinary temperature. Onnes later reversed the process and found that at 4.2 K, the resistance returned to the material. The next year, Onnes published more articles about the phenomenon. Initially, Onnes called the phenomenon "supraconductivity" (1913) and, only later, adopted the term "superconductivity." For his research, he was awarded the Nobel Prize in Physics in 1913.
+Onnes conducted an experiment, in 1912, on the usability of superconductivity. Onnes introduced an electric current into a superconductive ring and removed the battery that generated it. Upon measuring the electric current, Onnes found that its intensity did not diminish with the time. The current persisted due to the superconductive state of the conductive medium.
+In subsequent decades, superconductivity was found in several other materials; In 1913, lead at 7 K, in 1930's niobium at 10 K, and in 1941 niobium nitride at 16 K.
+
+== Enigmas and solutions (1933–1979) ==
+
+The next important step in understanding superconductivity occurred in 1933, when Walther Meissner and Robert Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon that has come to be known as the Meissner effect. In 1935, brothers Fritz London and Heinz London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current. 
+In 1937, Lev Shubnikov discovered a new type of superconductors (later called type-II superconductors), that presented a mixed phase between ordinary and superconductive properties.
+In 1950, the phenomenological Ginzburg–Landau theory of superconductivity was devised by Lev Landau and Vitaly Ginzburg. The Ginzburg–Landau theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Alexei Abrikosov showed that Ginzburg–Landau theory predicts the division of superconductors into the two categories now referred to as type I and type II superconductivity. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize in Physics for their work (Landau having died in 1968). Also in 1950, Emanuel Maxwell and, almost simultaneously, C.A. Reynolds et al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity.
+On the experimental side, collaborations of Bernd T. Matthias in the 1950s with John Kenneth Hulm and Theodore H. Geballe, led to the discovery of hundreds of low temperature superconductors using a technique based on the Meissner effect. Due to his experience, he came up with Matthias' rules in 1954, a set of empirical guidelines on how to find these types of superconductors.
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+---
+title: "History of superconductivity"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/History_of_superconductivity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:33.041097+00:00"
+instance: "kb-cron"
+---
+
+=== BCS theory ===
+The complete microscopic theory of superconductivity was finally proposed in 1957 by John Bardeen, Leon N. Cooper, and Robert Schrieffer. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in Physics in 1972. The BCS theory was set on a firmer footing in 1958, when Nikolay Bogolyubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Lev Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature. Gor'kov was the first to derive the superconducting phase evolution equation 
+  
+    
+      
+        2
+        e
+        V
+        =
+        ℏ
+        
+          
+            
+              ∂
+              ϕ
+            
+            
+              ∂
+              t
+            
+          
+        
+      
+    
+    {\displaystyle 2eV=\hbar {\frac {\partial \phi }{\partial t}}}
+  
+.
+
+=== Little–Parks effect ===
+The Little–Parks effect was discovered in 1962 in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field. The electrical resistance of such cylinders shows a periodic oscillation with the magnetic flux through the cylinder, the period being h/2e = 2.07×10−15 V·s. The explanation provided by William Little and Ronald Parks is that the resistance oscillation reflects a more fundamental phenomenon, i.e. periodic oscillation of the superconducting critical temperature (Tc). This is the temperature at which the sample becomes superconducting. The Little-Parks effect is a result of collective quantum behavior of superconducting electrons. It reflects the general fact that it is the fluxoid rather than the flux which is quantized in superconductors. The Little-Parks effect demonstrates that the vector potential couples to an observable physical quantity, namely the superconducting critical temperature.
+
+== Commercial activity ==
+
+Soon after discovering superconductivity in 1911, Kamerlingh Onnes attempted to make an electromagnet with superconducting windings but found that relatively low magnetic fields destroyed superconductivity in the materials he investigated. Much later, in 1955, George Yntema succeeded in constructing a small 0.7-tesla iron-core electromagnet with superconducting niobium wire windings. Then, in 1961, J. E. Kunzler, E. Buehler, F. S. L. Hsu, and J. H. Wernick made the startling discovery that at 4.2 kelvins, a compound consisting of three parts niobium and one part tin was capable of supporting a current density of more than 100,000 amperes per square centimeter in a magnetic field of 8.8 teslas. Despite being brittle and difficult to fabricate, niobium-tin has since proved extremely useful in supermagnets generating magnetic fields as high as 20 teslas. In 1962, Ted Berlincourt and Richard Hake discovered that less brittle alloys of niobium and titanium are suitable for applications up to 10 teslas. Promptly thereafter, commercial production of niobium-titanium supermagnet wire commenced at Westinghouse Electric Corporation and at Wah Chang Corporation. Although niobium-titanium boasts less-impressive superconducting properties than those of niobium-tin, niobium-titanium has, nevertheless, become the most widely used “workhorse” supermagnet material, in large measure a consequence of its very high ductility and ease of fabrication. However, both niobium-tin and niobium-titanium find wide application in MRI medical imagers, bending and focusing magnets for enormous high-energy particle accelerators, and a host of other applications. Conectus, a European consortium for superconductivity, estimated that in 2014, global economic activity, for which superconductivity was indispensable, amounted to about five billion euros, with MRI systems accounting for about 80% of that total.
+In 1962, Brian Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum h/2e, and thus (coupled with the quantum Hall resistivity) for the Planck constant h. Josephson was awarded the Nobel Prize in Physics for this work in 1973.
+In 1973 Nb3Ge found to have Tc of 23 K, which remained the highest ambient-pressure Tc until the discovery of the cuprate high-temperature superconductors in 1986 (see below).
+
+== Unconventional superconductivity. ==
+
+=== First unconventional superconductors ===
+In 1979, two new classes of superconductors were discovered that could not be explained by BCS theory: heavy fermion superconductors and organic superconductors.
+The first heavy fermion superconductor, CeCu2Si2, was discovered by Frank Steglich. Since then over 30 heavy fermion superconductors were found (in materials based on Ce, U), with a critical temperature up to 2.3 K (in CeCoIn5).
+Klaus Bechgaard and Denis Jérome synthesized the first organic superconductor (TMTSF)2PF6 (the corresponding material class was named after him later) with a transition temperature of TC = 0.9 K, at an external pressure of 11 kbar.
+
+=== High-temperature superconductors ===
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+---
+title: "History of superconductivity"
+chunk: 3/3
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:33.041097+00:00"
+instance: "kb-cron"
+---
+
+In 1986, J. Georg Bednorz and K. Alex Mueller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987) and was the first of the high-temperature superconductors. It was shortly found (by Ching-Wu Chu) that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K, which was important because liquid nitrogen could then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77 K).  This is important commercially because liquid nitrogen can be produced cheaply on-site with no raw materials, and is not prone to some of the problems (solid air plugs, etc.) of helium in piping. Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of theoretical condensed-matter physics.
+In March 2001, superconductivity of magnesium diboride (MgB2) was found with Tc = 39 K.
+In 2008, the oxypnictide or iron-based superconductors were discovered, which led to a flurry of work in the hope that studying them would provide a theory of the cuprate superconductors.
+In 2013, room-temperature superconductivity was attained in YBCO for picoseconds, using short pulses of infrared laser light to deform the material's crystal structure.
+In 2017 it was suggested that undiscovered superhard materials (e.g. critically doped beta-titanium Au) might be a candidate for a new superconductor with Tc, substantially higher than HgBaCuO (138 K), possibly up to 233 K, which would be higher even than H2S. A lot of research suggests that additionally nickel could replace copper in some perovskites, offering another route to room temperature. Li+ doped materials can also be used, i.e. the spinel battery material LiTi2Ox and the lattice pressure can increase Tc to over 13.8 K. Also LiHx has been theorized to metallise at a substantially lower pressure than H and could be a candidate for a Type 1 superconductor.
+
+== Historical publications ==
+Papers by H.K. Onnes
+
+"The resistance of pure mercury at helium temperatures". Comm. Leiden. April 28, 1911.
+"The disappearance of the resistivity of mercury". Comm. Leiden. May 27, 1911.
+"On the sudden change in the rate at which the resistance of mercury disappears". Comm. Leiden. November 25, 1911.
+"The imitation of an ampere molecular current or a permanent magnet by means of a supraconductor". Comm. Leiden. 1914.
+BCS theory
+
+Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. (1957-12-01). "Theory of Superconductivity". Physical Review. 108 (5). American Physical Society (APS): 1175–1204. Bibcode:1957PhRv..108.1175B. doi:10.1103/physrev.108.1175. ISSN 0031-899X. S2CID 73661301.
+Other key papers
+
+Meissner, W.; Ochsenfeld, R. (1933). "Ein neuer Effekt bei Eintritt der Supraleitfähigkeit". Die Naturwissenschaften (in German). 21 (44). Springer Science and Business Media LLC: 787–788. Bibcode:1933NW.....21..787M. doi:10.1007/bf01504252. ISSN 0028-1042. S2CID 37842752.
+F. London and H. London, "The electromagnetic equations of the supraconductor," Proc. Roy. Soc. (London) A149, 71 (1935), ISSN 0080-4630.
+V.L. Ginzburg and L.D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950)
+Maxwell, Emanuel (1950-05-15). "Isotope Effect in the Superconductivity of Mercury". Physical Review. 78 (4). American Physical Society (APS): 477. Bibcode:1950PhRv...78..477M. doi:10.1103/physrev.78.477. ISSN 0031-899X.
+Reynolds, C. A.; Serin, B.; Wright, W. H.; Nesbitt, L. B. (1950-05-15). "Superconductivity of Isotopes of Mercury". Physical Review. 78 (4). American Physical Society (APS): 487. Bibcode:1950PhRv...78..487R. doi:10.1103/physrev.78.487. ISSN 0031-899X.
+A.A. Abrikosov, "On the magnetic properties of superconductors of the second group," Soviet Physics JETP 5, 1174 (1957)
+Little, W. A.; Parks, R. D. (1962-07-01). "Observation of Quantum Periodicity in the Transition Temperature of a Superconducting Cylinder". Physical Review Letters. 9 (1). American Physical Society (APS): 9–12. Bibcode:1962PhRvL...9....9L. doi:10.1103/physrevlett.9.9. ISSN 0031-9007.
+Josephson, B.D. (1962). "Possible new effects in superconductive tunnelling". Physics Letters. 1 (7). Elsevier BV: 251–253. Bibcode:1962PhL.....1..251J. doi:10.1016/0031-9163(62)91369-0. ISSN 0031-9163.
+Patents
+
+Tesla, Nikola, U.S. patent 685,012 "Means for Increasing the Intensity of Electrical Oscillations", March 21, 1900.
+
+== See also ==
+Superconductivity
+Macroscopic quantum phenomena
+Timeline of low-temperature technology
+Technological applications of superconductivity
+High-temperature superconductivity
+
+== External links and references ==
+
+Heike Kamerlingh Onnes, "Investigations into the properties of substances at low temperatures, which have led, amongst other things, to the preparation of liquid helium," Nobel Lecture, December 11, 1913
+M. Tinkham, Introduction to Superconductivity, 2nd Ed., McGraw-Hill, NY, 1996, ISBN 0-486-43503-2
+T. Shachtman, Absolute Zero and the Conquest of Cold, Houghton Mifflin Co., 1999, ISBN 0-395-93888-0
+J. Matricon, G. Waysand and C. Glashausser, The Cold Wars: A History of Superconductivity, Rutgers University Press, 2003, ISBN 0-8135-3295-7
+J. Schmalian, Failed theories of superconductivity
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+
+In special relativity, the history of the twin paradox chronicles the development of the famous thought experiment known as the twin paradox, which started in 1905 when Albert Einstein showed that a clock returning from a round-trip is retarded with respect to a clock that remained at its place. By 1911, Einstein, Paul Langevin and Emil Wiechert had extended this result to life forms and human beings, with Hermann Weyl introducing twin brothers in 1918, see section § Round-trip experiment (1905).
+In 1911, Langevin, Wiechert and Max von Laue showed that asymmetric aging of clocks or life forms along closed paths directly corresponds to the fact, that the proper time is maximal along the straight worldlines of non-accelerated clocks (see § Maximal proper time (1911)). Laue pointed out that the relativity of time and asymmetric aging appears "paradoxical" to those who are still unfamiliar with relativity, while some even claimed that asymmetric aging contradicts the relativity principle, which was refuted by Laue himself and others such as Einstein (1918) who pointed out the meaning of the relativity principle and demonstrated the asymmetries between the twins (see §§ Relativity principle and asymmetry (1911/12)​ and Perspective of the traveler).
+
+== Round-trip experiment (1905) ==
+In 1905, Einstein derived the effect of time dilation which he applied to round-trips as follows:
+
+From this there ensues the following peculiar consequence. [...] If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting 
+  
+    
+      
+        t
+      
+    
+    {\displaystyle t}
+  
+ seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be 
+  
+    
+      
+        
+          
+            
+              1
+              2
+            
+          
+        
+        t
+        
+          v
+          
+            2
+          
+        
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle {\tfrac {1}{2}}tv^{2}/c^{2}}
+  
+ second slow. [Translation by Perret and Jefferies]
+In a lecture from January 1911 (published November), Einstein extended this result to life forms:
+
+If we placed a living organism in a box [...] one could arrange that the organism, after any arbitrary lengthy flight, could be returned to its original spot in a scarcely altered condition, while corresponding organisms which had remained in their original positions had already long since given way to new generations. For the moving organism, the lengthy time of the journey was a mere instant, provided the motion took place with approximately the speed of light. [Translation by Miller]
+Two participants of this lecture, Rudolf Lämmel in April 1911 and Fritz Müller in October 1911, reported in newspaper articles that Einstein also talked about human observers making a journey near light speed who practically didn't age during the journey, yet as they return they meet later generations (Lämmel) or old men with gray beards (Müller). This experiment became particularly known through a lecture by Langevin in April 1911 (published July), who independently stated that a portion of matter conducting a closed cycle will have aged less between its departure and its return than if it had not been accelerating, thus radium will have decayed less during the round-trip than a stationary sample, and a human traveler flying in a rocket and returning after 200 years Earth time will experience only 2 years during the flight. Independently, Wiechert in lectures between March and May 1911 (published July/September) discussed several round-trip clock experiments, including an experiment in which a human observer traveled for 300 Earth years on a circular path away and back to Earth, while he himself only experienced 75 years. Similarities between such experiments and fictional stories such as Rip Van Winkle, Urashima Tarō or When The Sleeper Wakes were noticed by several authors.
+The round-trip experiment was explicitly formulated in terms of twins, i.e. two life forms of equal age, by the following authors: Wiechert (1911) spoke about "two life forms that begin their life at the same time", Paul Gruner (1912) about "two persons of same age", Laue (1913) about "former agemates", Weyl (1918) about "twin brothers", Werner Bloch (1918) about "two humans of exactly same age", and Einstein (1920) about "twins". For instance, the description of Weyl reads:
+
+Suppose we have two twin-brothers who take leave from one another at a world-point A, and suppose one remains at home (that is, permanently at rest in an allowable reference-space), whilst the other sets out on voyages, during which he moves with velocities (relative to “home”) that approximate to that of light. When the wanderer returns home in later years he will appear appreciably younger than the one who stayed at home. [Translation by Henry Brose]
+
+== Maximal proper time (1911) ==
+After Einstein (1905) derived asymmetric clock aging along a closed polygonal path directly from the time dilation formula, more general treatments based on the proper time integral introduced by Hermann Minkowski (1907) followed. Langevin (1911–1919) showed that the integration of proper time leads to the result, that the time experienced by an accelerated observer traversing a closed path is shorter than for an observer in uniform motion. Also Wiechert (1911) noticed that the time difference in round-trip experiments can "easily" be derived by applying the proper time integral. Laue (December 1911) showed that asymmetric clock aging directly corresponds to the geometrical property of spacetime that among all time-like intervals connecting two events, the straight worldline has the maximal proper time as indicated by the clock that remained at rest in a single inertial frame, so differential aging is only about the different ways by which two points in spacetime are connected. Consequently, Laue (1912/13) employed the inequality
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-1.md b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-1.md
new file mode 100644
index 000000000..30abf8959
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-1.md
@@ -0,0 +1,345 @@
+---
+title: "History of the twin paradox"
+chunk: 2/8
+source: "https://en.wikipedia.org/wiki/History_of_the_twin_paradox"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:25.226599+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          
+            
+              1
+              c
+            
+          
+        
+        
+          ∫
+          
+            1
+          
+          
+            2
+          
+        
+        
+          
+            d
+            
+              u
+              
+                2
+              
+            
+            −
+            
+              (
+              
+                d
+                
+                  x
+                  
+                    2
+                  
+                
+                +
+                d
+                
+                  y
+                  
+                    2
+                  
+                
+                +
+                d
+                
+                  z
+                  
+                    2
+                  
+                
+              
+              )
+            
+          
+        
+        <
+        
+          
+            
+              1
+              c
+            
+          
+        
+        
+          ∫
+          
+            1
+          
+          
+            2
+          
+        
+        d
+        u
+      
+    
+    {\displaystyle {\tfrac {1}{c}}\int _{1}^{2}{\sqrt {du^{2}-\left(dx^{2}+dy^{2}+dz^{2}\right)}}<{\tfrac {1}{c}}\int _{1}^{2}du}
+  
+,
+in which the right-hand side represents the "maximal proper time" along a straight worldline, while the left-hand side represents smaller proper times of clocks along a broken worldline between the same events. This explanation was adopted by others such as Arnold Sommerfeld (1913), Weyl (1918), August Kopff (1921), Jean Becquerel (1922), with Wolfgang Pauli (1921) calling this the "four-dimensional formulation of the clock paradox".
+
+In the simplest case where the traveler only once changes his direction in a very small time, Laue's inequality reduces to the inverse triangle inequality in Minkowski space formulated by Alfred Robb (1914), stating that the length of a particular side is longer than the combined lengths of the other sides, if all sides represent time-like intervals. In 1920, Robb gave a numerical example in which the time-like intervals AB=10, AC=3, CB=3 form the sides of triangle with the inequality 
+  
+    
+      
+        A
+        C
+        +
+        C
+        B
+        <
+        A
+        B
+      
+    
+    {\displaystyle AC+CB<AB}
+  
+ (Fig. 1). Arthur Eddington (1922) described those relations as "time-triangles" formed by moving clocks.
+Several authors employed Minkowski diagrams to graphically demonstrate the round-trip experiment: Alexander von Brill (1920) demonstrated that the broken worldline 
+  
+    
+      
+        
+          
+            
+              O
+              A
+            
+            ¯
+          
+        
+      
+    
+    {\displaystyle {\overline {OA}}}
+  
+ + 
+  
+    
+      
+        
+          
+            
+              A
+              B
+            
+            ¯
+          
+        
+      
+    
+    {\displaystyle {\overline {AB}}}
+  
+ of the traveling clock has a smaller proper time than the straight one 
+  
+    
+      
+        
+          
+            
+              O
+              B
+            
+            ¯
+          
+        
+      
+    
+    {\displaystyle {\overline {OB}}}
+  
+ of the stationary clock; even though the worldlines drawn on paper apparently indicate the inequality 
+  
+    
+      
+        
+          
+            
+              O
+              A
+              B
+            
+            ¯
+          
+        
+        >
+        
+          
+            
+              O
+              B
+            
+            ¯
+          
+        
+      
+    
+    {\displaystyle {\overline {OAB}}>{\overline {OB}}}
+  
+, the computation of proper time actually gives 
+  
+    
+      
+        
+          
+            
+              O
+              B
+            
+            ¯
+          
+        
+        >
+        
+          
+            
+              O
+              A
+              B
+            
+            ¯
+          
+        
+      
+    
+    {\displaystyle {\overline {OB}}>{\overline {OAB}}}
+  
+ because the units on the traveler's axis are warped by 
+  
+    
+      
+        K
+        =
+        
+          
+            
+              
+                
+                  1
+                  −
+                  
+                    v
+                    
+                      2
+                    
+                  
+                
+                
+                  1
+                  +
+                  
+                    v
+                    
+                      2
+                    
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle K={\sqrt {\tfrac {1-v^{2}}{1+v^{2}}}}}
+  
+. Pauli (1921) described the round-trip experiment in terms of two diagrams: In the first, two points P and Q are connected by a straight worldline 
+  
+    
+      
+        
+          L
+          
+            1
+          
+        
+      
+    
+    {\displaystyle L_{1}}
+  
+ and a broken worldline 
+  
+    
+      
+        
+          L
+          
+            2
+          
+        
+      
+    
+    {\displaystyle L_{2}}
+  
+; in the second, two points A and B are connected by a straight worldline 
+  
+    
+      
+        L
+      
+    
+    {\displaystyle L}
+  
+ and by a continuously curved one. The diagram of Max Born (1921) showed that at the outbound journey, traveler B experiences proper time interval OU on the inclined 
+  
+    
+      
+        
+          t
+          ′
+        
+      
+    
+    {\displaystyle t'}
+  
+-axis while stationary observer A experiences proper time interval OQ on the vertical t-axis, with points U and Q located on the same hyperbola; at the inbound journey, however, observer B returns when his proper time is exactly the double of OU, whereas observer A returns when his proper time is more than the double of OQ.
+
+== Negligibility of proper acceleration (1913) ==
+
+It was pointed out that the acceleration experienced by the traveler (i.e. the proper acceleration) is neglectable when computing the round-trip experiment from the viewpoint of the inertial frame of the stay-at-home twin: Sommerfeld (1913) showed that the application of the proper time integral to the round-trip experiment rests on the "unprovable assumption" (which he attributed to Einstein) that the time indicated by the traveling clocks only depends on its momentary velocity (clock hypothesis). Laue (1912/13), Weyl (1918), Pauli (1921) avoided all practical problems related to the application of that integral to the travelling clock by demanding that the strength of acceleration must be sufficiently small. Einstein (1911, 1914, 1918), Laue (1913), Hans Thirring (1921), Born (1921) showed that even if there were an unknown influence of proper acceleration on the traveling clock's readings, this wouldn't necessarily change the conclusion that the traveling clock is retarded with respect to the stay-at-home clock when they reunite, because any such influence must be finite and therefore can be made arbitrarily small and negligible with respect to the effect of time dilation by arbitrarily elongating the duration of constant velocity motion. The same fact was demonstrated in an alternative way by Hendrik Lorentz (1913) who pointed out that any effect of acceleration of clock B at turnaround can be separated from the time dilation effect since only the latter depends on the distance traversed along the round-trip, and also Pauli (1921) argued that any influence of acceleration at turnaround must be independent of the total travel time along the round-trip and is therefore easy to eliminate.
+Wiechert (1911) showed that even when both clocks undergo the same velocity changes or accelerations in the round-trip experiment, asymmetric clock aging can arise when the clocks reunite: Clock A travels with 
+  
+    
+      
+        +
+        u
+      
+    
+    {\displaystyle +u}
+  
+ for a short time, then comes to rest at which it remains for a long time, and then returns with 
+  
+    
+      
+        −
+        u
+      
+    
+    {\displaystyle -u}
+  
+, while clock B traveled with 
+  
+    
+      
+        ±
+        u
+      
+    
+    {\displaystyle \pm u}
+  
+ for a long time (see Fig. 2), in which case B will be retarded with respect to A at reunion. Likewise, Wiechert 1921 (published 1922) described the round-trip of clock B along polygonal path away from stationary clock A and back again; then the experiment is repeated with exact same velocity changes as before, yet the size of the polygon should be arbitrarily increased; this implies that any influence on clocks during the velocity changes will affect the endresults of the two experiments in different proportion, which allows us to determine and eliminate that influence.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-2.md b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-2.md
new file mode 100644
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-2.md
@@ -0,0 +1,49 @@
+---
+title: "History of the twin paradox"
+chunk: 3/8
+source: "https://en.wikipedia.org/wiki/History_of_the_twin_paradox"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:25.226599+00:00"
+instance: "kb-cron"
+---
+
+While discussing a one-way time dilation experiment in which the first clock had to be accelerated at the start in order to reach the second clock, Fritz Grünbaum (1911) showed that problems related to unknown influences of acceleration can be avoided by replacing the accelerated clock with a third, non-accelerated clock that is synchronized with the accelerated clock when they are momentarily co-located. Wiechert in 1920 (published 1921) applied the same idea to round-trip experiments by replacing the clocks or twins with three non-accelerated bodies A, B, C, on which the time is measured either by counting light oscillations or by determining the aging of life forms; A is passed by B that moves away in some direction, later B is passed by C that moves with same speed in the opposite direction, and finally C passes A; it turns out that the combined time measured on bodies B+C during those periods is smaller than the time measured on A alone. In 1921 (published 1922) Wiechert extended what he described as "relay" experiment (German: Stafette) to arbitrary many non-accelerated bodies 
+  
+    
+      
+        A
+        ,
+        
+          B
+          
+            1
+          
+        
+        ,
+        
+          B
+          
+            2
+          
+        
+        ,
+        …
+      
+    
+    {\displaystyle A,B_{1},B_{2},\dots }
+  
+, in which the first B passes A at the beginning of the experiment and the last B passes A at the end of the experiment; it turns out that the combined time measured on all B bodies is smaller than the time measured on A alone (see Fig. 3 for the special case of three B clocks). Variants of this thought experiment became known as the three-brother experiments in which the traveling clocks synchronize their times when they pass each other, as discussed by Luise Lange (1927) or Lord Halsbury (1957).
+
+== Relativity principle and asymmetry (1911/12) ==
+
+=== Paradox? ===
+While Einstein (1905) described the round-trip experiment as "peculiar" (German: eigentümlich), Laue (1911/12) was the first to denote the round-trip experiment as "paradox":
+
+Of all apparently paradox consequences that stem from the time-transformation of the theory of relativity, there is probably none against which the common sense of anyone who is still unfamiliar with the matter is more reluctant, than the one according to which the time indication of a clock shall be dependent on its state of motion. Already in his fundamental paper, Einstein has driven this paradox to the extreme by a thought experiment, recently explained in a very nice way by Langevin in a lecture that is also very readable in other respects. [...] The opposition against this, which at first will probably be raised in the mind of everyone, has recently caused two authors [Laue cites Otto Berg and Wiechert] to object at this place. [Translation on Wikisource]
+Subsequently, Gruner (1912) and others including Einstein (1918) explicitly used the expression "clock paradox" (French: Paradoxe des horloges, German: Uhrenparadoxon), whereas Rudolf Seeliger (1913) spoke of the "familiar Einstein-Langevinian paradox" (German: "bekannte Einstein-Langevinsche Paradoxon"). Regarding the "twin paradox", Einstein (1920) is quoted as follows:
+
+In the case of these two twins, Einstein declared, we have merely a paradox of feeling. It would be a paradox of thought only if no sufficient ground could be suggested for the behavior of these two creatures. [Translation by Brose]
+In his relativity textbook, Born (1921) wrote
+
+If we take up arms against this result and call it paradoxical, we simply mean that it is unusual, or "peculiar," and time will help us to conquer this strange feeling. But there are also opponents to the theory of relativity who seek to make of these conclusions an objection against the logical consistency of the theory [Translation by Brose].
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-3.md b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-3.md
new file mode 100644
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-3.md
@@ -0,0 +1,22 @@
+---
+title: "History of the twin paradox"
+chunk: 4/8
+source: "https://en.wikipedia.org/wiki/History_of_the_twin_paradox"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:25.226599+00:00"
+instance: "kb-cron"
+---
+
+=== Objections and their refutations ===
+The papers of Laue ("Two Objections Against the Theory of Relativity and their Refutation", 1911) and Einstein ("Dialog about Objections against the Theory of Relativity", 1918) as well as the textbooks and papers of Bloch, Thirring, Born, etc. discuss and refute objections against the twin paradox such as:
+a) Otto Berg (1910) claimed that the relativity principle demands complete symmetry of motions and travel times throughout the round-trip in both clock rest frames, thus the clocks must indicate the same time at reunion; he warned that "illustrative ideas such as the retardation of clocks can easily lead to mistakes at this place". Even staunch supporters of special relativity such as Norman Robert Campbell (1911/12) or Joseph Petzoldt (1914) required full symmetry, claiming that any time difference during the outbound journey that emerges from the Lorentz transformation due to increasing velocity and distance, vanishes during the inbound journey as differences in velocity and distance are decreasing; this was popularized by the (then famous) philosopher Henri Bergson (1922) who claimed that relativity requires symmetric experience of "lived time" and therefore equal age for both twins during and after the round-trip, because temporal differences between frames are "fictions" which are just as real as the smaller height of a receding person who will regain his original height as he returns (see Einstein-Bergson debate). Similar arguments were also given during the Dingle controversy in 1955 and later.
+This was refuted by the historical authors in section § Maximal proper time (1911) who showed that relativity doesn't predict equal aging in the standard round-trip scenario, and in sections §§ Acceleration asymmetry​ and Frame distribution asymmetry they showed that asymmetric aging does not contradict the relativity principle.
+b) Wiechert (1911) demonstrated that asymmetric clock aging in the round-trip experiment definitely follows from the relativistic formulas; yet since this effect only depends on the periods of constant velocity motion while accelerations at turnaround can be neglected in the computation, he concluded that this proves the inequivalence or anisotropy of non-accelerated motions with respect to a Lorentzian aether in contradiction to Einstein's "unconditional" relativity principle that allegedly requires equivalence and symmetry of motions and frames along the round-trip. A similar mistake was made by the notorious anti-relativist Ernst Gehrcke (1912/13) who claimed that the slowing down of the rates of moving clocks requires recourse to "absolute translation" in contradiction to the relativity of uniform motion. Also Bergson (1922) claimed that when physicists derive asymmetric aging in the round-trip experiment, they inadvertently think in terms of Lorentz's "semi relativity" based on absolute space while forgetting that Einstein's "complete relativity" requires symmetry of motions and experienced time of both twins during uniform outbound and inbound journey.
+This was refuted by Laue in sections §§ Maximal proper time (1911)​ and Frame distribution asymmetry, who showed why asymmetric aging does not require any inequivalent/anisotropic non-accelerated motions with respect to an absolute space or aether by pointing out its geometric nature.
+c) Gruner (1912) claimed that the relativity principle requires complete symmetry of time dilation between the twins and therefore mutual attribution of younger age at reunion; this represents an "irreducible and inconceivable contradiction", because person A can say that B returns in a less developed state than A, while person B can say with same right that A returns in a less developed state than B. Similar mistakes were made by Gehrcke (1912), or by Paul Painlevé (1922) during a discussion with Einstein and Langevin.
+This was refuted by the historical authors in section § Perspective of the traveler, who showed where and why the symmetry of time dilation is broken during the round-trip.
+
+=== Acceleration asymmetry ===
+
+While it was known (see section § Negligibility of proper acceleration (1913)) that any influence of proper acceleration can be neglected in the context of computing the age difference in the inertial frame of the stay-at-home twin, the same authors noticed that acceleration is still useful as an absolute asymmetry indicator in the context of explaining why the symmetry between the twins is broken in the first place. Langevin (1911) described the twin paradox as "another example of the absolute character of acceleration" in which the "asymmetry occurred because only the traveler, in the middle of his journey, has undergone an acceleration that changes the direction of his velocity". Sommerfeld (1913) formulated the clock hypothesis according to which only momentary velocities count when the proper time is computed in the round-trip experiment; yet the time difference between the clocks at reunion doesn't indicate "motion" but rather "accelerated motion" since one of them had to be accelerated in order to come back, thus there is no contradiction to the relativity principle. Einstein (1914) explained that while accelerations are irrelevant for the computation of the time difference, their "presence nevertheless causes the slowing down of clock B and not that of clock A" because "accelerated motions are absolute in the theory of relativity". Lorentz (1913), Einstein (1918), Pauli (1921), Kopff (1921), Born (1921) all stated that the acceleration of the traveling clock can be neglected or eliminated in the computation of its retardation with respect to the stay-at-home clock; yet the fact that only the frame of A is inertial while the frame of B was temporarily accelerated shows that there is no contradiction to the special relativity principle, since it doesn't require symmetry between inertial and accelerated frames (see §§ Inertial frame analysis​ and Accelerated frame analysis for quantitative analyses). The different roles of acceleration were also discussed by Hans Thirring (1921) who showed that on one hand the acceleration of clock B can indeed be neglected in the computation of its retardation with respect to A; yet if A were the accelerated one, it would be A that is retarded with respect to B at reunion, thus acceleration is "responsible" for the time difference after all. Finally, Einstein summarized the reason why there is no contradiction as follows in an interview from 1920 as follows:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-4.md b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-4.md
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--- /dev/null
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@@ -0,0 +1,107 @@
+---
+title: "History of the twin paradox"
+chunk: 5/8
+source: "https://en.wikipedia.org/wiki/History_of_the_twin_paradox"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:25.226599+00:00"
+instance: "kb-cron"
+---
+
+In the case of these two twins, Einstein declared, we have merely a paradox of feeling. It would be a paradox of thought only if no sufficient ground could be suggested for the behavior of these two creatures. This ground, which accounts for the comparative youth of A, is given, from the point of view of the special theory of relativity, by the fact that the creature in question, and only this creature, has been subject to accelerations. [Translation by Brose]
+
+=== Frame distribution asymmetry ===
+Laue (1911–13) described the asymmetry in Fig. 4 purely in terms of spacetime geometry and the different distribution of inertial rest frames without emphasizing the role of acceleration: Only one clock rests in a single inertial frame throughout as it follows a straight worldline, while the other one rested in at least two inertial frames as it follows a broken worldline. Bloch (1918) represented the frames with three movable slots K, K' and K”, provided with hooks on which one can hang clocks at the origins of K and K'; while one clock always hangs on a hook of slot K, the other clock moved away with K' and after some time was transferred (neglecting any effect of acceleration) by a mechanical device to slot K” that moves in the other direction, by which it comes back; there is no contradiction to the relativity principle, as one clock rested in one inertial frame while the other one rested in two such frames. André Metz (1923) represented the three frames by using Earth and two mechanical sidewalks transporting people in opposite directions; Pierre remains on Earth, while Paul and Jean together travel away on the first sidewalk with uniform speed; while Jean continues his journey, Paul jumps (neglecting any effect of acceleration) to the other sidewalk and returns to Pierre where they discover that Paul's clock is retarded; thus while Jean remained symmetric with Pierre the entire time, Paul who changed sidewalks is neither symmetric with Jean nor with Pierre.
+Laue (1911/12) went on to show that this result does not imply anisotropy of non-accelerated motions as claimed by Wiechert (objection b) by restating the asymmetry in terms of spacetime geometry:
+
+The principle of relativity claims the equivalence of all time-like directions in [Minkowski space]. Einstein's experiment, however, is represented by a curved worldline, which in a worldpoint A decomposes into a row of curves, and all of them will be re-united at a worldpoint B to a single line. Of all curves connecting the points A and B having time-like direction throughout, the straight connection has the longest proper time; that is the meaning of Einstein's consideration. That of all time-like directions, one is preferred in this way, is to be admitted; however, this preference is not based on the natural laws employed, but only on the choice of world-points A and B, i.e. on the special assumptions of our example. [..] One of the most important physical findings is the physical equivalence of all directions in (three-dimensional) space; and one of the most elementary geometric laws says, that two points determine a straight line, and thus a direction as well. It would be in accordance with the previous objection [of Wiechert] against the relativity theory, when one would try to refute that law of the isotropy of space by the aid of that geometric theorem. [Translation on Wikisource]
+
+== Perspective of the traveler ==
+
+=== Inertial frame analysis ===
+
+Assuming that the turnaround happened in negligible time, the asymmetry in the perspective of the traveler has been described in terms of the two inertial frames in which he was at rest during the outbound and inbound journey: Langevin (1911) applied the relativistic Doppler effect to one-way signals and found, that the wavelength of signals sent from the rocket or Earth is seen by the latter to be elongated for 200 years before turnaround but contracted only for 2 days after turnaround; on the other hand, the traveler sees the wavelength of Earth's signals elongated for one year and immediately after turnaround he sees it contracted for another year; thus 200 years were spent on Earth but only 2 years in the rocket. Directly addressing and refuting objection c, Lorentz (1913) described both perspectives as follows: In the frame of the resting observer the ordinary time dilation formula predicts that the traveler's clock is retarded by the factor 
+  
+    
+      
+        
+          
+            1
+            −
+            
+              v
+              
+                2
+              
+            
+            
+              /
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\sqrt {1-v^{2}/c^{2}}}}
+  
+ throughout the journey; then he showed the perspective of the traveler in terms of two-way signals (radar) using three periods: In the first and the last, the stay-at-home clock is dilated by the factor 
+  
+    
+      
+        
+          
+            1
+            −
+            
+              v
+              
+                2
+              
+            
+            
+              /
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\sqrt {1-v^{2}/c^{2}}}}
+  
+, yet in the middle period the stay-at-home clock apparently ticks faster by the factor 
+  
+    
+      
+        
+          
+            
+              
+                
+                  c
+                  +
+                  v
+                
+                
+                  c
+                  −
+                  v
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\sqrt {\tfrac {c+v}{c-v}}}}
+  
+ which overcompensates the other periods and explains, why the traveler's clock is retarded at reunion even from his own perspective.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-5.md b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-5.md
new file mode 100644
index 000000000..47c89388c
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-5.md
@@ -0,0 +1,199 @@
+---
+title: "History of the twin paradox"
+chunk: 6/8
+source: "https://en.wikipedia.org/wiki/History_of_the_twin_paradox"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:25.226599+00:00"
+instance: "kb-cron"
+---
+
+Also addressing and refuting objection c, Thirring (1921) applied the Lorentz transformation and showed that relativity of simultaneity leads to desynchronization of all the traveler's clocks during turnaround from 
+  
+    
+      
+        
+          t
+          ′
+        
+        =
+        γ
+        
+          (
+          
+            t
+            −
+            v
+            x
+            
+              /
+            
+            
+              c
+              
+                2
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle t'=\gamma \left(t-vx/c^{2}\right)}
+  
+ to 
+  
+    
+      
+        
+          t
+          ′
+        
+        −
+        
+          t
+          
+            0
+          
+          ′
+        
+        =
+        γ
+        
+          (
+          
+            t
+            +
+            v
+            x
+            
+              /
+            
+            
+              c
+              
+                2
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle t'-t'_{0}=\gamma \left(t+vx/c^{2}\right)}
+  
+, in which 
+  
+    
+      
+        
+          t
+          
+            0
+          
+          ′
+        
+      
+    
+    {\displaystyle t'_{0}}
+  
+ is a constant that depends on the clock after which the other clocks should be resynchronised after turnaround; this leads to an apparent forward jump (Fig. 6) of the stay-at-home clock which overcompensates its time dilation during constant velocity motion, all of which was visualized by Thirring using diagrams. Similarly, Langevin (1922) gave a thorough algebraic treatment in terms of a train conductor clock moving along a railway; setting 
+  
+    
+      
+        x
+        =
+        v
+        t
+      
+    
+    {\displaystyle x=vt}
+  
+ as turnaround point and assuming that all clocks in the train are resynchronized after the train conductor clock, he determined Thirring's constant as 
+  
+    
+      
+        −
+        γ
+        2
+        t
+        
+          v
+          
+            2
+          
+        
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle -\gamma 2tv^{2}/c^{2}}
+  
+; the train conductor consequently notices that all clocks along the railway he passes by during the round-trip are advanced with respect to his own clock. Both of them showed the analogy to explanations employing the equivalence principle (see § Accelerated frame analysis): Thirring pointed out that his method gives an elementary explanation of the gravitational redshift at locations of lower potential since clocks at those locations fell behind due to desynchronization, and Langevin pointed out that even if the traveler would have slept during turnaround, the desynchronization of clocks would have informed him about the presence of a gravitational field.
+The explanation of Thirring and Langevin was used by other authors as well: Jean Becquerel (1923) described a rocket passing a row of desynchronized and advanced Earth clocks; at turnaround the rocket clock indicates 2 hours while a co-located Earth clock indicates 4 hours, and at reunion the rocket clock indicates 4 hours while the Earth clock indicates 8 hours. Metz (1923) used moving sidewalks of 100 million kilometers length that move along desynchronized and advanced Earth clocks; at turnaround the traveler's clock is 1 minute behind a co-located Earth clock, and at reunion the traveler's clock is 2 minutes behind the Earth clock. Alfred North Whitehead (1923) showed that while Earth conducts 200 times 365 revolutions from departure until return of the traveler, the traveler counted only 7.3 Earth revolutions during the outbound and inbound journey, whereas the remaining 72992.7 revolutions occurred during his frame/simultaneity jump.
+A simplified description that doesn't require the full Lorentz transformation was given by William McCrea (1951) using Lorentz contraction: The stay-at-home observer remains at rest and plots the length 
+  
+    
+      
+        X
+        =
+        v
+        T
+      
+    
+    {\displaystyle X=vT}
+  
+ during the outward as well as inward motion of the traveler, resulting in the total travel time 
+  
+    
+      
+        2
+        T
+      
+    
+    {\displaystyle 2T}
+  
+. As long as the traveler is at rest with respect to the stay-at-home observer, he will plot the same distance 
+  
+    
+      
+        X
+      
+    
+    {\displaystyle X}
+  
+, yet when he starts to move he will instantly plot the contracted distance 
+  
+    
+      
+        X
+        
+          /
+        
+        γ
+      
+    
+    {\displaystyle X/\gamma }
+  
+ in both the outward- and inward journey, thus the traveler will have experienced the shorter travel time 
+  
+    
+      
+        2
+        T
+        
+          /
+        
+        γ
+      
+    
+    {\displaystyle 2T/\gamma }
+  
+ when he returns.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-6.md b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-6.md
new file mode 100644
index 000000000..caf31c939
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-6.md
@@ -0,0 +1,181 @@
+---
+title: "History of the twin paradox"
+chunk: 7/8
+source: "https://en.wikipedia.org/wiki/History_of_the_twin_paradox"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:25.226599+00:00"
+instance: "kb-cron"
+---
+
+=== Accelerated frame analysis ===
+After completion of general relativity, the perspective of the traveler has also been described in terms the accelerated frame in which he rests even during turnaround: Einstein (1918) wrote a dialogue, in which the "critic" claimed that general relativity requires complete symmetry of motions and frames during the round-trip so that objection c "rises from the ashes" again, which was refuted by the "relativist" using the equivalence principle, according to which uniformly accelerated frames are equivalent to homogeneous gravitational fields. Einstein's solution published in a popular science journal didn't include formulas, but they can be found in one of his letters from the same year where he based his analysis on the approximate formulas that he derived as early as 1907/8 in his first paper on the equivalence principle. The solution was immediately adopted in the textbooks of Bloch (1920), Pauli (1921), Kopff (1921), Born (1921), Karl Bollert (1922a): In the frame of the traveling clock U2, a homogeneous gravitational field appears at turnaround, which is accompanied by gravitational time dilation 
+  
+    
+      
+        σ
+        =
+        τ
+        
+          (
+          
+            1
+            +
+            g
+            l
+            
+              /
+            
+            
+              c
+              
+                2
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle \sigma =\tau \left(1+gl/c^{2}\right)}
+  
+ with 
+  
+    
+      
+        l
+        =
+        v
+        t
+      
+    
+    {\displaystyle l=vt}
+  
+ as distance between the clocks and 
+  
+    
+      
+        g
+      
+    
+    {\displaystyle g}
+  
+ as acceleration and 
+  
+    
+      
+        g
+        l
+        =
+        Φ
+      
+    
+    {\displaystyle gl=\Phi }
+  
+ as gravitational potential. Since the "free-falling" stay-at-home clock U1 is at a location of higher potential than "stationary" clock U2 during turnaround, U1 advances by 
+  
+    
+      
+        2
+        l
+        v
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle 2lv/c^{2}}
+  
+ with respect to U2 (Fig. 6), which overcompensates U1's approximated retardation 
+  
+    
+      
+        l
+        v
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle lv/c^{2}}
+  
+ during its constant velocity motion. Subsequently, Bollert (1922b) described the solution in terms of the more general formula 
+  
+    
+      
+        
+          
+            d
+            τ
+            =
+            d
+            t
+            
+              
+                
+                  
+                    (
+                    
+                      1
+                      +
+                      g
+                      l
+                      
+                        /
+                      
+                      
+                        c
+                        
+                          2
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                −
+                
+                  
+                    (
+                    
+                      d
+                      x
+                      
+                        /
+                      
+                      d
+                      t
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\scriptstyle d\tau =dt{\sqrt {\left(1+gl/c^{2}\right)^{2}-\left(dx/dt\right)^{2}}}}}
+  
+ that also incorporates the velocity of U1 during free fall. An exact treatment was given by Christian Møller (1943) who discussed a case involving constant proper acceleration (hyperbolic motion), describing the accompanied accelerated frame and its homogeneous gravitational field in terms of Kottler–Møller coordinates.
+In order to explain the occurrence of gravitational fields in the traveler's frame at turnaround, Einstein (1918) invoked Mach's principle according to which those fields are generated by the relative acceleration of distant masses such as fixed stars. This was adopted by Kopff (1921) who pointed out that in the first case, the traveler experiences acceleration due to forces relative to the stay-at-home twin and the stationary masses of the universe, while in the second case, stay-at-home twin and the masses of the universe are accelerating while the traveler is held at rest by the same forces as before. Thirring (1921) added that the traveler's frame can be interpreted in two ways: Either it is considered as "accelerating" in which case inertial forces arise in it, or it is considered as being "at rest" in which case gravitational forces arise due to relative acceleration of the distant masses.
+Some authors argued that the accelerated frame analysis and general relativity are necessary in order to "complete" the solution indicated in section § Acceleration asymmetry: Einstein (1918) stated that there is no paradox in special relativity because only one clock is always at rest in an inertial frame while the other one is accelerated; yet after describing the accelerated frame at turnaround in terms of gravitational fields and general relativity, he stated that "by this consideration, the paradox is completely resolved." Einstein (1920) stated that in special relativity the reason of the asymmetry between the twins lies in the acceleration of one of them; yet he continued that "a proper grasp of the reason is furnished only when we adopt the general theory of relativity" which shows that a "centrifugal field" only arises in the frame of the traveler but not in the frame of the resting twin. Bloch (1920) stated that there is no paradox in special relativity since one of them is in two inertial frames; yet since the combination of two inertial frames constitutes an accelerated frame that cannot be dealt with in special relativity, only general relativity can provide the "proper and satisfying solution". Pauli (1921) stated that there is no paradox in special relativity since one of them is accelerating; yet in order to describe the accelerated frame of the traveler at turnaround, the influence of (coordinate) acceleration on the stay-at-home clock cannot be neglected as it is not caused by an external force but by an inertial force, thus he concluded that "the complete solution of the problem can naturally only been given in the framework of general relativity". Born (1921) stated that there is no paradox in special relativity since one of them is accelerating; then he gave "the complete explanation of the clock paradox" that also includes the accelerated frame of the traveler and concluded that "the clock paradox is due to a false application of the special theory of relativity to a case in which the general theory should be applied".
+However, many physicists reject the idea that general relativity is "necessary" to "complete" the solution: As the round-trip described above is entirely formulated in the framework of flat Minkowski space of special relativity, and because special relativity can perfectly handle accelerated frames such as Rindler coordinates, the accelerated frame solution is not even an application of general relativity as a theory of gravitation in curved spacetime, but rather relies on pseudo-gravitational fields that pop up by transforming into the accelerated frame, thus special relativity is sufficient to discuss the twin paradox. Regarding Mach's principle, it is not clear whether it is even compatible with the theory of relativity.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-7.md b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-7.md
new file mode 100644
index 000000000..e2fa7f9a3
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_the_twin_paradox-7.md
@@ -0,0 +1,118 @@
+---
+title: "History of the twin paradox"
+chunk: 8/8
+source: "https://en.wikipedia.org/wiki/History_of_the_twin_paradox"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:25.226599+00:00"
+instance: "kb-cron"
+---
+
+== Curved spacetime (1922) ==
+Contrary to the previous examples, general relativity is required when spacetime curvature caused by mass and energy cannot be neglected any longer. An early discussion of a round-trip experiment in curved spacetime was provided by Jean Becquerel (1922) in terms of the Schwarzschild formula 
+  
+    
+      
+        d
+        τ
+        =
+        
+          
+            1
+            −
+            
+              
+                
+                  
+                    2
+                    G
+                    M
+                  
+                  
+                    
+                      c
+                      
+                        2
+                      
+                    
+                    r
+                  
+                
+              
+            
+          
+        
+        d
+        t
+      
+    
+    {\displaystyle d\tau ={\sqrt {1-{\tfrac {2GM}{c^{2}r}}}}dt}
+  
+, where 
+  
+    
+      
+        G
+      
+    
+    {\displaystyle G}
+  
+ is the gravitational constant, 
+  
+    
+      
+        M
+      
+    
+    {\displaystyle M}
+  
+ the mass of the spherical central body, and 
+  
+    
+      
+        r
+      
+    
+    {\displaystyle r}
+  
+ the distance between test body and central body. In his example, two identical clocks A and B are placed next to each other at a point very far from the material center, initially marking the same time 
+  
+    
+      
+        t
+      
+    
+    {\displaystyle t}
+  
+; when A is transported closer to the central mass where the field is more intense, it will measure time 
+  
+    
+      
+        ∫
+        d
+        τ
+      
+    
+    {\displaystyle \int d\tau }
+  
+ which is shorter than 
+  
+    
+      
+        ∫
+        d
+        t
+      
+    
+    {\displaystyle \int dt}
+  
+ measured by B; when A is brought back to B, it will be retarded with respect to B. 
+Other authors investigated cases in which both twins are in free fall without experiencing proper acceleration, yet according to the Schwarzschild metric they will nevertheless age differently. For instance, Mikhail (1952) gave an "example in which the two observers are attached to two test-particles moving freely in the field of a gravitating mass; one of these makes complete revolutions in a circular orbit while the other moves radially outwards and inwards. The time-interval between two successive encounters is shorter in the reckoning of the former than in that of the latter."
+
+== References ==
+
+=== Historical papers and textbooks ===
+
+=== Recent papers and textbooks ===
+
+== External links ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_variational_principles_in_physics-0.md b/data/en.wikipedia.org/wiki/History_of_variational_principles_in_physics-0.md
new file mode 100644
index 000000000..33ba73c53
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_variational_principles_in_physics-0.md
@@ -0,0 +1,185 @@
+---
+title: "History of variational principles in physics"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/History_of_variational_principles_in_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:50.096276+00:00"
+instance: "kb-cron"
+---
+
+In physics, a variational principle is a method for describing the state or dynamics of a physical system, by identifying it as an extremum (minimum, maximum or saddle point) of a functional. Variational methods are exploited in many modern software applications to simulate matter and light.
+Since the development of analytical mechanics in the 18th century, the fundamental equations of physics can be expressed in terms of action principles, where the variational principle is applied to the action of a system in order to recover the fundamental equation of motion. Intuitively, instead of writing out the laws of motion in terms of local, instantaneous relationships using a differential equation, the same motions can be described as minimising some total cost.
+This article describes the historical development of such action principles and other variational methods applied in physics. See History of physics for an overview and Outline of the history of physics for related histories.
+
+== Antiquity ==
+Variational principles are found among earlier ideas in surveying and optics. The rope stretchers of ancient Egypt stretched corded ropes between two points to measure the path which minimized the distance of separation, and Claudius Ptolemy, in his Geographia (Bk 1, Ch 2), emphasized that one must correct for "deviations from a straight course"; in ancient Greece Euclid states in his Catoptrica that, for the path of light reflecting from a mirror, the angle of incidence equals the angle of reflection; and Hero of Alexandria later showed that this path was the shortest length and least time.
+
+== Early variational principles ==
+
+=== Principle of least time ===
+The earlier geometrical ideas in optics were generalized by Pierre de Fermat, who in the 1660s refined the principle to "light travels between two given points along the path of shortest time"; now known as the principle of least time or Fermat's principle. Fermat showed that principle predicts the observed law of refraction. His approach was metaphysical, arguing that Nature acts simply and economically.
+
+=== Principle of virtual work ===
+In the static analysis of objects under forces but fixed at mechanical equilibrium, the principle of virtual work imagines tiny mathematical shifts away from equilibrium. Each shift does work—energy lost or gained—against the forces, but the sum of all these bits of virtual work must be zero. This principle was developed by Johann Bernoulli in a letter to Pierre Varignon in 1715, but never separately published. Cornelius Lanczos uses a slightly different definition as the single postulate for all analytic mechanics, showing thereby the power of energy based variational principles over Newtonian mechanics.
+
+=== D'Alembert's principle ===
+In 1743 Jean le Rond d'Alembert generalized the concept we now call virtual work to dynamical systems with rigid constraints, like rods or string under tension, a form that became known as the d'Alembert principle. In the case of static (in equilibrium) rigid bodies without friction, the principle of virtual work says the net work of all applied forces (
+  
+    
+      
+        
+          F
+          
+            i
+          
+          
+            (
+            a
+            )
+          
+        
+      
+    
+    {\displaystyle F_{i}^{(a)}}
+  
+) under variation of positions (
+  
+    
+      
+        
+          r
+          
+            i
+          
+        
+      
+    
+    {\displaystyle r_{i}}
+  
+)  is zero:
+
+  
+    
+      
+        
+          Σ
+          
+            i
+          
+        
+        
+          F
+          
+            i
+          
+          
+            (
+            a
+            )
+          
+        
+        ⋅
+        δ
+        
+          r
+          
+            i
+          
+        
+        =
+        0
+      
+    
+    {\displaystyle \Sigma _{i}F_{i}^{(a)}\cdot \delta r_{i}=0}
+  
+
+A similar condition but valid for dynamics (systems in motion) introduces, for each force, the change in momentum 
+  
+    
+      
+        
+          
+            
+              
+                p
+                ˙
+              
+            
+          
+          
+            i
+          
+        
+      
+    
+    {\displaystyle {\dot {p}}_{i}}
+  
+:
+
+  
+    
+      
+        
+          Σ
+          
+            i
+          
+        
+        (
+        
+          F
+          
+            i
+          
+        
+        −
+        
+          
+            
+              
+                p
+                ˙
+              
+            
+          
+          
+            i
+          
+        
+        )
+        ⋅
+        δ
+        
+          r
+          
+            i
+          
+        
+        =
+        0
+      
+    
+    {\displaystyle \Sigma _{i}(F_{i}-{\dot {p}}_{i})\cdot \delta r_{i}=0}
+  
+
+which is d'Alembert's principle.
+
+=== Brachistochrone problem ===
+
+In 1696 Johann Bernoulli posed a puzzle to European mathematicians: derive a curve for motion of a frictionless bead falling between a higher and a lower point in the least possible time. He named the curve the "brachistochrone", (from brachystos, "shortest", and chronos, "time") Isaac Newton, Gottfried Wilhelm Leibniz and others contributed solutions, and in 1718 Johann Bernoulli published an analysis based on the solution created by his brother James Bernoulli. All of these works, especially the approach taken by the Bernoullis, involved reasoning about small deviations in the path taken by the falling bead. Thus this became the first application of the variational technique, albeit as a special-case rather than a general principle.
+
+=== Principle of least action ===
+
+In 1744 and 1746, Pierre Louis Maupertuis generalized Fermat's concept to mechanics, in the form of a principle of least action.  
+Maupertuis argued metaphysically, he felt that "Nature is thrifty in all its actions", and applied the principle broadly:
+
+The laws of movement and of rest deduced from this principle being precisely the same as those observed in nature, we can admire the application of it to all phenomena. The movement of animals, the vegetative growth of plants ... are only its consequences; and the spectacle of the universe becomes so much the grander, so much more beautiful, the worthier of its Author, when one knows that a small number of laws, most wisely established, suffice for all movements.
+This notion of Maupertuis, although somewhat deterministic today, does capture much of the essence of variational mechanics.
+In application to physics, Maupertuis suggested that the quantity to be minimized was the product of the duration (time) of movement within a system by the action; his definitions of action varied with the problems he discussed.
+One form he used was called "vis viva",
+
+which is the integral of twice what we now call the kinetic energy T of the system.
+
+=== Euler's refinement ===
+Leonhard Euler corresponded with Maupertuis from 1740 to 1744; in 1744 Euler proposed a refined formulation of the least action principle in 1744. In modern notation, Euler proposed a principle based on the abbreviated action:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_variational_principles_in_physics-1.md b/data/en.wikipedia.org/wiki/History_of_variational_principles_in_physics-1.md
new file mode 100644
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_variational_principles_in_physics-1.md
@@ -0,0 +1,283 @@
+---
+title: "History of variational principles in physics"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/History_of_variational_principles_in_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:50.096276+00:00"
+instance: "kb-cron"
+---
+
+In rather general terms he wrote that "Since the fabric of the Universe is most perfect and is the work of a most wise Creator, nothing whatsoever takes place in the Universe in which some relation of maximum and minimum does not appear."
+Euler continued to write on the topic; in his Reflexions sur quelques loix generales de la nature (1748), he called the quantity "effort". His expression corresponds to what we would now call potential energy, so that his statement of least action in statics is equivalent to the principle that a system of bodies at rest will adopt a configuration that minimizes total potential energy.
+
+=== Lagrangian mechanics ===
+The first use of the term "method of variations" came in 1755 through the work of a young Joseph Louis Lagrange; Euler presented Lagrange's approach to the Berlin Academy in 1756 as the "calculus of variations". Unlike Euler, Lagrange's approach was purely analytic rather than geometrical.  Lagrange introduced the idea of variation of entire curves or paths between the endpoints than of individual coordinates. For this he introduced a new form of a differential, written 
+  
+    
+      
+        δ
+      
+    
+    {\displaystyle \delta }
+  
+, that acts on integrals rather than 
+  
+    
+      
+        d
+      
+    
+    {\displaystyle d}
+  
+ acting on coordinates.  His notation continues to be used today.
+
+=== Hamilton-Jacobi mechanics ===
+
+The variational principle was not used to derive the equations of motion until almost 75 years later, when William Rowan Hamilton in 1834 and 1835  applied the variational principle to the Lagrangian function 
+  
+    
+      
+        L
+        =
+        T
+        −
+        V
+      
+    
+    {\displaystyle L=T-V}
+  
+ (where T is the kinetic energy and V the potential energy of an object) to obtain what are now called the Euler–Lagrange equations.  Hamilton believed his results were constrained by conservation of energy, which he called conservation of living force.
+While few German scientists read English papers in this era, in 1836 the German mathematician Carl Gustav Jacobi read of Hamilton's work and immediately began new mathematical work, publishing ground breaking work on the variational principle in the following year. Among Jacobi's results was the extension of Hamilton's method to time-dependent potentials (or "force functions" as they were known at that time).
+
+=== Extensions by Gauss and Hertz ===
+Other extremal principles of classical mechanics were formulated, such as Carl Friedrich Gauss's 1829 principle of least constraint and its corollary, Heinrich Hertz's 1896 principle of least curvature.
+
+== Action principle names ==
+
+Action principles were developed by trial and error over three centuries; the names of the principles are not self-describing. Richard Feynman, through his PhD thesis and later through his reinvention of the undergraduate physics course, reinvigorated the field of variational principles in physics. In the process he upended the terminology. Feynman called Hamilton's principal function simply the "action" and Hamilton's principle he called "the principle of least action". The table below summarizes the key terminology found in modern physics literature.
+
+The notation 
+  
+    
+      
+        (
+        δ
+        S
+        
+          )
+          
+            T
+          
+        
+        =
+        0
+      
+    
+    {\displaystyle (\delta S)_{T}=0}
+  
+ means variations on 
+  
+    
+      
+        S
+      
+    
+    {\displaystyle S}
+  
+ with 
+  
+    
+      
+        T
+        =
+        
+          t
+          
+            2
+          
+        
+        −
+        
+          t
+          
+            1
+          
+        
+      
+    
+    {\displaystyle T=t_{2}-t_{1}}
+  
+ fixed;  
+  
+    
+      
+        (
+        δ
+        W
+        
+          )
+          
+            E
+          
+        
+      
+    
+    {\displaystyle (\delta W)_{E}}
+  
+ means variation with constant energy. The abbreviated action is sometimes labeled 
+  
+    
+      
+        
+          S
+          
+            0
+          
+        
+      
+    
+    {\displaystyle S_{0}}
+  
+. Some authors use "stationary action" or "least action" to mean any variational principle involving action.
+
+== Modern action principles ==
+
+=== In relativity ===
+
+In 1915 David Hilbert applied variational principles to derive the gravitational field equations of general relativity in agreement with Albert Einstein's derivation. (Einstein and Hilbert discussed Einstein's work on general relativity in person and letters throughout 1915.) Hilbert's approach required accepting the variational principle as "axiomatic", a broadly accepted requirement today but questionable to the physicists of 1915. 
+Hilbert's variations were based on what became known as the Einstein–Hilbert action, given by
+
+  
+    
+      
+        
+          
+            S
+          
+        
+        [
+        g
+        ]
+        =
+        
+          
+            1
+            
+              2
+              κ
+            
+          
+        
+        ∫
+        R
+        
+          
+            −
+            g
+          
+        
+        
+        
+          
+            d
+          
+          
+            4
+          
+        
+        x
+      
+    
+    {\displaystyle {\mathcal {S}}[g]={\frac {1}{2\kappa }}\int R{\sqrt {-g}}\,\mathrm {d} ^{4}x}
+  
+,
+where κ is Einstein gravitational constant, 
+  
+    
+      
+        g
+        =
+        det
+        (
+        
+          g
+          
+            α
+            β
+          
+        
+        )
+      
+    
+    {\displaystyle g=\det(g_{\alpha \beta })}
+  
+ is the determinant of a spacetime Lorentz metric and 
+  
+    
+      
+        R
+      
+    
+    {\displaystyle R}
+  
+ is the scalar curvature.
+
+=== In quantum mechanics ===
+
+Variational principles played decisive roles at critical times in the development of quantum mechanics.
+
+==== Sommerfeld's atom ====
+
+Following Max Planck's proposal that quantum radiators explain the blackbody radiation spectrum and Albert Einstein hypothesis of quantum radiation to explain the photoelectric effect, Niels Bohr proposed quantized energy levels for the orbits in his model of the atom, thereby explaining the Balmer series for absorption of radiation by atoms. However this hypothesis involved no mechanical model. Arnold Sommerfeld then showed that quantization of the action of orbits for Hydrogen predicted the Balmer series, complete with relativistic corrections leading to fine structure in spectral lines. However, this approach could not be extended to atoms with more electrons and, more fundamentally, the quantum hypothesis itself had no explanation from this classical mechanics solution.
+
+==== Schrödinger's equation ====
+Combining Einstein's relativity and photoelectric effect results, De Broglie suggested that Sommerfeld's quantized action may relate to quantized wave effects; Erwin Schrödinger took up this idea, applying Hamilton's optico-mechanical analogy to connect the quantized action to Hamilton-Jacobi equations for the action. Hamilton's connection between light rays and light waves now became a connection between matter trajectories and de Broglie matter waves.  The resulting Schrödinger equation became the first successful quantum mechanics.
+
+==== Dirac's quantum action ====
+The work that built on Schrödinger's equation relied on analogies to Hamiltonian mechanics.
+In 1933 Paul Dirac published a paper seeking an alternative formulation based on Lagrangian mechanics. He was motivated by the power of the action principle and the relativistic invariance of the action itself. Dirac was able to show that the wavefunctions probability amplitude at 
+  
+    
+      
+        
+          x
+          
+            1
+          
+        
+        ,
+        
+          t
+          
+            2
+          
+        
+      
+    
+    {\displaystyle x_{1},t_{2}}
+  
+ was related to the amplitude at 
+  
+    
+      
+        
+          x
+          
+            2
+          
+        
+        ,
+        
+          t
+          
+            2
+          
+        
+      
+    
+    {\displaystyle x_{2},t_{2}}
+  
+ through a complex exponential function of the action.
+
+==== Feynman's least action mechanics ====
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_variational_principles_in_physics-2.md b/data/en.wikipedia.org/wiki/History_of_variational_principles_in_physics-2.md
new file mode 100644
index 000000000..cd30f2aa6
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_variational_principles_in_physics-2.md
@@ -0,0 +1,91 @@
+---
+title: "History of variational principles in physics"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/History_of_variational_principles_in_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:50.096276+00:00"
+instance: "kb-cron"
+---
+
+In 1942, nearly a decade after Dirac's work, Richard Feynman built a new quantum mechanics formulation on the action principle. Feynman interpreted Dirac's formula as a physical recipe for the probability amplitude contributions from every possible path between 
+  
+    
+      
+        
+          x
+          
+            1
+          
+        
+        ,
+        
+          t
+          
+            2
+          
+        
+      
+    
+    {\displaystyle x_{1},t_{2}}
+  
+ and 
+  
+    
+      
+        
+          x
+          
+            2
+          
+        
+        ,
+        
+          t
+          
+            2
+          
+        
+      
+    
+    {\displaystyle x_{2},t_{2}}
+  
+. These possibilities interfere; constructive interference gives the paths with the most amplitude. In the classical limit with large values of action compared to 
+  
+    
+      
+        h
+      
+    
+    {\displaystyle h}
+  
+, the single classical path given by the action principle results.
+
+==== Schwinger's quantum action principle ====
+
+In 1950, Julian Schwinger revisited Dirac's Lagrangian paper to develop the action principle in a different direction. Unlike Feynman's focus on paths, Schwinger's approach was "differential" or local.
+
+=== In particle physics ===
+The Standard Model is defined in terms of a Lagrangian density that includes all known elementary particles, the Higgs field and three of the fundamental interactions (electromagnetism, weak interaction and strong interaction, not including gravitational interaction). Its formulation started in the 1970s and has successfully explained almost all experimental results related to microscopic physics.
+
+== Teleology in action principles ==
+The breadth of physical phenomena subject to study by action principles lead scientists from all centuries to view these concepts as especially fundamental; the connection of two points by paths lead some to suggest a "purpose" to the selection of one particular path. This teleological viewpoint runs from the earliest physics through Fermat, Maupertuis, and on up to Max Planck,  without, however, any scientific backing. The use of colorful language continues in the modern era with phrases like "Nature's command (to) Explore all paths!" or "It isn't that a particle takes the path of least action but that it smells all the paths in the neighborhood...".
+
+== Variational methods ==
+
+=== Ritz's work on elasticity and waves ===
+Lord Rayleigh was the first to popularly adapt the variational principles for the search of eigenvalues and eigenvectors for the study of elasticity and classical waves in his 1877 Theory of Sound. The Rayleigh method allows approximation of the fundamental frequencies without full knowledge of the material composition and without the requirement of computational power. From 1903 to 1908, Walther Ritz introduced a series of improved methods for static and free vibration problems based on the optimization of an ansatz or trial function. Ritz demonstrated his use in the Euler–Bernoulli beam theory and the determination of Chladni figures.
+For years, Ritz works were poorly cited in Western Europe and would only become popular after Ritz death in 1909. In Russia, physicists like Ivan Bubnov (in 1913) and Boris Galerkin (in 1915) would rediscover and popularize some of Ritz's methods from 1908. In 1940, Georgii I. Petrov improved these approximations. These methods are now known under different names, including Bubnov–Galerkin, Petrov–Galerkin and Ritz–Galerkin methods.
+In 1911, Rayleigh complemented Ritz for his method for solving Chladni's problem, but complained for the lack of citation of his earlier work. However the similarity between Rayleigh's and Ritz's method has sometimes been challenged. Ritz's methods are sometimes referred as Rayleigh–Ritz method or simply Ritz method, depending on the procedure. Ritz's method led to the development of finite element method for the numerical solution of partial differential equations in physics.
+
+=== For quantum systems ===
+The variational method of Ritz would found his use quantum mechanics with the development of Hellmann–Feynman theorem. The theorem was first discussed by Schrödinger in 1926, the first proof was given by Paul Güttinger in 1932, and later rediscovered independently by Wolfgang Pauli and Hans Hellmann in 1933, and by Feynman in 1939.
+In quantum chemistry and condensed matter physics, variational methods were developed to study atoms, molecules, nuclei and solids under a quantum mechanical framework. Some of these include the use of Ritz methods for the determination of the spectra of the helium atom, 1930 Hartree–Fock method, 1964 density functional theory and variational Monte Carlo and 1992 density matrix renormalization group (DMRG).
+
+=== Quantum algorithms ===
+In 2014, variational principles were part of a hybrid strategy, called noisy intermediate-scale quantum (NISQ) computing, to combine powerful but imperfect quantum computers coupled with classical computers. The first proposals included a
+variational quantum eigensolver to exploit quantum phenomena to simulate atoms and small molecules using variational methods and an approximate optimization algorithm.
+
+== Footnote ==
+
+== References ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Hyperradiant_Fresnel_lens-0.md b/data/en.wikipedia.org/wiki/Hyperradiant_Fresnel_lens-0.md
new file mode 100644
index 000000000..336a4ea19
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Hyperradiant_Fresnel_lens-0.md
@@ -0,0 +1,28 @@
+---
+title: "Hyperradiant Fresnel lens"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Hyperradiant_Fresnel_lens"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:26.485729+00:00"
+instance: "kb-cron"
+---
+
+Hyper-radial or hyperradiant Fresnel lenses are Fresnel lenses used in lighthouses. They are larger than "first-order" lenses, having a focal length (radius) of 1330 mm (52.36 inches). The idea was mentioned by Thomas Stevenson in 1869 and first proposed by John Richardson Wigham in 1872, and again proposed by Thomas Stevenson in 1885 (infringing Wigham's patent).
+The hyper-radial lens was made in 1885 by the F. Barbier Company in Paris as a test lens for the lighthouse illumination trials then going on at the South Foreland Lighthouse in the United Kingdom (UK). Chance Brothers Glass Company made their first hyper-radial lens in 1887 in the UK.
+These lenses were originally named biform, and later triform and quadriform lenses, by Wigham. Thomas Stevenson used the term hyperradiant lens, and later they were renamed the hyper-radial lens by James Kenward of the Chance Brothers Glass Company.
+The hyper-radial Fresnel lenses were the largest ever put into use and were installed in about two dozen major "landfall" beacons around the world. The recipients include Makapu'u Point lighthouse on Oahu Island in Hawaii, Cabo de São Vicente in Portugal, Manora Point in Karachi, Pakistan, the Bishop Rock off the coast of Cornwall (in the UK), Cabo de Santa Marta in Brazil, and Cape Race, Newfoundland. By the 1920s, high-intensity lamp technology had rendered lenses of this size obsolete.
+
+
+== Lighthouses ==
+  
+Hyperradiant optics were installed in thirty-one lighthouses around the world. A large proportion were destined for lights around Great Britain and Ireland, with another four used at sites around Sri Lanka. Despite the improvements in lighting technology, a number are still in use. Others are in museums, either on display or in storage. The remainder have been broken up or lost.
+
+
+== References ==
+
+
+== External links ==
+
+Wikimap showing lighthouse locations
+Makapuu Point Archived 2007-03-04 at the Wayback Machine
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Hypotheses_non_fingo-0.md b/data/en.wikipedia.org/wiki/Hypotheses_non_fingo-0.md
index da14abc31..5636ce845 100644
--- a/data/en.wikipedia.org/wiki/Hypotheses_non_fingo-0.md
+++ b/data/en.wikipedia.org/wiki/Hypotheses_non_fingo-0.md
@@ -4,7 +4,7 @@ chunk: 1/1
 source: "https://en.wikipedia.org/wiki/Hypotheses_non_fingo"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T12:09:22.413312+00:00"
+date_saved: "2026-05-05T16:29:27.857688+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/J/psi_meson-0.md b/data/en.wikipedia.org/wiki/J/psi_meson-0.md
new file mode 100644
index 000000000..d0efe6b4e
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/J/psi_meson-0.md
@@ -0,0 +1,27 @@
+---
+title: "J/psi meson"
+chunk: 1/2
+source: "https://en.wikipedia.org/wiki/J/psi_meson"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:30.468827+00:00"
+instance: "kb-cron"
+---
+
+The J/ψ (J/psi) meson  is a subatomic particle, a flavor-neutral meson consisting of a charm quark and a charm antiquark.  Mesons formed by a bound state of a charm quark and a charm anti-quark are generally known as "charmonium" or psions.  The J/ψ is the most common form of charmonium, due to its spin of 1 and its low rest mass.  The J/ψ has a rest mass of 3.0969 GeV/c2, just above that of the ηc (2.9836 GeV/c2), and a mean lifetime of 7.2×10−21 s. This lifetime was about a thousand times longer than expected.
+Its discovery was made independently by two research groups, one at the Stanford Linear Accelerator Center, headed by Burton Richter, and one at the Brookhaven National Laboratory, headed by Samuel Ting of MIT. They discovered that they had found the same particle, and both announced their discoveries on 11 November 1974. The importance of this discovery is highlighted by the fact that the subsequent, rapid changes in high-energy physics at the time have become collectively known as the "November Revolution". Richter and Ting were awarded the 1976 Nobel Prize in Physics.
+
+== Background to discovery ==
+The background to the discovery of the J/ψ was both theoretical and experimental. In the 1960s, the first quark models of elementary particle physics were proposed, which said that protons, neutrons, and all other baryons, and also all mesons, are made from fractionally charged particles, the "quarks", originally with three types or "flavors", called up, down,  and strange. (Later the model was expanded to six quarks, adding the charm, top and bottom quarks.)  Despite the ability of quark models to bring order to the "elementary particle zoo", they were considered something like mathematical fiction at the time, a simple artifact of deeper physical reasons.
+Starting in 1969, deep inelastic scattering experiments at SLAC revealed surprising experimental evidence for particles inside of protons. Whether these were quarks or something else was not known at first. Many experiments were needed to fully identify the properties of the sub-protonic components. To a first approximation, they indeed were a match for the previously described quarks.
+On the theoretical front, gauge theories with broken symmetry became the first fully viable contenders for explaining the weak interaction after Gerardus 't Hooft discovered in 1971 how to calculate with them beyond tree level. The first experimental evidence for these electroweak unification theories was the discovery of the weak neutral current in 1973. Gauge theories with quarks became a viable contender for the strong interaction in 1973, when the concept of asymptotic freedom was identified.
+However, a naive mixture of electroweak theory and the quark model led to calculations about known decay modes that contradicted observation: In particular, it predicted Z boson-mediated flavor-changing decays of a strange quark into a down quark, which were not observed. A 1970 idea of Sheldon Glashow, John Iliopoulos, and Luciano Maiani, known as the GIM mechanism, showed that the flavor-changing decays would be strongly suppressed if there were a fourth quark (now called the charm quark) that was a complementary counterpart to the strange quark. By summer 1974 this work had led to theoretical predictions of what a charm + anticharm meson would be like.
+The group at Brookhaven, were the first to discern a peak at 3.1 GeV in plots of production rates. Ting named it the "J meson".
+
+== Decay modes ==
+Hadronic decay modes of J/ψ are strongly suppressed because of the OZI rule. This effect strongly increases the lifetime of the particle and thereby gives it its very narrow decay width of just 93.2±2.1 keV. Because of this strong suppression, electromagnetic decays begin to compete with hadronic decays. This is why the J/ψ has a significant branching fraction to leptons.
+The primary decay modes are:
+
+== J/ψ melting ==
+In a hot QCD medium, when the temperature is raised well beyond the Hagedorn temperature, the J/ψ and its excitations are expected to melt. This is one of the predicted signals of the formation of the quark–gluon plasma. Heavy-ion experiments at CERN's Super Proton Synchrotron and at BNL's Relativistic Heavy Ion Collider have studied this phenomenon without a conclusive outcome as of 2009. This is due to the requirement that the disappearance of J/ψ mesons is evaluated with respect to the baseline provided by the total production of all charm quark-containing subatomic particles, and because it is widely expected that some J/ψ are produced and/or destroyed at time of QGP hadronization. Thus, there is uncertainty in the prevailing conditions at the initial collisions.
+In fact, instead of suppression, enhanced production of J/ψ is expected in heavy ion experiments at LHC where the quark-combinant production mechanism should be dominant given the large abundance of charm quarks in the QGP. Aside of J/ψ, charmed B mesons (Bc), offer a signature that indicates that quarks move freely and bind at-will when combining to form hadrons.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/J/psi_meson-1.md b/data/en.wikipedia.org/wiki/J/psi_meson-1.md
new file mode 100644
index 000000000..ef94c51ff
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/J/psi_meson-1.md
@@ -0,0 +1,47 @@
+---
+title: "J/psi meson"
+chunk: 2/2
+source: "https://en.wikipedia.org/wiki/J/psi_meson"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:30.468827+00:00"
+instance: "kb-cron"
+---
+
+== Name ==
+Because of the nearly simultaneous discovery, the J/ψ is the only particle to have a two-letter name. Richter named it "SP", after the SPEAR accelerator used at SLAC; however, none of his coworkers liked that name. After consulting with Greek-born Leo Resvanis to see which Greek letters were still available, and rejecting "iota" because its name implies insignificance, Richter chose "psi" – a name which, as Gerson Goldhaber pointed out, contains the original name "SP", but in reverse order. Coincidentally, later spark chamber pictures often resembled the psi shape. Ting assigned the name "J" to it, saying that the more stable particles, such as the W and Z bosons had Roman names, as opposed to classical particles, which had Greek names. He also cited the symbol for electromagnetic current 
+  
+    
+      
+        
+          j
+          
+            μ
+          
+        
+        (
+        x
+        )
+      
+    
+    {\displaystyle j_{\mu }(x)}
+  
+ which much of their previous work was concentrated on to be one of the reasons.
+Much of the scientific community considered it unjust to give one of the two discoverers priority, so most subsequent publications have referred to the particle as the "J/ψ".
+The first excited state of the J/ψ was called the ψ′; it is now called the ψ(2S), indicating its quantum state. The next excited state was called the ψ″; it is now called ψ(3770), indicating mass in MeV/c2. Other vector charm–anticharm states are denoted similarly with ψ and the quantum state (if known) or the mass. The "J" is not used, since Richter's group alone first found excited states.
+The name charmonium is used for the J/ψ and other charm–anticharm bound states. This is by analogy with positronium, which also consists of a particle and its antiparticle (an electron and positron in the case of positronium).
+
+== See also ==
+OZI rule
+List of multiple discoveries
+
+== Footnotes ==
+
+== References ==
+
+== Sources ==
+Glashow, S. L.; Iliopoulos, J.; Maiani, L. (1970). "Weak Interactions with Lepton–Hadron Symmetry". Physical Review D. 2 (7): 1285–1292. Bibcode:1970PhRvD...2.1285G. doi:10.1103/PhysRevD.2.1285.
+Aubert, J.; et al. (1974). "Experimental Observation of a Heavy Particle J". Physical Review Letters. 33 (23): 1404–1406. Bibcode:1974PhRvL..33.1404A. doi:10.1103/PhysRevLett.33.1404.
+Augustin, J.; et al. (1974). "Discovery of a Narrow Resonance in e+e− Annihilation". Physical Review Letters. 33 (23): 1406–1408. Bibcode:1974PhRvL..33.1406A. doi:10.1103/PhysRevLett.33.1406.
+Bobra, M. (2005). "Logbook: J/ψ particle". Symmetry Magazine. 2 (7): 34.
+Yao, W.-M.; et al. (Particle Data Group) (2006). "Review of Particle Physics: Naming Scheme for Hadrons" (PDF). Journal of Physics G. 33 (1): 108. arXiv:astro-ph/0601168. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Kite_experiment-0.md b/data/en.wikipedia.org/wiki/Kite_experiment-0.md
new file mode 100644
index 000000000..db2bc0850
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Kite_experiment-0.md
@@ -0,0 +1,33 @@
+---
+title: "Kite experiment"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Kite_experiment"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:31.745202+00:00"
+instance: "kb-cron"
+---
+
+The kite experiment is a scientific experiment in which a kite with a pointed conductive wire attached to its apex is flown near thunder clouds to collect static electricity from the air and conduct it down the wet kite string to the ground. The experiment was first proposed in 1752 by Benjamin Franklin, who reportedly conducted the experiment with the assistance of his son William. The experiment's purpose was to investigate the nature of lightning and electricity, which were not yet understood. Combined with further experiments on the ground, the kite experiment demonstrated that lightning and electricity were the result of the same phenomenon.
+
+
+== Background ==
+Speculations of Jean-Antoine Nollet had led to the issue of the electrical nature of lightning being posed as a prize question at Bordeaux in 1749. In 1750, it was the subject of public discussion in France with a dissertation of Denis Barberet receiving a prize in Bordeaux. Barberet proposed a cause in line with the triboelectric effect. The same year, Franklin reversed his previous skepticism of electrical lightning's attraction to high points. The physicist Jacques de Romas also wrote a mémoire with similar ideas that year and later defended them as independent of Franklin's.
+
+
+== Lightning rod experiments ==
+In 1752, Franklin proposed an experiment with conductive rods to attract lightning to a leyden jar, an early form of capacitor, but there was no spire in Philadelphia that was high enough for him to try it out. Thomas-François Dalibard, however, did carry out such an experiment in Northern France in May 1752 at Marly-la-Ville. Then the following years, an attempt to replicate the experiment killed Georg Wilhelm Richmann in Saint Petersburg in August 1753; he was thought to be the victim of ball lightning.
+
+
+== Franklin's kite experiment ==
+Franklin then got the idea to use a kite to raise the lightning rod to a high height. His kite experiment was performed in Philadelphia in June 1752, according to the account by Joseph Priestley. Franklin described the experiment in the Pennsylvania Gazette on October 19, 1752, without mentioning that he had performed it. The account was read to the Royal Society on December 21 and printed as such in the Philosophical Transactions. A more complete account of Franklin's experiment was given by Priestley in 1767, who presumably learned the details directly from Franklin, who was in London while Priestley wrote the book.
+According to the 1767 Priestley account, Franklin realized the dangers of using conductive rods and instead used the conductivity of a wet hemp string attached to a kite. As a result, he was able to remain on the ground and let his son fly the kite from the cover of a shed close by. That enabled Franklin and his son to keep the silk string of the kite dry to insulate them while the hemp string to the kite was allowed to get wet in the rain to provide conductivity. A house key was attached to the hemp string and connected to a Leyden jar; a silk string was attached to that. "At this key he charged phials, and from the electric fire thus obtained, he kindled spirits, and performed all other electrical experiments which are usually exhibited by an excited globe or tube."
+Contrary to popular belief, the kite was not hit by visible lightning; otherwise Franklin would almost certainly have been killed. However, Franklin noticed that loose threads of the kite string were repelling one another and deduced that the Leyden jar was being charged. He moved his hand near the key and observed an electric spark, which proved the electric nature of lightning.
+
+
+== References ==
+
+
+== External links ==
+Philosophical Transactions: "A Letter of Benjamin Franklin, Esq; to Mr. Peter Collinson, F. R. S. concerning an Electrical Kite" (PDF).  Phil. Trans. 1751–1752 47, 565–567.
+pbs.org
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Koenig's_manometric_flame_apparatus-0.md b/data/en.wikipedia.org/wiki/Koenig's_manometric_flame_apparatus-0.md
new file mode 100644
index 000000000..b49b6b39a
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Koenig's_manometric_flame_apparatus-0.md
@@ -0,0 +1,30 @@
+---
+title: "Koenig's manometric flame apparatus"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Koenig's_manometric_flame_apparatus"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:33.051846+00:00"
+instance: "kb-cron"
+---
+
+Koenig's manometric flame apparatus was a laboratory  instrument invented in 1862 by the German physicist Rudolph Koenig, and  used to visualize sound waves. It was the nearest equivalent of the modern oscilloscope in the late nineteenth and early twentieth centuries.
+
+
+== Description ==
+The manometric flame apparatus consisted of a chamber which acted in the same way as a modern microphone. Sound from the source to be measured was concentrated by means of a horn or tube into one half of the capsule chamber. The chamber was divided in two by an elastic diaphragm, usually rubber. The sound caused the diaphragm to vibrate which modulated a flow of flammable illumination gas passing through the other half of the chamber. The illumination gas was passed to a Bunsen burner, the flame of which would then increase or decrease in size at the same frequency as the sound source.
+The change in flame size was too fast to be easily seen with the naked eye, and a stroboscope — usually in the form of a rotating many sided mirror — was used to view the flame. The frequency of the sound could then be calculated from the apparent distance between the flame images in the mirror and the known speed of its rotation. 
+
+Alexander Graham Bell used this type of equipment to study the performance of his microphones and demonstrated it in his display at the 1876 
+Philadelphia Centenarian Exhibition. He replaced the rubber diaphragm with an iron disc which was driven by an  electromagnet with current fed from a microphone. This apparatus was capable of giving quantitative measures of the performance of his microphones.
+A type of Fourier analyzer can be constructed by connecting a number of  manometric flame capsules each to a Helmholtz resonator tuned to either the fundamental frequency of the sound to be analyzed, or one of its harmonics. The flames produced from each capsule are then an indication of the strength of each of the Fourier components of the sound.
+
+
+== Notes ==
+
+
+== References ==
+1. The Koinge manometric flame apparatus  Jim & Rhoda Morris  at  SciTechAntiques. Accessed March 2008
+2.Manometric Flame Apparatus Kenyon College. Gambier, Ohio. Accessed March 2008
+3.Fourier Analysis Kenyon College. Gambier, Ohio. Accessed March 2008
+4.Flame manometer Case Western Reserve University Physics Department. Accessed March 2008
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Line_of_force-0.md b/data/en.wikipedia.org/wiki/Line_of_force-0.md
new file mode 100644
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@@ -0,0 +1,47 @@
+---
+title: "Line of force"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Line_of_force"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:34.303659+00:00"
+instance: "kb-cron"
+---
+
+In the history of physics, a line of force in Michael Faraday's extended sense is synonymous with James Clerk Maxwell's line of induction. According to J.J. Thomson, Faraday usually discusses lines of force as chains of polarized particles in a dielectric, yet sometimes Faraday discusses them as having an existence all their own as in stretching across a vacuum. In addition to lines of force, J.J. Thomson—similar to Maxwell—also calls them tubes of electrostatic inductance, or simply Faraday tubes.  From the 20th century perspective, lines of force are energy linkages embedded in a 19th-century field theory that led to more mathematically and experimentally sophisticated concepts and theories, including Maxwell's equations and Albert Einstein's theory of relativity.
+Lines of force originated with Michael Faraday, whose theory holds that all of reality is made up of force itself.  His theory predicts that electricity, light, and gravity have finite propagation delays.  The theories and experimental data of later scientific figures such as Maxwell, Heinrich Hertz, Einstein, and others are in agreement with the ramifications of Faraday's theory.  Nevertheless, Faraday's theory remains distinct. Unlike Faraday, Maxwell and others (e.g., J.J. Thomson) thought that light and electricity must propagate through an ether.  In Einstein's relativity, there is no ether, yet the physical reality of force is much weaker than in the theories of Faraday.
+Historian Nancy J. Nersessian in her paper "Faraday's Field Concept" distinguishes between the ideas of Maxwell and Faraday:
+
+The specific features of Faraday's field concept, in its 'favourite' and most complete form, are that force is a substance, that it is the only substance and that all forces are interconvertible through various motions of the lines of force. These features of Faraday's 'favourite notion' were not carried on. Maxwell, in his approach to the problem of finding a mathematical representation for the continuous transmission of electric and magnetic forces, considered these to be states of stress and strain in a mechanical aether. This was part of the quite different network of beliefs and problems with which Maxwell was working.
+
+
+== Views of Faraday ==
+At first Michael Faraday considered the physical reality of the lines of force as a possibility, yet several scholars agree that for Faraday their physical reality became a conviction. One scholar dates this change in the year 1838. Another scholar dates this final strengthening of his belief in 1852. Faraday experimentally studied lines of magnetic force and electrostatic force, showing them not to fit action at a distance models. In 1852 Faraday wrote the paper "On the Physical Character of the Lines of Magnetic Force" which examined gravity, radiation, and electricity, and their possible relationships with the transmission medium, transmission propagation, and the receiving entity.
+
+
+== Views of Maxwell ==
+Initially, James Clerk Maxwell took an agnostic approach in his mathematization of Faraday's theories.  This is seen in Maxwell's 1855 and 1856 papers:  "On Faraday's Lines of Force" and "On Faraday's Electrotontic State". In the 1864 paper "A Dynamical Theory of the Electromagnetic Field" Maxwell gives scientific priority of the electromagnetic theory of light to Faraday and his 1846 paper "Thoughts on Ray Vibrations". Maxwell wrote:
+
+Faraday discovered that when a plane polarized ray traverses a transparent diamagnetic medium in the direction of the lines of magnetic force produced by magnets or currents in the neighborhood, the plane of polarization is caused to rotate.The conception of the propagation of transverse magnetic disturbances to the exclusion of normal ones is distinctly set forth by Professor Faraday in his "Thoughts on Ray Vibrations." The electromagnetic theory of light, as proposed by him, is the same in substance as that which I have begun to develop in this paper, except that in 1846 there was no data to calculate the velocity of propagation.
+
+
+== Tube of force ==
+Maxwell changed Faraday's phrase lines of force to tubes of force, when expressing his fluidic assumptions involved in his mathematization of Faraday's theories.  A tube of force, also called a tube of electrostatic induction or field tube, are the lines of electric force which moves so that its beginning traces a closed curve on a positive surface, its end will trace a corresponding closed curve on the negative surface, and the line of force itself will generate an inductive tubular surface. Such a tube is called a "solenoid". There is a pressure at right angles to a tube of force of one half the product of the dielectric and magnetic density. If through the growth of a field the tubes of force are spread sideways or in width there is a magnetic reaction to that growth in intensity of electric current. However, if a tube of force is caused to move endwise there is little or no drag to limit velocity. Tubes of force are absorbed by bodies imparting momentum and gravitational mass. Tubes of force are a group of electric lines of force.
+
+
+== Magnetic curves ==
+Early on in his research (circa 1831), Faraday calls the patterns of apparently continuous curves traced out in metallic filings near a magnet magnetic curves.  Later on he refers to them as just an instance of magnetic lines of force or simply lines of force. Eventually Faraday would also begin to use the phrase "magnetic field".
+
+
+== See also ==
+Field line
+Flux tube
+Flux
+
+
+== Other relevant papers ==
+Faraday, Michael, "Thoughts on Ray Vibrations", Philosophical Magazine, May 1846, or Experimental Researches, iii, p. 447
+Faraday, Michael, Experimental Researches, Series 19.
+
+
+== Notes ==
\ No newline at end of file
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+date_saved: "2026-05-05T16:29:38.235700+00:00"
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diff --git a/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-0.md b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-0.md
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+---
+title: "Mathematical formulation of quantum mechanics"
+chunk: 1/7
+source: "https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:40.823856+00:00"
+instance: "kb-cron"
+---
+
+The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces. In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues; more precisely as spectral values of linear operators in Hilbert space.
+These formulations of quantum mechanics continue to be used today. At the heart of the description are ideas of quantum state and quantum observables, which are radically different from those used in previous models of physical reality. While the mathematics permits calculation of many quantities that can be measured experimentally, there is a definite theoretical limit to values that can be simultaneously measured. This limitation was first elucidated by Heisenberg through a thought experiment, and is represented mathematically in the new formalism by the non-commutativity of operators representing quantum observables.
+Prior to the development of quantum mechanics as a separate theory, the mathematics used in physics consisted mainly of formal mathematical analysis, beginning with calculus, and increasing in complexity up to differential geometry and partial differential equations. Probability theory was used in statistical mechanics. Geometric intuition played a strong role in the first two and, accordingly, theories of relativity were formulated entirely in terms of differential geometric concepts. The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the development of quantum mechanics (around 1925) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures. The most sophisticated example of this is the Sommerfeld–Wilson–Ishiwara quantization rule, which was formulated entirely on the classical phase space.
+
+== History of the formalism ==
+
+=== The "old quantum theory" and the need for new mathematics ===
+
+In the 1890s, Planck was able to derive the blackbody spectrum, which was later used to avoid the classical ultraviolet catastrophe by making the unorthodox assumption that, in the interaction of electromagnetic radiation with matter, energy could only be exchanged in discrete units which he called quanta. Planck postulated a direct proportionality between the frequency of radiation and the quantum of energy at that frequency. The proportionality constant, h, is now called the Planck constant in his honor.
+In 1905, Einstein explained certain features of the photoelectric effect by assuming that Planck's energy quanta were actual particles, which were later dubbed photons.
+
+All of these developments were phenomenological and challenged the theoretical physics of the time. Bohr and Sommerfeld went on to modify classical mechanics in an attempt to deduce the Bohr model from first principles. They proposed that, of all closed classical orbits traced by a mechanical system in its phase space, only the ones that enclosed an area which was a multiple of the Planck constant were actually allowed. The most sophisticated version of this formalism was the so-called Sommerfeld–Wilson–Ishiwara quantization. Although the Bohr model of the hydrogen atom could be explained in this way, the spectrum of the helium atom (classically an unsolvable 3-body problem) could not be predicted. The mathematical status of quantum theory remained uncertain for some time.
+In 1923, de Broglie proposed that wave–particle duality applied not only to photons but to electrons and every other physical system.
+The situation changed rapidly in the years 1925–1930, when working mathematical foundations were found through the groundbreaking work of Erwin Schrödinger, Werner Heisenberg, Max Born, Pascual Jordan, and the foundational work of John von Neumann, Hermann Weyl and Paul Dirac, and it became possible to unify several different approaches in terms of a fresh set of ideas. The physical interpretation of the theory was also clarified in these years after Werner Heisenberg discovered the uncertainty relations and Niels Bohr introduced the idea of complementarity.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-1.md b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-1.md
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+---
+title: "Mathematical formulation of quantum mechanics"
+chunk: 2/7
+source: "https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:40.823856+00:00"
+instance: "kb-cron"
+---
+
+=== The "new quantum theory" ===
+Werner Heisenberg's matrix mechanics was the first successful attempt at replicating the observed quantization of atomic spectra. Later in the same year, Schrödinger created his wave mechanics. Schrödinger's formalism was considered easier to understand, visualize and calculate as it led to differential equations, which physicists were already familiar with solving. Within a year, it was shown that the two theories were equivalent.
+Schrödinger himself initially did not understand the fundamental probabilistic nature of quantum mechanics, as he thought that the absolute square of the wave function of an electron should be interpreted as the charge density of an object smeared out over an extended, possibly infinite, volume of space. It was Max Born who introduced the interpretation of the absolute square of the wave function as the probability distribution of the position of a pointlike object. Born's idea was soon taken over by Niels Bohr in Copenhagen who then became the "father" of the Copenhagen interpretation of quantum mechanics. Schrödinger's wave function can be seen to be closely related to the classical Hamilton–Jacobi equation. The correspondence to classical mechanics was even more explicit, although somewhat more formal, in Heisenberg's matrix mechanics. In his PhD thesis project, Paul Dirac discovered that the equation for the operators in the Heisenberg representation, as it is now called, closely translates to classical equations for the dynamics of certain quantities in the Hamiltonian formalism of classical mechanics, when one expresses them through Poisson brackets, a procedure now known as canonical quantization.
+Already before Schrödinger, the young postdoctoral fellow Werner Heisenberg invented his matrix mechanics, which was the first correct quantum mechanics – the essential breakthrough. Heisenberg's matrix mechanics formulation was based on algebras of infinite matrices, a very radical formulation in light of the mathematics of classical physics, although he started from the index-terminology of the experimentalists of that time, not even aware that his "index-schemes" were matrices, as Born soon pointed out to him. In fact, in these early years, linear algebra was not generally popular with physicists in its present form.
+Although Schrödinger himself after a year proved the equivalence of his wave-mechanics and Heisenberg's matrix mechanics, the reconciliation of the two approaches and their modern abstraction as motions in Hilbert space is generally attributed to Paul Dirac, who wrote a lucid account in his 1930 classic The Principles of Quantum Mechanics. He is the third, and possibly most important, pillar of that field (he soon was the only one to have discovered a relativistic generalization of the theory). In his above-mentioned account, he introduced the bra–ket notation, together with an abstract formulation in terms of the Hilbert space used in functional analysis; he showed that Schrödinger's and Heisenberg's approaches were two different representations of the same theory, and found a third, most general one, which represented the dynamics of the system. His work was particularly fruitful in many types of generalizations of the field.
+The first complete mathematical formulation of this approach, known as the Dirac–von Neumann axioms, is generally credited to John von Neumann's 1932 book Mathematical Foundations of Quantum Mechanics, although Hermann Weyl had already referred to Hilbert spaces (which he called unitary spaces) in his 1927 classic paper and 1928 book. It was developed in parallel with a new approach to the mathematical spectral theory based on linear operators rather than the quadratic forms that were David Hilbert's approach a generation earlier. Though theories of quantum mechanics continue to evolve to this day, there is a basic framework for the mathematical formulation of quantum mechanics which underlies most approaches and can be traced back to the mathematical work of John von Neumann. In other words, discussions about interpretation of the theory, and extensions to it, are now mostly conducted on the basis of shared assumptions about the mathematical foundations.
+
+=== Later developments ===
+The application of the new quantum theory to electromagnetism resulted in quantum field theory, which was developed starting around 1930. Quantum field theory has driven the development of more sophisticated formulations of quantum mechanics, of which the ones presented here are simple special cases. 
+
+Path integral formulation
+Phase-space formulation of quantum mechanics & geometric quantization
+quantum field theory in curved spacetime
+axiomatic, algebraic and constructive quantum field theory
+C*-algebra formalism
+Generalized statistical model of quantum mechanics
+A related topic is the relationship to classical mechanics. Any new physical theory is supposed to reduce to successful old theories in some approximation. For quantum mechanics, this translates into the need to study the so-called classical limit of quantum mechanics. Also, as Bohr emphasized, human cognitive abilities and language are inextricably linked to the classical realm, and so classical descriptions are intuitively more accessible than quantum ones. In particular, quantization, namely the construction of a quantum theory whose classical limit is a given and known classical theory, becomes an important area of quantum physics in itself.
+Finally, some of the originators of quantum theory (notably Einstein and Schrödinger) were unhappy with what they thought were the philosophical implications of quantum mechanics. In particular, Einstein took the position that quantum mechanics must be incomplete, which motivated research into so-called hidden-variable theories. The issue of hidden variables has become in part an experimental issue with the help of quantum optics.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-2.md b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-2.md
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@@ -0,0 +1,521 @@
+---
+title: "Mathematical formulation of quantum mechanics"
+chunk: 3/7
+source: "https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:40.823856+00:00"
+instance: "kb-cron"
+---
+
+== Postulates of quantum mechanics ==
+A physical system is generally described by three basic ingredients: states; observables; and dynamics (or law of time evolution) or, more generally, a group of physical symmetries. A classical description can be given in a fairly direct way by a phase space model of mechanics: states are points in a phase space formulated by symplectic manifold, observables are real-valued functions on it, time evolution is given by a one-parameter group of symplectic transformations of the phase space, and physical symmetries are realized by symplectic transformations. A quantum description normally consists of a Hilbert space of states, observables are self-adjoint operators on the space of states, time evolution is given by a one-parameter group of unitary transformations on the Hilbert space of states, and physical symmetries are realized by unitary transformations. (It is possible, to map this Hilbert-space picture to a phase space formulation, invertibly. See below.)
+The following summary of the mathematical framework of quantum mechanics can be partly traced back to the Dirac–von Neumann axioms.
+
+=== Description of the state of a system ===
+Each isolated physical system is associated with a (topologically) separable complex Hilbert space H with inner product ⟨φ|ψ⟩.
+
+Separability is a mathematically convenient hypothesis, with the physical interpretation that the state is uniquely determined by countably many observations. Quantum states can be identified with equivalence classes in H, where two vectors (of length 1) represent the same state if they differ only by a phase factor:
+
+  
+    
+      
+        
+          |
+        
+        
+          ψ
+          
+            k
+          
+        
+        ⟩
+        ∼
+        
+          |
+        
+        
+          ψ
+          
+            l
+          
+        
+        ⟩
+        
+        
+        ⇔
+        
+        
+        
+          |
+        
+        
+          ψ
+          
+            k
+          
+        
+        ⟩
+        =
+        
+          e
+          
+            i
+            α
+          
+        
+        
+          |
+        
+        
+          ψ
+          
+            l
+          
+        
+        ⟩
+        ,
+        
+         
+        α
+        ∈
+        
+          R
+        
+        .
+      
+    
+    {\displaystyle |\psi _{k}\rangle \sim |\psi _{l}\rangle \;\;\Leftrightarrow \;\;|\psi _{k}\rangle =e^{i\alpha }|\psi _{l}\rangle ,\quad \ \alpha \in \mathbb {R} .}
+  
+
+As such, a quantum state is an element of a projective Hilbert space, conventionally termed a "ray".
+Accompanying Postulate I is the composite system postulate:
+
+In the presence of quantum entanglement, the quantum state of the composite system cannot be factored as a tensor product of states of its local constituents; Instead, it is expressed as a sum, or superposition, of tensor products of states of component subsystems. A subsystem in an entangled composite system generally cannot be described by a state vector (or a ray), but instead is described by a density operator; Such quantum state is known as a mixed state. The density operator of a mixed state is a trace class, nonnegative (positive semi-definite) self-adjoint operator 
+  
+    
+      
+        ρ
+      
+    
+    {\displaystyle \rho }
+  
+ normalized to be of trace 1. In turn, any density operator of a mixed state can be represented as a subsystem of a larger composite system in a pure state (see purification theorem).
+In the absence of quantum entanglement, the quantum state of the composite system is called a separable state. The density matrix of a bipartite system in a separable state can be expressed as 
+  
+    
+      
+        ρ
+        =
+        
+          ∑
+          
+            k
+          
+        
+        
+          p
+          
+            k
+          
+        
+        
+          ρ
+          
+            1
+          
+          
+            k
+          
+        
+        ⊗
+        
+          ρ
+          
+            2
+          
+          
+            k
+          
+        
+      
+    
+    {\displaystyle \rho =\sum _{k}p_{k}\rho _{1}^{k}\otimes \rho _{2}^{k}}
+  
+, where 
+  
+    
+      
+        
+        
+          ∑
+          
+            k
+          
+        
+        
+          p
+          
+            k
+          
+        
+        =
+        1
+      
+    
+    {\displaystyle \;\sum _{k}p_{k}=1}
+  
+. If there is only a single non-zero 
+  
+    
+      
+        
+          p
+          
+            k
+          
+        
+      
+    
+    {\displaystyle p_{k}}
+  
+, then the state can be expressed just as 
+  
+    
+      
+        ρ
+        =
+        
+          ρ
+          
+            1
+          
+        
+        ⊗
+        
+          ρ
+          
+            2
+          
+        
+        ,
+      
+    
+    {\textstyle \rho =\rho _{1}\otimes \rho _{2},}
+  
+ and is called simply separable or product state.
+
+=== Measurement on a system ===
+
+==== Description of physical quantities ====
+Physical observables are represented by Hermitian matrices on H. Since these operators are Hermitian, their eigenvalues are always real, and represent the possible outcomes/results from measuring the corresponding observable. If the spectrum of the observable is discrete, then the possible results are quantized.
+
+==== Results of measurement ====
+By spectral theory, we can associate a probability measure to the values of A in any state ψ. We can also show that the possible values of the observable A in any state must belong to the spectrum of A. The expectation value (in the sense of probability theory) of the observable A for the system in state represented by the unit vector ψ ∈ H is 
+  
+    
+      
+        ⟨
+        ψ
+        
+          |
+        
+        A
+        
+          |
+        
+        ψ
+        ⟩
+      
+    
+    {\displaystyle \langle \psi |A|\psi \rangle }
+  
+. If we represent the state ψ in the basis formed by the eigenvectors of A, then the square of the modulus of the component attached to a given eigenvector is the probability of observing its corresponding eigenvalue.
+
+For a mixed state ρ, the expected value of A in the state ρ is 
+  
+    
+      
+        tr
+        ⁡
+        (
+        A
+        ρ
+        )
+      
+    
+    {\displaystyle \operatorname {tr} (A\rho )}
+  
+, and the probability of obtaining an eigenvalue 
+  
+    
+      
+        
+          a
+          
+            n
+          
+        
+      
+    
+    {\displaystyle a_{n}}
+  
+ in a discrete, nondegenerate spectrum of the corresponding observable 
+  
+    
+      
+        A
+      
+    
+    {\displaystyle A}
+  
+ is given by 
+  
+    
+      
+        
+          P
+        
+        (
+        
+          a
+          
+            n
+          
+        
+        )
+        =
+        tr
+        ⁡
+        (
+        
+          |
+        
+        
+          a
+          
+            n
+          
+        
+        ⟩
+        ⟨
+        
+          a
+          
+            n
+          
+        
+        
+          |
+        
+        ρ
+        )
+        =
+        ⟨
+        
+          a
+          
+            n
+          
+        
+        
+          |
+        
+        ρ
+        
+          |
+        
+        
+          a
+          
+            n
+          
+        
+        ⟩
+      
+    
+    {\displaystyle \mathbb {P} (a_{n})=\operatorname {tr} (|a_{n}\rangle \langle a_{n}|\rho )=\langle a_{n}|\rho |a_{n}\rangle }
+  
+.
+If the eigenvalue 
+  
+    
+      
+        
+          a
+          
+            n
+          
+        
+      
+    
+    {\displaystyle a_{n}}
+  
+ has degenerate, orthonormal eigenvectors 
+  
+    
+      
+        {
+        
+          |
+        
+        
+          a
+          
+            n
+            1
+          
+        
+        ⟩
+        ,
+        
+          |
+        
+        
+          a
+          
+            n
+            2
+          
+        
+        ⟩
+        ,
+        …
+        ,
+        
+          |
+        
+        
+          a
+          
+            n
+            m
+          
+        
+        ⟩
+        }
+      
+    
+    {\displaystyle \{|a_{n1}\rangle ,|a_{n2}\rangle ,\dots ,|a_{nm}\rangle \}}
+  
+, then the projection operator onto the eigensubspace can be defined as the identity operator in the eigensubspace:
+
+  
+    
+      
+        
+          P
+          
+            n
+          
+        
+        =
+        
+          |
+        
+        
+          a
+          
+            n
+            1
+          
+        
+        ⟩
+        ⟨
+        
+          a
+          
+            n
+            1
+          
+        
+        
+          |
+        
+        +
+        
+          |
+        
+        
+          a
+          
+            n
+            2
+          
+        
+        ⟩
+        ⟨
+        
+          a
+          
+            n
+            2
+          
+        
+        
+          |
+        
+        +
+        ⋯
+        +
+        
+          |
+        
+        
+          a
+          
+            n
+            m
+          
+        
+        ⟩
+        ⟨
+        
+          a
+          
+            n
+            m
+          
+        
+        
+          |
+        
+        ,
+      
+    
+    {\displaystyle P_{n}=|a_{n1}\rangle \langle a_{n1}|+|a_{n2}\rangle \langle a_{n2}|+\dots +|a_{nm}\rangle \langle a_{nm}|,}
+  
+
+and then 
+  
+    
+      
+        
+          P
+        
+        (
+        
+          a
+          
+            n
+          
+        
+        )
+        =
+        tr
+        ⁡
+        (
+        
+          P
+          
+            n
+          
+        
+        ρ
+        )
+      
+    
+    {\displaystyle \mathbb {P} (a_{n})=\operatorname {tr} (P_{n}\rho )}
+  
+.
+Postulates II.a and II.b are collectively known as the Born rule of quantum mechanics.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-3.md b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-3.md
new file mode 100644
index 000000000..7bd53d0e9
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-3.md
@@ -0,0 +1,355 @@
+---
+title: "Mathematical formulation of quantum mechanics"
+chunk: 4/7
+source: "https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:40.823856+00:00"
+instance: "kb-cron"
+---
+
+==== Effect of measurement on the state ====
+When a measurement is performed, only one result is obtained (according to some interpretations of quantum mechanics). This is modeled mathematically as the processing of additional information from the measurement, confining the probabilities of an immediate second measurement of the same observable. In the case of a discrete, non-degenerate spectrum, two sequential measurements of the same observable will always give the same value assuming the second immediately follows the first. Therefore, the state vector must change as a result of measurement, and collapse onto the eigensubspace associated with the eigenvalue measured. 
+For a mixed state ρ, after obtaining an eigenvalue 
+  
+    
+      
+        
+          a
+          
+            n
+          
+        
+      
+    
+    {\displaystyle a_{n}}
+  
+ in a discrete, nondegenerate spectrum of the corresponding observable 
+  
+    
+      
+        A
+      
+    
+    {\displaystyle A}
+  
+, the updated state is given by 
+  
+    
+      
+        
+          ρ
+          ′
+        
+        =
+        
+          
+            
+              
+                P
+                
+                  n
+                
+              
+              ρ
+              
+                P
+                
+                  n
+                
+                
+                  †
+                
+              
+            
+            
+              tr
+              ⁡
+              (
+              
+                P
+                
+                  n
+                
+              
+              ρ
+              
+                P
+                
+                  n
+                
+                
+                  †
+                
+              
+              )
+            
+          
+        
+      
+    
+    {\textstyle \rho '={\frac {P_{n}\rho P_{n}^{\dagger }}{\operatorname {tr} (P_{n}\rho P_{n}^{\dagger })}}}
+  
+. If the eigenvalue 
+  
+    
+      
+        
+          a
+          
+            n
+          
+        
+      
+    
+    {\displaystyle a_{n}}
+  
+ has degenerate, orthonormal eigenvectors 
+  
+    
+      
+        {
+        
+          |
+        
+        
+          a
+          
+            n
+            1
+          
+        
+        ⟩
+        ,
+        
+          |
+        
+        
+          a
+          
+            n
+            2
+          
+        
+        ⟩
+        ,
+        …
+        ,
+        
+          |
+        
+        
+          a
+          
+            n
+            m
+          
+        
+        ⟩
+        }
+      
+    
+    {\displaystyle \{|a_{n1}\rangle ,|a_{n2}\rangle ,\dots ,|a_{nm}\rangle \}}
+  
+, then the projection operator onto the eigensubspace is 
+  
+    
+      
+        
+          P
+          
+            n
+          
+        
+        =
+        
+          |
+        
+        
+          a
+          
+            n
+            1
+          
+        
+        ⟩
+        ⟨
+        
+          a
+          
+            n
+            1
+          
+        
+        
+          |
+        
+        +
+        
+          |
+        
+        
+          a
+          
+            n
+            2
+          
+        
+        ⟩
+        ⟨
+        
+          a
+          
+            n
+            2
+          
+        
+        
+          |
+        
+        +
+        ⋯
+        +
+        
+          |
+        
+        
+          a
+          
+            n
+            m
+          
+        
+        ⟩
+        ⟨
+        
+          a
+          
+            n
+            m
+          
+        
+        
+          |
+        
+      
+    
+    {\displaystyle P_{n}=|a_{n1}\rangle \langle a_{n1}|+|a_{n2}\rangle \langle a_{n2}|+\dots +|a_{nm}\rangle \langle a_{nm}|}
+  
+.
+Postulates II.c is sometimes called the "state update rule" or "collapse rule"; Together with the Born rule (Postulates II.a and II.b), they form a complete representation of measurements, and are sometimes collectively called the measurement postulate(s).
+Note that the projection-valued measures (PVM) described in the measurement postulate(s) can be generalized to positive operator-valued measures (POVM), which is the most general kind of measurement in quantum mechanics. A POVM can be understood as the effect on a component subsystem when a PVM is performed on a larger, composite system (see Naimark's dilation theorem).
+
+=== Time evolution of a system ===
+The Schrödinger equation describes how a state vector evolves in time. Depending on the text, it may be derived from some other assumptions, motivated on heuristic grounds, or asserted as a postulate. Derivations include using the de Broglie relation between wavelength and momentum or path integrals.
+
+Equivalently, the time evolution postulate can be stated as:
+
+For a closed system in a mixed state ρ, the time evolution is 
+  
+    
+      
+        ρ
+        (
+        t
+        )
+        =
+        U
+        (
+        t
+        ;
+        
+          t
+          
+            0
+          
+        
+        )
+        ρ
+        (
+        
+          t
+          
+            0
+          
+        
+        )
+        
+          U
+          
+            †
+          
+        
+        (
+        t
+        ;
+        
+          t
+          
+            0
+          
+        
+        )
+      
+    
+    {\displaystyle \rho (t)=U(t;t_{0})\rho (t_{0})U^{\dagger }(t;t_{0})}
+  
+.
+The evolution of an open quantum system can be described by quantum operations (in an operator sum formalism) and quantum instruments, and generally does not have to be unitary.
+
+=== Other implications of the postulates ===
+Physical symmetries act on the Hilbert space of quantum states unitarily or antiunitarily due to Wigner's theorem (supersymmetry is another matter entirely).
+Density operators are those that are in the closure of the convex hull of the one-dimensional orthogonal projectors. Conversely, one-dimensional orthogonal projectors are extreme points of the set of density operators. Physicists also call one-dimensional orthogonal projectors pure states and other density operators mixed states.
+One can in this formalism state Heisenberg's uncertainty principle and prove it as a theorem, although the exact historical sequence of events, concerning who derived what and under which framework, is the subject of historical investigations outside the scope of this article.
+Furthermore, to the postulates of quantum mechanics one should also add basic statements on the properties of spin and Pauli's exclusion principle, see below.
+
+=== Spin ===
+In addition to their other properties, all particles possess a quantity called spin, an intrinsic angular momentum. Despite the name, particles do not literally spin around an axis, and quantum mechanical spin has no correspondence in classical physics. In the position representation, a spinless wavefunction has position r and time t as continuous variables, ψ = ψ(r, t). For spin wavefunctions the spin is an additional discrete variable: ψ = ψ(r, t, σ), where σ takes the values;
+
+  
+    
+      
+        σ
+        =
+        −
+        S
+        ℏ
+        ,
+        −
+        (
+        S
+        −
+        1
+        )
+        ℏ
+        ,
+        …
+        ,
+        0
+        ,
+        …
+        ,
+        +
+        (
+        S
+        −
+        1
+        )
+        ℏ
+        ,
+        +
+        S
+        ℏ
+        
+        .
+      
+    
+    {\displaystyle \sigma =-S\hbar ,-(S-1)\hbar ,\dots ,0,\dots ,+(S-1)\hbar ,+S\hbar \,.}
+  
+
+That is, the state of a single particle with spin S is represented by a (2S + 1)-component spinor of complex-valued wave functions.
+Two classes of particles with very different behaviour are bosons which have integer spin (S = 0, 1, 2, ...), and fermions possessing half-integer spin (S = 1⁄2, 3⁄2, 5⁄2, ...).
+
+=== Symmetrization postulate ===
+
+In quantum mechanics, two particles can be distinguished from one another using two methods. By performing a measurement of intrinsic properties of each particle, particles of different types can be distinguished. Otherwise, if the particles are identical, their trajectories can be tracked which distinguishes the particles based on the locality of each particle. While the second method is permitted in classical mechanics, (i.e. all classical particles are treated with distinguishability), the same cannot be said for quantum mechanical particles since the process is infeasible due to the fundamental uncertainty principles that govern small scales. Hence the requirement of indistinguishability of quantum particles is presented by the symmetrization postulate. The postulate is applicable to a system of bosons or fermions, for example, in predicting the spectra of helium atom. The postulate, explained in the following sections, can be stated as follows:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-4.md b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-4.md
new file mode 100644
index 000000000..99278ebea
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-4.md
@@ -0,0 +1,647 @@
+---
+title: "Mathematical formulation of quantum mechanics"
+chunk: 5/7
+source: "https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:40.823856+00:00"
+instance: "kb-cron"
+---
+
+Exceptions can occur when the particles are constrained to two spatial dimensions where existence of particles known as anyons are possible which are said to have a continuum of statistical properties spanning the range between fermions and bosons. The connection between behaviour of identical particles and their spin is given by spin statistics theorem.
+It can be shown that two particles localized in different regions of space can still be represented using a symmetrized/antisymmetrized wavefunction and that independent treatment of these wavefunctions gives the same result. Hence the symmetrization postulate is applicable in the general case of a system of identical particles.
+
+==== Exchange Degeneracy ====
+In a system of identical particles, let P be known as exchange operator that acts on the wavefunction as:
+
+  
+    
+      
+        P
+        
+          
+            (
+          
+        
+        ⋯
+        
+          |
+        
+        ψ
+        ⟩
+        
+          |
+        
+        ϕ
+        ⟩
+        ⋯
+        
+          
+            )
+          
+        
+        ≡
+        ⋯
+        
+          |
+        
+        ϕ
+        ⟩
+        
+          |
+        
+        ψ
+        ⟩
+        ⋯
+      
+    
+    {\displaystyle P{\bigg (}\cdots |\psi \rangle |\phi \rangle \cdots {\bigg )}\equiv \cdots |\phi \rangle |\psi \rangle \cdots }
+  
+
+If a physical system of identical particles is given, wavefunction of all particles can be well known from observation but these cannot be labelled to each particle. Thus, the above exchanged wavefunction represents the same physical state as the original state which implies that the wavefunction is not unique. This is known as exchange degeneracy.
+More generally, consider a linear combination of such states, 
+  
+    
+      
+        
+          |
+        
+        Ψ
+        ⟩
+      
+    
+    {\displaystyle |\Psi \rangle }
+  
+. For the best representation of the physical system, we expect this to be an eigenvector of P since exchange operator is not excepted to give completely different vectors in projective Hilbert space. Since 
+  
+    
+      
+        
+          P
+          
+            2
+          
+        
+        =
+        1
+      
+    
+    {\displaystyle P^{2}=1}
+  
+, the possible eigenvalues of P are +1 and −1. The 
+  
+    
+      
+        
+          |
+        
+        Ψ
+        ⟩
+      
+    
+    {\displaystyle |\Psi \rangle }
+  
+ states for identical particle system are represented as symmetric for +1 eigenvalue or antisymmetric for -1 eigenvalue as follows:
+
+  
+    
+      
+        P
+        
+          |
+        
+        ⋯
+        
+          n
+          
+            i
+          
+        
+        ,
+        
+          n
+          
+            j
+          
+        
+        ⋯
+        ;
+        S
+        ⟩
+        =
+        +
+        
+          |
+        
+        ⋯
+        
+          n
+          
+            i
+          
+        
+        ,
+        
+          n
+          
+            j
+          
+        
+        ⋯
+        ;
+        S
+        ⟩
+      
+    
+    {\displaystyle P|\cdots n_{i},n_{j}\cdots ;S\rangle =+|\cdots n_{i},n_{j}\cdots ;S\rangle }
+  
+
+  
+    
+      
+        P
+        
+          |
+        
+        ⋯
+        
+          n
+          
+            i
+          
+        
+        ,
+        
+          n
+          
+            j
+          
+        
+        ⋯
+        ;
+        A
+        ⟩
+        =
+        −
+        
+          |
+        
+        ⋯
+        
+          n
+          
+            i
+          
+        
+        ,
+        
+          n
+          
+            j
+          
+        
+        ⋯
+        ;
+        A
+        ⟩
+      
+    
+    {\displaystyle P|\cdots n_{i},n_{j}\cdots ;A\rangle =-|\cdots n_{i},n_{j}\cdots ;A\rangle }
+  
+
+The explicit symmetric/antisymmetric form of 
+  
+    
+      
+        
+          |
+        
+        Ψ
+        ⟩
+      
+    
+    {\displaystyle |\Psi \rangle }
+  
+ is constructed using a symmetrizer or antisymmetrizer operator. Particles that form symmetric states are called bosons and those that form antisymmetric states are called as fermions. The relation of spin with this classification is given from spin statistics theorem which shows that integer spin particles are bosons and half integer spin particles are fermions.
+
+==== Pauli exclusion principle ====
+The property of spin relates to another basic property concerning systems of N identical particles: the Pauli exclusion principle, which is a consequence of the following permutation behaviour of an N-particle wave function; again in the position representation one must postulate that for the transposition of any two of the N particles one always should have
+
+i.e., on transposition of the arguments of any two particles the wavefunction should reproduce, apart from a prefactor (−1)2S which is +1 for bosons, but (−1) for fermions.
+Electrons are fermions with S = 1/2; quanta of light are bosons with S = 1.
+Due to the form of anti-symmetrized wavefunction:
+
+  
+    
+      
+        
+          Ψ
+          
+            
+              n
+              
+                1
+              
+            
+            ⋯
+            
+              n
+              
+                N
+              
+            
+          
+          
+            (
+            A
+            )
+          
+        
+        (
+        
+          x
+          
+            1
+          
+        
+        ,
+        …
+        ,
+        
+          x
+          
+            N
+          
+        
+        )
+        =
+        
+          
+            1
+            
+              N
+              !
+            
+          
+        
+        
+          |
+          
+            
+              
+                
+                  
+                    ψ
+                    
+                      
+                        n
+                        
+                          1
+                        
+                      
+                    
+                  
+                  (
+                  
+                    x
+                    
+                      1
+                    
+                  
+                  )
+                
+                
+                  
+                    ψ
+                    
+                      
+                        n
+                        
+                          1
+                        
+                      
+                    
+                  
+                  (
+                  
+                    x
+                    
+                      2
+                    
+                  
+                  )
+                
+                
+                  ⋯
+                
+                
+                  
+                    ψ
+                    
+                      
+                        n
+                        
+                          1
+                        
+                      
+                    
+                  
+                  (
+                  
+                    x
+                    
+                      N
+                    
+                  
+                  )
+                
+              
+              
+                
+                  
+                    ψ
+                    
+                      
+                        n
+                        
+                          2
+                        
+                      
+                    
+                  
+                  (
+                  
+                    x
+                    
+                      1
+                    
+                  
+                  )
+                
+                
+                  
+                    ψ
+                    
+                      
+                        n
+                        
+                          2
+                        
+                      
+                    
+                  
+                  (
+                  
+                    x
+                    
+                      2
+                    
+                  
+                  )
+                
+                
+                  ⋯
+                
+                
+                  
+                    ψ
+                    
+                      
+                        n
+                        
+                          2
+                        
+                      
+                    
+                  
+                  (
+                  
+                    x
+                    
+                      N
+                    
+                  
+                  )
+                
+              
+              
+                
+                  ⋮
+                
+                
+                  ⋮
+                
+                
+                  ⋱
+                
+                
+                  ⋮
+                
+              
+              
+                
+                  
+                    ψ
+                    
+                      
+                        n
+                        
+                          N
+                        
+                      
+                    
+                  
+                  (
+                  
+                    x
+                    
+                      1
+                    
+                  
+                  )
+                
+                
+                  
+                    ψ
+                    
+                      
+                        n
+                        
+                          N
+                        
+                      
+                    
+                  
+                  (
+                  
+                    x
+                    
+                      2
+                    
+                  
+                  )
+                
+                
+                  ⋯
+                
+                
+                  
+                    ψ
+                    
+                      
+                        n
+                        
+                          N
+                        
+                      
+                    
+                  
+                  (
+                  
+                    x
+                    
+                      N
+                    
+                  
+                  )
+                
+              
+            
+          
+          |
+        
+      
+    
+    {\displaystyle \Psi _{n_{1}\cdots n_{N}}^{(A)}(x_{1},\ldots ,x_{N})={\frac {1}{\sqrt {N!}}}\left|{\begin{matrix}\psi _{n_{1}}(x_{1})&\psi _{n_{1}}(x_{2})&\cdots &\psi _{n_{1}}(x_{N})\\\psi _{n_{2}}(x_{1})&\psi _{n_{2}}(x_{2})&\cdots &\psi _{n_{2}}(x_{N})\\\vdots &\vdots &\ddots &\vdots \\\psi _{n_{N}}(x_{1})&\psi _{n_{N}}(x_{2})&\cdots &\psi _{n_{N}}(x_{N})\\\end{matrix}}\right|}
+  
+
+if the wavefunction of each particle is completely determined by a set of quantum numbers, then two fermions cannot share the same set of quantum numbers since the resulting function cannot be anti-symmetrized (i.e. above formula gives zero). The same cannot be said of Bosons since their wavefunction is:
+
+  
+    
+      
+        
+          |
+        
+        
+          x
+          
+            1
+          
+        
+        
+          x
+          
+            2
+          
+        
+        ⋯
+        
+          x
+          
+            N
+          
+        
+        ;
+        S
+        ⟩
+        =
+        
+          
+            
+              
+                ∏
+                
+                  j
+                
+              
+              
+                n
+                
+                  j
+                
+              
+              !
+            
+            
+              N
+              !
+            
+          
+        
+        
+          ∑
+          
+            p
+          
+        
+        
+          |
+          
+            x
+            
+              p
+              (
+              1
+              )
+            
+          
+          ⟩
+        
+        
+          |
+          
+            x
+            
+              p
+              (
+              2
+              )
+            
+          
+          ⟩
+        
+        ⋯
+        
+          |
+          
+            x
+            
+              p
+              (
+              N
+              )
+            
+          
+          ⟩
+        
+      
+    
+    {\displaystyle |x_{1}x_{2}\cdots x_{N};S\rangle ={\frac {\prod _{j}n_{j}!}{N!}}\sum _{p}\left|x_{p(1)}\right\rangle \left|x_{p(2)}\right\rangle \cdots \left|x_{p(N)}\right\rangle }
+  
+
+where 
+  
+    
+      
+        
+          n
+          
+            j
+          
+        
+      
+    
+    {\displaystyle n_{j}}
+  
+ is the number of particles with same wavefunction.
+
+==== Exceptions for symmetrization postulate ====
+In nonrelativistic quantum mechanics all particles are either bosons or fermions; in relativistic quantum theories also "supersymmetric" theories exist, where a particle is a linear combination of a bosonic and a fermionic part. Only in dimension d = 2 can one construct entities where (−1)2S is replaced by an arbitrary complex number with magnitude 1, called anyons. In relativistic quantum mechanics, spin statistic theorem can prove that under certain set of assumptions that the integer spins particles are classified as bosons and half spin particles are classified as fermions. Anyons which form neither symmetric nor antisymmetric states are said to have fractional spin.
+Although spin and the Pauli principle can only be derived from relativistic generalizations of quantum mechanics, the properties mentioned in the last two paragraphs belong to the basic postulates already in the non-relativistic limit. Especially, many important properties in natural science, e.g. the periodic system of chemistry, are consequences of the two properties.
+
+== Mathematical structure of quantum mechanics ==
+
+=== Pictures of dynamics ===
+
+Summary:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-5.md b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-5.md
new file mode 100644
index 000000000..19f0956ec
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-5.md
@@ -0,0 +1,315 @@
+---
+title: "Mathematical formulation of quantum mechanics"
+chunk: 6/7
+source: "https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:40.823856+00:00"
+instance: "kb-cron"
+---
+
+=== Representations ===
+The original form of the Schrödinger equation depends on choosing a particular representation of Heisenberg's canonical commutation relations. The Stone–von Neumann theorem dictates that all irreducible representations of the finite-dimensional Heisenberg commutation relations are unitarily equivalent. A systematic understanding of its consequences has led to the phase space formulation of quantum mechanics, which works in full phase space instead of Hilbert space, so then with a more intuitive link to the classical limit thereof. This picture also simplifies considerations
+of quantization, the deformation extension from classical to quantum mechanics.
+The quantum harmonic oscillator is an exactly solvable system where the different representations are easily compared. There, apart from the Heisenberg, or Schrödinger (position or momentum), or phase-space representations, one also encounters the Fock (number) representation and the Segal–Bargmann (Fock-space or coherent state) representation (named after Irving Segal and Valentine Bargmann). All four are unitarily equivalent.
+
+=== Time as an operator ===
+The framework presented so far singles out time as the parameter that everything depends on. It is possible to formulate mechanics in such a way that time becomes itself an observable associated with a self-adjoint operator. At the classical level, it is possible to arbitrarily parameterize the trajectories of particles in terms of an unphysical parameter s, and in that case the time t becomes an additional generalized coordinate of the physical system. At the quantum level, translations in s would be generated by a "Hamiltonian" H − E, where E is the energy operator and H is the "ordinary" Hamiltonian. However, since s is an unphysical parameter, physical states must be left invariant by "s-evolution", and so the physical state space is the kernel of H − E (this requires the use of a rigged Hilbert space and a renormalization of the norm).
+This is related to the quantization of constrained systems and quantization of gauge theories. It
+is also possible to formulate a quantum theory of "events" where time becomes an observable.
+
+== Problem of measurement ==
+
+The picture given in the preceding paragraphs is sufficient for description of a completely isolated system. However, it fails to account for one of the main differences between quantum mechanics and classical mechanics, that is, the effects of measurement. The von Neumann description of quantum measurement of an observable A, when the system is prepared in a pure state ψ is the following (note, however, that von Neumann's description dates back to the 1930s and is based on experiments as performed during that time – more specifically the Compton–Simon experiment; it is not applicable to most present-day measurements within the quantum domain):
+
+Let A have spectral resolution 
+  
+    
+      
+        A
+        =
+        ∫
+        λ
+        
+        d
+        
+          E
+          
+            A
+          
+        
+        ⁡
+        (
+        λ
+        )
+        ,
+      
+    
+    {\displaystyle A=\int \lambda \,d\operatorname {E} _{A}(\lambda ),}
+  
+ where EA is the resolution of the identity (also called projection-valued measure) associated with A. Then the probability of the measurement outcome lying in an interval B of R is |EA(B) ψ|2. In other words, the probability is obtained by integrating the characteristic function of B against the countably additive measure 
+  
+    
+      
+        ⟨
+        ψ
+        ∣
+        
+          E
+          
+            A
+          
+        
+        ⁡
+        ψ
+        ⟩
+        .
+      
+    
+    {\displaystyle \langle \psi \mid \operatorname {E} _{A}\psi \rangle .}
+  
+
+If the measured value is contained in B, then immediately after the measurement, the system will be in the (generally non-normalized) state EA(B)ψ. If the measured value does not lie in B, replace B by its complement for the above state.
+For example, suppose the state space is the n-dimensional complex Hilbert space Cn and A is a Hermitian matrix with eigenvalues λi, with corresponding eigenvectors ψi. The projection-valued measure associated with A, EA, is then
+
+  
+    
+      
+        
+          E
+          
+            A
+          
+        
+        ⁡
+        (
+        B
+        )
+        =
+        
+          |
+        
+        
+          ψ
+          
+            i
+          
+        
+        ⟩
+        ⟨
+        
+          ψ
+          
+            i
+          
+        
+        
+          |
+        
+        ,
+      
+    
+    {\displaystyle \operatorname {E} _{A}(B)=|\psi _{i}\rangle \langle \psi _{i}|,}
+  
+
+where B is a Borel set containing only the single eigenvalue λi. If the system is prepared in state
+
+  
+    
+      
+        
+          |
+        
+        ψ
+        ⟩
+      
+    
+    {\displaystyle |\psi \rangle }
+  
+
+Then the probability of a measurement returning the value λi can be calculated by integrating the spectral measure
+
+  
+    
+      
+        ⟨
+        ψ
+        ∣
+        
+          E
+          
+            A
+          
+        
+        ⁡
+        ψ
+        ⟩
+      
+    
+    {\displaystyle \langle \psi \mid \operatorname {E} _{A}\psi \rangle }
+  
+
+over Bi. This gives trivially
+
+  
+    
+      
+        ⟨
+        ψ
+        
+          |
+        
+        
+          ψ
+          
+            i
+          
+        
+        ⟩
+        ⟨
+        
+          ψ
+          
+            i
+          
+        
+        ∣
+        ψ
+        ⟩
+        =
+        
+          |
+        
+        ⟨
+        ψ
+        ∣
+        
+          ψ
+          
+            i
+          
+        
+        ⟩
+        
+          
+            |
+          
+          
+            2
+          
+        
+        .
+      
+    
+    {\displaystyle \langle \psi |\psi _{i}\rangle \langle \psi _{i}\mid \psi \rangle =|\langle \psi \mid \psi _{i}\rangle |^{2}.}
+  
+
+The characteristic property of the von Neumann measurement scheme is that repeating the same measurement will give the same results. This is also called the projection postulate.
+A more general formulation replaces the projection-valued measure with a positive-operator valued measure (POVM). To illustrate, take again the finite-dimensional case. Here we would replace the rank-1 projections
+
+  
+    
+      
+        
+          |
+        
+        
+          ψ
+          
+            i
+          
+        
+        ⟩
+        ⟨
+        
+          ψ
+          
+            i
+          
+        
+        
+          |
+        
+      
+    
+    {\displaystyle |\psi _{i}\rangle \langle \psi _{i}|}
+  
+
+by a finite set of positive operators
+
+  
+    
+      
+        
+          F
+          
+            i
+          
+        
+        
+          F
+          
+            i
+          
+          
+            ∗
+          
+        
+      
+    
+    {\displaystyle F_{i}F_{i}^{*}}
+  
+
+whose sum is still the identity operator as before (the resolution of identity). Just as a set of possible outcomes {λ1 ... λn}  is associated to a projection-valued measure, the same can be said for a POVM. Suppose the measurement outcome is λi. Instead of collapsing to the (unnormalized) state
+
+  
+    
+      
+        
+          |
+        
+        
+          ψ
+          
+            i
+          
+        
+        ⟩
+        ⟨
+        
+          ψ
+          
+            i
+          
+        
+        
+          |
+        
+        ψ
+        ⟩
+      
+    
+    {\displaystyle |\psi _{i}\rangle \langle \psi _{i}|\psi \rangle }
+  
+
+after the measurement, the system now will be in the state
+
+  
+    
+      
+        
+          F
+          
+            i
+          
+        
+        
+          |
+        
+        ψ
+        ⟩
+        .
+      
+    
+    {\displaystyle F_{i}|\psi \rangle .}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-6.md b/data/en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics-6.md
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+---
+title: "Mathematical formulation of quantum mechanics"
+chunk: 7/7
+source: "https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:40.823856+00:00"
+instance: "kb-cron"
+---
+
+Since the Fi Fi* operators need not be mutually orthogonal projections, the projection postulate of von Neumann no longer holds.
+The same formulation applies to general mixed states.
+In von Neumann's approach, the state transformation due to measurement is distinct from that due to time evolution in several ways. For example, time evolution is deterministic and unitary whereas measurement is non-deterministic and non-unitary. However, since both types of state transformation take one quantum state to another, this difference was viewed by many as unsatisfactory. The POVM formalism views measurement as one among many other quantum operations, which are described by completely positive maps which do not increase the trace.
+
+== List of mathematical tools ==
+Part of the folklore of the subject concerns the mathematical physics textbook Methods of Mathematical Physics put together by Richard Courant from David Hilbert's Göttingen University courses. The story is told (by mathematicians) that physicists had dismissed the material as not interesting in the current research areas, until the advent of Schrödinger's equation. At that point it was realised that the mathematics of the new quantum mechanics was already laid out in it. It is also said that Heisenberg had consulted Hilbert about his matrix mechanics, and Hilbert observed that his own experience with infinite-dimensional matrices had derived from differential equations, advice which Heisenberg ignored, missing the opportunity to unify the theory as Weyl and Dirac did a few years later. Whatever the basis of the anecdotes, the mathematics of the theory was conventional at the time, whereas the physics was radically new.
+The main tools include:
+
+linear algebra: complex numbers, eigenvectors, eigenvalues
+functional analysis: Hilbert spaces, linear operators, spectral theory
+differential equations: partial differential equations, separation of variables, ordinary differential equations, Sturm–Liouville theory, eigenfunctions
+harmonic analysis: Fourier transforms
+
+== See also ==
+List of mathematical topics in quantum theory
+Quantum foundations
+Symmetry in quantum mechanics
+
+== Notes ==
+
+== References ==
+Bäuerle, Gerard G. A.; de Kerf, Eddy A. (1990). Lie Algebras, Part 1: Finite and Infinite Dimensional Lie Algebras and Applications in Physics. Studies in Mathematical Physics. Amsterdam: North Holland. ISBN 0-444-88776-8.
+Byron, Frederick W.; Fuller, Robert W. (1992). Mathematics of Classical and Quantum Physics. New York: Courier Corporation. ISBN 978-0-486-67164-2.
+Cohen-Tannoudji, Claude; Diu, Bernard; Laloë, Franck (2020). Quantum mechanics. Volume 2: Angular momentum, spin, and approximation methods. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA. ISBN 978-3-527-82272-0.
+Dirac, P. A. M. (1925). "The Fundamental Equations of Quantum Mechanics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 109 (752): 642–653. Bibcode:1925RSPSA.109..642D. doi:10.1098/rspa.1925.0150.
+Edwards, David A. (1979). "The mathematical foundations of quantum mechanics". Synthese. 42 (1). Springer Science and Business Media LLC: 1–70. doi:10.1007/bf00413704. ISSN 0039-7857. S2CID 46969028.
+Greenstein, George; Zajonc, Arthur (2006). The Quantum Challenge. Sudbury, Mass.: Jones & Bartlett Learning. ISBN 978-0-7637-2470-2.
+Jauch, J. M.; Wigner, E. P.; Yanase, M. M. (1997). "Some Comments Concerning Measurements in Quantum Mechanics". Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 475–482. doi:10.1007/978-3-662-09203-3_52. ISBN 978-3-642-08179-8.
+Solem, J. C.; Biedenharn, L. C. (1993). "Understanding geometrical phases in quantum mechanics: An elementary example". Foundations of Physics. 23 (2): 185–195. Bibcode:1993FoPh...23..185S. doi:10.1007/BF01883623. S2CID 121930907.
+Streater, Raymond Frederick; Wightman, Arthur Strong (2000). PCT, Spin and Statistics, and All that. Princeton, NJ: Princeton University Press. ISBN 978-0-691-07062-9.
+Sakurai, Jun John; Napolitano, Jim (2021). Modern quantum mechanics (3rd ed.). Cambridge: Cambridge University Press. ISBN 978-1-108-47322-4.
+Weyl, Hermann (1950) [1931]. The Theory of Groups and Quantum Mechanics. Translated by Robertson, H. P. Dover. Bibcode:1950tgqm.book.....W.
+
+== Further reading ==
+Auyang, Sunny Y. (1995). How is Quantum Field Theory Possible?. New York, NY: Oxford University Press on Demand. ISBN 978-0-19-509344-5.
+Emch, Gérard G. (1972). Algebraic Methods in Statistical Mechanics and Quantum Field Theory. New York: John Wiley & Sons. ISBN 0-471-23900-3.
+Giachetta, Giovanni; Mangiarotti, Luigi; Sardanashvily, Gennadi (2005). Geometric and Algebraic Topological Methods in Quantum Mechanics. WORLD SCIENTIFIC. arXiv:math-ph/0410040. doi:10.1142/5731. ISBN 978-981-256-129-9.
+Gleason, Andrew M. (1957). "Measures on the Closed Subspaces of a Hilbert Space". Journal of Mathematics and Mechanics. 6 (6). Indiana University Mathematics Department: 885–893. JSTOR 24900629.
+Hall, Brian C. (2013). Quantum Theory for Mathematicians. Graduate Texts in Mathematics. Vol. 267. New York, NY: Springer New York. Bibcode:2013qtm..book.....H. doi:10.1007/978-1-4614-7116-5. ISBN 978-1-4614-7115-8. ISSN 0072-5285. S2CID 117837329.
+Jauch, Josef Maria (1968). Foundations of Quantum Mechanics. Reading, Mass.: Addison-Wesley. ISBN 0-201-03298-8.
+Jost, R. (1965). The General Theory of Quantized Fields. Lectures in applied mathematics. American Mathematical Society.
+Kuhn, Thomas S. (1987). Black-Body Theory and the Quantum Discontinuity, 1894-1912. Chicago: University of Chicago Press. ISBN 978-0-226-45800-7.
+Landsman, Klaas (2017). Foundations of Quantum Theory. Fundamental Theories of Physics. Vol. 188. Cham: Springer International Publishing. doi:10.1007/978-3-319-51777-3. ISBN 978-3-319-51776-6. ISSN 0168-1222.
+Mackey, George W. (2004). Mathematical Foundations of Quantum Mechanics. Mineola, N.Y: Courier Corporation. ISBN 978-0-486-43517-6.
+McMahon, David (2013). Quantum Mechanics Demystified, 2nd Edition (PDF). New York, NY: McGraw-Hill Prof Med/Tech. ISBN 978-0-07-176563-3.
+Moretti, Valter (2017). Spectral Theory and Quantum Mechanics. Unitext. Vol. 110. Cham: Springer International Publishing. doi:10.1007/978-3-319-70706-8. ISBN 978-3-319-70705-1. ISSN 2038-5714. S2CID 125121522.
+Moretti, Valter (2019). Fundamental Mathematical Structures of Quantum Theory. Cham: Springer International Publishing. doi:10.1007/978-3-030-18346-2. ISBN 978-3-030-18345-5. S2CID 197485828.
+Prugovecki, Eduard (2006). Quantum Mechanics in Hilbert Space. Mineola, NY: Courier Dover Publications. ISBN 978-0-486-45327-9.
+Reed, Michael; Simon, Barry (1972). Methods of Modern Mathematical Physics. New York: Academic Press. ISBN 978-0-12-585001-8.
+Shankar, R. (2013). Principles of Quantum Mechanics (PDF). Springer. ISBN 978-1-4615-7675-4.
+Teschl, Gerald (2009). Mathematical Methods in Quantum Mechanics (PDF). Providence, R.I: American Mathematical Soc. ISBN 978-0-8218-4660-5.
+von Neumann, John (2018). Mathematical Foundations of Quantum Mechanics. Princeton Oxford: Princeton University Press. ISBN 978-0-691-17856-1.
+Weaver, Nik (2001). Mathematical Quantization. Chapman and Hall/CRC. doi:10.1201/9781420036237. ISBN 978-0-429-07514-8.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Matthias_rules-0.md b/data/en.wikipedia.org/wiki/Matthias_rules-0.md
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+++ b/data/en.wikipedia.org/wiki/Matthias_rules-0.md
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+---
+title: "Matthias rules"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Matthias_rules"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:42.092869+00:00"
+instance: "kb-cron"
+---
+
+In physics, the Matthias rules refers to a historical set of empirical guidelines on how to find superconductors. These rules were authored Bernd T. Matthias who discovered hundreds of superconductors using these principles in the 1950s and 1960s. Deviations from these rules have been found since the end of the 1970s with the discovery of unconventional superconductors.
+
+
+== History ==
+
+Superconductivity was first discovered in solid mercury in 1911 by Heike Kamerlingh Onnes and Gilles Holst, who had developed new techniques to reach near-absolute zero temperatures.
+In subsequent decades, superconductivity was found in several other materials; In 1913, lead at 7 K, in 1930's niobium at 10 K, and in 1941 niobium nitride at 16 K.
+In 1933, Walther Meissner and Robert Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon that has come to be known as the Meissner effect. 
+Bernd T. Matthias and John Kenneth Hulm were encouraged by Enrico Fermi to start a systematic experimental investigation in the 1950s, looking for superconductors in different elements and compounds. For this reason, they developed a technique based on the Meissner effect. 
+In collaboration with Theodore H. Geballe, Matthias broke the record in 1954, with the discovery of superconductivity in niobium–tin (Nb3Sn) which had the highest known transition temperature of about 18 K. Later Matthias would try to come up with general empirical properties to find superconducting alloys. In the same year he published a first version of his famous guidelines which came to be known, as the "Mathias rules". Matthias was able to show in 1962 that some deviations from his rules where due to impurities or defects in the materials. Using his rules, Matthias and collaborators found in 1965 that niobium–germanium (Nb3Ge) with a record critical temperature above 20 K.
+Matthias published a first outline his rules in 1957. A successful microscopic theory of superconductivity would no come up until the same year, with the development of the BCS theory by John Bardeen, Leon Cooper, and John Robert Schrieffer.
+Geballe and Matthias won the Oliver E. Buckley Condensed Matter Prize in 1970 for "For their joint experimental investigations of superconductivity which have challenged theoretical understanding and opened up the technology of high field superconductors."
+One of the first deviations of Matthias' rules was found with the discovery of superconductivity in molybdenum sulfide and selenides. Matthias postulated an additional criterion in 1976 at the Rochester Conference on superconductivity to include these materials.
+Another violation of Matthias rules appeared in 1979, with the discovery of heavy fermion superconductors by Frank Steglich where magnetism was expected to play a role, contrary to the Matthias rules.
+Matthias held the record of highest critical temperature superconductor found until the discovery of high-temperature superconductors were discovered in 1986 by Georg Bednorz and K. Alex Müller.
+
+
+== Description ==
+The Matthias rules are a set of guidelines to find low temperature superconductors but were never provided in list form by Matthias. 
+A popular summarized version of these rules reads:
+
+High symmetry is good, cubic symmetry is the best.
+High density of electronic states is good.
+Stay away from oxygen.
+Stay away from magnetism
+Stay away from insulators.
+Stay away from theorists!
+Rule 2, rules out materials near metal-insulator transition like oxides. Rule 4, rules out material that are in close vicinity to ferromagnetism or antiferromagnetism. Rule 6 is not an official rule and is often added to indicate skepticism of the theories of the time.
+Other equivalent principles as stated by Matthias, indicate to work mainly with d-electron metals; with the average number of valence electrons, preferably odd numbers 3, 5, and 7 and high electron density or high electron density of state at the Fermi level.
+In 1976, Mattias added the criterion to include "elements which will not react at all with molybdenum alone form superconducting compounds with Mo3S4 and Mo3Se4, S or Se" due to deviations in molybdenum compounds.
+
+
+== Failure and extensions ==
+It has been argued that all of Matthias' rules have been shown to not be completely valid. Specially the rules are not valid for high-temperature superconductors, alternative rules for these materials have been suggested.
+
+
+== References ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Mechanical_equivalent_of_heat-0.md b/data/en.wikipedia.org/wiki/Mechanical_equivalent_of_heat-0.md
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+---
+title: "Mechanical equivalent of heat"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Mechanical_equivalent_of_heat"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:44.670641+00:00"
+instance: "kb-cron"
+---
+
+In the history of science, the mechanical equivalent of heat states that motion and heat are mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat, provided the work done is totally converted to heat energy.  The mechanical equivalent of heat was a concept that had an important part in the development and acceptance of the conservation of energy and the establishment of the science of thermodynamics in the 19th century. Its independent and simultaneous discovery by James Prescott Joule and by Julius Robert von Mayer led to a priority dispute.
+
+
+== History and priority dispute ==
+
+Benjamin Thompson, Count Rumford, had observed the frictional heat generated by boring cannon at the arsenal in Munich, Bavaria, circa 1797. Rumford immersed a cannon barrel in water and arranged for a specially blunted boring tool. He showed that the water could be boiled within roughly two and a half hours and that the supply of frictional heat was seemingly inexhaustible.
+Based on his experiments, he published "An Inquiry Concerning the Source of the Heat Which Is Excited by Friction", (1798), Philosophical Transactions of the Royal Society p. 102. This scientific paper provided a substantial challenge to established theories of heat and began the 19th century revolution in thermodynamics. The experiment inspired the work of James Prescott Joule in the 1840s. Joule's more exact measurements on equivalence were pivotal in establishing the kinetic theory at the expense of the caloric theory. The idea that heat and work are equivalent was also proposed by Julius Robert von Mayer in 1842 in the leading German physics journal and independently by James Prescott Joule in 1843, in the leading British physics journal. Similar work was carried out by Ludwig A. Colding in 1840–1843, though Colding's work was little known outside his native Denmark.
+A collaboration between Nicolas Clément and Sadi Carnot in the 1820s had some related thinking near the same lines. In 1845, Joule published a paper entitled "The Mechanical Equivalent of Heat", in which he specified a numerical value for the amount of mechanical work required to produce a unit of heat. In particular Joule had experimented on the amount of mechanical work generated by friction needed to raise the temperature of a pound of water by one degree Fahrenheit and found a consistent value of 778.24 foot pound force (4.1550 J·cal−1). Joule contended that motion and heat were mutually interchangeable and that, in every case, a given amount of work would generate the same amount of heat. Von Mayer also published a numerical value for mechanical equivalent of heat in 1845 but his experimental method wasn't as convincing.
+Though a standardised value of 4.1860 J·cal−1 was established in the early 20th century, in the 1920s, it was ultimately realised that the constant has magnitude close to the specific heat of water, a quantity that varies with temperature between the values of 4.17 and 4.22 J·g−1·°C−1. The change in unit was the result of the demise of the calorie as a unit in physics and chemistry.
+Both von Mayer and Joule met with initial neglect and resistance despite having published in leading European physics journals, but by 1847, a lot of leading scientists of the day were paying attention. Hermann Helmholtz in 1847 published what is considered a definitive declaration of the conservation of energy. Helmholtz had learned from reading Joule's publications, though Helmholtz eventually came around to crediting both Joule and von Mayer for priority.
+Also in 1847, Joule made a well-attended presentation at the annual meeting of British Association for the Advancement of Science. Among those in attendance was William Thomson. Thomson was intrigued but initially skeptical. Over the next two years, Thomson became increasingly convinced of Joule's theory, finally admitting his conviction in print in 1851, simultaneously crediting von Mayer. Thomson collaborated with Joule, mainly by correspondence, Joule conducting experiments, Thomson analysing the results and suggesting further experiments. The collaboration lasted from 1852 to 1856. Its published results did much to bring about general acceptance of Joule's work and the kinetic theory.
+However, in 1848, von Mayer had first had sight of Joule's papers and wrote to the French Académie des Sciences to assert priority. His letter was published in the Comptes Rendus and Joule was quick to react. Thomson's close relationship with Joule allowed him to become dragged into the controversy. The pair planned that Joule would admit von Mayer's priority for the idea of the mechanical equivalent but to claim that experimental verification rested with Joule. Thomson's associates, co-workers and relatives such as William John Macquorn Rankine, James Thomson, James Clerk Maxwell, and Peter Guthrie Tait joined to champion Joule's cause.
+However, in 1862, John Tyndall, in one of his many excursions into popular science and many public disputes with Thomson and his circle, gave a lecture at the Royal Institution entitled On Force[1] in which he credited von Mayer with conceiving and measuring the mechanical equivalent of heat. Thomson and Tait were angered, and an undignified public exchange of correspondence took place in the pages of the Philosophical Magazine, and the rather more popular Good Words. Tait even resorted to championing Colding's cause in an attempt to undermine von Mayer.
+Though Tyndall again pressed von Mayer's cause in Heat: A Mode of Motion (1863) with the publication of Sir Henry Enfield Roscoe's Edinburgh Review article Thermo-Dynamics in January 1864, Joule's reputation was sealed while that of von Mayer entered a period of obscurity.
+
+
+== Notes ==
+^The usage of terms such as work, force, energy, power, etc. in the 18th and 19th centuries by scientific workers does not necessarily reflect the standardised modern usage.
+
+
+== References ==
+
+
+== Further reading ==
+Foucault, L. (1854) “Equivalent mécanique de la chaleur. M. Mayer, M. Joule. Chaleur spécifique des gaz sous volume constant. M. Victor Regnault”, Journal des débats politiques et littéraires, Thursday 8 June
+Lloyd, J.T. (1970). "Background to the Joule-Mayer Controversy". Notes and Records of the Royal Society. 25 (2): 211–225. doi:10.1098/rsnr.1970.0030. S2CID 71802199.
+Sharlin, H.I. (1979). Lord Kelvin: The Dynamic Victorian. Pennsylvania State University Press. ISBN 0-271-00203-4., pp. 154–5
+Smith, C. (1998). The Science of Energy: A Cultural History of Energy Physics in Victorian Britain. Chicago University Press. ISBN 0-226-76421-4.
+Smith, C. (2004) "Joule, James Prescott (1818-1889)", Oxford Dictionary of National Biography, Oxford University Press, <http://www.oxforddnb.com/view/article/15139, accessed 27 July 2005> (subscription required)
+Zemansky, M.W. (1968) Heat and Thermodynamics: An Intermediate Textbook, McGraw-Hill, pp. 86–87
+
+
+== External links ==
+ Media related to Mechanical equivalent of heat at Wikimedia Commons
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation-0.md b/data/en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation-0.md
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--- a/data/en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation-0.md
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 category: "reference"
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+date_saved: "2026-05-05T16:29:46.123272+00:00"
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diff --git a/data/en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation-1.md b/data/en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation-1.md
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--- a/data/en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation-1.md
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@@ -4,7 +4,7 @@ chunk: 2/3
 source: "https://en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T09:34:29.920491+00:00"
+date_saved: "2026-05-05T16:29:46.123272+00:00"
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diff --git a/data/en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation-2.md b/data/en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation-2.md
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--- a/data/en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation-2.md
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 source: "https://en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T09:34:29.920491+00:00"
+date_saved: "2026-05-05T16:29:46.123272+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Meitner–Hupfeld_effect-0.md b/data/en.wikipedia.org/wiki/Meitner–Hupfeld_effect-0.md
new file mode 100644
index 000000000..1143cadb6
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Meitner–Hupfeld_effect-0.md
@@ -0,0 +1,20 @@
+---
+title: "Meitner–Hupfeld effect"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Meitner–Hupfeld_effect"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:47.379446+00:00"
+instance: "kb-cron"
+---
+
+The Meitner–Hupfeld effect, named after Lise Meitner and Hans-Hermann Hupfeld, is an anomalously large scattering of gamma rays by heavy elements. The effect was later explained by a broad theory from which evolved the Standard Model, a theory for explaining the structure of the atomic nucleus. The anomalous gamma-ray behaviour was eventually ascribed to electron–positron pair production and annihilation.
+Although Meitner was recognised for her work, Hupfeld's contribution is largely ignored, and little or no account of his life exists.
+
+
+== See also ==
+Pair production
+Electron-positron annihilation
+
+
+== References ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Milan_school_of_physics-0.md b/data/en.wikipedia.org/wiki/Milan_school_of_physics-0.md
new file mode 100644
index 000000000..6acce37f2
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Milan_school_of_physics-0.md
@@ -0,0 +1,20 @@
+---
+title: "Milan school of physics"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Milan_school_of_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:48.602702+00:00"
+instance: "kb-cron"
+---
+
+The Milan school of physics indicates the tradition of research in the field of physics in Milan, with particular reference to the first and second half of the 20th century, when under the impulse of Orso Mario Corbino and Antonio Garbasso, and with the chair of theoretical physics by Aldo Pontremoli, the so-called Institute of Complementary Physics of Milan was formed at the University of Milan.
+
+== History ==
+Until the eighteenth century, the teaching of physics in Milan and generically in Italy, developed significantly in the confessional institutes, which represented, to some extent, the secular thought on the one hand and the religious tradition on the other, to then follow in the Twentieth century the events of the university. The first signs of studies, mainly based on astronomy, took place in 1764, when the Brera Astronomical Observatory was founded within the Jesuit College of Milan with the help of La Grange and subsequently of Ruggero Boscovich. It was then with Schiaparelli, a pupil of Quintino Sella and Luigi Menabrea, that the foundations were laid for modern astronomy that made Milan an astronomical center of world excellence.
+
+=== First half of the 20th century (1900-1948) ===
+In 1924 the first three absolute chairs of theoretical physics were assigned in Italy. The competition was won by Enrico Fermi, Aldo Pontremoli and Enrico Persico, who were appointed to the three chairs of some of the most prestigious Italian universities. This led Pontremoli himself to be assigned to the Lombard university, where he formed the so-called Institute of Complementary Physics, which he founded and directed, from 1924 to 1928, with the aim of founding a pole that would respond to the needs of science and technology, such as it suited the greatest Italian industrial center. Having had a part of the school building in via Sacchini available, he took care of the adaptation and the fixed installations so that the new Institute could carry out scientific and didactic activities effectively and without interference. With the means obtained by the university, he constituted the first nucleus of devices essential for the functioning of the new institution; through his relationships in the industrial field, he was able to complete these endowments with materials received as a gift. In this way the Institute in a short time was able to fully fulfill the task assigned to it. In November 1925 the institute was the organizer of the II Assembly of the International Federation of the Intellectual Union. Among the grants received by Pontremoli, the one received from Banca Popolare di Milano in 1926, which allowed the foundation of the radiology laboratory, specialized in ultraviolet radiation, and radioactive substances, should be noted. The foundation of the school, which later became part of the Physics Department of the University of Milan, was published in the physics magazine Il Nuovo Cimento, of the Italian Physics Society. Pontremoli's studies were particularly concerned with optics, radioactivity and hydrodynamics and were mainly published in the Rendiconti dei Lincei of the homonymous Academy and in the Reports of the Lombard Academy of Sciences and Letters. Some popular writings appeared in the magazine La Fiera Letteraria. In 1929, after the death of Aldo Pontremoli who died in the tragedy of the airship Italia who disappeared in the ice of Antarctica in May of the previous year, Giovanni Polvani replaced him in the chair of Experimental Physics of the Institute which became part of the University of Milan . The Polvani Archive, containing historical volumes, is still kept in the Physics Library of the University of Milan. A classroom in the university department was then named after him. In Milan, Polvani, already before the Second World War, is committed with Bolla and also with Gentile to find new tools to develop research on cosmic rays. Starting from 1936 the physical institute suffered a constant decline due to the conflicts between its protagonists and the fascist regime, many of which, following the fascist racial laws, left Italy to continue their research studies in the United States of America.
+
+=== Second half of the 20th century (1949-1998) ===
+After the war, the department returned to obtain particular successes thanks to the return to Italy of many influential personalities. In 1949, lectures were given by the Nobel laureate Enrico Fermi, collected by the assistants of the universities of Rome and Milan, and were then published in 1950 by the Accademia Nazionale dei Lincei. In 1952, Giuseppe Occhialini, who returned to Italy, taught higher physics and founded the Laboratory of Cosmic Physics and Related Technologies of the CNR and the Astrophysics Section of the Physics Department of the University of Milan. Here he creates a leading school in the research of cosmic rays with the use of nuclear emulsions exposed at high altitudes, an experience that culminated in 1954 with the G-Stack experiment. He also founded the Space Group, so called because it conducted high altitude observations with stratospheric balloons first, then with rockets and finally with artificial satellites. It is also through these activities that Italy and Milan have quickly acquired positions of excellence in the field of High Energy Astrophysics and more particularly in X-ray and Gamma-ray astronomy. To allow this type of activity, Beppo Occhialini also took action on the organizational level, founding various sections of various research institutes still present, and taking charge of both the theoretical and experimental direction of the department.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Milan_school_of_physics-1.md b/data/en.wikipedia.org/wiki/Milan_school_of_physics-1.md
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--- /dev/null
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@@ -0,0 +1,13 @@
+---
+title: "Milan school of physics"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Milan_school_of_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:48.602702+00:00"
+instance: "kb-cron"
+---
+
+==== The Occhialini case ====
+Occhialini was involved in two Nobel Prize-winning works: the discovery of the positron and the discovery of the pion. However, as he was an anti-fascist, during the publication of most of his studies he was an exile in England, and could not publish only in his name, and therefore the articles he did were also signed by Patrick Maynard Stuart Blackett in '32 when there was the work del positron and Cecil Frank Powell in '47 on the occasion of the work on the pion. Both of these works were awarded the Nobel but were awarded to Blacket and Powell. Blacket was honest enough to say that he had nothing to do with it and that Occhialini had done the job. Only many years later it was discovered, from the documents of the Nobel Foundation that there had been an explicit veto on the name Occhialini. In fact, Occhialini, since he had not collaborated in the atomic enterprise during the war, could not be awarded the Nobel. Occhialini was then awarded the Wolf Prize for physics in 1979.
+Occhialini himself in the period between '52 and '55 supervises Riccardo Giacconi, who will then be awarded the Nobel Prize for physics in 2002 for his pioneering contributions to astrophysics, which led to the discovery of the first cosmic sources in X-rays, and Giovanni Bignami, then president of ASI, INAF, COSPAR and SKA. With the advent of particle accelerators, Occhialini explores new fields of research, including space physics, making a decisive contribution to the foundation of the Italian Space Agency (ASI) and the European Space Agency (ESA), as well as to the INAF-IASF section of Milan. From 1947 to 1961 Polvani was president of the Italian Physics Society and in this capacity contributed to the reorganization of Italian research after the war and, in 1953, he founded the International School of Physics of Varenna in the municipality of the same name, in the province of Lecco, subsequently named after Enrico Fermi, site of periodic meetings between established scientists and young physicists. Fermi himself, in the summer of 1954, gave a lecture on the physics of π mesons. To date, the school has hosted speeches by over thirty-four Nobel laureates.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Milan_school_of_physics-2.md b/data/en.wikipedia.org/wiki/Milan_school_of_physics-2.md
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Milan_school_of_physics-2.md
@@ -0,0 +1,52 @@
+---
+title: "Milan school of physics"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Milan_school_of_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:48.602702+00:00"
+instance: "kb-cron"
+---
+
+==== The cyclotron of Milan ====
+After World War II, Italian physicists felt the need to build accelerator machines for research purposes in the field of particles. After long discussions, two machines were built: one in Frascati - the 1000 Mev synchrotron - intended for high energy physics and one in Milan - the 45 Mev cyclotron - intended for low energy physics. While the construction of the Frascati machine was financed by the National Institute of Nuclear Physics, the Milan machine was built with local funding from companies and the Municipality of Milan.
+It is interesting to underline the great willingness of the Lombard business world to finance basic research activities, without immediate technological repercussions. Evidently, a favorable climate had been created for scientific research as a factor of progress and it is within this strategy that we can also place the interest that the industrial world showed for the construction of the first Italian technical-scientific museum, the Leonardo da Vinci Museum.
+Between 1960 and 1965, the first Italian cyclotron was designed and built at the Institute of Physical Sciences of the University of Milan. It belonged to the category of fixed frequency cyclotrons, variable azimuth field (A.V.F.) and was of the Thomas strong focus type. A special shed and other buildings were built to house the machine and the research laboratories. The machine worked until the early 1980s and was subsequently dismantled when construction of the superconducting cyclotron was started in Segrate. The 1: 5 scale model of the cyclotron is kept at the Museum of Science and Technology in Milan. It was created at the time, in particular, to study the most suitable and economical shape of the magnets to guarantee the necessary field.
+In 1949 Piero Caldirola moved as full professor of theoretical physics at the University of Milan, where he always remained afterwards, as full professor of general physics from 1966 to 1976 and full professor of theoretical physics institutions starting from 1974. From a scientific interest for the problems of the propagation of electromagnetic waves in weakly ionized gases began his involvement in Milan in plasma physics, also becoming president of the Euratom committee for fusion studies at the Frascati Laboratories. In the following years Caldirola, after having created the Italian school of theoretical solid state physics, founded the research group for quantum electronics, and the plasma physics laboratory, as well as the International School of Plasma Physics in Varenna in Milan. He was also director of the Institute of Physics, and of the Postgraduate Schools in "Atomic and Nuclear Physics" and in "Health and Hospital Physics" of the university. In November 1966 Giovanni Polvani, now at the end of his career, was elected Rector of the Milanese university; it's the first time for a physicist. In the 1980s, the group led by Occhialini made numerous progress, collaborating in the design and construction of the first European satellites for astronomy: Cos-B, Exosat, XMM and Beppo-SAX. After 1984, Giuliano Preparata, who has recently returned to Italy after a long period in the United States and a short period in Bari, where he has aroused current controversy among theoretical physicists on cold fusion, is called to the chair of high energy nuclear physics of the 'University of Milan, where he creates, with some young collaborators, his own independent research group with the best students of the department. Here Preparata appears to be the only one who manages to bring a breath of fresh air into what is narrated as the stale world of Italian theoretical physics, giving prestige to the Milanese university. In the same period Preparata met Emilio Del Giudice in Milan, from which a fruitful friendship and collaboration was born aimed at developing a cold fusion theory, which will give him international fame in the following years. However, the collaboration stopped unexpectedly in 2000 with the premature death of Preparata. The duo was also interested in the properties of electromagnetic fields in water, in a series of experimental works then resumed in 2009 by the Nobel Prize for Medicine Luc Montagnier. Between 1982 and 1991 Ugo Amaldi received a professorship at the University of Milan. Here for a decade he headed an international collaboration of over 400 scientists who designed and implemented the DELPHI experiment at the LEP accelerator at CERN. In this same period Fabiola Gianotti studied at the Milanese university, before becoming director of the ATLAS experiment, and then general director of CERN in Geneva. Meanwhile, Giovanni Bignami, after twenty years of work, managed to identify and understand Geminga, the first neutron star without radio emission, and the American Astronomical Society in 1993 awarded it the Bruno Rossi Award for this discovery.
+
+=== Present (1998-present) ===
+Under the activity of Ugo Amaldi, in the 2000s the first National Center for Oncological Hadrotherapy was created in Italy and fourth in the world, which houses a synchrotron of 25 meters in diameter, capable of accelerating both protons and ions of carbon. In 1995 Marco Bersanelli, who returned to Italy from the Berkeley laboratories after having studied and collaborated with the Nobel laureate George Smoot, creates an observational cosmology group for the study of the cosmic microwave background at the University of Milan, which becomes one of the main executive and scientific managers of the space missions of ESA Planck, launched in 2009, and of the Euclid space telescope, scheduled for launch in 2021. In the same period Giuseppe Bertin won a chair at the University of Milan where he focuses on studies on the growth dynamics of galaxies; earned him the "National Prize of the President of the Republic" of the Accademia dei Lincei. He is the third professor of the physics department of the University of Milan to receive him, after Giuseppe Occhialini (in '49) and Piero Caldirola (in '56).
+
+== Exponents ==
+Aldo Pontremoli
+Giovanni Schiaparelli
+Giuseppe Occhialini
+Giovanni Polvani
+Riccardo Giacconi
+Piero Caldirola
+Giovanni Bignami
+Patrizia Caraveo
+Marco Bersanelli
+Ugo Amaldi
+Giuliano Preparata
+Emilio Del Giudice
+Emilio Gatti
+Fabiola Gianotti
+Giuseppe Bertin
+Lucio Rossi
+Alessio Zaccone
+
+== Bibliography ==
+Il nuovo cimento, organo della società italiana di fisica, anno VII-1930; Zanichelli (Bologna).
+Giuseppe Occhialini. Biografia di un fisico italiano, Gruppo Editoriale Muzzio (2009) ISBN 978-88-96159-02-6.
+Giordana G.P. - VITA DI ALDO PONTREMOLI, ASIN B00KPD0R4G; Editore : Formiggini (1 gennaio 1933).
+
+== See also ==
+
+University of Milan
+
+== External links ==
+University of Milan Website (in English)
+Università degli Studi di Milano (in Italian)
+
+== References ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Modern_physics-0.md b/data/en.wikipedia.org/wiki/Modern_physics-0.md
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@@ -0,0 +1,35 @@
+---
+title: "Modern physics"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Modern_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:49.903466+00:00"
+instance: "kb-cron"
+---
+
+Modern physics is a branch of physics that developed in the early 20th century and onward or branches greatly influenced by early 20th century physics. Notable branches of modern physics include quantum mechanics, special relativity, and general relativity.
+Classical physics is typically concerned with everyday conditions: speeds are much lower than the speed of light, sizes are much greater than that of atoms, and energies are relatively small. Modern physics, however, is concerned with more extreme conditions, such as high velocities that are comparable to the speed of light (special relativity), small distances comparable to the atomic radius (quantum mechanics), and very high energies (relativity). In general, quantum and relativistic effects are believed to exist across all scales, although these effects may be very small at human scale. While quantum mechanics is compatible with special relativity (See: Relativistic quantum mechanics), one of the unsolved problems in physics is the unification of quantum mechanics and general relativity, which the Standard Model of particle physics currently cannot account for.
+Modern physics is an effort to understand the underlying processes of the interactions of matter using the tools of science and engineering. In a literal sense, the term modern physics means up-to-date physics. In this sense, a significant portion of so-called classical physics is modern. However, since roughly 1890, new discoveries have caused significant paradigm shifts: especially the advent of quantum mechanics (QM) and relativity (ER). Physics that incorporates elements of either QM or ER (or both) is said to be modern physics. It is in this latter sense that the term is generally used.
+Modern physics is often encountered when dealing with extreme conditions. Quantum mechanical effects tend to appear when dealing with "lows" (low temperatures, small distances), while relativistic effects tend to appear when dealing with "highs" (high velocities, large distances), the "middles" being classical behavior. For example, when analyzing the behavior of a gas at room temperature, most phenomena will involve the (classical) Maxwell–Boltzmann distribution. However, near absolute zero, the Maxwell–Boltzmann distribution fails to account for the observed behavior of the gas, and the (modern) Fermi–Dirac or Bose–Einstein distributions have to be used instead.
+
+Very often, it is possible to find – or "retrieve" – the classical behavior from the modern description by analyzing the modern description at low speeds and large distances (by taking a limit, or by making an approximation). When doing so, the result is called the classical limit.
+
+
+== Hallmark experiments ==
+
+These are generally considered to be experiments regarded leading to the foundation of modern physics:
+
+
+== See also ==
+
+
+== References ==
+A. Beiser (2003). Concepts of Modern Physics (6th ed.). McGraw-Hill. ISBN 978-0-07-123460-3.
+P. Tipler, R. Llewellyn (2002). Modern Physics (4th ed.). W. H. Freeman. ISBN 978-0-7167-4345-3.
+
+
+== Notes ==
+
+
+== External links ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Moseley's_law-0.md b/data/en.wikipedia.org/wiki/Moseley's_law-0.md
new file mode 100644
index 000000000..b78538053
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@@ -0,0 +1,747 @@
+---
+title: "Moseley's law"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Moseley's_law"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:51.144728+00:00"
+instance: "kb-cron"
+---
+
+Moseley's law is an empirical law concerning the characteristic X-rays emitted by atoms. The law was discovered and published by the English physicist Henry Moseley in 1913–1914. Until Moseley's work, "atomic number" was merely an element's place in the periodic table and was not known to be associated with any measurable physical quantity. In brief, the law states that the square root of the frequency of the emitted X-ray is approximately proportional to the atomic number: 
+  
+    
+      
+        
+          
+            ν
+          
+        
+        ∝
+        Z
+        .
+      
+    
+    {\displaystyle {\sqrt {\nu }}\varpropto Z.}
+  
+
+
+== History ==
+
+The historic periodic table was roughly ordered by increasing atomic weight, but in a few famous cases the physical properties of two elements suggested that the heavier ought to precede the lighter.  An example is cobalt having the atomic weight of 58.9 and nickel having the atomic weight of 58.7.
+Henry Moseley and other physicists used X-ray diffraction to study the elements, and the results of their experiments led to organizing the periodic table by proton count.
+
+
+== Apparatus ==
+Since the spectral emissions for the lighter elements would be in the soft X-ray range (absorbed by air), the spectrometry apparatus had to be enclosed inside a vacuum. Details of the experimental setup are documented in the journal articles "The High-Frequency Spectra of the Elements" Part I and Part II.
+
+
+== Results ==
+Moseley found that the 
+  
+    
+      
+        K
+        α
+      
+    
+    {\displaystyle K\alpha }
+  
+ lines (in Siegbahn notation) were indeed related to the atomic number, Z.
+Following Bohr's lead, Moseley found that for the spectral lines, this relationship could be approximated by a simple formula, later called Moseley's Law.
+
+  
+    
+      
+        ν
+        =
+        A
+        ⋅
+        
+          
+            (
+            
+              Z
+              −
+              b
+            
+            )
+          
+          
+            2
+          
+        
+      
+    
+    {\displaystyle \nu =A\cdot \left(Z-b\right)^{2}}
+  
+
+where:
+
+  
+    
+      
+        ν
+      
+    
+    {\displaystyle \nu }
+  
+ is the frequency of the observed X-ray emission line
+
+  
+    
+      
+        A
+      
+    
+    {\displaystyle A}
+  
+ and 
+  
+    
+      
+        b
+      
+    
+    {\displaystyle b}
+  
+ are constants that depend on the type of line (that is, K, L, etc. in X-ray notation)
+
+  
+    
+      
+        A
+        =
+        
+          (
+          
+            
+              
+                1
+                
+                  1
+                  
+                    2
+                  
+                
+              
+            
+            −
+            
+              
+                1
+                
+                  2
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+        ⋅
+      
+    
+    {\displaystyle A=\left({\frac {1}{1^{2}}}-{\frac {1}{2^{2}}}\right)\cdot }
+  
+  Rydberg frequency and  
+  
+    
+      
+        b
+         
+      
+    
+    {\displaystyle b\ }
+  
+= 1 for 
+  
+    
+      
+        K
+        α
+      
+    
+    {\displaystyle K\alpha }
+  
+ lines, and 
+  
+    
+      
+        A
+        =
+        
+          (
+          
+            
+              
+                1
+                
+                  2
+                  
+                    2
+                  
+                
+              
+            
+            −
+            
+              
+                1
+                
+                  3
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+        ⋅
+      
+    
+    {\displaystyle A=\left({\frac {1}{2^{2}}}-{\frac {1}{3^{2}}}\right)\cdot }
+  
+ Rydberg frequency and 
+  
+    
+      
+        b
+        =
+        7.4
+      
+    
+    {\displaystyle b=7.4}
+  
+ for 
+  
+    
+      
+        L
+        α
+      
+    
+    {\displaystyle L\alpha }
+  
+ lines.
+
+
+== Derivation ==
+Moseley derived his formula empirically by fitting the square root of the X-ray frequency plotted against the atomic number. This formula can be explained based on the Bohr model of the atom, namely, 
+
+  
+    
+      
+        E
+        =
+        h
+        ν
+        =
+        
+          E
+          
+            i
+          
+        
+        −
+        
+          E
+          
+            f
+          
+        
+        =
+        
+          
+            
+              
+                m
+                
+                  e
+                
+              
+              
+                q
+                
+                  e
+                
+                
+                  2
+                
+              
+              
+                q
+                
+                  Z
+                
+                
+                  2
+                
+              
+            
+            
+              8
+              
+                h
+                
+                  2
+                
+              
+              
+                ε
+                
+                  0
+                
+                
+                  2
+                
+              
+            
+          
+        
+        
+          (
+          
+            
+              
+                1
+                
+                  n
+                  
+                    f
+                  
+                  
+                    2
+                  
+                
+              
+            
+            −
+            
+              
+                1
+                
+                  n
+                  
+                    i
+                  
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+        ,
+      
+    
+    {\displaystyle E=h\nu =E_{\text{i}}-E_{\text{f}}={\frac {m_{\text{e}}q_{\text{e}}^{2}q_{Z}^{2}}{8h^{2}\varepsilon _{0}^{2}}}\left({\frac {1}{n_{\text{f}}^{2}}}-{\frac {1}{n_{\text{i}}^{2}}}\right),}
+  
+
+where
+
+  
+    
+      
+        
+          ε
+          
+            0
+          
+        
+      
+    
+    {\displaystyle \varepsilon _{0}}
+  
+ is the permittivity of free space
+
+  
+    
+      
+        
+          m
+          
+            e
+          
+        
+      
+    
+    {\displaystyle m_{\text{e}}}
+  
+ is the mass of an electron
+
+  
+    
+      
+        
+          q
+          
+            e
+          
+        
+      
+    
+    {\displaystyle q_{\text{e}}}
+  
+ is the charge of an electron
+
+  
+    
+      
+        
+          q
+          
+            Z
+          
+        
+      
+    
+    {\displaystyle q_{Z}}
+  
+ is an effective charge of the nucleus, expressed as 
+  
+    
+      
+        (
+        Z
+        −
+        b
+        )
+        
+          q
+          
+            e
+          
+        
+      
+    
+    {\displaystyle (Z-b)q_{e}}
+  
+
+  
+    
+      
+        
+          n
+          
+            f
+          
+        
+      
+    
+    {\displaystyle n_{\text{f}}}
+  
+ is the quantum number of final energy level
+
+  
+    
+      
+        
+          n
+          
+            i
+          
+        
+      
+    
+    {\displaystyle n_{\text{i}}}
+  
+ is the quantum number of initial energy level (
+  
+    
+      
+        
+          n
+          
+            i
+          
+        
+        >
+        
+          n
+          
+            f
+          
+        
+      
+    
+    {\displaystyle n_{\text{i}}>n_{\text{f}}}
+  
+)
+
+  
+    
+      
+        h
+      
+    
+    {\displaystyle h}
+  
+ is the Planck constant
+Taking into account the empirically found b constant that reduced (or  "screened") the nucleus charge, Bohr's formula for 
+  
+    
+      
+        K
+        α
+      
+    
+    {\displaystyle K\alpha }
+  
+ transitions becomes
+
+  
+    
+      
+        E
+        =
+        h
+        ν
+        =
+        
+          E
+          
+            i
+          
+        
+        −
+        
+          E
+          
+            f
+          
+        
+        =
+        
+          
+            
+              
+                m
+                
+                  e
+                
+              
+              
+                q
+                
+                  e
+                
+                
+                  4
+                
+              
+            
+            
+              8
+              
+                h
+                
+                  2
+                
+              
+              
+                ε
+                
+                  0
+                
+                
+                  2
+                
+              
+            
+          
+        
+        
+          (
+          
+            
+              
+                1
+                
+                  1
+                  
+                    2
+                  
+                
+              
+            
+            −
+            
+              
+                1
+                
+                  2
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+        (
+        Z
+        −
+        1
+        
+          )
+          
+            2
+          
+        
+        ≈
+        
+          
+            3
+            4
+          
+        
+        (
+        Z
+        −
+        1
+        
+          )
+          
+            2
+          
+        
+        ×
+        13.6
+         
+        
+          e
+          V
+        
+        .
+      
+    
+    {\displaystyle E=h\nu =E_{\text{i}}-E_{\text{f}}={\frac {m_{\text{e}}q_{\text{e}}^{4}}{8h^{2}\varepsilon _{0}^{2}}}\left({\frac {1}{1^{2}}}-{\frac {1}{2^{2}}}\right)(Z-1)^{2}\approx {\frac {3}{4}}(Z-1)^{2}\times 13.6\ \mathrm {eV} .}
+  
+
+Dividing both sides by h to convert to the frequency units, one obtains
+
+  
+    
+      
+        ν
+        =
+        
+          
+            E
+            h
+          
+        
+        =
+        
+          
+            
+              
+                m
+                
+                  e
+                
+              
+              
+                q
+                
+                  e
+                
+                
+                  4
+                
+              
+            
+            
+              8
+              
+                h
+                
+                  3
+                
+              
+              
+                ε
+                
+                  0
+                
+                
+                  2
+                
+              
+            
+          
+        
+        
+          
+            3
+            4
+          
+        
+        (
+        Z
+        −
+        1
+        
+          )
+          
+            2
+          
+        
+        ≈
+        (
+        Z
+        −
+        1
+        
+          )
+          
+            2
+          
+        
+        ×
+        (
+        2.47
+        ⋅
+        
+          10
+          
+            15
+          
+        
+         
+        
+          H
+          z
+        
+        )
+        .
+      
+    
+    {\displaystyle \nu ={\frac {E}{h}}={\frac {m_{\text{e}}q_{\text{e}}^{4}}{8h^{3}\varepsilon _{0}^{2}}}{\frac {3}{4}}(Z-1)^{2}\approx (Z-1)^{2}\times (2.47\cdot 10^{15}\ \mathrm {Hz} ).}
+  
+
+
+== Screening ==
+A simplified explanation for the effective charge of a nucleus being one less than its actual charge is that an unpaired electron in the K-shell screens it. An elaborate discussion criticizing Moseley's interpretation of screening can be found in a paper by Whitaker which is repeated in most modern texts.
+A list of experimentally found and theoretically calculated X-ray transition energies is available at NIST. Nowadays, theoretical energies are computed with much greater accuracy than Moseley's law allows, using modern computational models such as the Dirac–Fock method (the Hartree–Fock method with the relativistic effects accounted for).
+
+
+== See also ==
+Moseley's periodic law, concerning the modern periodic table.
+Auger electron spectroscopy, a similar phenomenon with increased X-ray yield from species of higher atomic number.
+Discovery of the neutron Mosley's law was an important step in the development of the understanding of the atom.
+
+
+== References ==
+
+
+== External links ==
+Oxford Physics Teaching - History Archive, "Exhibit 12 - Moseley's graph Archived 2016-03-03 at the Wayback Machine" (Reproduction of the original Moseley diagram showing the square root frequency dependence)
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-0.md b/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-0.md
index 225ab16a4..a83d78c14 100644
--- a/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-0.md
+++ b/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-0.md
@@ -4,7 +4,7 @@ chunk: 1/3
 source: "https://en.wikipedia.org/wiki/Newton's_law_of_cooling"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T10:01:23.867206+00:00"
+date_saved: "2026-05-05T16:29:52.450911+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-1.md b/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-1.md
index d85774914..3b78e46f2 100644
--- a/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-1.md
+++ b/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-1.md
@@ -4,7 +4,7 @@ chunk: 2/3
 source: "https://en.wikipedia.org/wiki/Newton's_law_of_cooling"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T10:01:23.867206+00:00"
+date_saved: "2026-05-05T16:29:52.450911+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-2.md b/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-2.md
index 373e6879c..05793ae97 100644
--- a/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-2.md
+++ b/data/en.wikipedia.org/wiki/Newton's_law_of_cooling-2.md
@@ -4,7 +4,7 @@ chunk: 3/3
 source: "https://en.wikipedia.org/wiki/Newton's_law_of_cooling"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T10:01:23.867206+00:00"
+date_saved: "2026-05-05T16:29:52.450911+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Old_quantum_theory-0.md b/data/en.wikipedia.org/wiki/Old_quantum_theory-0.md
new file mode 100644
index 000000000..489c4dae5
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Old_quantum_theory-0.md
@@ -0,0 +1,91 @@
+---
+title: "Old quantum theory"
+chunk: 1/5
+source: "https://en.wikipedia.org/wiki/Old_quantum_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:54.976606+00:00"
+instance: "kb-cron"
+---
+
+The old quantum theory is a collection of results from the years 1900–1925, which predate modern quantum mechanics. The theory was never complete or self-consistent, but was instead a set of heuristic corrections to classical mechanics. The theory has come to be understood as the semi-classical approximation to modern quantum mechanics. The main and final accomplishments of the old quantum theory were the determination of the modern form of the periodic table by Edmund Stoner and the Pauli exclusion principle, both of which were premised on Arnold Sommerfeld's enhancements to the Bohr model of the atom.
+The main tool of the old quantum theory was the Bohr–Sommerfeld quantization condition, a procedure for selection of certain allowed states of a classical system: the system can then only exist in one of the allowed states and not in any other state.
+
+== History ==
+The old quantum theory was instigated by the 1900 work of Max Planck on the emission and absorption of light in a black body with his discovery of Planck's law introducing his quantum of action, and began in earnest after the work of Albert Einstein on the specific heats of solids in 1907 brought him to the attention of Walther Nernst. Einstein solid, followed by the Debye model in 1912, applied quantum principles to the motion of atoms, explaining the specific heat anomaly.
+In 1910, Arthur Erich Haas further developed J. J. Thomson's atomic model in a paper that outlined a treatment of the hydrogen atom involving quantization of electronic orbitals, thus anticipating the Bohr model (1913) by three years.
+John William Nicholson is noted as the first to create an atomic model that quantized angular momentum as 
+  
+    
+      
+        h
+        
+          /
+        
+        (
+        2
+        π
+        )
+      
+    
+    {\displaystyle h/(2\pi )}
+  
+. Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.
+In 1913, Bohr displayed rudiments of the later defined correspondence principle and used it to formulate a model of the hydrogen atom which explained the line spectrum. In the next few years Arnold Sommerfeld extended the quantum rule to arbitrary integrable systems making use of the principle of adiabatic invariance of the quantum numbers introduced by Hendrik Lorentz and Einstein. Sommerfeld made a crucial contribution by quantizing the z-component of the angular momentum, which in the old quantum era was called "space quantization" (German: Richtungsquantelung). This model, which became known as the Bohr–Sommerfeld model, allowed the orbits of the electron to be ellipses instead of circles, and introduced the concept of quantum degeneracy. The theory would have correctly explained the Zeeman effect, except for the issue of electron spin. Sommerfeld's model was much closer to the modern quantum mechanical picture than Bohr's.
+Throughout the 1910s and well into the 1920s, many problems were attacked using the old quantum theory with mixed results. Molecular rotation and vibration spectra were understood and the electron's spin was discovered, leading to the confusion of half-integer quantum numbers. Planck introduced the zero point energy and Sommerfeld semiclassically quantized the relativistic hydrogen atom. Hendrik Kramers explained the Stark effect. Satyendra Nath Bose and Einstein developed the Bose–Einstein statistics for bosons. Einstein also refined the quantization condition in 1917.
+
+=== End of old theory ===
+In 1924, Bohr, Kramers and John C. Slater promoted what was known as the BKS theory which considered systems as quantum mechanical but the electromagnetic field as a classical field. However the theory was rejected by the Bothe–Geiger coincidence experiment.
+Kramers prescriptions for calculating transition probabilities between quantum states in terms of Fourier components of the motion, were extended in collaboration with Werner Heisenberg to a semiclassical matrix-like description of atomic transition probabilities. Heisenberg went on to reformulate all of quantum theory in his 1925 Umdeutung paper, in terms these transition rules, later creating matrix mechanics with Max Born and Pascual Jordan.
+In parallel in 1924, Louis de Broglie introduced the wave theory of matter, which was extended to a semiclassical equation for matter waves by Einstein a short time later. In 1926 Erwin Schrödinger found a completely quantum mechanical wave-equation, which reproduced all the successes of the old quantum theory without ambiguities and inconsistencies. The Schrödinger equation developed separately from matrix mechanics until Schrödinger and others proved that the two methods predicted the same experimental consequences. Paul Dirac later proved in 1926 that both methods can be obtained from a more general method called transformation theory.
+The mathematical formalism of modern quantum mechanics was developed by Dirac and John von Neumann.
+
+=== Other developments ===
+In the 1950s Joseph Keller updated Bohr–Sommerfeld quantization using Einstein's interpretation of 1917, now known as Einstein–Brillouin–Keller method. In 1971, Martin Gutzwiller took into account that this method only works for integrable systems and derived a semiclassical way of quantizing chaotic systems from path integrals.
+
+== Basic principles ==
+
+The basic idea of the old quantum theory is that the motion in an atomic system is quantized, or discrete. The system obeys classical mechanics except that not every motion is allowed, only those motions which obey the quantization condition:
+
+  
+    
+      
+        
+          ∮
+          
+            H
+            (
+            p
+            ,
+            q
+            )
+            =
+            E
+          
+        
+        
+          p
+          
+            i
+          
+        
+        
+        d
+        
+          q
+          
+            i
+          
+        
+        =
+        
+          n
+          
+            i
+          
+        
+        h
+      
+    
+    {\displaystyle \oint _{H(p,q)=E}p_{i}\,dq_{i}=n_{i}h}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Old_quantum_theory-1.md b/data/en.wikipedia.org/wiki/Old_quantum_theory-1.md
new file mode 100644
index 000000000..c6fee33ae
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Old_quantum_theory-1.md
@@ -0,0 +1,323 @@
+---
+title: "Old quantum theory"
+chunk: 2/5
+source: "https://en.wikipedia.org/wiki/Old_quantum_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:54.976606+00:00"
+instance: "kb-cron"
+---
+
+where the 
+  
+    
+      
+        
+          p
+          
+            i
+          
+        
+      
+    
+    {\displaystyle p_{i}}
+  
+ are the momenta of the system and the 
+  
+    
+      
+        
+          q
+          
+            i
+          
+        
+      
+    
+    {\displaystyle q_{i}}
+  
+ are the corresponding coordinates. The quantum numbers 
+  
+    
+      
+        
+          n
+          
+            i
+          
+        
+      
+    
+    {\displaystyle n_{i}}
+  
+ are integers and the integral is taken over one period of the motion at constant energy (as described by the Hamiltonian). The integral is an area in phase space, which is a quantity called the action and is quantized in units of the (unreduced) Planck constant. For this reason, the Planck constant was often called the quantum of action.
+In order for the old quantum condition to make sense, the classical motion must be separable, meaning that there are separate coordinates 
+  
+    
+      
+        
+          q
+          
+            i
+          
+        
+      
+    
+    {\displaystyle q_{i}}
+  
+ in terms of which the motion is periodic. The periods of the different motions do not have to be the same, they can even be incommensurate, but there must be a set of coordinates where the motion decomposes in a multi-periodic way.
+The motivation for the old quantum condition was the correspondence principle, complemented by the physical observation that the quantities which are quantized must be adiabatic invariants. Given Planck's quantization rule for the harmonic oscillator, either condition determines the correct classical quantity to quantize in a general system up to an additive constant.
+This quantization condition is often known as the Wilson–Sommerfeld rule, proposed independently by William Wilson and Arnold Sommerfeld.
+
+== Examples ==
+
+=== Thermal properties of the harmonic oscillator ===
+The simplest system in the old quantum theory is the harmonic oscillator, whose Hamiltonian is:
+
+  
+    
+      
+        H
+        =
+        
+          
+            
+              p
+              
+                2
+              
+            
+            
+              2
+              m
+            
+          
+        
+        +
+        
+          
+            
+              m
+              
+                ω
+                
+                  2
+                
+              
+              
+                q
+                
+                  2
+                
+              
+            
+            2
+          
+        
+        .
+      
+    
+    {\displaystyle H={p^{2} \over 2m}+{m\omega ^{2}q^{2} \over 2}.}
+  
+
+The old quantum theory yields a recipe for the quantization of the energy levels of the harmonic oscillator, which, when combined with the Boltzmann probability distribution of thermodynamics, yields the correct expression for the stored energy and specific heat of a quantum oscillator both at low and at ordinary temperatures. Applied as a model for the specific heat of solids, this resolved a discrepancy in pre-quantum thermodynamics that had troubled 19th-century scientists. Let us now describe this.
+The level sets of H are the orbits, and the quantum condition is that the area enclosed by an orbit in phase space is an integer. It follows that the energy is quantized according to the Planck rule:
+
+  
+    
+      
+        E
+        =
+        n
+        ℏ
+        ω
+        ,
+        
+      
+    
+    {\displaystyle E=n\hbar \omega ,\,}
+  
+
+a result which was known well before, and used to formulate the old quantum condition. This result differs by 
+  
+    
+      
+        
+          
+            
+              1
+              2
+            
+          
+        
+        ℏ
+        ω
+      
+    
+    {\displaystyle {\tfrac {1}{2}}\hbar \omega }
+  
+ from the results found with the help of quantum mechanics. This constant is neglected in the derivation of the old quantum theory, and its value cannot be determined using it.
+The thermal properties of a quantized oscillator may be found by averaging the energy in each of the discrete states assuming that they are occupied with a Boltzmann weight:
+
+  
+    
+      
+        U
+        =
+        
+          
+            
+              
+                ∑
+                
+                  n
+                
+              
+              ℏ
+              ω
+              n
+              
+                e
+                
+                  −
+                  β
+                  n
+                  ℏ
+                  ω
+                
+              
+            
+            
+              
+                ∑
+                
+                  n
+                
+              
+              
+                e
+                
+                  −
+                  β
+                  n
+                  ℏ
+                  ω
+                
+              
+            
+          
+        
+        =
+        
+          
+            
+              ℏ
+              ω
+              
+                e
+                
+                  −
+                  β
+                  ℏ
+                  ω
+                
+              
+            
+            
+              1
+              −
+              
+                e
+                
+                  −
+                  β
+                  ℏ
+                  ω
+                
+              
+            
+          
+        
+        ,
+        
+        
+        
+        
+          
+            w
+            h
+            e
+            r
+            e
+          
+        
+        
+        
+        β
+        =
+        
+          
+            1
+            
+              k
+              T
+            
+          
+        
+        ,
+      
+    
+    {\displaystyle U={\sum _{n}\hbar \omega ne^{-\beta n\hbar \omega } \over \sum _{n}e^{-\beta n\hbar \omega }}={\hbar \omega e^{-\beta \hbar \omega } \over 1-e^{-\beta \hbar \omega }},\;\;\;{\rm {where}}\;\;\beta ={\frac {1}{kT}},}
+  
+
+kT is Boltzmann constant times the absolute temperature, which is the temperature as measured in more natural units of energy. The quantity 
+  
+    
+      
+        β
+      
+    
+    {\displaystyle \beta }
+  
+ is more fundamental in thermodynamics than the temperature, because it is the thermodynamic potential associated to the energy.
+From this expression, it is easy to see that for large values of 
+  
+    
+      
+        β
+      
+    
+    {\displaystyle \beta }
+  
+, for very low temperatures, the average energy U in the harmonic oscillator approaches zero very quickly, exponentially fast. The reason is that kT is the typical energy of random motion at temperature T, and when this is smaller than 
+  
+    
+      
+        ℏ
+        ω
+      
+    
+    {\displaystyle \hbar \omega }
+  
+, there is not enough energy to give the oscillator even one quantum of energy. So the oscillator stays in its ground state, storing next to no energy at all.
+This means that at very cold temperatures, the change in energy with respect to beta, or equivalently the change in energy with respect to temperature, is also exponentially small. The change in energy with respect to temperature is the specific heat, so the specific heat is exponentially small at low temperatures, going to zero like
+
+  
+    
+      
+        exp
+        ⁡
+        (
+        −
+        ℏ
+        ω
+        
+          /
+        
+        k
+        T
+        )
+      
+    
+    {\displaystyle \exp(-\hbar \omega /kT)}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Old_quantum_theory-2.md b/data/en.wikipedia.org/wiki/Old_quantum_theory-2.md
new file mode 100644
index 000000000..e3fa486f4
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Old_quantum_theory-2.md
@@ -0,0 +1,658 @@
+---
+title: "Old quantum theory"
+chunk: 3/5
+source: "https://en.wikipedia.org/wiki/Old_quantum_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:54.976606+00:00"
+instance: "kb-cron"
+---
+
+At small values of 
+  
+    
+      
+        β
+      
+    
+    {\displaystyle \beta }
+  
+, at high temperatures, the average energy U is equal to 
+  
+    
+      
+        1
+        
+          /
+        
+        β
+        =
+        k
+        T
+      
+    
+    {\displaystyle 1/\beta =kT}
+  
+. This reproduces the equipartition theorem of classical thermodynamics: every harmonic oscillator at temperature T has energy kT on average. This means that the specific heat of an oscillator is constant in classical mechanics and equal to k. For a collection of atoms connected by springs, a reasonable model of a solid, the total specific heat is equal to the total number of oscillators times k. There are overall three oscillators for each atom, corresponding to the three possible directions of independent oscillations in three dimensions. So the specific heat of a classical solid is always 3k per atom, or in chemistry units, 3R per mole of atoms.
+Monatomic solids at room temperatures have approximately the same specific heat of 3k per atom, but at low temperatures they don't. The specific heat is smaller at colder temperatures, and it goes to zero at absolute zero. This is true for all material systems, and this observation is called the third law of thermodynamics. Classical mechanics cannot explain the third law, because in classical mechanics the specific heat is independent of the temperature.
+This contradiction between classical mechanics and the specific heat of cold materials was noted by James Clerk Maxwell in the 19th century, and remained a deep puzzle for those who advocated an atomic theory of matter. Einstein resolved this problem in 1906 by proposing that atomic motion is quantized. This was the first application of quantum theory to mechanical systems. A short while later, Peter Debye gave a quantitative theory of solid specific heats in terms of quantized oscillators with various frequencies (see Einstein solid and Debye model).
+
+=== One-dimensional potential: U = 0 ===
+One-dimensional problems are easy to solve. At any energy E, the value of the momentum p is found from the conservation equation:
+
+  
+    
+      
+        
+          
+            2
+            m
+            (
+            E
+            −
+            U
+            (
+            q
+            )
+            )
+          
+        
+        =
+        
+          
+            2
+            m
+            E
+          
+        
+        =
+        p
+        =
+        
+          const.
+        
+      
+    
+    {\displaystyle {\sqrt {2m(E-U(q))}}={\sqrt {2mE}}=p={\text{const.}}}
+  
+
+which is integrated over all values of q between the classical turning points, the places where the momentum vanishes. The integral is easiest for a particle in a box of length L, where the quantum condition is:
+
+  
+    
+      
+        2
+        
+          ∫
+          
+            0
+          
+          
+            L
+          
+        
+        p
+        
+        d
+        q
+        =
+        n
+        h
+      
+    
+    {\displaystyle 2\int _{0}^{L}p\,dq=nh}
+  
+
+which gives the allowed momenta:
+
+  
+    
+      
+        p
+        =
+        
+          
+            
+              n
+              h
+            
+            
+              2
+              L
+            
+          
+        
+      
+    
+    {\displaystyle p={nh \over 2L}}
+  
+
+and the energy levels
+
+  
+    
+      
+        
+          E
+          
+            n
+          
+        
+        =
+        
+          
+            
+              p
+              
+                2
+              
+            
+            
+              2
+              m
+            
+          
+        
+        =
+        
+          
+            
+              
+                n
+                
+                  2
+                
+              
+              
+                h
+                
+                  2
+                
+              
+            
+            
+              8
+              m
+              
+                L
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle E_{n}={p^{2} \over 2m}={n^{2}h^{2} \over 8mL^{2}}}
+  
+
+=== One-dimensional potential: U = Fx ===
+Another easy case to solve with the old quantum theory is a linear potential on the positive halfline, the constant confining force F binding a particle to an impenetrable wall. This case is much more difficult in the full quantum mechanical treatment, and unlike the other examples, the semiclassical answer here is not exact but approximate, becoming more accurate at large quantum numbers.
+
+  
+    
+      
+        2
+        
+          ∫
+          
+            0
+          
+          
+            
+              E
+              F
+            
+          
+        
+        
+          
+            2
+            m
+            (
+            E
+            −
+            F
+            x
+            )
+          
+        
+         
+        d
+        x
+        =
+        n
+        h
+      
+    
+    {\displaystyle 2\int _{0}^{\frac {E}{F}}{\sqrt {2m(E-Fx)}}\ dx=nh}
+  
+
+so that the quantum condition is
+
+  
+    
+      
+        
+          
+            4
+            3
+          
+        
+        
+          
+            2
+            m
+          
+        
+        
+          
+            
+              E
+              
+                3
+                
+                  /
+                
+                2
+              
+            
+            F
+          
+        
+        =
+        n
+        h
+      
+    
+    {\displaystyle {4 \over 3}{\sqrt {2m}}{E^{3/2} \over F}=nh}
+  
+
+which determines the energy levels,
+
+  
+    
+      
+        
+          E
+          
+            n
+          
+        
+        =
+        
+          
+            (
+            
+              
+                
+                  3
+                  n
+                  h
+                  F
+                
+                
+                  4
+                  
+                    
+                      2
+                      m
+                    
+                  
+                
+              
+            
+            )
+          
+          
+            2
+            
+              /
+            
+            3
+          
+        
+      
+    
+    {\displaystyle E_{n}=\left({3nhF \over 4{\sqrt {2m}}}\right)^{2/3}}
+  
+
+In the specific case F=mg, the particle is confined by the gravitational potential of the earth and the "wall" here is the surface of the earth.
+
+=== One-dimensional potential: U = 1⁄2kx2 ===
+This case is also easy to solve, and the semiclassical answer here agrees with the quantum one to within the ground-state energy. Its quantization-condition integral is
+
+  
+    
+      
+        2
+        
+          ∫
+          
+            −
+            
+              
+                
+                  
+                    2
+                    E
+                  
+                  k
+                
+              
+            
+          
+          
+            
+              
+                
+                  2
+                  E
+                
+                k
+              
+            
+          
+        
+        
+          
+            2
+            m
+            
+              (
+              
+                E
+                −
+                
+                  
+                    1
+                    2
+                  
+                
+                k
+                
+                  x
+                  
+                    2
+                  
+                
+              
+              )
+            
+          
+        
+         
+        d
+        x
+        =
+        n
+        h
+      
+    
+    {\displaystyle 2\int _{-{\sqrt {\frac {2E}{k}}}}^{\sqrt {\frac {2E}{k}}}{\sqrt {2m\left(E-{\frac {1}{2}}kx^{2}\right)}}\ dx=nh}
+  
+
+with solution
+
+  
+    
+      
+        E
+        =
+        n
+        
+          
+            h
+            
+              2
+              π
+            
+          
+        
+        
+          
+            
+              k
+              m
+            
+          
+        
+        =
+        n
+        ℏ
+        ω
+      
+    
+    {\displaystyle E=n{\frac {h}{2\pi }}{\sqrt {\frac {k}{m}}}=n\hbar \omega }
+  
+
+for oscillation angular frequency 
+  
+    
+      
+        ω
+      
+    
+    {\displaystyle \omega }
+  
+, as before.
+
+=== Rotator ===
+Another simple system is the rotator. A rotator consists of a mass M at the end of a massless rigid rod of length R and in two dimensions has the Lagrangian:
+
+  
+    
+      
+        L
+        =
+        
+          
+            
+              M
+              
+                R
+                
+                  2
+                
+              
+            
+            2
+          
+        
+        
+          
+            
+              
+                θ
+                ˙
+              
+            
+          
+          
+            2
+          
+        
+      
+    
+    {\displaystyle L={MR^{2} \over 2}{\dot {\theta }}^{2}}
+  
+
+which determines that the angular momentum J conjugate to 
+  
+    
+      
+        θ
+      
+    
+    {\displaystyle \theta }
+  
+, the polar angle, 
+  
+    
+      
+        J
+        =
+        M
+        
+          R
+          
+            2
+          
+        
+        
+          
+            
+              θ
+              ˙
+            
+          
+        
+      
+    
+    {\displaystyle J=MR^{2}{\dot {\theta }}}
+  
+. The old quantum condition requires that J multiplied by the period of 
+  
+    
+      
+        θ
+      
+    
+    {\displaystyle \theta }
+  
+ is an integer multiple of the Planck constant:
+
+  
+    
+      
+        2
+        π
+        J
+        =
+        n
+        h
+      
+    
+    {\displaystyle 2\pi J=nh}
+  
+
+the angular momentum to be an integer multiple of 
+  
+    
+      
+        ℏ
+      
+    
+    {\displaystyle \hbar }
+  
+. In the Bohr model, this restriction imposed on circular orbits was enough to determine the energy levels.
+In three dimensions, a rigid rotator can be described by two angles — 
+  
+    
+      
+        θ
+      
+    
+    {\displaystyle \theta }
+  
+ and 
+  
+    
+      
+        ϕ
+      
+    
+    {\displaystyle \phi }
+  
+, where 
+  
+    
+      
+        θ
+      
+    
+    {\displaystyle \theta }
+  
+ is the inclination relative to an arbitrarily chosen z-axis while 
+  
+    
+      
+        ϕ
+      
+    
+    {\displaystyle \phi }
+  
+ is the rotator angle in the projection to the x–y plane. The kinetic energy is again the only contribution to the Lagrangian:
+
+  
+    
+      
+        L
+        =
+        
+          
+            
+              M
+              
+                R
+                
+                  2
+                
+              
+            
+            2
+          
+        
+        
+          
+            
+              
+                θ
+                ˙
+              
+            
+          
+          
+            2
+          
+        
+        +
+        
+          
+            
+              M
+              
+                R
+                
+                  2
+                
+              
+            
+            2
+          
+        
+        (
+        sin
+        ⁡
+        (
+        θ
+        )
+        
+          
+            
+              ϕ
+              ˙
+            
+          
+        
+        
+          )
+          
+            2
+          
+        
+      
+    
+    {\displaystyle L={MR^{2} \over 2}{\dot {\theta }}^{2}+{MR^{2} \over 2}(\sin(\theta ){\dot {\phi }})^{2}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Old_quantum_theory-3.md b/data/en.wikipedia.org/wiki/Old_quantum_theory-3.md
new file mode 100644
index 000000000..7ec23a513
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Old_quantum_theory-3.md
@@ -0,0 +1,462 @@
+---
+title: "Old quantum theory"
+chunk: 4/5
+source: "https://en.wikipedia.org/wiki/Old_quantum_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:54.976606+00:00"
+instance: "kb-cron"
+---
+
+And the conjugate momenta are 
+  
+    
+      
+        
+          p
+          
+            θ
+          
+        
+        =
+        
+          
+            
+              θ
+              ˙
+            
+          
+        
+      
+    
+    {\displaystyle p_{\theta }={\dot {\theta }}}
+  
+ and 
+  
+    
+      
+        
+          p
+          
+            ϕ
+          
+        
+        =
+        sin
+        ⁡
+        (
+        θ
+        
+          )
+          
+            2
+          
+        
+        
+          
+            
+              ϕ
+              ˙
+            
+          
+        
+      
+    
+    {\displaystyle p_{\phi }=\sin(\theta )^{2}{\dot {\phi }}}
+  
+. The equation of motion for 
+  
+    
+      
+        ϕ
+      
+    
+    {\displaystyle \phi }
+  
+ is trivial: 
+  
+    
+      
+        
+          p
+          
+            ϕ
+          
+        
+      
+    
+    {\displaystyle p_{\phi }}
+  
+ is a constant:
+
+  
+    
+      
+        
+          p
+          
+            ϕ
+          
+        
+        =
+        
+          l
+          
+            ϕ
+          
+        
+      
+    
+    {\displaystyle p_{\phi }=l_{\phi }}
+  
+
+which is the z-component of the angular momentum. The quantum condition demands that the integral of the constant 
+  
+    
+      
+        
+          l
+          
+            ϕ
+          
+        
+      
+    
+    {\displaystyle l_{\phi }}
+  
+ as 
+  
+    
+      
+        ϕ
+      
+    
+    {\displaystyle \phi }
+  
+ varies from 0 to 
+  
+    
+      
+        2
+        π
+      
+    
+    {\displaystyle 2\pi }
+  
+ is an integer multiple of h:
+
+  
+    
+      
+        
+          l
+          
+            ϕ
+          
+        
+        =
+        m
+        ℏ
+      
+    
+    {\displaystyle l_{\phi }=m\hbar }
+  
+
+And m is called the magnetic quantum number, because the z component of the angular momentum is the magnetic moment of the rotator along the z direction in the case where the particle at the end of the rotator is charged.
+Since the three-dimensional rotator is rotating about an axis, the total angular momentum should be restricted in the same way as the two-dimensional rotator. The two quantum conditions restrict the total angular momentum and the z-component of the angular momentum to be the integers l,m. This condition is reproduced in modern quantum mechanics, but in the era of the old quantum theory it led to a paradox: how can the orientation of the angular momentum relative to the arbitrarily chosen z-axis be quantized? This seems to pick out a direction in space.
+This phenomenon, the quantization of angular momentum about an axis, was given the name space quantization, because it seemed incompatible with rotational invariance. In modern quantum mechanics, the angular momentum is quantized the same way, but the discrete states of definite angular momentum in any one orientation are quantum superpositions of the states in other orientations, so that the process of quantization does not pick out a preferred axis. For this reason, the name "space quantization" fell out of favor, and the same phenomenon is now called the quantization of angular momentum.
+
+=== Hydrogen atom ===
+The angular part of the hydrogen atom is just the rotator, and gives the quantum numbers l and m. The only remaining variable is the radial coordinate, which executes a periodic one-dimensional potential motion, which can be solved.
+For a fixed value of the total angular momentum L, the Hamiltonian for a classical Kepler problem is (the unit of mass and unit of energy redefined to absorb two constants):
+
+  
+    
+      
+        H
+        =
+        
+          
+            
+              p
+              
+                r
+              
+              
+                2
+              
+            
+            2
+          
+        
+        +
+        
+          
+            
+              l
+              
+                2
+              
+            
+            
+              2
+              
+                r
+                
+                  2
+                
+              
+            
+          
+        
+        −
+        
+          
+            1
+            r
+          
+        
+        .
+      
+    
+    {\displaystyle H={p_{r}^{2} \over 2}+{l^{2} \over 2r^{2}}-{1 \over r}.}
+  
+
+Fixing the energy to be (a negative) constant and solving for the radial momentum 
+  
+    
+      
+        
+          p
+          
+            r
+          
+        
+      
+    
+    {\displaystyle p_{r}}
+  
+, the quantum condition integral is:
+
+  
+    
+      
+        ∮
+        
+          
+            2
+            E
+            −
+            
+              
+                
+                  l
+                  
+                    2
+                  
+                
+                
+                  r
+                  
+                    2
+                  
+                
+              
+            
+            +
+            
+              
+                2
+                r
+              
+            
+          
+        
+         
+        d
+        r
+        =
+        k
+        h
+      
+    
+    {\displaystyle \oint {\sqrt {2E-{l^{2} \over r^{2}}+{2 \over r}}}\ dr=kh}
+  
+
+which can be solved with the method of residues, and gives a new quantum number 
+  
+    
+      
+        k
+      
+    
+    {\displaystyle k}
+  
+ which determines the energy in combination with 
+  
+    
+      
+        l
+      
+    
+    {\displaystyle l}
+  
+. The energy is:
+
+  
+    
+      
+        E
+        =
+        −
+        
+          
+            1
+            
+              2
+              (
+              k
+              +
+              l
+              
+                )
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle E=-{1 \over 2(k+l)^{2}}}
+  
+
+and it only depends on the sum of k and l, which is the principal quantum number n. Since k is positive, the allowed values of l for any given n are no bigger than n. The energies reproduce those in the Bohr model, except with the correct quantum mechanical multiplicities, with some ambiguity at the extreme values.
+
+== De Broglie waves ==
+In 1905, Einstein noted that the entropy of the quantized electromagnetic field oscillators in a box is, for short wavelength, equal to the entropy of a gas of point particles in the same box. The number of point particles is equal to the number of quanta. Einstein concluded that the quanta could be treated as if they were localizable objects 
+(see page 139/140), particles of light. Today we call them photons (a name coined by Gilbert N. Lewis in a letter to Nature.)
+Einstein's theoretical argument was based on thermodynamics, on counting the number of states, and so was not completely convincing. Nevertheless, he concluded that light had attributes of both waves and particles, more precisely that an electromagnetic standing wave with frequency 
+  
+    
+      
+        ω
+      
+    
+    {\displaystyle \omega }
+  
+ with the quantized energy:
+
+  
+    
+      
+        E
+        =
+        n
+        ℏ
+        ω
+        
+      
+    
+    {\displaystyle E=n\hbar \omega \,}
+  
+
+should be thought of as consisting of n photons each with an energy 
+  
+    
+      
+        ℏ
+        ω
+      
+    
+    {\displaystyle \hbar \omega }
+  
+. Einstein could not describe how the photons were related to the wave.
+The photons have momentum as well as energy, and the momentum had to be 
+  
+    
+      
+        ℏ
+        k
+      
+    
+    {\displaystyle \hbar k}
+  
+ where 
+  
+    
+      
+        k
+      
+    
+    {\displaystyle k}
+  
+ is the wavenumber of the electromagnetic wave. This is required by relativity, because the momentum and energy form a four-vector, as do the frequency and wave-number.
+In 1924, as a PhD candidate, Louis de Broglie proposed a new interpretation of the quantum condition. He suggested that all matter, electrons as well as photons, are described by waves obeying the relations.
+
+  
+    
+      
+        p
+        =
+        ℏ
+        k
+      
+    
+    {\displaystyle p=\hbar k}
+  
+
+or, expressed in terms of wavelength 
+  
+    
+      
+        λ
+      
+    
+    {\displaystyle \lambda }
+  
+ instead,
+
+  
+    
+      
+        p
+        =
+        
+          
+            h
+            λ
+          
+        
+      
+    
+    {\displaystyle p={h \over \lambda }}
+  
+
+He then noted that the quantum condition:
+
+  
+    
+      
+        ∫
+        p
+        
+        d
+        x
+        =
+        ℏ
+        ∫
+        k
+        
+        d
+        x
+        =
+        2
+        π
+        ℏ
+        n
+      
+    
+    {\displaystyle \int p\,dx=\hbar \int k\,dx=2\pi \hbar n}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Old_quantum_theory-4.md b/data/en.wikipedia.org/wiki/Old_quantum_theory-4.md
new file mode 100644
index 000000000..8d5c5ab33
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Old_quantum_theory-4.md
@@ -0,0 +1,206 @@
+---
+title: "Old quantum theory"
+chunk: 5/5
+source: "https://en.wikipedia.org/wiki/Old_quantum_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:54.976606+00:00"
+instance: "kb-cron"
+---
+
+counts the change in phase for the wave as it travels along the classical orbit, and requires that it be an integer multiple of 
+  
+    
+      
+        2
+        π
+      
+    
+    {\displaystyle 2\pi }
+  
+. Expressed in wavelengths, the number of wavelengths along a classical orbit must be an integer. This is the condition for constructive interference, and it explained the reason for quantized orbits—the matter waves make standing waves only at discrete frequencies, at discrete energies.
+For example, for a particle confined in a box, a standing wave must fit an integer number of wavelengths between twice the distance between the walls. The condition becomes:
+
+  
+    
+      
+        n
+        λ
+        =
+        2
+        L
+      
+    
+    {\displaystyle n\lambda =2L}
+  
+
+so that the quantized momenta are:
+
+  
+    
+      
+        p
+        =
+        
+          
+            
+              n
+              h
+            
+            
+              2
+              L
+            
+          
+        
+      
+    
+    {\displaystyle p={\frac {nh}{2L}}}
+  
+
+reproducing the old quantum energy levels.
+This development was given a more mathematical form by Einstein, who noted that the phase function for the waves, 
+  
+    
+      
+        θ
+        (
+        J
+        ,
+        x
+        )
+      
+    
+    {\displaystyle \theta (J,x)}
+  
+, in a mechanical system should be identified with the solution to the Hamilton–Jacobi equation, an equation which William Rowan Hamilton believed to be a short-wavelength limit of a sort of wave mechanics in the 19th century. Schrödinger then found the proper wave equation which matched the Hamilton–Jacobi equation for the phase; this is now known as the Schrödinger equation.
+
+== Kramers transition matrix ==
+The old quantum theory was formulated only for special mechanical systems which could be separated into action angle variables which were periodic. It did not deal with the emission and absorption of radiation. Nevertheless, Hendrik Kramers was able to find heuristics for describing how emission and absorption should be calculated.
+Kramers suggested that the orbits of a quantum system should be Fourier analyzed, decomposed into harmonics at multiples of the orbit frequency:
+
+  
+    
+      
+        
+          X
+          
+            n
+          
+        
+        (
+        t
+        )
+        =
+        
+          ∑
+          
+            k
+            =
+            −
+            ∞
+          
+          
+            ∞
+          
+        
+        
+          e
+          
+            i
+            k
+            ω
+            t
+          
+        
+        
+          X
+          
+            n
+            ;
+            k
+          
+        
+      
+    
+    {\displaystyle X_{n}(t)=\sum _{k=-\infty }^{\infty }e^{ik\omega t}X_{n;k}}
+  
+
+The index n describes the quantum numbers of the orbit, it would be n–l–m in the Sommerfeld model. The frequency 
+  
+    
+      
+        ω
+      
+    
+    {\displaystyle \omega }
+  
+ is the angular frequency of the orbit 
+  
+    
+      
+        2
+        π
+        
+          /
+        
+        
+          T
+          
+            n
+          
+        
+      
+    
+    {\displaystyle 2\pi /T_{n}}
+  
+ while k is an index for the Fourier mode. Bohr had suggested that the k-th harmonic of the classical motion correspond to the transition from level n to level n−k.
+Kramers proposed that the transition between states were analogous to classical emission of radiation, which happens at frequencies at multiples of the orbit frequencies. The rate of emission of radiation is proportional to 
+  
+    
+      
+        
+          |
+        
+        
+          X
+          
+            k
+          
+        
+        
+          
+            |
+          
+          
+            2
+          
+        
+      
+    
+    {\displaystyle |X_{k}|^{2}}
+  
+, as it would be in classical mechanics. The description was approximate, since the Fourier components did not have frequencies that exactly match the energy spacings between levels.
+This idea led to the development of matrix mechanics.
+
+== Limitations ==
+The old quantum theory had some limitations:
+
+The old quantum theory provides no means to calculate the intensities of the spectral lines.
+It fails to explain the anomalous Zeeman effect (that is, where the spin of the electron cannot be neglected).
+It cannot quantize "chaotic" systems, i.e. dynamical systems in which trajectories are neither closed nor periodic and whose analytical form does not exist. This presents a problem for systems as simple as a 2-electron atom which is classically chaotic analogously to the famous gravitational three-body problem.
+However it can be used to describe atoms with more than one electron (e.g. Helium) and the Zeeman effect. 
+It was later proposed that the old quantum theory is in fact the semi-classical approximation to the canonical quantum mechanics but its limitations are still under investigation.
+
+== See also ==
+
+Bohr model
+Bohr–Sommerfeld model
+BKS theory
+
+== References ==
+
+== Further reading ==
+Thewlis, J., ed. (1962). Encyclopaedic Dictionary of Physics.
+Pais, Abraham (1982). "Max Born's Statistical Interpretation of Quantum Mechanics" (PDF). Science. 218 (4578): 1193–8. Bibcode:1982Sci...218.1193P. doi:10.1126/science.218.4578.1193. PMID 17802457. S2CID 34406257. Address to annual meeting of the Optical Society of America October 21, 1982 (Tucson AZ). Retrieved 2013-09-08.
+Planck, Max (1922). The origin and development of the quantum theory. Translated by Silberstein, L.; Clarke, H. T. Oxford: Clarendon Press.
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+title: "Oxford Calculators"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Oxford_Calculators"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:58.839669+00:00"
+instance: "kb-cron"
+---
+
+The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford; for this reason they were dubbed "The Merton School". Their work incorporated a logical and mathematical approach to philosophical problems.
+The key "calculators", writing in the second quarter of the 14th century, were Thomas Bradwardine, William Heytesbury, Richard Swineshead, and John Dumbleton.
+Using the slightly earlier works of Walter Burley, Gerard of Brussels, and Nicole Oresme, these individuals expanded upon the concepts of 'latitudes' and what real world applications they could apply them to.
+
+== Science ==
+
+The Oxford Calculators' advances were initially purely mathematical but later became relevant to mechanics. Using Aristotelian logic and physics, they studied and attempted to quantify physical and observable characteristics such as: heat, force, color, density, and light. Aristotle believed that only length and motion were able to be quantified. However, they used his philosophy and proved it untrue by being able to calculate things such as temperature and power. Although they attempted to quantify these observable characteristics, their interests lay more in the philosophical and logical aspects than in natural world. They used numbers to disagree philosophically and prove the reasoning of "why" something worked the way it did and not only "how" something functioned the way that it did.
+Historian David C. Lindberg and professor Michael H. Shank in their 2013 book, Cambridge History of Science, Volume 2: Medieval Science, wrote:
+
+Like Bradwardine's theorem, the methods and results of the other Oxford Calculators spread to the continent over the next generation, appearing most notably at the University of Paris in the works of Albert of Saxony, Nicole Oresme, and Marsilius of Inghen.Lawrence M. Principe wrote:A group known as the Oxford Calculators had begun applying mathematics to motion in the 1300s; in fact, Galileo begins his exposition of kinematics in the Two New Sciences with a theorem they enunciated. But Galileo went much further by linking mathematical abstraction tightly with experimental observation.
+
+=== Mean Speed Theorem ===
+The Oxford Calculators distinguished kinematics from dynamics, emphasizing kinematics, and investigating instantaneous velocity. It is through their understanding of geometry and how different shapes could be used to represent a body in motion. The Calculators related these bodies in relative motion to geometrical shapes and also understood that a right triangle's area would be equivalent to a rectangle's if the rectangle's height was half of the triangle's. This, and developing Al-Battani's work on trigonometry is what led to the formulating of the mean speed theorem (though it was later credited to Galileo) which is also known as "The Law of Falling Bodies".  A basic definition of the mean speed theorem is; a body moving with constant speed will travel the same distance as an accelerated body in the same period of time as long as the body with constant speed travels at half of the sum of initial and final velocities for the accelerated body. Its earliest known mention is found in Heytesbury's Rules for Solving Sophisms: a body uniformly accelerated or decelerated for a given time covers the same distance as it would if it were to travel for the same time uniformly with the speed of the middle instant of its motion, which is defined as its mean speed. Relative motion, also referred to as local motion, can be defined as motion relative to another object where the values for acceleration, velocity, and position are dependent upon a predetermined reference point. 
+The mathematical physicist and historian of science Clifford Truesdell, wrote:
+
+The now published sources prove to us, beyond contention, that the main kinematical properties of uniformly accelerated motions, still attributed to Galileo by the physics texts, were discovered and proved by scholars of Merton college.... In principle, the qualities of Greek physics were replaced, at least for motions, by the numerical quantities that have ruled Western science ever since. The work was quickly diffused into France, Italy, and other parts of Europe. Almost immediately, Giovanni di Casale and Nicole Oresme found how to represent the results by geometrical graphs, introducing the connection between geometry and the physical world that became a second characteristic habit of Western thought ...
+
+=== Boethian Theory ===
+In Tractatus de proportionibus (1328), Bradwardine extended the theory of proportions of Eudoxus to anticipate the concept of exponential growth, later developed by Bernoulli and Euler, with compound interest as a special case. Arguments for the mean speed theorem (above) require the modern concept of limit, so Bradwardine had to use arguments of his day. Mathematician and mathematical historian Carl Benjamin Boyer writes, "Bradwardine developed the Boethian theory of double or triple or, more generally, what we would call 'n-tuple' proportion".
+Boyer also writes that "the works of Bradwardine had contained some fundamentals of trigonometry". Yet "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science." The most essential missing tool was algebra.
+
+A group known as the Oxford Calculators had begun applying mathematics to motion in the 1300s; in fact, Galileo begins his exposition of kinematics in the Two New Sciences with a theorem they enunciated. But Galileo went much further by linking mathematical abstraction tightly with experimental observation.
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+title: "Oxford Calculators"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Oxford_Calculators"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:58.839669+00:00"
+instance: "kb-cron"
+---
+
+=== Bradwardine's Rule ===
+Lindberg and Shank also wrote:In Book VII of Physics, Aristotle had treated in general the relation between powers, moved bodies, distance, and time, but his suggestions there were sufficiently ambiguous to give rise to considerable discussion and
+disagreement among his medieval commentators. The most successful theory, as well as the most mathematically sophisticated, was proposed by Thomas Bradwardine in his Treatise on the Ratios of Speeds in Motions. In this tour de force of medieval natural philosophy, Bradwardine devised a single simple rule to govern the relationship between moving and resisting powers and speeds that was both a brilliant application of mathematics to motion and also a tolerable interpretation of Aristotle's text.The initial goal of Bradwardine's Rule was to come up with a single rule in a general form that would show the relationship between moving and resisting powers and speed while at the same time precluded motion when the moving power is less than or equal to the resisting power. Before Bradwardine decided to use his own theory of compounded ratios in his own rule he considered and rejected four other opinions on the relationship between powers, resistances, and speeds. He then went on to use his own rule of compounded ratios which says that the ratio of speeds follows the ratios of motive to resistive powers. By applying medieval ratio theory to a controversial topic in Aristotle's Physics, Brawardine was able to make a simple, definite, and sophisticated mathematical rule for the relationship between speeds, powers, and resistances. Bradwardine's Rule was quickly accepted in the fourteenth century, first among his contemporaries at Oxford, where Richard Swineshead and John Dumbleton used it for solving sophisms, the logical and physical puzzles that were just beginning to assume and important place in the undergraduate arts curriculum.
+
+=== Latitude of Forms ===
+The Latitude of Forms is a topic that many of the Oxford Calculators published volumes on. Developed by Nicole Oresme, a “Latitude" is an abstract concept of a range that forms may vary inside of. Before latitudes were introduced into mechanics, they were used in both medical and philosophical fields. Medical authors Galen and Avicenna can be given credit for the origin of the concept. “Galen says, for instance, that there is a latitude of health which is divided into three parts, each in turn having some latitude. First, there is the latitude of healthy bodies, second the latitude of neither health nor sickness, and third the latitude of sickness.” The calculators attempted to measure and explain these changes in latitude concretely and mathematically. John Dumbleton discusses latitudes in Part II and Part III of his work the Summa. He is critical of earlier philosophers in Part II as he believes latitudes are measurable and quantifiable and later in Part III of the Summa attempts to use latitudes to measure local motion. Roger Swineshead defines five latitudes for local motion being: First, the latitude of local motion, Second, the latitude of velocity of local motion, Third, the latitude of slowness of the local motion, Fourth, the latitude of the acquisition of the latitude of local motion, and the Fifth being, the latitude of the loss of the latitude of local motion. Each of these latitudes are infinite and are comparable to the velocity, acceleration, and deceleration of the local motion of an object.
+
+== People ==
+
+=== Thomas Bradwardine ===
+Thomas Bradwardine was born in 1290 in Sussex, England. An attending student educated at Balliol College, Oxford, he earned various degrees. He was a secular cleric, a scholar, a theologist, a mathematician, and a physicist. He became chancellor of the diocese of London and Dean of St Paul's, as well as chaplain and confessor to Edward III. During his time at Oxford, he authored many books including: De Geometria Speculativa (printed in Paris, 1530), De Arithmetica Practica (printed in Paris, 1502), and De Proportionibus Velocitatum in Motibus (printed in Paris in 1495). Bradwardine furthered the study of using mathematics to explain physical reality. Drawing on the work of Robert Grosseteste, Robert Kilwardby and Roger Bacon, his work was in direct opposition to William of Ockham.
+Aristotle suggested that velocity was proportional to force and inversely proportional to resistance, doubling the force would double the velocity but doubling the resistance would halve the velocity (V ∝ F/R). Bradwardine objected saying that this is not observed because the velocity does not equal zero when the resistance exceeds the force. Instead, he proposed a new theory that, in modern terms, would be written as (V ∝ log F/R), which was widely accepted until the late sixteenth century.
+
+=== William Heytesbury ===
+William Heytesbury was a bursar at Merton until the late 1330s and he administered the college properties in Northumberland. Later in his life he was a chancellor of Oxford. He was the first to discover the mean-speed theorem, later "The Law of Falling Bodies". Unlike Bradwardine's theory, the theorem, also known as "The Merton Rule" is a probable truth.
+His most noted work was Regulae Solvendi Sophismata (Rules for Solving Sophisms). Sophisma is a statement which one can argue to be both true and false. The resolution of these arguments and determination of the real state of affairs forces one to deal with logical matters such as the analysis of the meaning of the statement in question, and the application of logical rules to specific cases. An example would be the statement, "The compound H2O is both a solid and a liquid". When the temperature is low enough this statement is true. But it may be argued and proven false at a higher temperature. In his time, this work was logically advanced.
+He was a second generation calculator. He built on Richard Klivingston's "Sophistimata and Bradwardine's "Insolubilia". Later, his work went on to influence Peter of Mantura and Paul of Venice.
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+---
+title: "Oxford Calculators"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Oxford_Calculators"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:29:58.839669+00:00"
+instance: "kb-cron"
+---
+
+=== Richard Swineshead ===
+Richard Swineshead was also an English mathematician, logician, and natural philosopher. The sixteenth-century polymath Girolamo Cardano placed him in the top-ten intellects of all time, alongside Archimedes, Aristotle, and Euclid.
+He became a member of the Oxford calculators in 1344. His main work was a series of treatises written in 1350. This work earned him the title of "The Calculator". His treatises were named Liber Calculationum, which means "Book of Calculations". His book dealt in exhaustive detail with quantitative physics and he had over fifty variations of Bradwardine's law.
+
+=== John Dumbleton ===
+John Dumbleton became a member of the calculators in 1338–39. After becoming a member, he left the calculators for a brief period of time to study theology in Paris in 1345–47. After his study there he returned to his work with the calculators in 1347–48. One of his main pieces of work, Summa logicae et philosophiae naturalis, focused on explaining the natural world in a coherent and realistic manner, unlike some of his colleagues, claiming that they were making light of serious endeavors. Dumbleton attempted many solutions to the latitude of things, most were refuted by Richard Swineshead in his Liber Calculationum.
+
+== See also ==
+Jean Buridan
+John Cantius
+Gerard of Brussels
+Henry of Langenstein
+Scholasticism
+Science in the Middle Ages
+Domingo de Soto
+
+== Notes ==
+
+== References ==
+Weisheipl, James A. (1959) "The Place of John Dumbleton in the Merton School"
+Clagett, Marshall (1964) “Nicole Oresme and Medieval Scientific Thought.” Proceedings of the American Philosophical Society
+Sylla, Edith D. (1973) "MEDIEVAL CONCEPTS OF THE LATITUDE OF FORMS: THE OXFORD CALCULATORS"
+Sylla, Edith D. (1999) "Oxford Calculators", in The Cambridge Dictionary of Philosophy.
+Gavroglu, Kostas; Renn, Jurgen (2007) "Positioning the History of Science".
+Agutter, Paul S.; Wheatley, Denys N. (2008) "Thinking About Life"
+Principe, Lawrence M. (2011) "The Scientific Revolution: A Very Short Introduction"
+
+== Further reading ==
+Carl B. Boyer (1949), The History of Calculus and Its Conceptual Development, New York: Hafner, reprinted in 1959, New York:  Dover.
+John Longeway, (2003), "William Heytesbury", in The Stanford Encyclopedia of Philosophy.  Accessed 2012 January 3.
+Uta C. Merzbach and Carl B. Boyer (2011), A History of Mathematics, Third Edition, Hoboken, NJ:  Wiley.
+Edith Sylla (1982), "The Oxford Calculators", in Norman Kretzmann, Anthony Kenny, and Jan Pinborg, edd. The Cambridge History of Later Medieval Philosophy: From the Rediscovery of Aristotle to the Disintegration of Scholasticism, 1100-1600, New York:  Cambridge.
+Boccaletti, Dino (2016). Galileo and the Equations of Motion. Heidelberg, New York: Springer. ISBN 978-3-319-20134-4.
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+---
+title: "Oxford Electric Bell"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Oxford_Electric_Bell"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:00.141199+00:00"
+instance: "kb-cron"
+---
+
+The Oxford Electric Bell or Clarendon Dry Pile is an experimental electric bell, in particular a type of bell that uses the electrostatic clock principle that was set up in 1840 and which has run nearly continuously ever since. It was one of the first pieces purchased for a collection of apparatus by clergyman and physicist Robert Walker. It is located in a corridor adjacent to the foyer of the Clarendon Laboratory at the University of Oxford, England, and is still ringing every half second, albeit inaudibly due to being behind two layers of glass.
+
+
+== Design ==
+The experiment consists of two brass bells, each positioned beneath a dry pile (a form of battery), the pair of piles connected in series, giving the bells opposite electric charges. The clapper is a metal sphere approximately 4 mm (3⁄16 in) in diameter suspended between the piles, which rings the bells alternately due to electrostatic forces. When the clapper touches one bell, it is charged by that pile. It is then repelled from that bell due to having the same charge and attracted to the other bell, which has the opposite charge. The clapper then touches the other bell and the process reverses, leading to oscillation. The use of electrostatic forces means that while high voltage is required to create motion, only a tiny amount of charge is carried from one bell to the other. As a result, the batteries drain very slowly, which is why the piles have been able to last since the apparatus was set up in 1840. Its oscillation frequency is 2 hertz, or every half second.
+The exact composition of the dry piles is unknown, but it is known that they have been coated with molten sulfur for insulation and it is thought that they may be Zamboni piles.
+At one point this sort of device played an important role in distinguishing between two different theories of electrical action: the theory of contact tension and the theory of chemical action.
+The Oxford Electric Bell does not demonstrate perpetual motion. The bell will eventually stop when the dry piles have distributed their charges equally if the clapper does not wear out first. The Bell has produced approximately 10 billion rings since 1840 and holds the Guinness World Record as "the world's most durable battery [delivering] ceaseless tintinnabulation".
+
+
+== Operation ==
+Apart from occasional short interruptions caused by high humidity, the bell has rung continuously since 1840. The bell may have been constructed in 1825.
+
+
+== See also ==
+Long-term experiment
+Franklin bells
+Beverly Clock (1864)
+Pitch drop experiment (1927)
+Clock of the Long Now
+
+
+== References ==
+
+
+== Further reading ==
+Willem Hackmann, "The Enigma of Volta's 'Contact Tension' and the Development of the 'Dry Pile'", appearing in Nuova Voltiana: Studies on Volta and His Times, nb Volume 3 (Fabio Bevilacqua; Lucio Frenonese (Editors)), 2000, pp. 103–119.
+"Exhibit 1 - The Clarendon Dry Pile". Oxford Physics Teaching, History Archive. Retrieved 14 June 2021.
+Croft, A. J. (1984). "The Oxford electric bell". European Journal of Physics. 5 (4): 193–194. Bibcode:1984EJPh....5..193C. doi:10.1088/0143-0807/5/4/001.
+Croft, A. J. (1985). "The Oxford electric bell". European Journal of Physics. 6 (2): 128. Bibcode:1985EJPh....6..128C. doi:10.1088/0143-0807/6/2/511.
+
+
+== External links ==
+Oxford Electric Bell, YouTube video with David Glover-Aoki (18 October 2011)
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+---
+title: "Philosophy of artificial intelligence"
+chunk: 1/7
+source: "https://en.wikipedia.org/wiki/Philosophy_of_artificial_intelligence"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:55.691404+00:00"
+instance: "kb-cron"
+---
+
+The philosophy of artificial intelligence is a branch of the philosophy of mind and the philosophy of computer science that explores artificial intelligence and its implications for knowledge and understanding of intelligence, ethics, consciousness, epistemology,  and free will. Furthermore, the technology is concerned with the creation of artificial animals or artificial people (or, at least, artificial creatures; see artificial life) so the discipline is of considerable interest to philosophers. These factors contributed to the emergence of the philosophy of artificial intelligence.
+The philosophy of artificial intelligence attempts to answer such questions as follows:
+
+Can a machine act intelligently? Can it solve any problem that a person would solve by thinking?
+Are human intelligence and machine intelligence the same? Is the human brain essentially a computer?
+Can a machine have a mind, mental states, and consciousness in the same sense that a human being can? Can it feel how things are? (i.e. does it have qualia?)
+Questions like these reflect the divergent interests of AI researchers, cognitive scientists and philosophers respectively. The scientific answers to these questions depend on the definition of "intelligence" and "consciousness" and exactly which "machines" are under discussion.
+Important propositions in the philosophy of AI include some of the following:
+
+Turing's "polite convention": If a machine behaves as intelligently as a human being, then it is as intelligent as a human being.
+The Dartmouth proposal: "Every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it."
+Allen Newell and Herbert A. Simon's physical symbol system hypothesis: "A physical symbol system has the necessary and sufficient means of general intelligent action."
+John Searle's strong AI hypothesis: "The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds."
+Hobbes' mechanism: "For 'reason' ... is nothing but 'reckoning,' that is adding and subtracting, of the consequences of general names agreed upon for the 'marking' and 'signifying' of our thoughts..."
+
+== Machine intelligence ==
+In AI research, questions about "intelligence" are concerned with the behavior of machines, and is not generally concerned with the concept of thought.
+
+=== Definitions of intelligence ===
+
+==== Turing test ====
+
+In 1949, computer scientist Alan Turing reduced the problem of defining intelligence to a simple question about conversation. He suggests that if a machine can answer any question posed to it, using the same words that an ordinary person would, then we may call that machine intelligent. A modern version of his experimental design would use an online chat room, where one of the participants is a real person and one of the participants is a computer program. The program passes the test if no one can tell which of the two participants is human. Turing notes that no one (except philosophers) ever asks the question "can people think?" He writes "instead of arguing continually over this point, it is usual to have a polite convention that everyone thinks". Turing's test extends this polite convention to machines, proposing that if a machine acts as intelligently as a human being, then it is as intelligent as a human being.
+One criticism of the Turing test is that it only measures the "humanness" of the machine's behavior, rather than the "intelligence" of the behavior. Since human behavior and intelligent behavior are not exactly the same thing, the test fails to measure intelligence. Stuart J. Russell and Peter Norvig write that "aeronautical engineering texts do not define the goal of their field as 'making machines that fly so exactly like pigeons that they can fool other pigeons'".
+
+==== Intelligence as achieving goals ====
+
+Twenty-first century AI research defines intelligence in terms of goal-directed behavior. It views intelligence as a set of problems that the machine is expected to solve – the more problems it can solve, and the better its solutions are, the more intelligent the program is. AI founder John McCarthy defined intelligence as "the computational part of the ability to achieve goals in the world."
+Stuart Russell and Peter Norvig formalized this definition using abstract intelligent agents. An "agent" is something which perceives and acts in an environment. A "performance measure" defines what counts as success for the agent. 
+
+"If an agent acts so as to maximize the expected value of a performance measure based on past experience and knowledge then it is intelligent."
+Definitions like this one try to capture the essence of intelligence. They have the advantage that, unlike the Turing test, they do not also test for unintelligent human traits such as making typing mistakes. 
+They have the disadvantage that they can fail to differentiate between "things that think" and "things that do not". By this definition, even a thermostat has a rudimentary intelligence.
+
+=== Arguments that a machine can display general intelligence ===
+
+==== The brain can be simulated ====
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+title: "Philosophy of artificial intelligence"
+chunk: 2/7
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:55.691404+00:00"
+instance: "kb-cron"
+---
+
+Hubert Dreyfus describes this argument as claiming that "if the nervous system obeys the laws of physics and chemistry, which we have every reason to suppose it does, then ... we ... ought to be able to reproduce the behavior of the nervous system with some physical device". This argument, first introduced as early as 1943 and vividly described by Hans Moravec in 1988, 
+is now associated with futurist Ray Kurzweil, who estimates that computer power will be sufficient for a complete brain simulation by the year 2029. A non-real-time simulation of a thalamocortical model that has the size of the human brain (1011 neurons) was performed in 2005, and it took 50 days to simulate 1 second of brain dynamics on a cluster of 27 processors.
+Even AI's harshest critics (such as Hubert Dreyfus and John Searle) agree that a brain simulation is possible in theory.
+However, Searle points out that, in principle, anything can be simulated by a computer; thus, bringing the definition to its breaking point leads to the conclusion that any process at all can technically be considered "computation". "What we wanted to know is what distinguishes the mind from thermostats and livers," he writes. Thus, merely simulating the functioning of a living brain would in itself be an admission of ignorance regarding intelligence and the nature of the mind, like trying to build a jet airliner by copying a living bird precisely, feather by feather, with no theoretical understanding of aeronautical engineering.
+
+==== Human thinking is symbol processing ====
+
+In 1963, Allen Newell and Herbert A. Simon proposed that "symbol manipulation" was the essence of both human and machine intelligence. They wrote: 
+
+"A physical symbol system has the necessary and sufficient means of general intelligent action."
+This claim is very strong: it implies both that human thinking is a kind of symbol manipulation (because a symbol system is necessary for intelligence) and that machines can be intelligent (because a symbol system is sufficient for intelligence).
+Another version of this position was described by philosopher Hubert Dreyfus, who called it "the psychological assumption":
+
+"The mind can be viewed as a device operating on bits of information according to formal rules."
+The "symbols" that Newell, Simon and Dreyfus discussed were word-like and high level—symbols that directly correspond with objects in the world, such as <dog> and <tail>. Most AI programs written between 1956 and 1990 used this kind of symbol. Modern AI, based on statistics and mathematical optimization, does not use the high-level "symbol processing" that Newell and Simon discussed.
+
+==== Arguments against symbol processing ====
+These arguments show that human thinking does not consist (solely) of high level symbol manipulation. They do not show that artificial intelligence is impossible, only that more than symbol processing is required.
+
+===== Gödelian anti-mechanist arguments =====
+
+In 1931, Kurt Gödel proved with an incompleteness theorem that it is always possible to construct a "Gödel statement" that a given consistent formal system of logic (such as a high-level symbol manipulation program) could not prove. Despite being a true statement, the constructed Gödel statement is unprovable in the given system. (The truth of the constructed Gödel statement is contingent on the consistency of the given system; applying the same process to a subtly inconsistent system will appear to succeed, but will actually yield a false "Gödel statement" instead.) More speculatively, Gödel conjectured that the human mind can eventually correctly determine the truth or falsity of any well-grounded mathematical statement (including any possible Gödel statement), and that therefore the human mind's power is not reducible to a mechanism. Philosopher John Lucas (since 1961) and Roger Penrose (since 1989) have championed this philosophical anti-mechanist argument.
+Gödelian anti-mechanist arguments tend to rely on the innocuous-seeming claim that a system of human mathematicians (or some idealization of human mathematicians) is both consistent (completely free of error) and believes fully in its own consistency (and can make all logical inferences that follow from its own consistency, including belief in its Gödel statement) . This is probably impossible for a Turing machine to do (see Halting problem); therefore, the Gödelian concludes that human reasoning is too powerful to be captured by a Turing machine, and by extension, any digital mechanical device.
+However, the modern consensus in the scientific and mathematical community is that actual human reasoning is inconsistent; that any consistent "idealized version" H of human reasoning would logically be forced to adopt a healthy but counter-intuitive open-minded skepticism about the consistency of H (otherwise H is provably inconsistent); and that Gödel's theorems do not lead to any valid argument that humans have mathematical reasoning capabilities beyond what a machine could ever duplicate. This consensus that Gödelian anti-mechanist arguments are doomed to failure is laid out strongly in Artificial Intelligence: "any attempt to utilize (Gödel's incompleteness results) to attack the computationalist thesis is bound to be illegitimate, since these results are quite consistent with the computationalist thesis."
+Stuart Russell and Peter Norvig agree that Gödel's argument does not consider the nature of real-world human reasoning. It applies to what can theoretically be proved, given an infinite amount of memory and time. In practice, real machines (including humans) have finite resources and will have difficulty proving many theorems. It is not necessary to be able to prove everything in order to be an intelligent person.
+Less formally, Douglas Hofstadter, in his Pulitzer Prize winning book Gödel, Escher, Bach: An Eternal Golden Braid, states that these "Gödel-statements" always refer to the system itself, drawing an analogy to the way the Epimenides paradox uses statements that refer to themselves, such as "this statement is false" or "I am lying". But, of course, the Epimenides paradox applies to anything that makes statements, whether it is a machine or a human, even Lucas himself. Consider:
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+title: "Philosophy of artificial intelligence"
+chunk: 3/7
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+---
+
+Lucas can't assert the truth of this statement.
+This statement is true but cannot be asserted by Lucas. This shows that Lucas himself is subject to the same limits that he describes for machines, as are all people, and so Lucas's argument is pointless.
+After concluding that human reasoning is non-computable, Penrose went on to controversially speculate that some kind of hypothetical non-computable processes involving the collapse of quantum mechanical states give humans a special advantage over existing computers. Existing quantum computers are only capable of reducing the complexity of Turing computable tasks and are still restricted to tasks within the scope of Turing machines.  . By Penrose and Lucas's arguments, the fact that quantum computers are only able to complete Turing computable tasks implies that they cannot be sufficient for emulating the human mind. Therefore, Penrose seeks for some other process involving new physics, for instance quantum gravity which might manifest new physics at the scale of the Planck mass via spontaneous quantum collapse of the wave function. These states, he suggested, occur both within neurons and also spanning more than one neuron. However, other scientists point out that there is no plausible organic mechanism in the brain for harnessing any sort of quantum computation, and furthermore that the timescale of quantum decoherence seems too fast to influence neuron firing.
+
+===== Dreyfus: the primacy of implicit skills =====
+
+Hubert Dreyfus argued that human intelligence and expertise depended primarily on fast intuitive judgements rather than step-by-step symbolic manipulation, and argued that these skills would never be captured in formal rules.
+Dreyfus's argument had been anticipated by Turing in his 1950 paper Computing machinery and intelligence, where he had classified this as the "argument from the informality of behavior." Turing argued in response that, just because we do not know the rules that govern a complex behavior, this does not mean that no such rules exist. He wrote: "we cannot so easily convince ourselves of the absence of complete laws of behaviour ... The only way we know of for finding such laws is scientific observation, and we certainly know of no circumstances under which we could say, 'We have searched enough. There are no such laws.'"
+Russell and Norvig point out that, in the years since Dreyfus published his critique, progress has been made towards discovering the "rules" that govern unconscious reasoning. The situated movement in robotics research attempts to capture our unconscious skills at perception and attention. Computational intelligence paradigms, such as neural nets, evolutionary algorithms and so on are mostly directed at simulated unconscious reasoning and learning. Statistical approaches to AI can make predictions which approach the accuracy of human intuitive guesses. Research into commonsense knowledge has focused on reproducing the "background" or context of knowledge. In fact, AI research in general has moved away from high level symbol manipulation, towards new models that are intended to capture more of our intuitive reasoning.
+Cognitive science and psychology eventually came to agree with Dreyfus' description of human expertise. Daniel Kahnemann and others developed a similar theory where they identified two "systems" that humans use to solve problems, which he called "System 1" (fast intuitive judgements) and "System 2" (slow deliberate step by step thinking).
+Although Dreyfus' views have been vindicated in many ways, the work in cognitive science and in AI was in response to specific problems in those fields and was not directly influenced by Dreyfus. Historian and AI researcher Daniel Crevier wrote that "time has proven the accuracy and perceptiveness of some of Dreyfus's comments. Had he formulated them less aggressively, constructive actions they suggested might have been taken much earlier."
+
+== Can a machine have a mind, consciousness, and mental states? ==
+This is a philosophical question, related to the problem of other minds and the hard problem of consciousness. The question revolves around a position defined by John Searle as "strong AI":
+
+A physical symbol system can have a mind and mental states.
+Searle distinguished this position from what he called "weak AI":
+
+A physical symbol system can act intelligently.
+Searle introduced the terms to isolate strong AI from weak AI so he could focus on what he thought was the more interesting and debatable issue. He argued that even if we assume that we had a computer program that acted exactly like a human mind, there would still be a difficult philosophical question that needed to be answered.
+Neither of Searle's two positions are of great concern to AI research, since they do not directly answer the question "can a machine display general intelligence?" (unless it can also be shown that consciousness is necessary for intelligence). Turing wrote "I do not wish to give the impression that I think there is no mystery about consciousness… [b]ut I do not think these mysteries necessarily need to be solved before we can answer the question [of whether machines can think]." Russell and Norvig agree: "Most AI researchers take the weak AI hypothesis for granted, and don't care about the strong AI hypothesis."
+There are a few researchers who believe that consciousness is an essential element in intelligence, such as Igor Aleksander, Stan Franklin, Ron Sun, and Pentti Haikonen, although their definition of "consciousness" strays very close to "intelligence". (See artificial consciousness.)
+Before we can answer this question, we must be clear what we mean by "minds", "mental states" and "consciousness".
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+instance: "kb-cron"
+---
+
+=== Consciousness, minds, mental states, meaning ===
+The words "mind" and "consciousness" are used by different communities in different ways. Some new age thinkers, for example, use the word "consciousness" to describe something similar to Bergson's "élan vital": an invisible, energetic fluid that permeates life and especially the mind. Science fiction writers use the word to describe some essential property that makes us human: a machine or alien that is "conscious" will be presented as a fully human character, with intelligence, desires, will, insight, pride and so on. (Science fiction writers also use the words "sentience", "sapience", "self-awareness" or "ghost"—as in the Ghost in the Shell manga and anime series—to describe this essential human property). For others , the words "mind" or "consciousness" are used as a kind of secular synonym for the soul.
+For philosophers, neuroscientists and cognitive scientists, the words are used in a way that is both more precise and more mundane: they refer to the familiar, everyday experience of having a "thought in your head", like a perception, a dream, an intention or a plan, and to the way we see something, know something, mean something or understand something. "It's not hard to give a commonsense definition of consciousness" observes philosopher John Searle. What is mysterious and fascinating is not so much what it is but how it is: how does a lump of fatty tissue and electricity give rise to this (familiar) experience of perceiving, meaning or thinking?
+Philosophers call this the hard problem of consciousness. It is the latest version of a classic problem in the philosophy of mind called the "mind-body problem". A related problem is the problem of meaning or understanding (which philosophers call "intentionality"): what is the connection between our thoughts and what we are thinking about (i.e. objects and situations out in the world)? A third issue is the problem of experience (or "phenomenology"): If two people see the same thing, do they have the same experience? Or are there things "inside their head" (called "qualia") that can be different from person to person?
+Neurobiologists believe all these problems will be solved as we begin to identify the neural correlates of consciousness: the actual relationship between the machinery in our heads and its collective properties; such as the mind, experience and understanding. Some of the harshest critics of artificial intelligence agree that the brain is just a machine, and that consciousness and intelligence are the result of physical processes in the brain. The difficult philosophical question is this: can a computer program, running on a digital machine that shuffles the binary digits of zero and one, duplicate the ability of the neurons to create minds, with mental states (like understanding or perceiving), and ultimately, the experience of consciousness?
+
+=== Arguments that a computer cannot have a mind and mental states ===
+
+==== Searle's Chinese room ====
+
+John Searle asks us to consider a thought experiment: suppose we have written a computer program that passes the Turing test and demonstrates general intelligent action. Suppose, specifically that the program can converse in fluent Chinese. Write the program on 3x5 cards and give them to an ordinary person who does not speak Chinese. Lock the person into a room and have him follow the instructions on the cards. He will copy out Chinese characters and pass them in and out of the room through a slot. From the outside, it will appear that the Chinese room contains a fully intelligent person who speaks Chinese. The question is this: is there anyone (or anything) in the room that understands Chinese? That is, is there anything that has the mental state of understanding, or which has conscious awareness of what is being discussed in Chinese? The man is clearly not aware. The room cannot be aware. The cards certainly are not aware. Searle concludes that the Chinese room, or any other physical symbol system, cannot have a mind.
+Searle goes on to argue that actual mental states and consciousness require (yet to be described) "actual physical-chemical properties of actual human brains." He argues there are special "causal properties" of brains and neurons that gives rise to minds: in his words "brains cause minds."
+
+==== Related arguments: Leibniz' mill, Davis's telephone exchange, Block's Chinese nation and Blockhead ====
+Gottfried Leibniz made essentially the same argument as Searle in 1714, using the thought experiment of expanding the brain until it was the size of a mill. In 1974, Lawrence Davis imagined duplicating the brain using telephone lines and offices staffed by people, and in 1978 Ned Block envisioned the entire population of China involved in such a brain simulation. This thought experiment is called "the Chinese Nation" or "the Chinese Gym". Ned Block also proposed his Blockhead argument, which is a version of the Chinese room in which the program has been re-factored into a simple set of rules of the form "see this, do that", removing all mystery from the program.
+
+==== Responses to the Chinese room ====
+Responses to the Chinese room emphasize several different points. 
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+---
+
+The systems reply and the virtual mind reply: This reply argues that the system, including the man, the program, the room, and the cards, is what understands Chinese. Searle claims that the man in the room is the only thing which could possibly "have a mind" or "understand", but others disagree, arguing that it is possible for there to be two minds in the same physical place, similar to the way a computer can simultaneously "be" two machines at once: one physical (like a Macintosh) and one "virtual" (like a word processor).
+Speed, power and complexity replies: Several critics point out that the man in the room would probably take millions of years to respond to a simple question, and would require "filing cabinets" of astronomical proportions. This brings the clarity of Searle's intuition into doubt.
+Robot reply: To truly understand, some believe the Chinese Room needs eyes and hands. Hans Moravec writes: "If we could graft a robot to a reasoning program, we wouldn't need a person to provide the meaning anymore: it would come from the physical world."
+Brain simulator reply: What if the program simulates the sequence of nerve firings at the synapses of an actual brain of an actual Chinese speaker? The man in the room would be simulating an actual brain. This is a variation on the "systems reply" that appears more plausible because "the system" now clearly operates like a human brain, which strengthens the intuition that there is something besides the man in the room that could understand Chinese.
+Other minds reply and the epiphenomena reply: Several people have noted that Searle's argument is just a version of the problem of other minds, applied to machines. Since it is difficult to decide if people are "actually" thinking, we should not be surprised that it is difficult to answer the same question about machines.
+A related question is whether "consciousness" (as Searle understands it) exists. Searle argues that the experience of consciousness cannot be detected by examining the behavior of a machine, a human being or any other animal. Daniel Dennett points out that natural selection cannot preserve a feature of an animal that has no effect on the behavior of the animal, and thus consciousness (as Searle understands it) cannot be produced by natural selection. Therefore, either natural selection did not produce consciousness, or "strong AI" is correct in that consciousness can be detected by suitably designed Turing test.
+
+== Is thinking a kind of computation? ==
+
+The computational theory of mind or "computationalism" claims that the relationship between mind and brain is similar (if not identical) to the relationship between a running program (software) and a computer (hardware). The idea has philosophical roots in Hobbes (who claimed reasoning was "nothing more than reckoning"), Leibniz (who attempted to create a logical calculus of all human ideas), Hume (who thought perception could be reduced to "atomic impressions") and even Kant (who analyzed all experience as controlled by formal rules). The latest version is associated with philosophers Hilary Putnam and Jerry Fodor.
+This question bears on our earlier questions: if the human brain is a kind of computer then computers can be both intelligent and conscious, answering both the practical and philosophical questions of AI. In terms of the practical question of AI ("Can a machine display general intelligence?"), some versions of computationalism make the claim that (as Hobbes wrote):
+
+Reasoning is nothing but reckoning.
+In other words, our intelligence derives from a form of calculation, similar to arithmetic. This is the physical symbol system hypothesis discussed above, and it implies that artificial intelligence is possible. In terms of the philosophical question of AI ("Can a machine have mind, mental states and consciousness?"), most versions of computationalism claim that (as Stevan Harnad characterizes it):
+
+Mental states are just implementations of (the right) computer programs.
+This is John Searle's "strong AI" discussed above, and it is the real target of the Chinese room argument (according to Harnad).
+
+== Other related questions ==
+
+=== Can a machine have emotions? ===
+If "emotions" are defined only in terms of their effect on behavior or on how they function inside an organism, then emotions can be viewed as a mechanism that an intelligent agent uses to maximize the utility of its actions. Given this definition of emotion, Hans Moravec believes that "robots in general will be quite emotional about being nice people". Fear is a source of urgency. Empathy is a necessary component of good human computer interaction. He says robots "will try to please you in an apparently selfless manner because it will get a thrill out of this positive reinforcement. You can interpret this as a kind of love." Daniel Crevier writes "Moravec's point is that emotions are just devices for channeling behavior in a direction beneficial to the survival of one's species."
+
+=== Can a machine be self-aware? ===
+"Self-awareness", as noted above, is sometimes used by science fiction writers as a name for the essential human property that makes a character fully human. Turing strips away all other properties of human beings and reduces the question to "can a machine be the subject of its own thought?" Can it think about itself? Viewed in this way, a program can be written that can report on its own internal states, such as a debugger.
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+title: "Philosophy of artificial intelligence"
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+tags: "science, encyclopedia"
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+instance: "kb-cron"
+---
+
+=== Can a machine be original or creative? ===
+Turing reduces this to the question of whether a machine can "take us by surprise" and argues that this is obviously true, as any programmer can attest. He notes that, with enough storage capacity, a computer can behave in an astronomical number of different ways. It must be possible, even trivial, for a computer that can represent ideas to combine them in new ways. (Douglas Lenat's Automated Mathematician, as one example, combined ideas to discover new mathematical truths.) Kaplan and Haenlein suggest that machines can display scientific creativity, while it seems likely that humans will have the upper hand where artistic creativity is concerned.
+In 2009, scientists at Aberystwyth University in Wales and the U.K's University of Cambridge designed a robot called Adam that they believe to be the first machine to independently come up with new scientific findings. Also in 2009, researchers at Cornell developed Eureqa, a computer program that extrapolates formulas to fit the data inputted, such as finding the laws of motion from a pendulum's motion.
+
+=== Can a machine be benevolent or hostile? ===
+
+This question (like many others in the philosophy of artificial intelligence) can be presented in two forms. "Hostility" can be defined in terms function or behavior, in which case "hostile" becomes synonymous with "dangerous". Or it can be defined in terms of intent: can a machine "deliberately" set out to do harm? The latter is the question "can a machine have conscious states?" (such as intentions) in another form.
+The question of whether highly intelligent and completely autonomous machines would be dangerous has been examined in detail by futurists (such as the Machine Intelligence Research Institute). The obvious element of drama has also made the subject popular in science fiction, which has considered many differently possible scenarios where intelligent machines pose a threat to mankind; see Artificial intelligence in fiction.
+One issue is that machines may acquire the autonomy and intelligence required to be dangerous very quickly. Vernor Vinge has suggested that over just a few years, computers will suddenly become thousands or millions of times more intelligent than humans. He calls this "the Singularity". He suggests that it may be somewhat or possibly very dangerous for humans. This is discussed by a philosophy called Singularitarianism.
+In 2009, academics and technical experts attended a conference to discuss the potential impact of robots and computers and the impact of the hypothetical possibility that they could become self-sufficient and able to make their own decisions. They discussed the possibility and the extent to which computers and robots might be able to acquire any level of autonomy, and to what degree they could use such abilities to possibly pose any threat or hazard. They noted that some machines have acquired various forms of semi-autonomy, including being able to find power sources on their own and being able to independently choose targets to attack with weapons. They also noted that some computer viruses can evade elimination and have achieved "cockroach intelligence". They noted that self-awareness as depicted in science-fiction is probably unlikely, but that there were other potential hazards and pitfalls.
+Some experts and academics have questioned the use of robots for military combat, especially when such robots are given some degree of autonomous functions. The US Navy has funded a report which indicates that as military robots become more complex, there should be greater attention to implications of their ability to make autonomous decisions.
+The President of the Association for the Advancement of Artificial Intelligence has commissioned a study to look at this issue. They point to programs like the Language Acquisition Device which can emulate human interaction.
+Some have suggested a need to build "Friendly AI", a term coined by Eliezer Yudkowsky, meaning that the advances which are already occurring with AI should also include an effort to make AI intrinsically friendly and humane.
+
+=== Can a machine imitate all human characteristics? ===
+Turing said "It is customary ... to offer a grain of comfort, in the form of a statement that some peculiarly human characteristic could never be imitated by a machine. ... I cannot offer any such comfort, for I believe that no such bounds can be set."
+Turing noted that there are many arguments of the form "a machine will never do X", where X can be many things, such as:
+
+Be kind, resourceful, beautiful, friendly, have initiative, have a sense of humor, tell right from wrong, make mistakes, fall in love, enjoy strawberries and cream, make someone fall in love with it, learn from experience, use words properly, be the subject of its own thought, have as much diversity of behaviour as a man, do something really new.
+Turing argues that these objections are often based on naive assumptions about the versatility of machines or are "disguised forms of the argument from consciousness". Writing a program that exhibits one of these behaviors "will not make much of an impression." All of these arguments are tangential to the basic premise of AI, unless it can be shown that one of these traits is essential for general intelligence.
+
+=== Theological argument ===
+According to Turing, the argument that "thinking is a function of man's immortal soul" is "the theological objection". He writes:
+
+In attempting to construct such machines we should not be irreverently usurping His power of creating souls, any more than we are in the procreation of children: rather we are, in either case, instruments of His will providing mansions for the souls that He creates.
+
+== Views on the role of philosophy ==
+Some scholars argue that the AI community's dismissal of philosophy is detrimental. In the Stanford Encyclopedia of Philosophy, some philosophers argue that the role of philosophy in AI is underappreciated. Physicist David Deutsch argues that without an understanding of philosophy or its concepts, AI development would suffer from a lack of progress.
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+title: "Philosophy of artificial intelligence"
+chunk: 7/7
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:55.691404+00:00"
+instance: "kb-cron"
+---
+
+== Conferences and literature ==
+The main conference series on the issue is "Philosophy and Theory of AI" (PT-AI), run by Vincent C. Müller.
+The main bibliography on the subject, with several sub-sections, is on PhilPapers.
+A recent survey for Philosophy of AI is Müller (2025).
+
+== See also ==
+
+== Notes ==
+
+== References ==
+
+=== Works cited ===
+Adam, Alison (1989). Artificial Knowing: Gender and the Thinking Machine. Routledge & CRC Press. ISBN 978-0-415-12963-3
+Benjamin, Ruha (2019). Race After Technology: Abolitionist Tools for the New Jim Code. Wiley. ISBN 978-1-509-52643-7
+Blackmore, Susan (2005), Consciousness: A Very Short Introduction, Oxford University Press
+Bostrom, Nick (2014), Superintelligence: Paths, Dangers, Strategies, Oxford University Press, ISBN 978-0-19-967811-2
+Brooks, Rodney (1990), "Elephants Don't Play Chess" (PDF), Robotics and Autonomous Systems, 6 (1–2): 3–15, CiteSeerX 10.1.1.588.7539, doi:10.1016/S0921-8890(05)80025-9, retrieved 2007-08-30
+Bryson, Joanna (2019). The Artificial Intelligence of the Ethics of Artificial Intelligence: An Introductory Overview for Law and Regulation, p. 34
+Chalmers, David J (1996), The Conscious Mind: In Search of a Fundamental Theory, Oxford University Press, New York, ISBN 978-0-19-511789-9
+Cole, David (Fall 2004), "The Chinese Room Argument", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy
+Crawford, Kate (2021). Atlas of AI: Power, Politics, and the Planetary Costs of Artificial Intelligence. Yale University Press
+Crevier, Daniel (1993). AI: The Tumultuous Search for Artificial Intelligence. New York, NY: BasicBooks. ISBN 0-465-02997-3.
+Dennett, Daniel (1991), Consciousness Explained, The Penguin Press, ISBN 978-0-7139-9037-9
+Dreyfus, Hubert (1972), What Computers Can't Do, New York: MIT Press, ISBN 978-0-06-011082-6
+Dreyfus, Hubert (1979), What Computers Still Can't Do, New York: MIT Press
+Dreyfus, Hubert; Dreyfus, Stuart (1986), Mind over Machine: The Power of Human Intuition and Expertise in the Era of the Computer, Oxford, UK: Blackwell
+Fearn, Nicholas (2005), Philosophy: The Latest Answers to the Oldest Questions, London: Atlantic Books, ISBN 1-84354-066-5
+Gladwell, Malcolm (2005), Blink: The Power of Thinking Without Thinking, Boston, Massachusetts: Little, Brown, ISBN 978-0-316-17232-5
+Harnad, Stevan (2001), "What's Wrong and Right About Searle's Chinese Room Argument?", in Bishop, M.; Preston, J. (eds.), Essays on Searle's Chinese Room Argument, Oxford University Press
+Haraway, Donna (1985). A Cyborg Manifesto
+Haugeland, John (1985), Artificial Intelligence: The Very Idea, Cambridge, Massachusetts: MIT Press
+Hobbes, Thomas (1651), Leviathan
+Hofstadter, Douglas (1979), Gödel, Escher, Bach: an Eternal Golden Braid
+Horst, Steven (Fall 2005), "The Computational Theory of Mind", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy, archived from the original on 2021-03-04, retrieved 2012-03-22
+Kaplan, Andreas; Haenlein, Michael (2018), "Siri, Siri in my Hand, who's the Fairest in the Land? On the Interpretations, Illustrations and Implications of Artificial Intelligence", Business Horizons, 62: 15–25, doi:10.1016/j.bushor.2018.08.004, S2CID 158433736
+Kurzweil, Ray (2005), The Singularity is Near, New York: Viking Press, ISBN 978-0-670-03384-3
+Leibniz, Gottfried (1714), Monadology, translated by Ross, George MacDonald, archived from the original on July 3, 2011
+Lucas, John (1961), "Minds, Machines and Gödel", in Anderson, A. R. (ed.), Minds and Machines, archived from the original on 2007-08-19, retrieved 2007-09-28
+Malabou, Catherine (2019). Morphing Intelligence: From IQ Measurement to Artificial Brains. (C. Shread, Trans.). Columbia University Press
+McCarthy, John; Minsky, Marvin; Rochester, Nathan; Shannon, Claude (1955), A Proposal for the Dartmouth Summer Research Project on Artificial Intelligence, archived from the original on 2008-09-30
+McCarthy, John (1999), What is AI?, archived from the original on 4 December 2022, retrieved 4 December 2022
+McCulloch, Warren S.; Pitts, Walter (1 December 1943). "A logical calculus of the ideas immanent in nervous activity". Bulletin of Mathematical Biophysics. 5 (4): 115–133. Bibcode:1943BMaB....5..115M. doi:10.1007/BF02478259. ISSN 1522-9602.
+McDermott, Drew (May 14, 1997), "How Intelligent is Deep Blue", New York Times, archived from the original on October 4, 2007, retrieved October 10, 2007
+Moravec, Hans (1988), Mind Children, Harvard University Press
+Newell, Allen; Simon, H. A. (1976). "Computer Science as Empirical Inquiry: Symbols and Search". Communications of the ACM. 19 (3): 113–126. doi:10.1145/360018.360022.
+Penrose, Roger (1989), The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics, Oxford University Press, Bibcode:1989esnm.book.....P, ISBN 978-0-14-014534-2c
+Rescorla, Michael, "The Computational Theory of Mind", in:Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2020 Edition)
+Russell, Stuart J.; Norvig, Peter (2003), Artificial Intelligence: A Modern Approach (2nd ed.), Upper Saddle River, New Jersey: Prentice Hall, ISBN 0-13-790395-2
+Saygin, A. P.; Cicekli, I.; Akman, V. (2000), "Turing Test: 50 Years Later" (PDF), Minds and Machines, 10 (4): 463–518, doi:10.1023/A:1011288000451, hdl:11693/24987, S2CID 990084, archived from the original (PDF) on 9 April 2011, retrieved 7 January 2004
+Searle, John (1980), "Minds, Brains and Programs" (PDF), Behavioral and Brain Sciences, 3 (3): 417–457, doi:10.1017/S0140525X00005756, S2CID 55303721, archived from the original (PDF) on 2015-09-23
+Searle, John (1984), Minds, Brains and Science: The 1984 Reith Lectures, Harvard University Press, ISBN 978-0-674-57631-5
+Searle, John (1992), The Rediscovery of the Mind, Cambridge, Massachusetts: M.I.T. Press
+Searle, John (1999), Mind, language and society, New York, NY: Basic Books, ISBN 978-0-465-04521-1, OCLC 231867665
+Yudkowsky, Eliezer (2008), "Artificial Intelligence as a Positive and Negative Factor in Global Risk" (PDF), Global Catastrophic Risks, Oxford University Press, 2008, Bibcode:2008gcr..book..303Y, archived (PDF) from the original on 19 October 2013, retrieved 24 September 2021
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diff --git a/data/en.wikipedia.org/wiki/Physics_in_the_medieval_Islamic_world-0.md b/data/en.wikipedia.org/wiki/Physics_in_the_medieval_Islamic_world-0.md
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+title: "Physics in the medieval Islamic world"
+chunk: 1/2
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+---
+
+The natural sciences saw various advancements during the Golden Age of Islam (from roughly the mid 8th to the mid 13th centuries), adding a number of innovations to the Transmission of the Classics (such as Aristotle, Ptolemy, Euclid, Neoplatonism). During this period, Islamic theology was encouraging of thinkers to find knowledge. Thinkers from this period included Al-Farabi, Abu Bishr Matta, Ibn Sina, al-Hassan Ibn al-Haytham and Ibn Bajjah. These works and the important commentaries on them were the wellspring of science during the medieval period. They were translated into Arabic, the lingua franca of this period.
+Islamic scholarship in the sciences had inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further. However the Islamic world had a greater respect for knowledge gained from empirical observation, and believed that the universe is governed by a single set of laws. Their use of empirical observation led to the formation of crude forms of the scientific method. The study of physics in the Islamic world started in Iraq and Egypt. 
+Fields of physics studied in this period include optics, mechanics (including statics, dynamics, kinematics and motion), and astronomy.
+
+== Physics ==
+Islamic scholarship had inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further, especially placing emphasis on observation and a priori reasoning, developing early forms of the scientific method. With Aristotelian physics, physics was seen as lower than demonstrative mathematical sciences, but in terms of a larger theory of knowledge, physics was higher than astronomy; many of whose principles derive from physics and metaphysics. The primary subject of physics, according to Aristotle, was motion or change; there were three factors involved with this change, underlying thing, privation, and form. In his Metaphysics, Aristotle believed that the Unmoved Mover was responsible for the movement of the cosmos, which Neoplatonists later generalized as the cosmos were eternal. Al-Kindi argued against the idea of the cosmos being eternal by claiming that the eternality of the world lands one in a different sort of absurdity involving the infinite; Al-Kindi asserted that the cosmos must have a temporal origin because traversing an infinite was impossible.
+One of the first commentaries of Aristotle's Metaphysics is by Al-Farabi. In "'The Aims of Aristotle's Metaphysics", Al-Farabi argues that metaphysics is not specific to natural beings, but at the same time, metaphysics is higher in universality than natural beings.
+
+== Optics ==
+
+One field in physics, optics, developed rapidly in this period. By the ninth century, there were works on physiological optics as well as mirror reflections, and geometrical and physical optics. In the eleventh century, Ibn al-Haytham not only rejected the Greek idea about vision, he came up with a new theory.
+Ibn Sahl (c. 940–1000), a mathematician and physicist connected with the court of Baghdad, wrote a treatise On Burning Mirrors and Lenses in 984 in which he set out his understanding of how curved mirrors and lenses bend and focus light. Ibn Sahl is credited with discovering the law of refraction, now usually called Snell's law. He used this law to work out the shapes of lenses that focus light with no geometric aberrations, known as anaclastic lenses.
+Ibn al-Haytham (known in Western Europe as Alhacen or Alhazen) (965-1040), often regarded as the "father of optics" and a pioneer of the scientific method, formulated "the first comprehensive and systematic alternative to Greek optical theories." He postulated in his "Book of Optics" that light was reflected upon different surfaces in different directions, thus causing different light signatures for a certain object that we see. It was a different approach than that which was previously thought by Greek scientists, such as Euclid or Ptolemy, who believed rays were emitted from the eye to an object and back again. Al-Haytham, with this new theory of optics, was able to study the geometric aspects of the visual cone theories without explaining the physiology of perception. Also in his Book of Optics, Ibn al-Haytham used mechanics to try and understand optics. Using projectiles, he observed that objects that hit a target perpendicularly exert much more force than projectiles that hit at an angle. Al-Haytham applied this discovery to optics and tried to explain why direct light hurts the eye, because direct light approaches perpendicularly and not at an oblique angle. He developed a camera obscura to demonstrate that light and color from different candles can be passed through a single aperture in straight lines, without intermingling at the aperture. His theories were transmitted to the West. His work influenced Roger Bacon, John Peckham and Vitello, who built upon his work and ultimately transmitted it to Kepler.
+Taqī al-Dīn tried to disprove the widely held belief that light is emitted by the eye and not the object that is being observed. He explained that, if light came from our eyes at a constant velocity it would take much too long to illuminate the stars for us to see them while we are still looking at them, because they are so far away. Therefore, the illumination must be coming from the stars so we can see them as soon as we open our eyes.
+
+== Astronomy ==
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+title: "Physics in the medieval Islamic world"
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+---
+
+The Islamic understanding of the astronomical model was based on the Greek Ptolemaic system. However, many early astronomers had started to question the model. It was not always accurate in its predictions and was over complicated because astronomers were trying to mathematically describe the movement of the heavenly bodies. Ibn al-Haytham published Al-Shukuk ala Batiamyus ("Doubts on Ptolemy"), which outlined his many criticisms of the Ptolemaic paradigm. This book encouraged other astronomers to develop new models to explain celestial movement better than Ptolemy. In al-Haytham's Book of Optics he argues that the celestial spheres were not made of solid matter, and that the heavens are less dense than air. Some astronomers theorized about gravity too, al-Khazini suggests that the gravity an object contains varies depending on its distance from the center of the universe. The center of the universe in this case refers to the center of the Earth.
+
+== Mechanics ==
+
+=== Impetus ===
+John Philoponus had rejected the Aristotelian view of motion, and argued that an object acquires an inclination to move when it has a motive power impressed on it. In the eleventh century Ibn Sina had roughly adopted this idea, believing that a moving object has force which is dissipated by external agents like air resistance.
+Ibn Sina made distinction between 'force' and 'inclination' (called "mayl"), he claimed that an object gained mayl when the object is in opposition to its natural motion. So he concluded that continuation of motion is attributed to the inclination that is transferred to the object, and that object will be in motion until the mayl is spent. He also claimed that projectile in a vacuum would not stop unless it is acted upon. This conception of motion is consistent with Newton's first law of motion, inertia, which states that an object in motion will stay in motion unless it is acted on by an external force. This idea which dissented from the Aristotelian view was basically abandoned until it was described as "impetus" by John Buridan, who may have been influenced by Ibn Sina.
+
+=== Acceleration ===
+In Abū Rayḥān al-Bīrūnī text Shadows, he recognizes that non-uniform motion is the result of acceleration. Ibn-Sina's theory of mayl tried to relate the velocity and weight of a moving object, this idea closely resembled the concept of momentum Aristotle's theory of motion stated that a constant force produces a uniform motion, Abu'l-Barakāt al-Baghdādī contradicted this and developed his own theory of motion. In his theory he showed that velocity and acceleration are two different things and force is proportional to acceleration and not velocity.
+
+== See also ==
+Astronomy in the medieval Islamic world
+History of optics
+History of physics
+History of scientific method
+Islamic world contributions to Medieval Europe
+Islamic Golden Age
+Science in the medieval Islamic world
+Science in the Middle Ages
+
+== References ==
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+---
+
+For light and other electromagnetic radiation, the plane of polarization is the plane spanned by the direction of propagation and either the electric vector or the magnetic vector, depending on the convention. It can be defined for polarized light, remains fixed in space for linearly-polarized light, and undergoes axial rotation for circularly-polarized light.
+Unfortunately the two conventions are contradictory. As originally defined by Étienne-Louis Malus in 1811, the plane of polarization coincided (although this was not known at the time) with the plane containing the direction of propagation and the magnetic vector. In modern literature, the term plane of polarization, if it is used at all, is likely to mean the plane containing the direction of propagation and the electric vector, because the electric field has the greater propensity to interact with matter.
+For waves in a birefringent (doubly-refractive) crystal, under the old definition, one must also specify whether the direction of propagation means the ray direction (Poynting vector) or the wave-normal direction, because these directions generally differ and are both perpendicular to the magnetic vector (Fig. 1). Malus, as an adherent of the corpuscular theory of light, could only choose the ray direction. But Augustin-Jean Fresnel, in his successful effort to explain double refraction under the wave theory (1822 onward), found it more useful to choose the wave-normal direction, with the result that the supposed vibrations of the medium were then consistently perpendicular to the plane of polarization. In an isotropic medium such as air, the ray and wave-normal directions are the same, and Fresnel's modification makes no difference.
+Fresnel also admitted that, had he not felt constrained by the received terminology, it would have been more natural to define the plane of polarization as the plane containing the vibrations and the direction of propagation. That plane, which became known as the plane of vibration, is perpendicular to Fresnel's "plane of polarization" but identical with the plane that modern writers tend to call by that name!
+It has been argued that the term plane of polarization, because of its historical ambiguity, should be avoided in original writing. One can easily specify the orientation of a particular field vector; and even the term plane of vibration carries less risk of confusion than plane of polarization.
+
+== Physics of the term ==
+
+For electromagnetic (EM) waves in an isotropic medium (that is, a medium whose properties are independent of direction), the electric field vectors (E and D) are in one direction, and the magnetic field vectors (B and H) are in another direction, perpendicular to the first, and the direction of propagation is perpendicular to both the electric and the magnetic vectors. In this case the direction of propagation is both the ray direction and the wave-normal direction (the direction perpendicular to the wavefront). For a linearly-polarized wave (also called a plane-polarized wave), the orientations of the field vectors are fixed (Fig. 2).
+Because innumerable materials are dielectrics or conductors while comparatively few are ferromagnets, the reflection or refraction of EM waves (including light) is more often due to differences in the electric properties of media than to differences in their magnetic properties. That circumstance tends to draw attention to the electric vectors, so that we tend to think of the direction of polarization as the direction of the electric vectors, and the "plane of polarization" as the plane containing the electric vectors and the direction of propagation.
+
+Indeed, that is the convention used in the online Encyclopædia Britannica, and in Feynman's lecture on polarization. In the latter case one must infer the convention from the context: Feynman keeps emphasizing the direction of the electric (E) vector and leaves the reader to presume that the "plane of polarization" contains that vector — and this interpretation indeed fits the examples he gives. The same vector is used to describe the polarization of radio signals and antennas (Fig. 3).
+If the medium is magnetically isotropic but electrically non-isotropic (like a doubly-refracting crystal), the magnetic vectors B and H are still parallel, and the electric vectors E and D are still perpendicular to both, and the ray direction is still perpendicular to E and the magnetic vectors, and the wave-normal direction is still perpendicular to D and the magnetic vectors; but there is generally a small angle between the electric vectors E and D, hence the same angle between the ray direction and the wave-normal direction (Fig. 1).  Hence D, E, the wave-normal direction, and the ray direction are all in the same plane, and it is all the more natural to define that plane as the "plane of polarization".
+This "natural" definition, however, depends on the theory of EM waves developed by James Clerk Maxwell in the 1860s — whereas the word polarization was coined about 50 years earlier, and the associated mystery dates back even further.
+
+== History of the term ==
+
+=== Three candidates ===
+Whether by accident or by design, the plane of polarization has always been defined as the plane containing a field vector and a direction of propagation. In Fig. 1, there are three such planes, to which we may assign numbers for ease of reference:
+
+(1)  the plane containing both electric vectors and both propagation directions  (i.e., the plane normal to the magnetic vectors);
+(2a)  the plane containing the magnetic vectors and the wave-normal  (i.e., the plane normal to D);
+(2b)  the plane containing the magnetic vectors and the ray  (i.e., the plane normal to E).
+In an isotropic medium, E and D have the same direction, so that the ray and wave-normal directions merge, and the planes (2a) and (2b) become one:
+
+(2)  the plane containing both magnetic vectors and both propagation directions  (i.e., the plane normal to the electric vectors).
+
+=== Malus's choice ===
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+---
+
+Polarization was discovered — but not named or understood — by Christiaan Huygens, as he investigated the double refraction of "Iceland crystal" (transparent calcite, now called Iceland spar). The essence of his discovery, published in his Treatise on Light (1690), was as follows. When a ray (meaning a narrow beam of light) passes through two similarly oriented calcite crystals at normal incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second. But when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa. At intermediate positions of the second crystal, each ray emerging from the first is doubly refracted by the second, giving four rays in total; and as the crystal is rotated from the initial orientation to the perpendicular one, the brightnesses of the rays vary, giving a smooth transition between the extreme cases in which there are only two final rays.
+Huygens defined a principal section of a calcite crystal as a plane normal to a natural surface and parallel to the axis of the obtuse solid angle. This axis was parallel to the axes of the spheroidal secondary waves by which he (correctly) explained the directions of the extraordinary refraction.
+
+The term polarization was coined by Étienne-Louis Malus in 1811.  In 1808, in the midst of confirming Huygens' geometric description of double refraction (while disputing his physical explanation), Malus had discovered that when a ray of light is reflected off a non-metallic surface at the appropriate angle, it behaves like one of the two rays emerging from a calcite crystal. As this behavior had previously been known only in connection with double refraction, Malus described it in that context. In particular, he defined the plane of polarization of a polarized ray as the plane, containing the ray, in which a principal section of a calcite crystal must lie in order to cause only ordinary refraction. This definition was all the more reasonable because it meant that when a ray was polarized by reflection (off an isotopic medium), the plane of polarization was the plane of incidence and reflection — that is, the plane containing the incident ray, the normal to the reflective surface, and the polarized reflected ray. But, as we now know, this plane happens to contain the magnetic vectors of the polarized ray, not the electric vectors.
+The plane of the ray and the magnetic vectors is the one numbered (2b) above. The implication that the plane of polarization contains the magnetic vectors is still found in the definition given in the online Merriam-Webster dictionary. Even Julius Adams Stratton, having said that "It is customary to define the polarization in terms of E", promptly adds: "In optics, however, the orientation of the vectors is specified traditionally by the 'plane of polarization,' by which is meant the plane normal to E containing both H and the axis of propagation." That definition is identical with Malus's.
+
+=== Fresnel's choice ===
+
+In 1821, Augustin-Jean Fresnel announced his hypothesis that light waves are exclusively transverse and therefore always polarized in the sense of having a particular transverse orientation, and that what we call unpolarized light is in fact light whose orientation is rapidly and randomly changing. Supposing that light waves were analogous to shear waves in elastic solids, and that a higher refractive index corresponded to a higher density of the luminiferous aether, he found that he could account for the partial reflection (including polarization by reflection) at the interface between two transparent isotropic media, provided that the vibrations of the aether were perpendicular to the plane of polarization. Thus the polarization, according to the received definition, was "in" a certain plane if the vibrations were perpendicular to that plane!
+Fresnel himself found this implication inconvenient; later that year he wrote:
+
+Adopting this hypothesis, it would have been more natural to have called the plane of polarisation that in which the oscillations are supposed to be made: but I wished to avoid making any change in the received appellations.
+But he soon felt obliged to make a less radical change. In his successful model of double refraction, the displacement of the medium was constrained to be tangential to the wavefront, while the force was allowed to deviate from the displacement and from the wavefront. Hence, if the vibrations were perpendicular to the plane of polarization, then the plane of polarization contained the wave-normal but not necessarily the ray. In his "Second Memoir" on double refraction, Fresnel formally adopted this new definition, acknowledging that it agreed with the old definition in an isotropic medium such as air, but not in a birefringent crystal.
+The vibrations normal to Malus's plane of polarization are electric, and the electric vibration tangential to the wavefront is D (Fig. 1). Thus, in terms of the above numbering, Fresnel changed the "plane of polarization" from (2b) to (2a). Fresnel's definition remains compatible with the Merriam-Webster definition, which fails to specify the propagation direction. And it remains compatible with Stratton's definition, because that is given in the context of an isotropic medium, in which planes (2a) and (2b) merge into (2).
+What Fresnel called the "more natural" choice was a plane containing D and a direction of propagation. In Fig. 1, the only plane meeting that specification is the one labeled "Plane of vibration" and later numbered (1) — that is, the one that modern authors tend to identify with the "plane of polarization". We might therefore wish that Fresnel had been less deferential to his predecessors. That scenario, however, is less realistic than it may seem, because even after Fresnel's transverse-wave theory was generally accepted, the direction of the vibrations was the subject of continuing debate.
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+---
+title: "Plane of polarization"
+chunk: 3/4
+source: "https://en.wikipedia.org/wiki/Plane_of_polarization"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:06.819271+00:00"
+instance: "kb-cron"
+---
+
+=== "Plane of vibration" ===
+The principle that refractive index depended on the density of the aether was essential to Fresnel's aether drag hypothesis. But it could not be extended to birefringent crystals — in which at least one refractive index varies with direction — because density is not directional. Hence his explanation of refraction required a directional variation in stiffness of the aether within a birefringent medium, plus a variation in density between media.
+James MacCullagh and Franz Ernst Neumann avoided this complication by supposing that a higher refractive index corresponded always to the same density but a greater elastic compliance (lower stiffness). To obtain results that agreed with observations on partial reflection, they had to suppose, contrary to Fresnel, that the vibrations were within the plane of polarization.
+
+The question called for an experimental determination of the direction of vibration, and the challenge was answered by George Gabriel Stokes. He defined the plane of vibration as "the plane passing through the ray and the direction of vibration" (in agreement with Fig. 1). Now suppose that a fine diffraction grating is illuminated at normal incidence. At large angles of diffraction, the grating will appear somewhat edge-on, so that the directions of vibration will be crowded towards the direction parallel to the plane of the grating. If the planes of polarization coincide with the planes of vibration (as MacCullagh and Neumann said), they will be crowded in the same direction; and if the planes of polarization are normal to the planes of vibration (as Fresnel said), the planes of polarization will be crowded in the normal direction. To find the direction of the crowding, one could vary the polarization of the incident light in equal steps, and determine the planes of polarization of the diffracted light in the usual manner. Stokes performed such an experiment in 1849, and it found in favor of Fresnel.
+In 1852, Stokes noted a much simpler experiment that leads to the same conclusion. Sunlight scattered from a patch of blue sky 90° from the sun is found, by the methods of Malus, to be polarized in the plane containing the line of sight and the sun. But it is obvious from the geometry that the vibrations of that light can only be perpendicular to that plane.
+There was, however, a sense in which MacCullagh and Neumann were correct. If we attempt an analogy between shear waves in a non-isotropic elastic solid, and EM waves in a magnetically isotropic but electrically non-isotropic crystal, the density must correspond to the magnetic permeability (both being non-directional), and the compliance must correspond to the electric permittivity (both being directional). The result is that the velocity of the solid corresponds to the H field, so that the mechanical vibrations of the shear wave are in the direction of the magnetic vibrations of the EM wave. But Stokes's experiments were bound to detect the electric vibrations, because those have the greater propensity to interact with matter. In short, the MacCullagh-Neumann vibrations were the ones that had a mechanical analog, but Fresnel's vibrations were the ones that were more likely to be detected in experiments.
+
+=== Modern practice ===
+The electromagnetic theory of light further emphasized the electric vibrations because of their interactions with matter, whereas the old "plane of polarization" contained the magnetic vectors. Hence the electromagnetic theory would have reinforced the convention that the vibrations were normal to the plane of polarization — provided, of course, that one was familiar with the historical definition of the plane of polarization. But if one was influenced by physical considerations alone, then, as Feynman and the Britannica illustrate, one would pay attention to the electric vectors and assume that the "plane" of polarization (if one needed such a concept) contained those vectors.
+However, it is not clear that a "plane of polarization" is needed at all: knowing what field vectors are involved, one can specify the polarization by specifying the orientation of a particular vector, or, as Born and Wolf suggest, by specifying the "plane of vibration" of that vector.  Hecht also prefers the term plane of vibration (or, more usually, plane-of-vibration), which he defines as the plane of E and the wave-normal, in agreement with Fig. 1 above.
+
+== Remaining uses ==
+In an optically chiral medium — that is, one in which the direction of polarization gradually rotates as the wave propagates — the choice of definition of the "plane of polarization" does not affect the existence or direction ("handedness") of the rotation. This is one context in which the ambiguity of the term plane of polarization causes no further confusion.
+There is also a context in which the original definition might still suggest itself. In a non-magnetic non-chiral crystal of the biaxial class (in which there is no ordinary refraction, but both refractions violate Snell's law), there are three mutually perpendicular planes for which the speed of light is isotropic within the plane provided that the electric vectors are normal to the plane. This situation naturally draws attention to a plane normal to the vibrations as envisaged by Fresnel, and that plane is indeed the plane of polarization as defined by Fresnel or Malus.
+In most contexts, however, the concept of a "plane of polarization" distinct from a plane containing the electric "vibrations" has arguably become redundant, and has certainly become a source of confusion. In the words of Born & Wolf, "it is… better not to use this term."
+
+== See also ==
+E-plane and H-plane
+Plane of incidence
+
+== Notes ==
+
+== References ==
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+---
+title: "Plane of polarization"
+chunk: 4/4
+source: "https://en.wikipedia.org/wiki/Plane_of_polarization"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:06.819271+00:00"
+instance: "kb-cron"
+---
+
+== Bibliography ==
+W.S. Aldis, 1879, A Chapter on Fresnel's Theory of Double Refraction, 2nd Ed., Cambridge: Deighton, Bell, & Co. / London: George Bell & Sons.
+M. Born and E. Wolf, 1970, Principles of Optics, 4th Ed., Oxford: Pergamon Press.
+J.Z. Buchwald, 1989, The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century, University of Chicago Press, ISBN 0-226-07886-8.
+O. Darrigol, 2012, A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford, ISBN 978-0-19-964437-7.
+A. Fresnel, 1822, De la Lumière (On Light), in J. Riffault (ed.), Supplément à la traduction française de la cinquième édition du "Système de Chimie" par Th. Thomson, Paris: Chez Méquignon-Marvis, 1822, pp. 1–137, 535–9; reprinted in Fresnel, 1866–70, vol. 2, pp. 3–146; translated by T. Young as "Elementary view of the undulatory theory of light", Quarterly Journal of Science, Literature, and Art, vol. 22 (Jan.– Jun. 1827), pp. 127–41, 441–54; vol. 23 (Jul.– Dec. 1827), pp. 113–35, 431–48; vol. 24 (Jan.– Jun. 1828), pp. 198–215; vol. 25 (Jul.– Dec. 1828), pp. 168–91, 389–407; vol. 26 (Jan.– Jun. 1829), pp. 159–65.
+A. Fresnel, 1827, "Mémoire sur la double réfraction", Mémoires de l'Académie Royale des Sciences de l'Institut de France, vol. VII (for 1824, printed 1827), pp. 45–176; reprinted as "Second mémoire…" in Fresnel, 1866–70, vol. 2, pp. 479–596; translated by A.W. Hobson as "Memoir on double refraction", in R. Taylor (ed.), Scientific Memoirs, vol. V (London: Taylor & Francis, 1852), pp. 238–333. (Cited page numbers are from the translation.)
+A. Fresnel (ed.  H. de Senarmont, E. Verdet, and L. Fresnel), 1866–70, Oeuvres complètes d'Augustin Fresnel (3 volumes), Paris: Imprimerie Impériale; vol. 1 (1866), vol. 2 (1868), vol. 3 (1870).
+E. Hecht, 2017, Optics, 5th Ed., Pearson Education, ISBN 978-1-292-09693-3.
+C. Huygens, 1690, Traité de la Lumière (Leiden: Van der Aa), translated by S.P. Thompson as Treatise on Light, University of Chicago Press, 1912; Project Gutenberg, 2005. (Cited page numbers match the 1912 edition and the Gutenberg HTML edition.)
+B. Powell (July 1856), "On the demonstration of Fresnel's formulas for reflected and refracted light; and their applications", Philosophical Magazine and Journal of Science, Series 4, vol. 12, no. 76, pp. 1–20.
+J.A. Stratton, 1941, Electromagnetic Theory, New York: McGraw-Hill.
+E. T. Whittaker, 1910, A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century, London: Longmans, Green, & Co.
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diff --git a/data/en.wikipedia.org/wiki/Quaestiones_quaedam_philosophicae-0.md b/data/en.wikipedia.org/wiki/Quaestiones_quaedam_philosophicae-0.md
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+---
+title: "Quaestiones quaedam philosophicae"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Quaestiones_quaedam_philosophicae"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:08.113404+00:00"
+instance: "kb-cron"
+---
+
+Quaestiones quaedam philosophicae (Certain philosophical questions) is the name given to a set of notes that Isaac Newton kept for himself during his earlier years in Cambridge. They concern questions in the natural philosophy of the day that interested him. Apart from the light it throws on the formation of his own agenda for research, the major interest in these notes is the documentation of the unaided development of the scientific method in the mind of Newton, whereby every question is put to experimental test.
+
+
+== Introduction ==
+The Quaestiones are contained in an octavo notebook, currently in the Cambridge University Library, which was Newton's basic notebook in which he set down in 1661 his readings in the required curriculum in Cambridge and his later readings in mechanical philosophy. He entered notes from both ends. The initial notes, in Greek, were on Aristotle's logic at one end and his ethics, at the other.
+But following this, he drew a line across the page, below which appears his first notes on the new natural philosophy of his day— a compendium of limits on the radii of stars as determined by Galileo and Auzout. At the other end of the book, he interrupted his notes on Aristotle with two pages of notes on Descartes' metaphysics.
+Following this, the central approximately hundred pages of this notebook is entitled Questiones quadem Philosophcae [sic], and a later motto over the title Amicus Plato amicus Aristotle magis amica veritas (Plato is my friend, Aristotle is my friend, but my best friend is truth).
+
+
+== Dating ==
+The start of Quaestiones is definitely after 8 July 1661, the date on which Newton arrived at Trinity College. It is also definitely before 9 December 1664, on which day (and the following) he made notes of his observations of a comet. Other datings of the first entries are based on his handwriting—which changed drastically between the early notes of 1661 and later notes which can be dated independently to 1665. The transitional handwriting which characterizes the early parts of Quaestiones can only be independently dated to roughly 1664. This was written during a period when Newton was actively developing the notion of calculus, but mathematics made no real appearance in this notebook.
+
+
+== Contents ==
+The Quaestiones contains notes from Newton's thorough reading of Descartes, Walter Charlton's translation of Gassendi into English, Galileo Galilei's Dialogue Concerning the Two Chief World Systems, Robert Boyle, Thomas Hobbes, Kenelm Digby, Joseph Glanvill and Henry More, and others. These were set down under 45 section headings which he used to organize his readings. They began with the nature of matter, place, time and motion and went on to the organization of the universe. This was followed by what would be classed today as properties of condensed matter, for example, rarity, fluidity, hardness etc. These were followed by questions on violent motion, light, colour, vision, and other sensations. The last part contains miscellaneous topics which presumably occurred to him later during his readings: "Of God", "Of ye Creation", "Of ye soule" and "Of Sleepe and Dreams &c". Some headings were followed by vast entries, which had to be continued elsewhere; others were blank. The earlier essays were organized into questions and outlines of possible experiments which roughly fit into modern notions of science, not the broader ancient notion of philosophy.
+
+
+=== Gravity ===
+The topic of gravity was not dealt with in a single section, showing that his understanding of the matter was still far from well developed. In a section on perpetual motion machines (folio 121) he wrote
+
+Whether ye rays of gravity may be stopped by reflecting or refracting ym, if so a perpetual motion may be made one of these ways.
+
+Elsewhere, in his notes on Kepler's laws of planetary motion that he read about in the book Astronomiae carolina by Thomas Streete, he reached the conclusion that gravity must not merely act on the surfaces of bodies but on their interiors.
+
+
+=== On violent motion ===
+In Aristotelian physics, bodies are subject to either natural motion, such as when a heavy body falls, or violent motion such as when a heavy body is thrown up. Although this essay was written following his reading of Descartes and Galileo, by its title it shows that Newton did not reject pre-Galilean mechanics tout court.
+
+
+=== Nature of light ===
+Descartes believed that he was the first to obtain the law of refraction of light and paid great attention to it as well as to the well-known classical law of reflection. Descartes hypothesized that light is pressure, transmitted instantaneously through a transparent medium. Gassendi, on the contrary, held that light is a stream of tiny particles traveling with immense speed. Newton questioned Descartes' theory in many ways; in folio 103 he wrote—
+
+Light cannot be pressure for we should see in the night as well or better in the day we should be a bright light above us because we are pressed downwards ... there could be no refraction since same matter cannot press 2 ways. a little body interposed could not hinder us from seeing pressure could not render shapes so distinct. sun could not be quite eclipsed Moone & planets would shine like suns. When a fire or candle is extinguished we looking another way should see a light.
+
+
+=== Nature of colour ===
+The then-current theory of color held that white light was elementary and that colors arose from mixtures of light and dark. Newton criticised this theory by noting that in that case a printed page, with its juxtaposition of light and dark, would look colored. In folio 122 he recorded for the first time his notion that white light is heterogeneous and colors arise, not through the modification of a homogeneous white light, but from the separation of this mixture into its components. Newton also mentions Hooke's theory of color, including his idea that it is a wave. Newton dismisses this theory with the remark that then light should bend around edges of objects as sounds do.
+
+
+=== Of atoms ===
+Newton seems to have come across the idea of atomism through his knowledge of Gassendi gained by reading Charleton's Physiologia. He argued against continua and asserted the need for atoms. His acceptance of the corpuscular theory of light may have been affected by this.
+
+
+== See also ==
+Aristotelian physics, Galileo and Descartes
+Isaac Newton, the Philosophiae Naturalis Principia Mathematica and Opticks
+
+
+== References ==
+
+"Portsmouth Papers", additional manuscripts of Isaac Newton in the Cambridge University library.
+J. A. Lohne, "Isaac Newton: the rise of a scientist, 1661—1671" Notes and records of the Royal Society, vol 20 (1965) pp 125–139.
+Never at rest: a biography of Isaac Newton, by Richard S. Westfall, Cambridge University Press, 1980 ISBN 0-521-23143-4
+Westfall, Richard S. “The Foundations of Newton’s Philosophy of Nature.” The British Journal for the History of Science, vol. 1, no. 2, 1962, pp. 171–82. JSTOR.
+
+
+== External links ==
+Text of Quaestiones at Newton Project
+Newton Papers (Cambridge Digital Library): Trinity College Notebook (MS Add.3996); a famous section of this manuscript is 'Questiones quaedam Philosophiae'
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+---
+title: "Relativity of simultaneity"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Relativity_of_simultaneity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:14.866265+00:00"
+instance: "kb-cron"
+---
+
+In physics, the relativity of simultaneity is the concept that distant simultaneity –  whether two spatially separated events occur at the same time –  is not absolute, but depends on the observer's reference frame. This possibility was raised by mathematician Henri Poincaré in 1900, and thereafter became a central idea in the special theory of relativity.
+
+== Description ==
+According to the special theory of relativity introduced by Albert Einstein, it is impossible to say in an absolute sense that two distinct events occur at the same time if those events are separated in space. If one reference frame assigns precisely the same time to two events that are at different points in space, a reference frame that is moving relative to the first will generally assign different times to the two events (the only exception being when motion is exactly perpendicular to the line connecting the locations of both events).
+For example, a car crash in London and another in New York that appear to happen at the same time to an observer on Earth will appear to have occurred at slightly different times to an observer on an airplane flying between London and New York. Furthermore, if the two events cannot be causally connected, depending on the state of motion, the crash in London may appear to occur first in a given frame, and the New York crash may appear to occur first in another. However, if the events can be causally connected, precedence order is preserved in all frames of reference.
+
+== History ==
+
+In 1892 and 1895, Hendrik Lorentz used a mathematical method called "local time" t′ = t − v x/c2 for explaining the negative aether drift experiments. However, Lorentz gave no physical explanation of this effect. This was done by Henri Poincaré who already emphasized in 1898 the conventional nature of simultaneity and who argued that it is convenient to postulate the constancy of the speed of light in all directions. However, this paper did not contain any discussion of Lorentz's theory or the possible difference in defining simultaneity for observers in different states of motion.
+This was done in 1900, when Poincaré derived local time by assuming that the speed of light is invariant within the aether. Due to the "principle of relative motion", moving observers within the aether also assume that they are at rest and that the speed of light is constant in all directions (only to first order in v/c). Therefore, if they synchronize their clocks by using light signals, they will only consider the transit time for the signals, but not their motion in respect to the aether. So the moving clocks are not synchronous and do not indicate the "true" time. Poincaré calculated that this synchronization error corresponds to Lorentz's local time.
+In 1904, Poincaré emphasized the connection between the principle of relativity, "local time", and light speed invariance; however, the reasoning in that paper was presented in a qualitative and conjectural manner.
+Albert Einstein used a similar method in 1905 to derive the time transformation for all orders in v/c, i.e., the complete Lorentz transformation. Poincaré obtained the full transformation earlier in 1905 but in the papers of that year he did not mention his synchronization procedure. This derivation was completely based on light speed invariance and the relativity principle, so Einstein noted that for the electrodynamics of moving bodies the aether is superfluous. Thus, the separation into "true" and "local" times of Lorentz and Poincaré vanishes –  all times are equally valid and therefore the relativity of length and time is a natural consequence.
+In 1908, Hermann Minkowski introduced the concept of a world line of a particle in his model of the cosmos called Minkowski space. In Minkowski's view, the naïve notion of velocity is replaced with rapidity, and the ordinary sense of simultaneity becomes dependent on hyperbolic orthogonality of spatial directions to the worldline associated to the rapidity. Then every inertial frame of reference has a rapidity and a simultaneous hyperplane.
+In 1987, Robert Goldblatt published Orthogonality and Spacetime Geometry, directly addressing the structure Minkowski had put in place for simultaneity. In 2006, Max Jammer, through Project MUSE, published Concepts of Simultaneity: from antiquity to Einstein and beyond. The book culminates in chapter 6, "The transition to the relativistic conception of simultaneity". Jammer indicates that Ernst Mach demythologized the absolute time of Newtonian physics.
+Naturally the mathematical notions preceded physical interpretation. For instance, conjugate diameters of conjugate hyperbolas are related as space and time. The principle of relativity can be expressed as the arbitrariness of which pair are taken to represent space and time in a plane.
+
+== Thought experiments ==
+
+=== Einstein's train ===
+
+Einstein's version of the experiment presumed that one observer was sitting midway inside a speeding traincar and another was standing on a platform as the train moved past. As measured by the standing observer, the train is struck by two bolts of lightning simultaneously, but at different positions along the axis of train movement (back and front of the train car). In the inertial frame of the standing observer, there are three events which are spatially dislocated, but simultaneous: standing observer facing the moving observer (i.e., the center of the train), lightning striking the front of the train car, and lightning striking the back of the car.
+Since the events are placed along the axis of train movement, their time coordinates become projected to different time coordinates in the moving train's inertial frame. Events which occurred at space coordinates in the direction of train movement happen earlier than events at coordinates opposite to the direction of train movement. In the moving train's inertial frame, this means that lightning will strike the front of the train car before the two observers align (face each other).
+
+=== The train-and-platform ===
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+---
+title: "Relativity of simultaneity"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Relativity_of_simultaneity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:14.866265+00:00"
+instance: "kb-cron"
+---
+
+A popular picture for understanding this idea is provided by a thought experiment similar to those suggested by Daniel Frost Comstock in 1910 and Einstein in 1917. It also consists of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past. 
+A flash of light is given off at the center of the traincar just as the two observers pass each other. For the observer on board the train, the front and back of the traincar are at fixed distances from the light source and as such, according to this observer, the light will reach the front and back of the traincar at the same time.
+For the observer standing on the platform, on the other hand, the rear of the traincar is moving (catching up) toward the point at which the flash was given off, and the front of the traincar is moving away from it. As the speed of light is, according to the second postulate of special relativity, same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times.
+
+==== Spacetime diagrams ====
+It may be helpful to visualize this situation using spacetime diagrams.  For a given observer, the t-axis is defined to be a point traced out in time by the origin of the spatial coordinate x, and is drawn vertically.  The x-axis is defined as the set of all points in space at the time t = 0, and is drawn horizontally.  The statement that the speed of light is the same for all observers is represented by drawing a light ray as a 45° line, regardless of the speed of the source relative to the speed of the observer.
+In the first diagram, the two ends of the train are drawn as grey lines. Because the ends of the train are stationary with respect to the observer on the train, these lines are just vertical lines, showing their motion through time but not space. The flash of light is shown as the 45° red lines. The points at which the two light flashes hit the ends of the train are at the same level in the diagram. This means that the events are simultaneous.
+In the second diagram, the two ends of the train moving to the right, are shown by parallel lines. The flash of light is given off at a point exactly halfway between the two ends of the train, and again form two 45° lines, expressing the constancy of the speed of light.  In this picture, however, the points at which the light flashes hit the ends of the train are not at the same level; they are not simultaneous.
+
+== Lorentz transformation ==
+
+The relativity of simultaneity can be demonstrated using the Lorentz transformation, which relates the coordinates used by one observer to coordinates used by another in uniform relative motion with respect to the first.
+Assume that the first observer uses coordinates labeled t, x, y, and z, while the second observer uses coordinates labeled t′, x′, y′, and y′. Now suppose that the first observer sees the second observer moving in the x-direction at a velocity v. And suppose that the observers' coordinate axes are parallel and that they have the same origin. Then the Lorentz transformation expresses how the coordinates are related:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  t
+                  ′
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      t
+                      −
+                      
+                        v
+                        
+                        x
+                        
+                          /
+                        
+                        
+                          c
+                          
+                            2
+                          
+                        
+                      
+                    
+                    
+                      1
+                      −
+                      
+                        v
+                        
+                          2
+                        
+                      
+                      
+                        /
+                      
+                      
+                        c
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+              
+            
+            
+              
+                
+                  x
+                  ′
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      x
+                      −
+                      v
+                      
+                      t
+                    
+                    
+                      1
+                      −
+                      
+                        v
+                        
+                          2
+                        
+                      
+                      
+                        /
+                      
+                      
+                        c
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+              
+            
+            
+              
+                
+                  y
+                  ′
+                
+              
+              
+                
+                =
+                y
+                ,
+              
+            
+            
+              
+                
+                  z
+                  ′
+                
+              
+              
+                
+                =
+                z
+                ,
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}t'&={\frac {t-{v\,x/c^{2}}}{\sqrt {1-v^{2}/c^{2}}}},\\x'&={\frac {x-v\,t}{\sqrt {1-v^{2}/c^{2}}}},\\y'&=y,\\z'&=z,\end{aligned}}}
+  
+
+where c is the speed of light.  If two events happen at the same time in the frame of the first observer, they will have identical values of the t-coordinate.  However, if they have different values of the x-coordinate (different positions in the x-direction), they will have different values of the t′ coordinate, so they will happen at different times in that frame. The term that accounts for the failure of absolute simultaneity is the vx/c2.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Relativity_of_simultaneity-2.md b/data/en.wikipedia.org/wiki/Relativity_of_simultaneity-2.md
new file mode 100644
index 000000000..14edc7db2
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Relativity_of_simultaneity-2.md
@@ -0,0 +1,30 @@
+---
+title: "Relativity of simultaneity"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Relativity_of_simultaneity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:14.866265+00:00"
+instance: "kb-cron"
+---
+
+The equation t′ = constant defines a "line of simultaneity" in the (x′, t′) coordinate system for the second (moving) observer, just as the equation t = constant defines the "line of simultaneity" for the first (stationary) observer in the (x, t) coordinate system. From the above equations for the Lorentz transform it can be seen that t′ is constant if and only if t − vx/c2 = constant. Thus the set of points that make t constant are different from the set of points that makes t′ constant. That is, the set of events which are regarded as simultaneous depends on the frame of reference used to make the comparison.
+Graphically, this can be represented on a spacetime diagram by the fact that a plot of the set of points regarded as simultaneous generates a line which depends on the observer.  In the spacetime diagram, the dashed line represents a set of points considered to be simultaneous with the origin by an observer moving with a velocity v of one-quarter of the speed of light.  The dotted horizontal line represents the set of points regarded as simultaneous with the origin by a stationary observer.  This diagram is drawn using the (x, t) coordinates of the stationary observer, and is scaled so that the speed of light is one, i.e., so that a ray of light would be represented by a line with a 45° angle from the x axis.  From our previous analysis, given that v = 0.25 and c = 1, the equation of the dashed line of simultaneity is t − 0.25x = 0 and with v = 0, the equation of the dotted line of simultaneity is t = 0.
+In general the second observer traces out a worldline in the spacetime of the first observer described by t = x/v, and the set of simultaneous events for the second observer (at the origin) is described by the line t = vx. Note the multiplicative inverse relation of the slopes of the worldline and simultaneous events, in accord with the principle of hyperbolic orthogonality.
+
+== Accelerated observers ==
+
+The Lorentz-transform calculation above uses a definition of extended-simultaneity (i.e. of when and where events occur at which you were not present) that might be referred to as the co-moving or "tangent free-float-frame" definition. This definition is naturally extrapolated to events in gravitationally-curved spacetimes, and to accelerated observers, through use of a radar-time/distance definition that (unlike the tangent free-float-frame definition for accelerated frames) assigns a unique time and position to any event.
+The radar-time definition of extended-simultaneity further facilitates visualization of the way that acceleration curves spacetime for travelers in the absence of any gravitating objects. This is illustrated in the figure at right, which shows radar time/position isocontours for events in flat spacetime as experienced by a traveler (red trajectory) taking a constant proper-acceleration roundtrip. One caveat of this approach is that the time and place of remote events are not fully defined until light from such an event is able to reach our traveler.
+
+== See also ==
+Andromeda paradox
+Causal structure
+Einstein's thought experiments
+Ehrenfest's paradox
+Einstein synchronisation
+
+== References ==
+
+== External links ==
+ Special relativity at Wikibooks
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Ritz_ballistic_theory-0.md b/data/en.wikipedia.org/wiki/Ritz_ballistic_theory-0.md
new file mode 100644
index 000000000..47badc529
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Ritz_ballistic_theory-0.md
@@ -0,0 +1,1258 @@
+---
+title: "Ritz ballistic theory"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Ritz_ballistic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:16.167205+00:00"
+instance: "kb-cron"
+---
+
+Ritz ballistic theory is an emission theory in physics, first published in 1908 by Swiss physicist Walther Ritz. In 1908, Ritz published Recherches critiques sur l'Électrodynamique générale, a lengthy criticism of Maxwell-Lorentz electromagnetic theory, in which he contended that the theory's connection with the luminiferous aether (see Lorentz ether theory) made it "essentially inappropriate to express the comprehensive laws for the propagation of electrodynamic actions." He argued that, among its difficulties, is that there are too many solutions. Problems admit both advanced and retarded solutions, but advanced solutions are unphysical, since they allow the future to influence the past.
+Ritz also rejected special relativity. He proposed to preserve classical mechanics, and modify the equations of electromagnetism instead. He argued that the advanced solution is unacceptable, but cannot be excluded based on the mere Maxwell equations. Therefore, he proposed to add another assumption, that only the retarded solution is physically allowed. He proposed a new equation, derived from the principles of the ballistic theory of electromagnetic waves, a theory competing with the special theory of relativity. The equation relates the force between two charged particles with a radial separation r relative velocity v and relative acceleration a, where k is an undetermined parameter from the general form of Ampere's force law as proposed by Maxwell. The equation obeys Newton's third law and forms the basis of Ritz's electrodynamics.
+
+  
+    
+      
+        
+          F
+        
+        =
+        
+          
+            
+              
+                q
+                
+                  1
+                
+              
+              
+                q
+                
+                  2
+                
+              
+            
+            
+              4
+              π
+              
+                ϵ
+                
+                  0
+                
+              
+              
+                r
+                
+                  2
+                
+              
+            
+          
+        
+        
+          [
+          
+            
+              [
+              
+                1
+                +
+                
+                  
+                    
+                      3
+                      −
+                      k
+                    
+                    4
+                  
+                
+                
+                  
+                    (
+                    
+                      
+                        v
+                        c
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                −
+                
+                  
+                    
+                      3
+                      (
+                      1
+                      −
+                      k
+                      )
+                    
+                    4
+                  
+                
+                
+                  
+                    (
+                    
+                      
+                        
+                          v
+                          ⋅
+                          r
+                        
+                        
+                          c
+                          
+                            2
+                          
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                −
+                
+                  
+                    r
+                    
+                      2
+                      
+                        c
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                (
+                
+                  a
+                  ⋅
+                  r
+                
+                )
+              
+              ]
+            
+            
+              
+                
+                  r
+                
+                r
+              
+            
+            −
+            
+              
+                
+                  k
+                  +
+                  1
+                
+                
+                  2
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+            
+            (
+            
+              v
+              ⋅
+              r
+            
+            )
+            
+              v
+            
+            −
+            
+              
+                r
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+            (
+            
+              a
+            
+            )
+          
+          ]
+        
+      
+    
+    {\displaystyle \mathbf {F} ={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}r^{2}}}\left[\left[1+{\frac {3-k}{4}}\left({\frac {v}{c}}\right)^{2}-{\frac {3(1-k)}{4}}\left({\frac {\mathbf {v\cdot r} }{c^{2}}}\right)^{2}-{\frac {r}{2c^{2}}}(\mathbf {a\cdot r} )\right]{\frac {\mathbf {r} }{r}}-{\frac {k+1}{2c^{2}}}(\mathbf {v\cdot r} )\mathbf {v} -{\frac {r}{c^{2}}}(\mathbf {a} )\right]}
+  
+
+== Derivation of Ritz's equation ==
+On the assumption of an emission theory, the force acting between two moving charges should depend on the density of the messenger particles emitted by the charges (
+  
+    
+      
+        D
+      
+    
+    {\displaystyle D}
+  
+), the radial distance between the charges (ρ), the velocity of the emission relative to the receiver, (
+  
+    
+      
+        
+          U
+          
+            x
+          
+        
+      
+    
+    {\displaystyle U_{x}}
+  
+ and 
+  
+    
+      
+        
+          U
+          
+            r
+          
+        
+      
+    
+    {\displaystyle U_{r}}
+  
+ for the x and r components, respectively), and the acceleration of the particles relative to each other (
+  
+    
+      
+        
+          a
+          
+            x
+          
+        
+      
+    
+    {\displaystyle a_{x}}
+  
+). This gives us an equation of the form:
+
+  
+    
+      
+        
+          F
+          
+            x
+          
+        
+        =
+        e
+        D
+        
+          [
+          
+            
+              A
+              
+                1
+              
+            
+            c
+            o
+            s
+            (
+            ρ
+            x
+            )
+            +
+            
+              B
+              
+                1
+              
+            
+            
+              
+                
+                  
+                    U
+                    
+                      x
+                    
+                  
+                  
+                    U
+                    
+                      r
+                    
+                  
+                
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+            +
+            
+              C
+              
+                1
+              
+            
+            
+              
+                
+                  ρ
+                  
+                    a
+                    
+                      x
+                    
+                  
+                
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+          
+          ]
+        
+      
+    
+    {\displaystyle F_{x}=eD\left[A_{1}cos(\rho x)+B_{1}{\frac {U_{x}U_{r}}{c^{2}}}+C_{1}{\frac {\rho a_{x}}{c^{2}}}\right]}
+  
+.
+where the coefficients 
+  
+    
+      
+        
+          A
+          
+            1
+          
+        
+      
+    
+    {\displaystyle A_{1}}
+  
+, 
+  
+    
+      
+        
+          B
+          
+            1
+          
+        
+      
+    
+    {\displaystyle B_{1}}
+  
+ and 
+  
+    
+      
+        
+          C
+          
+            1
+          
+        
+      
+    
+    {\displaystyle C_{1}}
+  
+ are independent of the coordinate system and are functions of 
+  
+    
+      
+        
+          u
+          
+            2
+          
+        
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle u^{2}/c^{2}}
+  
+ and 
+  
+    
+      
+        
+          u
+          
+            ρ
+          
+          
+            2
+          
+        
+        
+          /
+        
+        
+          c
+          
+            2
+          
+        
+      
+    
+    {\displaystyle u_{\rho }^{2}/c^{2}}
+  
+. The stationary coordinates of the observer relate to the moving frame of the charge as follows
+
+  
+    
+      
+        X
+        +
+        x
+        (
+        
+          t
+          ′
+        
+        )
+        =
+        
+          X
+          ′
+        
+        +
+        
+          x
+          ′
+        
+        (
+        
+          t
+          ′
+        
+        )
+        −
+        (
+        t
+        −
+        
+          t
+          ′
+        
+        )
+        
+          v
+          
+            x
+          
+          ′
+        
+      
+    
+    {\displaystyle X+x(t')=X'+x'(t')-(t-t')v'_{x}}
+  
+
+Developing the terms in the force equation, we find that the density of particles is given by
+
+  
+    
+      
+        D
+        α
+        
+          
+            
+              d
+              
+                t
+                ′
+              
+              
+                e
+                ′
+              
+              d
+              S
+            
+            
+              ρ
+              
+                2
+              
+            
+          
+        
+        =
+        −
+        
+          
+            
+              
+                e
+                ′
+              
+              ∂
+              ρ
+            
+            
+              c
+              
+                ρ
+                
+                  2
+                
+              
+              ∂
+              n
+            
+          
+        
+        d
+        S
+        d
+        n
+      
+    
+    {\displaystyle D\alpha {\frac {dt'e'dS}{\rho ^{2}}}=-{\frac {e'\partial \rho }{c\rho ^{2}\partial n}}dSdn}
+  
+
+The tangent plane of the shell of emitted particles in the stationary coordinate is given by the Jacobian of the transformation from 
+  
+    
+      
+        
+          X
+          ′
+        
+      
+    
+    {\displaystyle X'}
+  
+ to 
+  
+    
+      
+        X
+      
+    
+    {\displaystyle X}
+  
+:
+
+  
+    
+      
+        
+          
+            
+              ∂
+              ρ
+            
+            
+              ∂
+              n
+            
+          
+        
+        =
+        
+          
+            
+              ∂
+              (
+              X
+              Y
+              Z
+              )
+            
+            
+              ∂
+              (
+              
+                X
+                ′
+              
+              
+                Y
+                ′
+              
+              
+                Z
+                ′
+              
+              )
+            
+          
+        
+        =
+        
+          
+            
+              a
+              
+                e
+                ′
+              
+            
+            
+              ρ
+              
+                2
+              
+            
+          
+        
+        
+          (
+          
+            1
+            +
+            
+              
+                
+                  ρ
+                  
+                    a
+                    
+                      ρ
+                    
+                    ′
+                  
+                
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle {\frac {\partial \rho }{\partial n}}={\frac {\partial (XYZ)}{\partial (X'Y'Z')}}={\frac {ae'}{\rho ^{2}}}\left(1+{\frac {\rho a'_{\rho }}{c^{2}}}\right)}
+  
+
+We can also develop expressions for the retarded radius 
+  
+    
+      
+        ρ
+      
+    
+    {\displaystyle \rho }
+  
+ and velocity 
+  
+    
+      
+        
+          U
+          
+            ρ
+          
+        
+        <
+        ρ
+        >
+      
+    
+    {\displaystyle U_{\rho }<\rho >}
+  
+ using Taylor series expansions
+
+  
+    
+      
+        ρ
+        =
+        r
+        
+          
+            (
+            
+              1
+              +
+              
+                
+                  
+                    r
+                    
+                      a
+                      
+                        r
+                      
+                      ′
+                    
+                  
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+            
+            )
+          
+          
+            1
+            
+              /
+            
+            2
+          
+        
+      
+    
+    {\displaystyle \rho =r\left(1+{\frac {ra'_{r}}{c^{2}}}\right)^{1/2}}
+  
+
+  
+    
+      
+        
+          ρ
+          
+            x
+          
+        
+        =
+        
+          r
+          
+            x
+          
+        
+        +
+        
+          
+            
+              
+                r
+                
+                  2
+                
+              
+              
+                a
+                
+                  x
+                
+                ′
+              
+            
+            
+              2
+              
+                c
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle \rho _{x}=r_{x}+{\frac {r^{2}a'_{x}}{2c^{2}}}}
+  
+
+  
+    
+      
+        
+          U
+          
+            ρ
+          
+        
+        =
+        
+          v
+          
+            r
+          
+        
+        −
+        
+          v
+          
+            r
+          
+          ′
+        
+        +
+        
+          
+            
+              r
+              
+                a
+                
+                  r
+                
+                ′
+              
+            
+            c
+          
+        
+      
+    
+    {\displaystyle U_{\rho }=v_{r}-v'_{r}+{\frac {ra'_{r}}{c}}}
+  
+
+With these substitutions, we find that the force equation is now
+
+  
+    
+      
+        
+          F
+          
+            x
+          
+        
+        =
+        
+          
+            
+              e
+              
+                e
+                ′
+              
+            
+            
+              r
+              
+                2
+              
+            
+          
+        
+        
+          (
+          
+            1
+            +
+            
+              
+                
+                  r
+                  
+                    a
+                    
+                      r
+                    
+                    ′
+                  
+                
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+        
+          [
+          
+            A
+            c
+            o
+            s
+            (
+            r
+            x
+            )
+            
+              (
+              
+                1
+                −
+                
+                  
+                    
+                      3
+                      r
+                      
+                        a
+                        
+                          r
+                        
+                        ′
+                      
+                    
+                    
+                      2
+                      
+                        c
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+              
+              )
+            
+            +
+            A
+            
+              (
+              
+                
+                  
+                    r
+                    
+                      a
+                      
+                        x
+                      
+                      ′
+                    
+                  
+                  
+                    2
+                    
+                      c
+                      
+                        2
+                      
+                    
+                  
+                
+              
+              )
+            
+            −
+            B
+            
+              (
+              
+                
+                  
+                    
+                      u
+                      
+                        x
+                      
+                    
+                    
+                      u
+                      
+                        r
+                      
+                    
+                  
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+              )
+            
+            −
+            C
+            
+              (
+              
+                
+                  
+                    r
+                    
+                      a
+                      
+                        x
+                      
+                      ′
+                    
+                  
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+              )
+            
+          
+          ]
+        
+      
+    
+    {\displaystyle F_{x}={\frac {ee'}{r^{2}}}\left(1+{\frac {ra'_{r}}{c^{2}}}\right)\left[Acos(rx)\left(1-{\frac {3ra'_{r}}{2c^{2}}}\right)+A\left({\frac {ra'_{x}}{2c^{2}}}\right)-B\left({\frac {u_{x}u_{r}}{c^{2}}}\right)-C\left({\frac {ra'_{x}}{c^{2}}}\right)\right]}
+  
+
+Next we develop the series representations of the coefficients
+
+  
+    
+      
+        A
+        =
+        
+          α
+          
+            0
+          
+        
+        +
+        
+          α
+          
+            1
+          
+        
+        
+          
+            
+              u
+              
+                2
+              
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+        +
+        
+          α
+          
+            2
+          
+        
+        
+          
+            
+              u
+              
+                r
+              
+              
+                2
+              
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+        +
+        .
+        .
+        .
+      
+    
+    {\displaystyle A=\alpha _{0}+\alpha _{1}{\frac {u^{2}}{c^{2}}}+\alpha _{2}{\frac {u_{r}^{2}}{c^{2}}}+...}
+  
+
+  
+    
+      
+        B
+        =
+        
+          β
+          
+            0
+          
+        
+        +
+        
+          β
+          
+            1
+          
+        
+        
+          
+            
+              u
+              
+                2
+              
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+        +
+        
+          β
+          
+            2
+          
+        
+        
+          
+            
+              u
+              
+                r
+              
+              
+                2
+              
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+        +
+        .
+        .
+        .
+      
+    
+    {\displaystyle B=\beta _{0}+\beta _{1}{\frac {u^{2}}{c^{2}}}+\beta _{2}{\frac {u_{r}^{2}}{c^{2}}}+...}
+  
+
+  
+    
+      
+        C
+        =
+        
+          γ
+          
+            0
+          
+        
+        +
+        
+          γ
+          
+            1
+          
+        
+        
+          
+            
+              u
+              
+                2
+              
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+        +
+        
+          γ
+          
+            2
+          
+        
+        
+          
+            
+              u
+              
+                r
+              
+              
+                2
+              
+            
+            
+              c
+              
+                2
+              
+            
+          
+        
+        +
+        .
+        .
+        .
+      
+    
+    {\displaystyle C=\gamma _{0}+\gamma _{1}{\frac {u^{2}}{c^{2}}}+\gamma _{2}{\frac {u_{r}^{2}}{c^{2}}}+...}
+  
+
+With these substitutions, the force equation becomes
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Ritz_ballistic_theory-1.md b/data/en.wikipedia.org/wiki/Ritz_ballistic_theory-1.md
new file mode 100644
index 000000000..34512310e
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Ritz_ballistic_theory-1.md
@@ -0,0 +1,1550 @@
+---
+title: "Ritz ballistic theory"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Ritz_ballistic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:16.167205+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          F
+          
+            x
+          
+        
+        =
+        
+          
+            
+              e
+              
+                e
+                ′
+              
+            
+            
+              r
+              
+                2
+              
+            
+          
+        
+        
+          [
+          
+            
+              (
+              
+                
+                  α
+                  
+                    0
+                  
+                
+                +
+                
+                  α
+                  
+                    1
+                  
+                
+                
+                  
+                    
+                      u
+                      
+                        x
+                      
+                      
+                        2
+                      
+                    
+                    
+                      c
+                      
+                        2
+                      
+                    
+                  
+                
+                +
+                
+                  α
+                  
+                    2
+                  
+                
+                
+                  
+                    
+                      u
+                      
+                        r
+                      
+                      
+                        2
+                      
+                    
+                    
+                      c
+                      
+                        2
+                      
+                    
+                  
+                
+              
+              )
+            
+            c
+            o
+            s
+            (
+            r
+            x
+            )
+            −
+            
+              β
+              
+                0
+              
+            
+            
+              
+                
+                  
+                    u
+                    
+                      x
+                    
+                  
+                  
+                    u
+                    
+                      r
+                    
+                  
+                
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+            −
+            
+              α
+              
+                0
+              
+            
+            
+              
+                
+                  r
+                  
+                    a
+                    
+                      r
+                    
+                    ′
+                  
+                
+                
+                  2
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+            
+            +
+            
+              (
+              
+                
+                  
+                    r
+                    
+                      a
+                      
+                        x
+                      
+                      ′
+                    
+                  
+                  
+                    2
+                    
+                      c
+                      
+                        2
+                      
+                    
+                  
+                
+              
+              )
+            
+            (
+            
+              α
+              
+                0
+              
+            
+            −
+            2
+            
+              γ
+              
+                0
+              
+            
+            )
+          
+          ]
+        
+      
+    
+    {\displaystyle F_{x}={\frac {ee'}{r^{2}}}\left[\left(\alpha _{0}+\alpha _{1}{\frac {u_{x}^{2}}{c^{2}}}+\alpha _{2}{\frac {u_{r}^{2}}{c^{2}}}\right)cos(rx)-\beta _{0}{\frac {u_{x}u_{r}}{c^{2}}}-\alpha _{0}{\frac {ra'_{r}}{2c^{2}}}+\left({\frac {ra'_{x}}{2c^{2}}}\right)(\alpha _{0}-2\gamma _{0})\right]}
+  
+
+Since the equation must reduce to the Coulomb force law when the relative velocities are zero, we immediately know that 
+  
+    
+      
+        
+          α
+          
+            0
+          
+        
+        =
+        1
+      
+    
+    {\displaystyle \alpha _{0}=1}
+  
+. Furthermore, to obtain the correct expression for electromagnetic mass, we may deduce that 
+  
+    
+      
+        2
+        
+          γ
+          
+            0
+          
+        
+        −
+        1
+        =
+        1
+      
+    
+    {\displaystyle 2\gamma _{0}-1=1}
+  
+ or 
+  
+    
+      
+        
+          γ
+          
+            0
+          
+        
+        =
+        1
+      
+    
+    {\displaystyle \gamma _{0}=1}
+  
+.
+To determine the other coefficients, we consider the force on a linear circuit using Ritz's expression, and compare the terms with the general form of Ampere's law. The second derivative of Ritz's equation is
+
+  
+    
+      
+        
+          d
+          
+            2
+          
+        
+        
+          F
+          
+            x
+          
+        
+        =
+        
+          ∑
+          
+            i
+            ,
+            j
+          
+        
+        
+          
+            
+              d
+              
+                e
+                
+                  i
+                
+              
+              d
+              
+                e
+                
+                  j
+                
+                ′
+              
+            
+            
+              r
+              
+                2
+              
+            
+          
+        
+        
+          [
+          
+            
+              (
+              
+                1
+                +
+                
+                  α
+                  
+                    1
+                  
+                
+                
+                  
+                    
+                      u
+                      
+                        x
+                      
+                      
+                        2
+                      
+                    
+                    
+                      c
+                      
+                        2
+                      
+                    
+                  
+                
+                +
+                
+                  α
+                  
+                    2
+                  
+                
+                
+                  
+                    
+                      u
+                      
+                        r
+                      
+                      
+                        2
+                      
+                    
+                    
+                      c
+                      
+                        2
+                      
+                    
+                  
+                
+              
+              )
+            
+            c
+            o
+            s
+            (
+            r
+            x
+            )
+            −
+            
+              β
+              
+                0
+              
+            
+            
+              
+                
+                  
+                    u
+                    
+                      x
+                    
+                  
+                  
+                    u
+                    
+                      r
+                    
+                  
+                
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+            −
+            
+              α
+              
+                0
+              
+            
+            
+              
+                
+                  r
+                  
+                    a
+                    
+                      r
+                    
+                    ′
+                  
+                
+                
+                  2
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+            
+            +
+            
+              
+                
+                  r
+                  
+                    a
+                    
+                      x
+                    
+                    ′
+                  
+                
+                
+                  2
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+            
+          
+          ]
+        
+      
+    
+    {\displaystyle d^{2}F_{x}=\sum _{i,j}{\frac {de_{i}de_{j}'}{r^{2}}}\left[\left(1+\alpha _{1}{\frac {u_{x}^{2}}{c^{2}}}+\alpha _{2}{\frac {u_{r}^{2}}{c^{2}}}\right)cos(rx)-\beta _{0}{\frac {u_{x}u_{r}}{c^{2}}}-\alpha _{0}{\frac {ra'_{r}}{2c^{2}}}+{\frac {ra'_{x}}{2c^{2}}}\right]}
+  
+
+Consider the diagram on the right, and note that 
+  
+    
+      
+        d
+        q
+        v
+        =
+        I
+        d
+        l
+      
+    
+    {\displaystyle dqv=Idl}
+  
+,
+
+  
+    
+      
+        
+          ∑
+          
+            i
+            ,
+            j
+          
+        
+        d
+        
+          e
+          
+            i
+          
+        
+        d
+        
+          e
+          
+            j
+          
+          ′
+        
+        =
+        0
+      
+    
+    {\displaystyle \sum _{i,j}de_{i}de_{j}'=0}
+  
+
+  
+    
+      
+        
+          ∑
+          
+            i
+            ,
+            j
+          
+        
+        d
+        
+          e
+          
+            i
+          
+        
+        d
+        
+          e
+          
+            j
+          
+          ′
+        
+        
+          u
+          
+            x
+          
+          
+            2
+          
+        
+        =
+        −
+        2
+        d
+        q
+        d
+        
+          q
+          ′
+        
+        
+          w
+          
+            x
+          
+        
+        
+          w
+          
+            x
+          
+          ′
+        
+      
+    
+    {\displaystyle \sum _{i,j}de_{i}de_{j}'u_{x}^{2}=-2dqdq'w_{x}w'_{x}}
+  
+
+  
+    
+      
+        =
+        −
+        2
+        I
+        
+          I
+          ′
+        
+        d
+        s
+        d
+        
+          s
+          ′
+        
+        c
+        o
+        s
+        ϵ
+      
+    
+    {\displaystyle =-2II'dsds'cos\epsilon }
+  
+
+  
+    
+      
+        
+          ∑
+          
+            i
+            ,
+            j
+          
+        
+        d
+        
+          e
+          
+            i
+          
+        
+        d
+        
+          e
+          
+            j
+          
+          ′
+        
+        
+          u
+          
+            r
+          
+          
+            2
+          
+        
+        =
+        −
+        2
+        d
+        q
+        d
+        
+          q
+          ′
+        
+        
+          w
+          
+            r
+          
+        
+        
+          w
+          
+            r
+          
+          ′
+        
+      
+    
+    {\displaystyle \sum _{i,j}de_{i}de_{j}'u_{r}^{2}=-2dqdq'w_{r}w'_{r}}
+  
+
+  
+    
+      
+        =
+        −
+        2
+        I
+        
+          I
+          ′
+        
+        d
+        s
+        d
+        
+          s
+          ′
+        
+        c
+        o
+        s
+        (
+        r
+        d
+        s
+        )
+        c
+        o
+        s
+        (
+        r
+        d
+        s
+        )
+      
+    
+    {\displaystyle =-2II'dsds'cos(rds)cos(rds)}
+  
+
+  
+    
+      
+        
+          ∑
+          
+            i
+            ,
+            j
+          
+        
+        d
+        
+          e
+          
+            i
+          
+        
+        d
+        
+          e
+          
+            j
+          
+          ′
+        
+        
+          u
+          
+            x
+          
+        
+        
+          u
+          
+            r
+          
+        
+        =
+        −
+        d
+        q
+        d
+        
+          q
+          ′
+        
+        (
+        
+          w
+          
+            x
+          
+        
+        
+          w
+          
+            r
+          
+          ′
+        
+        +
+        
+          w
+          
+            x
+          
+          ′
+        
+        
+          w
+          
+            r
+          
+        
+        )
+      
+    
+    {\displaystyle \sum _{i,j}de_{i}de_{j}'u_{x}u_{r}=-dqdq'(w_{x}w'_{r}+w'_{x}w_{r})}
+  
+
+  
+    
+      
+        =
+        −
+        I
+        
+          I
+          ′
+        
+        d
+        s
+        d
+        
+          s
+          ′
+        
+        
+          [
+          
+            c
+            o
+            s
+            (
+            x
+            d
+            s
+            )
+            c
+            o
+            s
+            (
+            r
+            d
+            s
+            )
+            +
+            c
+            o
+            s
+            (
+            r
+            d
+            s
+            )
+            c
+            o
+            s
+            (
+            x
+            d
+            
+              s
+              ′
+            
+            )
+          
+          ]
+        
+      
+    
+    {\displaystyle =-II'dsds'\left[cos(xds)cos(rds)+cos(rds)cos(xds')\right]}
+  
+
+  
+    
+      
+        
+          ∑
+          
+            i
+            ,
+            j
+          
+        
+        d
+        
+          e
+          
+            i
+          
+        
+        d
+        
+          e
+          
+            j
+          
+          ′
+        
+        
+          a
+          
+            r
+          
+          ′
+        
+        =
+        0
+      
+    
+    {\displaystyle \sum _{i,j}de_{i}de_{j}'a'_{r}=0}
+  
+
+  
+    
+      
+        
+          ∑
+          
+            i
+            ,
+            j
+          
+        
+        d
+        
+          e
+          
+            i
+          
+        
+        d
+        
+          e
+          
+            j
+          
+          ′
+        
+        
+          a
+          
+            x
+          
+          ′
+        
+        =
+        0
+      
+    
+    {\displaystyle \sum _{i,j}de_{i}de_{j}'a'_{x}=0}
+  
+
+Plugging these expressions into Ritz's equation, we obtain the following
+
+  
+    
+      
+        
+          d
+          
+            2
+          
+        
+        
+          F
+          
+            x
+          
+        
+        =
+        
+          
+            
+              I
+              
+                I
+                ′
+              
+              d
+              s
+              d
+              
+                s
+                ′
+              
+            
+            
+              r
+              
+                2
+              
+            
+          
+        
+        
+          [
+          
+            
+              [
+              
+                2
+                
+                  α
+                  
+                    1
+                  
+                
+                c
+                o
+                s
+                ϵ
+                +
+                2
+                
+                  α
+                  
+                    2
+                  
+                
+                c
+                o
+                s
+                (
+                r
+                d
+                s
+                )
+                c
+                o
+                s
+                (
+                r
+                d
+                
+                  s
+                  ′
+                
+                )
+              
+              ]
+            
+            c
+            o
+            s
+            (
+            r
+            x
+            )
+            −
+            
+              β
+              
+                0
+              
+            
+            c
+            o
+            s
+            (
+            r
+            d
+            
+              s
+              ′
+            
+            )
+            c
+            o
+            s
+            (
+            x
+            d
+            s
+            )
+            −
+            
+              β
+              
+                0
+              
+            
+            c
+            o
+            s
+            (
+            r
+            d
+            s
+            )
+            c
+            o
+            s
+            (
+            x
+            d
+            
+              s
+              ′
+            
+            )
+          
+          ]
+        
+      
+    
+    {\displaystyle d^{2}F_{x}={\frac {II'dsds'}{r^{2}}}\left[\left[2\alpha _{1}cos\epsilon +2\alpha _{2}cos(rds)cos(rds')\right]cos(rx)-\beta _{0}cos(rds')cos(xds)-\beta _{0}cos(rds)cos(xds')\right]}
+  
+
+Comparing to the original expression for Ampere's force law
+
+  
+    
+      
+        
+          d
+          
+            2
+          
+        
+        
+          F
+          
+            x
+          
+        
+        =
+        −
+        
+          
+            
+              I
+              
+                I
+                ′
+              
+              d
+              s
+              d
+              
+                s
+                ′
+              
+            
+            
+              2
+              
+                r
+                
+                  2
+                
+              
+            
+          
+        
+        
+          [
+          
+            
+              [
+              
+                (
+                3
+                −
+                k
+                )
+                c
+                o
+                s
+                ϵ
+                −
+                3
+                (
+                1
+                −
+                k
+                )
+                c
+                o
+                s
+                (
+                r
+                d
+                s
+                )
+                c
+                o
+                s
+                (
+                r
+                d
+                
+                  s
+                  ′
+                
+                )
+              
+              ]
+            
+            c
+            o
+            s
+            (
+            r
+            x
+            )
+            −
+            (
+            1
+            +
+            k
+            )
+            c
+            o
+            s
+            (
+            r
+            d
+            
+              s
+              ′
+            
+            )
+            c
+            o
+            s
+            (
+            x
+            d
+            s
+            )
+            −
+            (
+            1
+            +
+            k
+            )
+            c
+            o
+            s
+            (
+            r
+            d
+            s
+            )
+            c
+            o
+            s
+            (
+            x
+            d
+            
+              s
+              ′
+            
+            )
+          
+          ]
+        
+      
+    
+    {\displaystyle d^{2}F_{x}=-{\frac {II'dsds'}{2r^{2}}}\left[\left[(3-k)cos\epsilon -3(1-k)cos(rds)cos(rds')\right]cos(rx)-(1+k)cos(rds')cos(xds)-(1+k)cos(rds)cos(xds')\right]}
+  
+
+we obtain the coefficients in Ritz's equation
+
+  
+    
+      
+        
+          α
+          
+            1
+          
+        
+        =
+        
+          
+            
+              3
+              −
+              k
+            
+            4
+          
+        
+      
+    
+    {\displaystyle \alpha _{1}={\frac {3-k}{4}}}
+  
+
+  
+    
+      
+        
+          α
+          
+            2
+          
+        
+        =
+        −
+        
+          
+            
+              3
+              (
+              1
+              −
+              k
+              )
+            
+            4
+          
+        
+      
+    
+    {\displaystyle \alpha _{2}=-{\frac {3(1-k)}{4}}}
+  
+
+  
+    
+      
+        
+          β
+          
+            0
+          
+        
+        =
+        
+          
+            
+              1
+              +
+              k
+            
+            2
+          
+        
+      
+    
+    {\displaystyle \beta _{0}={\frac {1+k}{2}}}
+  
+
+From this we obtain the full expression of Ritz's electrodynamic equation with one unknown
+
+  
+    
+      
+        
+          F
+        
+        =
+        
+          
+            
+              
+                q
+                
+                  1
+                
+              
+              
+                q
+                
+                  2
+                
+              
+            
+            
+              4
+              π
+              
+                ϵ
+                
+                  0
+                
+              
+              
+                r
+                
+                  2
+                
+              
+            
+          
+        
+        
+          [
+          
+            
+              [
+              
+                1
+                +
+                
+                  
+                    
+                      3
+                      −
+                      k
+                    
+                    4
+                  
+                
+                
+                  
+                    (
+                    
+                      
+                        v
+                        c
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                −
+                
+                  
+                    
+                      3
+                      (
+                      1
+                      −
+                      k
+                      )
+                    
+                    4
+                  
+                
+                
+                  
+                    (
+                    
+                      
+                        
+                          v
+                          ⋅
+                          r
+                        
+                        
+                          c
+                          
+                            2
+                          
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                −
+                
+                  
+                    r
+                    
+                      2
+                      
+                        c
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                (
+                
+                  a
+                  ⋅
+                  r
+                
+                )
+              
+              ]
+            
+            
+              
+                
+                  r
+                
+                r
+              
+            
+            −
+            
+              
+                
+                  k
+                  +
+                  1
+                
+                
+                  2
+                  
+                    c
+                    
+                      2
+                    
+                  
+                
+              
+            
+            (
+            
+              v
+              ⋅
+              r
+            
+            )
+            
+              v
+            
+            −
+            
+              
+                r
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+            (
+            
+              a
+            
+            )
+          
+          ]
+        
+      
+    
+    {\displaystyle \mathbf {F} ={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}r^{2}}}\left[\left[1+{\frac {3-k}{4}}\left({\frac {v}{c}}\right)^{2}-{\frac {3(1-k)}{4}}\left({\frac {\mathbf {v\cdot r} }{c^{2}}}\right)^{2}-{\frac {r}{2c^{2}}}(\mathbf {a\cdot r} )\right]{\frac {\mathbf {r} }{r}}-{\frac {k+1}{2c^{2}}}(\mathbf {v\cdot r} )\mathbf {v} -{\frac {r}{c^{2}}}(\mathbf {a} )\right]}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Ritz_ballistic_theory-2.md b/data/en.wikipedia.org/wiki/Ritz_ballistic_theory-2.md
new file mode 100644
index 000000000..0bd06d8dc
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Ritz_ballistic_theory-2.md
@@ -0,0 +1,187 @@
+---
+title: "Ritz ballistic theory"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Ritz_ballistic_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:16.167205+00:00"
+instance: "kb-cron"
+---
+
+In a footnote at the end of Ritz's section on Gravitation  ( English translation) the editor says, "Ritz used k = 6.4 to reconcile his formula (to calculate the angle of advancement of perihelion of planets per century) with the observed anomaly for Mercury (41") however recent data give 43.1", which leads to k = 7. Substituting this result into Ritz's formula yields exactly the general relativity formula." Using this same integer value for k in Ritz's electrodynamic equation we get:
+
+  
+    
+      
+        
+          F
+        
+        =
+        
+          
+            
+              
+                q
+                
+                  1
+                
+              
+              
+                q
+                
+                  2
+                
+              
+            
+            
+              4
+              π
+              
+                ϵ
+                
+                  0
+                
+              
+              
+                r
+                
+                  2
+                
+              
+            
+          
+        
+        
+          [
+          
+            
+              [
+              
+                1
+                −
+                
+                  
+                    (
+                    
+                      
+                        v
+                        c
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                +
+                4.5
+                
+                  
+                    (
+                    
+                      
+                        
+                          v
+                          ⋅
+                          r
+                        
+                        
+                          c
+                          
+                            2
+                          
+                        
+                      
+                    
+                    )
+                  
+                  
+                    2
+                  
+                
+                −
+                
+                  
+                    r
+                    
+                      2
+                      
+                        c
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                (
+                
+                  a
+                  ⋅
+                  r
+                
+                )
+              
+              ]
+            
+            
+              
+                
+                  r
+                
+                r
+              
+            
+            −
+            
+              
+                4
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+            (
+            
+              v
+              ⋅
+              r
+            
+            )
+            
+              v
+            
+            −
+            
+              
+                r
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+            (
+            
+              a
+            
+            )
+          
+          ]
+        
+      
+    
+    {\displaystyle \mathbf {F} ={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}r^{2}}}\left[\left[1-\left({\frac {v}{c}}\right)^{2}+4.5\left({\frac {\mathbf {v\cdot r} }{c^{2}}}\right)^{2}-{\frac {r}{2c^{2}}}(\mathbf {a\cdot r} )\right]{\frac {\mathbf {r} }{r}}-{\frac {4}{c^{2}}}(\mathbf {v\cdot r} )\mathbf {v} -{\frac {r}{c^{2}}}(\mathbf {a} )\right]}
+  
+
+== References and notes ==
+
+== Further reading ==
+Fritzius, Robert S. (2001). "Abbreviated Biographical Sketch of Walter Ritz (1878–1909)". In Hsu, Jong-Ping; Zhang, Yuan-Zhong (eds.). Lorentz and Poincaré Invariance: 100 Years of Relativity. World Scientific. pp. 572–573. ISBN 978-981-281-098-4.
+Martínez, Alberto A. (2004). "Ritz, Einstein, and the Emission Hypothesis". Physics in Perspective. 6 (1): 4–28. Bibcode:2004PhP.....6....4M. doi:10.1007/s00016-003-0195-6. S2CID 123043585.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Round_Hill_generator-0.md b/data/en.wikipedia.org/wiki/Round_Hill_generator-0.md
index ee1d441b4..fbd5c160a 100644
--- a/data/en.wikipedia.org/wiki/Round_Hill_generator-0.md
+++ b/data/en.wikipedia.org/wiki/Round_Hill_generator-0.md
@@ -4,7 +4,7 @@ chunk: 1/3
 source: "https://en.wikipedia.org/wiki/Round_Hill_generator"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T09:56:50.995002+00:00"
+date_saved: "2026-05-05T16:30:17.585867+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Round_Hill_generator-1.md b/data/en.wikipedia.org/wiki/Round_Hill_generator-1.md
index 3c4d7cad0..305f8c2a6 100644
--- a/data/en.wikipedia.org/wiki/Round_Hill_generator-1.md
+++ b/data/en.wikipedia.org/wiki/Round_Hill_generator-1.md
@@ -4,7 +4,7 @@ chunk: 2/3
 source: "https://en.wikipedia.org/wiki/Round_Hill_generator"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T09:56:50.995002+00:00"
+date_saved: "2026-05-05T16:30:17.585867+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Round_Hill_generator-2.md b/data/en.wikipedia.org/wiki/Round_Hill_generator-2.md
index d6590ba79..41f2edb5a 100644
--- a/data/en.wikipedia.org/wiki/Round_Hill_generator-2.md
+++ b/data/en.wikipedia.org/wiki/Round_Hill_generator-2.md
@@ -4,7 +4,7 @@ chunk: 3/3
 source: "https://en.wikipedia.org/wiki/Round_Hill_generator"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T09:56:50.995002+00:00"
+date_saved: "2026-05-05T16:30:17.585867+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Rydberg_formula-0.md b/data/en.wikipedia.org/wiki/Rydberg_formula-0.md
new file mode 100644
index 000000000..38c0fe4a6
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Rydberg_formula-0.md
@@ -0,0 +1,514 @@
+---
+title: "Rydberg formula"
+chunk: 1/2
+source: "https://en.wikipedia.org/wiki/Rydberg_formula"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:19.993038+00:00"
+instance: "kb-cron"
+---
+
+In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It was first empirically stated in 1888 by the Swedish physicist Johannes Rydberg, then theoretically by Niels Bohr in 1913, who used a primitive form of quantum mechanics. The formula directly generalizes the equations used to calculate the wavelengths of the hydrogen spectral series.
+
+== History ==
+In 1890, Rydberg proposed on a formula describing the relation between the wavelengths in spectral lines of alkali metals. He noticed that lines came in series and he found that he could simplify his calculations by specifying the lines in terms of their wavenumber (the number of waves occupying the unit length, equal to 1/λ, the inverse of the wavelength) rather than their wavelength. He plotted the wavenumbers (n) of successive lines in each series against consecutive integers which represented the order of the lines in that particular series. Finding that the resulting curves were similarly shaped, he sought a single function which could generate all of them, when appropriate constants were inserted.
+First he tried the formula: 
+  
+    
+      
+        
+          n
+          =
+          
+            n
+            
+              0
+            
+          
+          −
+          
+            
+              
+                C
+                
+                  0
+                
+              
+              
+                m
+                +
+                
+                  m
+                  ′
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle \textstyle n=n_{0}-{\frac {C_{0}}{m+m'}}}
+  
+, where n is the line's wavenumber, n0 is the series limit, m is the line's ordinal number in the series, m′ is a constant different for different series and C0 is a universal constant. This did not work very well.
+Rydberg was trying: 
+  
+    
+      
+        
+          n
+          =
+          
+            n
+            
+              0
+            
+          
+          −
+          
+            
+              
+                C
+                
+                  0
+                
+              
+              
+                
+                  (
+                  
+                    m
+                    +
+                    
+                      m
+                      ′
+                    
+                  
+                  )
+                
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle \textstyle n=n_{0}-{\frac {C_{0}}{\left(m+m'\right)^{2}}}}
+  
+ when he became aware of Balmer's formula for the hydrogen spectrum 
+  
+    
+      
+        
+          λ
+          =
+          
+            
+              
+                h
+                
+                  m
+                  
+                    2
+                  
+                
+              
+              
+                
+                  m
+                  
+                    2
+                  
+                
+                −
+                4
+              
+            
+          
+        
+      
+    
+    {\displaystyle \textstyle \lambda ={hm^{2} \over m^{2}-4}}
+  
+ In this equation, m is an integer and h is a constant (not to be confused with the later Planck constant).
+Rydberg therefore rewrote Balmer's formula in terms of wavenumbers, as 
+  
+    
+      
+        
+          n
+          =
+          
+            n
+            
+              0
+            
+          
+          −
+          
+            
+              
+                4
+                
+                  n
+                  
+                    0
+                  
+                
+              
+              
+                m
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle \textstyle n=n_{0}-{4n_{0} \over m^{2}}}
+  
+.
+This suggested that the Balmer formula for hydrogen might be a special case with 
+  
+    
+      
+        
+          
+            m
+            ′
+          
+          =
+          0
+        
+      
+    
+    {\displaystyle \textstyle m'=0}
+  
+   and   
+  
+    
+      
+        
+          
+            C
+          
+          
+            0
+          
+        
+        =
+        4
+        
+          n
+          
+            0
+          
+        
+      
+    
+    {\displaystyle {\text{C}}_{0}=4n_{0}}
+  
+, where 
+  
+    
+      
+        
+          
+            n
+            
+              0
+            
+          
+          =
+          
+            
+              1
+              h
+            
+          
+        
+      
+    
+    {\displaystyle \textstyle n_{0}={\frac {1}{h}}}
+  
+, the reciprocal of Balmer's constant (this constant h is written B in the Balmer equation article, again to avoid confusion with the Planck constant).
+The term 
+  
+    
+      
+        
+          
+            C
+          
+          
+            0
+          
+        
+      
+    
+    {\displaystyle {\text{C}}_{0}}
+  
+ was found to be a universal constant common to all elements, equal to 4/h. This constant is now known as the Rydberg constant, and m′ is known as the quantum defect.
+As stressed by Niels Bohr, expressing results in terms of wavenumber, not wavelength, was the key to Rydberg's discovery. The fundamental role of wavenumbers was also emphasized by the Rydberg-Ritz combination principle of 1908. The fundamental reason for this lies in quantum mechanics. Light's wavenumber is proportional to frequency 
+  
+    
+      
+        
+          
+            
+              1
+              λ
+            
+          
+          =
+          
+            
+              f
+              c
+            
+          
+        
+      
+    
+    {\displaystyle \textstyle {\frac {1}{\lambda }}={\frac {f}{c}}}
+  
+, and therefore also proportional to light's quantum energy E. Thus, 
+  
+    
+      
+        
+          
+            
+              1
+              λ
+            
+          
+          =
+          
+            
+              E
+              
+                h
+                c
+              
+            
+          
+        
+      
+    
+    {\displaystyle \textstyle {\frac {1}{\lambda }}={\frac {E}{hc}}}
+  
+ (in this formula the h represents the Planck constant). Modern and legitimate understanding is that Rydberg's findings were a reflection of the underlying simplicity of the behavior of spectral lines, in terms of fixed (quantized) energy differences between electron orbitals in atoms. Rydberg's 1888 classical expression for the form of the spectral series was not accompanied by a physical explanation. Walther Ritz's pre-quantum 1908 explanation for the mechanism underlying the spectral series was that atomic electrons behaved like magnets and that the magnets could vibrate with respect to the atomic nucleus (at least temporarily) to produce electromagnetic radiation, but this theory was superseded in 1913 by Niels Bohr's model of the atom.
+
+=== Bohr's interpretation and derivation of the constant ===
+Rydberg's published formula was
+
+  
+    
+      
+        ±
+        
+          
+            n
+            
+              N
+              
+                0
+              
+            
+          
+        
+        =
+        
+          
+            1
+            
+              (
+              
+                m
+                
+                  1
+                
+              
+              +
+              
+                μ
+                
+                  1
+                
+              
+              
+                )
+                
+                  2
+                
+              
+            
+          
+        
+        −
+        
+          
+            1
+            
+              (
+              
+                m
+                
+                  2
+                
+              
+              +
+              
+                μ
+                
+                  2
+                
+              
+              
+                )
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle \pm {\frac {n}{N_{0}}}={\frac {1}{(m_{1}+\mu _{1})^{2}}}-{\frac {1}{(m_{2}+\mu _{2})^{2}}}}
+  
+
+where 
+  
+    
+      
+        n
+      
+    
+    {\displaystyle n}
+  
+ is the observed wavenumber, 
+  
+    
+      
+        
+          N
+          
+            0
+          
+        
+      
+    
+    {\displaystyle N_{0}}
+  
+ is a constant for all spectral series and elements, and the remaining values, 
+  
+    
+      
+        
+          m
+          
+            1
+          
+        
+        ,
+        
+          μ
+          
+            1
+          
+        
+        ,
+        
+          m
+          
+            2
+          
+        
+        ,
+        
+          μ
+          
+            2
+          
+        
+      
+    
+    {\displaystyle m_{1},\mu _{1},m_{2},\mu _{2}}
+  
+ are integers indexing the various lines. When Bohr analyzes his model for the atom he writes
+
+  
+    
+      
+        ν
+        =
+        
+          
+            
+              2
+              
+                π
+                
+                  2
+                
+              
+              m
+              
+                e
+                
+                  4
+                
+              
+            
+            
+              h
+              
+                3
+              
+            
+          
+        
+        
+          (
+          
+            
+              
+                1
+                
+                  τ
+                  
+                    2
+                  
+                  
+                    2
+                  
+                
+              
+            
+            −
+            
+              
+                1
+                
+                  τ
+                  
+                    1
+                  
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle \nu ={\frac {2\pi ^{2}me^{4}}{h^{3}}}\left({\frac {1}{\tau _{2}^{2}}}-{\frac {1}{\tau _{1}^{2}}}\right)}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Rydberg_formula-1.md b/data/en.wikipedia.org/wiki/Rydberg_formula-1.md
new file mode 100644
index 000000000..722f96e64
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Rydberg_formula-1.md
@@ -0,0 +1,423 @@
+---
+title: "Rydberg formula"
+chunk: 2/2
+source: "https://en.wikipedia.org/wiki/Rydberg_formula"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:19.993038+00:00"
+instance: "kb-cron"
+---
+
+where he uses frequency 
+  
+    
+      
+        ν
+      
+    
+    {\displaystyle \nu }
+  
+ (proportional to wavenumber). 
+Thus he has been able to compute the value of Rydberg's heuristic constant 
+  
+    
+      
+        
+          N
+          
+            0
+          
+        
+      
+    
+    {\displaystyle N_{0}}
+  
+ from his atom theory and set the integers 
+  
+    
+      
+        
+          μ
+          
+            1
+          
+        
+      
+    
+    {\displaystyle \mu _{1}}
+  
+ and 
+  
+    
+      
+        
+          μ
+          
+            2
+          
+        
+      
+    
+    {\displaystyle \mu _{2}}
+  
+ to zero. The effect is to predict new series corresponding to 
+  
+    
+      
+        
+          τ
+          
+            2
+          
+        
+        =
+        1
+      
+    
+    {\displaystyle \tau _{2}=1}
+  
+ in the extreme ultraviolet unknown to Rydberg.
+In Bohr's conception of the atom, the integer Rydberg (and Balmer) n numbers represent electron orbitals at different integral distances from the atom. A frequency (or spectral energy) emitted in a transition from n1 to n2 therefore represents the photon energy emitted or absorbed when an electron makes a jump from orbital 1 to orbital 2.
+Later models found that the values for n1 and n2 corresponded to the principal quantum numbers of the two orbitals.
+The Rydberg formula can be interpreted both through the semi-classical Bohr model and through fully quantum-mechanical treatments of the hydrogen atom. In the Bohr model, electrons occupy quantized orbits whose energies vary. When an electron transitions from a higher level to a lower level a photon is emitted with a wavelength matching the Rydberg expression. Modern quantum mechanics arrives at the same result from the Schrödinger equation for an electron bound by a Coulomb potential. Differences in the energy eigenvalues of the hydrogen atom reproduce the observed Rydberg dependence, while relativistic and spin corrections appear when the Dirac equation, fine-structure interactions, and quantum electrodynamics (QED) effects are included. These refinements explain small deviations from the simple formula, such as the Lamb shift and hyperfine splittings in hydrogen-like systems.
+
+== For hydrogen ==
+For hydrogen, the energy of the atomic electron transition is given by
+
+  
+    
+      
+        
+          
+            1
+            
+              λ
+              
+                
+                  v
+                  a
+                  c
+                
+              
+            
+          
+        
+        =
+        
+          R
+          
+            H
+          
+        
+        
+          (
+          
+            
+              
+                1
+                
+                  n
+                  
+                    1
+                  
+                  
+                    2
+                  
+                
+              
+            
+            −
+            
+              
+                1
+                
+                  n
+                  
+                    2
+                  
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+        ,
+      
+    
+    {\displaystyle {\frac {1}{\lambda _{\mathrm {vac} }}}=R_{\text{H}}\left({\frac {1}{n_{1}^{2}}}-{\frac {1}{n_{2}^{2}}}\right),}
+  
+
+where
+
+  
+    
+      
+        
+          λ
+          
+            
+              v
+              a
+              c
+            
+          
+        
+      
+    
+    {\displaystyle \lambda _{\mathrm {vac} }}
+  
+ is the wavelength of electromagnetic radiation emitted in vacuum,
+
+  
+    
+      
+        
+          R
+          
+            H
+          
+        
+      
+    
+    {\displaystyle R_{\text{H}}}
+  
+ is the Rydberg constant for hydrogen, approximately 1.09677583×107 m−1,
+
+  
+    
+      
+        
+          n
+          
+            1
+          
+        
+      
+    
+    {\displaystyle n_{1}}
+  
+, 
+  
+    
+      
+        
+          n
+          
+            2
+          
+        
+      
+    
+    {\displaystyle n_{2}}
+  
+ are principal quantum numbers for energy levels, with 
+  
+    
+      
+        
+          n
+          
+            2
+          
+        
+        >
+        
+          n
+          
+            1
+          
+        
+      
+    
+    {\displaystyle n_{2}>n_{1}}
+  
+.
+By setting 
+  
+    
+      
+        
+          n
+          
+            1
+          
+        
+      
+    
+    {\displaystyle n_{1}}
+  
+ to 1 and letting 
+  
+    
+      
+        
+          n
+          
+            2
+          
+        
+      
+    
+    {\displaystyle n_{2}}
+  
+ run from 2 to infinity, the spectral lines known as the Lyman series converging to 91 nm are obtained. Other named series correspond to increasingly higher values of 
+  
+    
+      
+        
+          n
+          
+            1
+          
+        
+      
+    
+    {\displaystyle n_{1}}
+  
+.
+
+== For any hydrogen-like element ==
+
+The formula above can be extended for use with any hydrogen-like chemical elements with
+
+  
+    
+      
+        
+          
+            1
+            λ
+          
+        
+        =
+        R
+        
+          Z
+          
+            2
+          
+        
+        
+          (
+          
+            
+              
+                1
+                
+                  n
+                  
+                    1
+                  
+                  
+                    2
+                  
+                
+              
+            
+            −
+            
+              
+                1
+                
+                  n
+                  
+                    2
+                  
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+        ,
+      
+    
+    {\displaystyle {\frac {1}{\lambda }}=RZ^{2}\left({\frac {1}{n_{1}^{2}}}-{\frac {1}{n_{2}^{2}}}\right),}
+  
+
+where
+
+  
+    
+      
+        λ
+      
+    
+    {\displaystyle \lambda }
+  
+ is the wavelength (in vacuum) of the light emitted,
+
+  
+    
+      
+        R
+      
+    
+    {\displaystyle R}
+  
+ is the Rydberg constant for this element,
+
+  
+    
+      
+        Z
+      
+    
+    {\displaystyle Z}
+  
+ is the atomic number, i.e. the number of protons in the atomic nucleus of this element,
+
+  
+    
+      
+        
+          n
+          
+            1
+          
+        
+      
+    
+    {\displaystyle n_{1}}
+  
+ is the principal quantum number of the lower energy level, and
+
+  
+    
+      
+        
+          n
+          
+            2
+          
+        
+      
+    
+    {\displaystyle n_{2}}
+  
+ is the principal quantum number of the higher energy level for the atomic electron transition.
+This formula can be directly applied only to hydrogen-like, also called hydrogenic atoms of chemical elements, i.e. atoms with only one electron being affected by an effective nuclear charge (which is easily estimated). Examples would include He+, Li2+, Be3+ etc., where no other electrons exist in the atom.
+But the Rydberg formula also provides correct wavelengths for distant electrons, where the effective nuclear charge can be estimated as the same as that for hydrogen, since all but one of the nuclear charges have been screened by other electrons, and the core of the atom has an effective positive charge of +1.
+Finally, with certain modifications (replacement of Z by Z − 1, and use of the integers 1 and 2 for the ns to give a numerical value of 3⁄4 for the difference of their inverse squares), the Rydberg formula provides correct values in the special case of K-alpha lines, since the transition in question is the K-alpha transition of the electron from the 1s orbital to the 2p orbital. This is analogous to the Lyman-alpha line transition for hydrogen, and has the same frequency factor. Because the 2p electron is not screened by any other electrons in the atom from the nucleus, the nuclear charge is diminished only by the single remaining 1s electron, causing the system to be effectively a hydrogenic atom, but with a diminished nuclear charge Z − 1. Its frequency is thus the Lyman-alpha hydrogen frequency, increased by a factor of (Z − 1)2. This formula of f = c / λ = (Lyman-alpha frequency) ⋅ (Z − 1)2 is historically known as Moseley's law (having added a factor c to convert wavelength to frequency), and can be used to predict wavelengths of the Kα (K-alpha) X-ray spectral emission lines of chemical elements from aluminum to gold. See the biography of Henry Moseley for the historical importance of this law, which was derived empirically at about the same time it was explained by the Bohr model of the atom.
+For other spectral transitions in multi-electron atoms, the Rydberg formula generally provides incorrect results, since the magnitude of the screening of inner electrons for outer-electron transitions is variable and cannot be compensated for in the simple manner above.  The correction to the Rydberg formula for these atoms is known as the quantum defect.
+
+== Reduced Mass and Precision Corrections ==
+The classical Rydberg formula assumes an infinitely massive nucleus; however, in real atoms the nucleus has finite mass. In the Bohr model the electron and nucleus should orbit their mutual center of mass. In quantum mechanical calculations this leads to the introduction of a reduced mass, producing a slightly modified Rydberg constant that varies depending on the isotope. Additional corrections arise from relativistic motion of the electron, vacuum polarization, self-energy contributions, and other QED effects, all of which are essential in high-precision spectroscopy. These corrections become especially important for high-Z hydrogen-like ions, where relativistic velocities and strong Coulomb fields generate observable deviations from the nonrelativistic prediction.
+
+== See also ==
+Balmer series
+Hydrogen line
+Rydberg–Ritz combination principle
+Bohr atom
+Bohr–Sommerfeld model
+
+== References ==
+
+Sutton, Mike (July 2004). "Getting the numbers right: The lonely struggle of the 19th century physicist/chemist Johannes Rydberg". Chemistry World. 1 (7): 38–41. ISSN 1473-7604.
+Martinson, I.; Curtis, L.J. (2005). "Janne Rydberg – his life and work". Nuclear Instruments and Methods in Physics Research Section B. 235 (1–4): 17–22. Bibcode:2005NIMPB.235...17M. CiteSeerX 10.1.1.602.6210. doi:10.1016/j.nimb.2005.03.137.
\ No newline at end of file
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diff --git a/data/en.wikipedia.org/wiki/Schiehallion_experiment-3.md b/data/en.wikipedia.org/wiki/Schiehallion_experiment-3.md
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diff --git a/data/en.wikipedia.org/wiki/Search_for_the_Higgs_boson-0.md b/data/en.wikipedia.org/wiki/Search_for_the_Higgs_boson-0.md
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+---
+title: "Search for the Higgs boson"
+chunk: 1/5
+source: "https://en.wikipedia.org/wiki/Search_for_the_Higgs_boson"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:22.733870+00:00"
+instance: "kb-cron"
+---
+
+The search for the Higgs boson was a 40-year effort by physicists to prove the existence or non-existence of the Higgs boson, first theorised in the 1960s. The Higgs boson was the last unobserved fundamental particle in the Standard Model of particle physics, and its discovery was described as being the "ultimate verification" of the Standard Model. In March 2013, the Higgs boson was officially confirmed to exist.
+This confirmed answer proved the existence of the hypothetical Higgs field—a field of immense significance that is hypothesised as the source of electroweak symmetry breaking and the means by which elementary particles acquire mass. Symmetry breaking is considered proven but confirming exactly how this occurs in nature is a major unanswered question in physics. Proof of the Higgs field (by observing the associated particle) validates the final unconfirmed part of the Standard Model as essentially correct, avoiding the need for alternative sources for the Higgs mechanism. Evidence of its properties is likely to greatly affect human understanding of the universe and open up "new" physics beyond current theories.
+Despite their importance, the search and the proof were extremely difficult and took decades, because direct production, detection and verification of the Higgs boson on the scale needed to confirm the discovery and learn its properties required a very large experimental project and huge computing resources. For this reason, most experiments until around 2011 aimed to exclude ranges of masses that the Higgs could not have. Ultimately the search led to the construction of the Large Hadron Collider (LHC) in Geneva, Switzerland, the largest particle accelerator in the world, designed especially for this and other high-energy tests of the Standard Model.
+
+== Background ==
+
+=== The Higgs boson ===
+
+The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin, even (positive)  parity, no electric charge, and no colour charge, that couples to (interacts with) mass. It is also very unstable, decaying into other particles almost immediately.
+
+=== Experimental requirements ===
+Like other massive particles (e.g. the top quark and W and Z bosons), Higgs bosons decay to other particles almost immediately, long before they can be observed directly. However, the Standard Model precisely predicts the possible modes of decay and their probabilities. This allows the creation and decay of a Higgs boson to be shown by careful examination of the decay products of collisions.
+Therefore, although approaches to proving the Higgs were studied in early research from the 1960s, when the particle was proposed, large-scale experimental searches only commenced in the 1980s, with the opening of particle accelerators sufficiently powerful to provide evidence related to the Higgs boson.
+Since the Higgs boson, if it existed, could have any mass in a very wide range, a number of very advanced facilities were eventually required for the search. These included very powerful particle accelerator and detectors (in order to create Higgs bosons and detect their decay, if possible), and processing and analysis of vast amounts of data, requiring very large worldwide computing facilities. For example, over 300 trillion (3 × 1014) proton-proton collisions at the LHC were analysed in confirming the July 2012 particle's discovery, requiring construction of the so-called LHC Computing Grid, the world's largest computing grid (as of 2012) comprising over 170 computing facilities in 36 countries. Experimental techniques included examination of a wide range of possible masses (often quoted in GeV) in order to gradually narrow down the search area and rule out possible masses where the Higgs was unlikely, statistical analysis, and operation of multiple experiments and teams in order to see if the results from all were in agreement.
+
+== Experimental search and discovery of unknown boson ==
+
+=== Early limits ===
+During the early 1970s there were only few constraints on the existence of the Higgs boson. The limits that did exist came from the absence of the observation of Higgs related effects in nuclear physics, neutron stars, and neutron scattering experiments. This resulted in the conclusion that the Higgs—if it existed—was heavier than 18.3 MeV/c2.
+
+=== Early collider phenomenology ===
+In the mid-1970s, the first studies exploring how the Higgs boson may show itself in particle collision experiments were published. However, the prospect of actually finding the particle were not very good; the authors of one of the first articles on Higgs phenomenology warned:
+
+We should perhaps finish our paper with an apology and a caution. We apologize to experimentalists for having no idea what is the mass of the Higgs boson, ..., and for not being sure of its couplings to other particles, except that they are probably all very small. For these reasons, we do not want to encourage big experimental searches for the Higgs boson, but we do feel that people doing experiments vulnerable to the Higgs boson should know how it may turn up.
+One of the problems was that at the time there was almost no clue to the mass of the Higgs boson. Theoretical considerations left open a very wide range somewhere between 10 GeV/c2 and 1000 GeV/c2 with no real indication where to look.
+
+=== Large Electron–Positron Collider ===
+In the early planning studies for the Large Electron–Positron Collider (LEP) at CERN, the Higgs boson played no role. In fact, it does not appear to be mentioned in any of the reports until 1979. The first detailed study examining the possibilities of discovering the Higgs boson at LEP appeared in 1986. Thereafter the search for the Higgs boson became firmly established within the LEP program.
+As its name implies, the Large Electron–Positron Collider collided electrons with positrons. The three most important ways in which such a collision could lead to the production of a Higgs boson were:
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+---
+title: "Search for the Higgs boson"
+chunk: 2/5
+source: "https://en.wikipedia.org/wiki/Search_for_the_Higgs_boson"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:22.733870+00:00"
+instance: "kb-cron"
+---
+
+The electron and the positron together produce a Z boson which in turn decay to a Higgs boson and a pair of fermions.
+The electron and the positron together produce a Z boson which in turn radiates away a Higgs boson. (Higgs strahlung)
+The electron and the positron exchange a W or Z boson which along the way emits a Higgs boson.
+The fact that no decays of the Z boson to the Higgs were observed at LEP immediately implies that the Higgs boson, if it existed, must be heavier than the Z boson (~91 GeV/c2). Subsequently, with each successive energy upgrade of the LEP, hope re-emerged that discovery of the Higgs was just around the corner. Just prior to the planned shut down of LEP in 2000, few events that resemble a Higgs boson with a mass of ~115 GeV/c2 were observed. This led to extension of the final LEP run by a few months. But in the end the data was inconclusive and insufficient to justify another run after the winter break and the difficult decision was made to shut down and dismantle LEP to make room for the new Large Hadron Collider in November 2000. The inconclusive results of the direct search for the Higgs boson at LEP resulted in a final lower bound of the Higgs mass 114.4 GeV/c2 at the 95% confidence level.
+In parallel to the direct search program, LEP made precision measurements of many observables of the weak interactions. These observables are sensitive to the value of the Higgs mass through contributions of processes containing loops of virtual Higgs bosons. This allowed for the first time a direct estimate of the Higgs mass of about 100±30 GeV/c2. This estimate however is subject to the condition that the Standard Model is all there is, and no physics beyond the Standard Model come into play at these energy levels. New physical effects could potentially alter this estimate substantially.
+
+=== Superconducting Super Collider ===
+Planning for a new powerful collider to explore new physics at the >1 TeV scale had already started in 1983. The Superconducting Super Collider was to accelerate protons in an underground 87.1 km circular tunnel just outside Dallas, Texas to energies of 20 TeV each. One of the primary goals of this megaproject was finding the Higgs boson.
+In preparation for this machine, extensive phenomenological studies were produced for the production of Higgs bosons in hadron colliders. The big downside of hadron colliders for search for the Higgs is that they collide composite particles, and as a consequence produce many more background events and provide less information about the initial state of the collision. On the other hand, they provide a much higher centre-of-mass energy than lepton colliders (such as LEP) of a similar technological level. However, hadron colliders also provide another way producing a Higgs boson through the collision of two gluons mediated by a triangle of heavy (top or bottom) quarks.
+The Superconducting Super Collider project however was plagued by budget problems, and in 1993 Congress decided to pull the plug on the project, despite $2 billion having already been spent.
+
+=== Tevatron ===
+
+On 1 March 2001, the Tevatron Proton-antiproton (pp) collider at Fermilab near Chicago commenced its run 2. After run 1 (1992–1996), in which the collider had discovered the top quark, Tevatron had shut down for significant upgrades focused on improving the potential for finding the Higgs boson; the energies of the protons and antiprotons was bumped up to 0.98 TeV, and the number of collisions per second was increased by an order of magnitude (with further increases planned as the run continued). Even with the upgrades Tevatron was not guaranteed to find the Higgs. If the Higgs were too heavy (>180 GeV), then the collisions would not have enough energy to produce a Higgs boson. If it were too light (<140 GeV), then the Higgs would predominantly decay to pairs of bottom quarks—a signal that would be swamped by background events, and the Tevatron would not produce enough collisions to filter out the statistics. Nonetheless, the Tevatron was at the time the only operational particle collider that was sufficiently powerful to be capable of seeking the Higgs particle.
+Operation was planned to continue until the Tevatron could no longer keep up with the Large Hadron Collider. This point was reached on 30 September 2011, when the Tevatron was shut down. In their final analyses, the collaborations of the two detectors at Tevatron (CDF and DØ) report that based on their data they can exclude the possibility of a Higgs boson with a mass between 100 GeV/c2 and 103 GeV/c2 and between 147 GeV/c2 and 180 GeV/c2 at a 95% confidence level. In addition, they found an excess of events that could be from a Higgs boson in the range 115–140 GeV/c2. However, the significance of the statistics is deemed too low to base any conclusions on.
+On 22 December 2011, the DØ collaboration also reported limitations on the Higgs boson within the Minimal Supersymmetric Standard Model, an extension to the Standard Model. Proton-antiproton (pp) collisions with a centre-of-mass energy of 1.96 TeV had allowed them to set an upper limit for Higgs boson production within MSSM ranging from 90 to 300 GeV, and excluding tanβ > 20–30 for masses of the Higgs boson below 180 GeV (tanβ is the ratio of the two Higgs doublet vacuum expectation values).
\ No newline at end of file
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+---
+title: "Search for the Higgs boson"
+chunk: 3/5
+source: "https://en.wikipedia.org/wiki/Search_for_the_Higgs_boson"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:22.733870+00:00"
+instance: "kb-cron"
+---
+
+=== Large Hadron Collider ===
+Full operation at the LHC was delayed for 14 months from its initial successful tests, on 10 September 2008, until mid-November 2009, following a magnet quench event nine days after its inaugural tests that damaged over 50 superconducting magnets and contaminated the vacuum system. The quench was traced to a faulty electrical connection and repairs took several months; electrical fault detection and rapid quench-handling systems were also upgraded.
+Data collection and analysis in search of Higgs intensified from 30 March 2010 when the LHC began operating at 7 Tev (2 x 3.5 TeV). Preliminary results from the ATLAS and CMS experiments at the LHC as of July 2011 excluded a Standard Model Higgs boson in the mass range 155-190 GeV/c2 and 149-206 GeV/c2, respectively, at 95% CL. All of the above confidence intervals were derived using the CLs method.
+As of December 2011 the search had narrowed to the approximate region to 115–130 GeV, with a specific focus around 125 GeV, where both the ATLAS and CMS experiments had independently reported an excess of events, meaning that a higher than expected number of particle patterns compatible with the decay of a Higgs boson were detected in this energy range. The data was insufficient to show whether or not these excesses were due to background fluctuations (i.e. random chance or other causes), and its statistical significance was not large enough to draw conclusions yet or even formally to count as an "observation", but the fact that two independent experiments had both shown excesses at around the same mass led to considerable excitement in the particle physics community.
+At the end of December 2011, it was therefore widely expected that the LHC would provide sufficient data to either exclude or confirm the existence of the Standard Model Higgs boson by the end of 2012, when their 2012 collision data (at energies of 8 TeV) had been examined.
+Updates from the two LHC teams continued during the first part of 2012, with the tentative December 2011 data largely being confirmed and developed further. Updates were also available from the team analysing the final data from the Tevatron. All of these continued to highlight and narrow down the 125 GeV region as showing interesting features.
+On 2 July 2012, the ATLAS collaboration published additional analyses of their 2011 data, excluding boson mass ranges of 111.4 GeV to 116.6 GeV, 119.4 GeV to 122.1 GeV, and 129.2 GeV to 541 GeV. They observed an excess of events corresponding to the Higgs boson mass hypotheses around 126 GeV with a local significance of 2.9 sigma. On the same date, the DØ and CDF collaborations announced further analysis that increased their confidence. The significance of the excesses at energies between 115 and 140 GeV was now quantified as 2.9 standard deviations, corresponding to a 1 in 550 probability of being due to a statistical fluctuation. However, this still fell short of the 5 sigma confidence, therefore the results of the LHC experiments were necessary to establish a discovery. They excluded Higgs mass ranges at 100–103 and 147–180 GeV.
+
+=== Discovery of new boson ===
+
+On 22 June 2012 CERN announced an upcoming seminar covering tentative findings for 2012, and shortly afterwards rumours began to spread in the media that this would include a major announcement, but it was unclear whether this would be a stronger signal or a formal discovery. Speculation escalated to a "fevered" pitch when reports emerged that Peter Higgs, who proposed the particle, was to be attending the seminar. On 4 July 2012 CMS announced the discovery of a previously unknown boson with mass 125.3 ± 0.6 GeV/c2 and ATLAS of a boson with mass 126.5 GeV/c2.
+Using the combined analysis of two decay modes (known as 'channels'), both experiments reached a local significance of 5 sigma — or less than a 1 in one million chance of a statistical fluctuation being that strong. When additional channels were taken into account, the CMS significance was 4.9 sigma.
+The two teams had been working independent from each other, meaning they did not discuss their results with each other, providing additional certainty that any common finding was genuine validation of a particle. This level of evidence, confirmed independently by two separate teams and experiments, meets the formal level of proof required to announce a confirmed discovery of a new particle. CERN has been cautious, and stated only that the new particle is "consistent with" the Higgs boson, but scientists have not positively identified it as being the Higgs boson, pending further data collection and analysis.
+On July 31, the ATLAS collaboration presented further data analysis, including a third channel. They improved the significance to 5.9 sigma, and described it as an "observation of a new particle" with mass 126 ± 0.4 (stat.) ± 0.4 (sys) GeV/c2. Also CMS improved the significance to 5 sigma with the boson's mass at 125.3 ± 0.4 (stat) ± 0.5 (sys) GeV/c2.
+On 14 March 2013 CERN confirmed that:
+
+"CMS and ATLAS have compared a number of options for the spin-parity of this particle, and these all prefer no spin and even parity [two fundamental criteria of a Higgs boson consistent with the Standard Model]. This, coupled with the measured interactions of the new particle with other particles, strongly indicates that it is a Higgs boson."
+
+== Events in 2012 ==
\ No newline at end of file
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+---
+title: "Search for the Higgs boson"
+chunk: 4/5
+source: "https://en.wikipedia.org/wiki/Search_for_the_Higgs_boson"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:22.733870+00:00"
+instance: "kb-cron"
+---
+
+=== 2012 (post-discovery) ===
+In 2012, observations were considered consistent with the observed particle being the Standard Model Higgs boson. The particle decays into at least some of the predicted channels. Moreover, the production rates and branching ratios for the observed channels match the predictions by the Standard Model within the experimental uncertainties. However, the experimental uncertainties still left room for alternative explanations. It was therefore considered too early to conclude that the found particle was indeed the Standard Model Higgs boson.
+Further confirmation required more precise data on some of the characteristic of the new particle, including its other decay channels and various quantum numbers such as its parity. To allow for further data gathering, the LHC proton-proton collision run had been extended by seven weeks, postponing the planned long shutdown for upgrades in 2013.
+In November 2012, in a conference in Tokyo researchers said evidence gathered since July was falling into line with the basic Standard Model more than its alternatives, with a range of results for several interactions matching that theory's predictions. Physicist Matt Strassler highlighted "considerable" evidence that the new particle is not a pseudoscalar negative parity particle (a required finding for a Higgs boson), "evaporation" or lack of increased significance for previous hints of non-Standard Model findings, expected Standard Model interactions with W and Z bosons, absence of "significant new implications" for or against supersymmetry, and in general no significant deviations to date from the results expected of a Standard Model Higgs boson. However some kinds of extensions to the Standard Model would also show very similar results; based on other particles that are still being understood long after their discovery, it could take many years to know for sure, and decades to understand the particle that has been found.
+
+=== Premature media reports of confirmation as a Higgs boson ===
+In late 2012, Time, Forbes, Slate, NPR, and others announced incorrectly that the existence of the Higgs boson had been confirmed. Numerous statements by the discoverers at CERN and other experts since July 2012 had reiterated that a particle was discovered but it was not yet confirmed to be a Higgs boson. It was only in March 2013 that it was announced officially. This was followed by the making of a documentary film about the hunt.
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+---
+title: "Search for the Higgs boson"
+chunk: 5/5
+source: "https://en.wikipedia.org/wiki/Search_for_the_Higgs_boson"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:22.733870+00:00"
+instance: "kb-cron"
+---
+
+== Timeline of experimental evidence ==
+All results refer to the Standard Model Higgs boson, unless otherwise stated.
+2000–2004 – using data collected before 2000, in 2003–2004 Large Electron–Positron Collider experiments published papers which set a lower bound for the Higgs boson of 114.4 GeV/c2 at the 95% confidence level (CL), with a small number of events around 115 GeV.
+July 2010 – data from CDF (Fermilab) and DØ (Tevatron) experiments exclude the Higgs boson in the range 158–175 GeV/c2 at 95% CL.
+24 April 2011 – media reports "rumors" of a find; these were debunked by May 2011. They had not been a hoax, but were based on unofficial, unreviewed results.
+24 July 2011 – the LHC reported possible signs of the particle, the ATLAS Note concluding: "In the low mass range (c. 120–140 GeV) an excess of events with a significance of approximately 2.8 sigma above the background expectation is observed" and the BBC reporting that "interesting particle events at a mass of between 140 and 145 GeV" were found. These findings were repeated shortly thereafter by researchers at the Tevatron with a spokesman stating that: "There are some intriguing things going on around a mass of 140GeV." On 22 August 2011 it was reported that these anomalous results had become insignificant on the inclusion of more data from ATLAS and CMS and that the non-existence of the particle had been confirmed by LHC collisions to 95% certainty between 145 and 466 GeV (except for a few small islands around 250 GeV).
+23–24 July 2011 – Preliminary LHC results exclude the ranges 155–190 GeV/c2 (ATLAS) and 149–206 GeV/c2 (CMS) at 95% CL.
+27 July 2011 – preliminary CDF/DØ results extend the excluded range to 156–177 GeV/c2 at 95% CL.
+18 November 2011 – a combined analysis of ATLAS and CMS data further narrowed the window for the allowed values of the Higgs boson mass to 114–141 GeV.
+13 December 2011 – experimental results were announced from the ATLAS and CMS experiments, indicating that if the Higgs boson exists, its mass is limited to the range 116–130 GeV (ATLAS) or 115–127 GeV (CMS), with other masses excluded at 95% CL. Observed excesses of events at around 124 GeV (CMS) and 125–126 GeV (ATLAS) are consistent with the presence of a Higgs boson signal, but also consistent with fluctuations in the background. The global statistical significances of the excesses are 1.9 sigma (CMS) and 2.6 sigma (ATLAS) after correction for the look elsewhere effect.
+22 December 2011 – the DØ collaboration also sets limits on Higgs boson masses within the Minimal Supersymmetric Standard Model (an extension of the Standard Model), with an upper limit for production ranging from 90 to 300 GeV, and excluding tanβ>20–30 for Higgs boson masses below 180 GeV at 95% CL.
+7 February 2012 – updating the December results, the ATLAS and CMS experiments constrain the Standard Model Higgs boson, if it exists, to the range 116–131 GeV and 115–127 GeV, respectively, with the same statistical significance as before.
+7 March 2012 – the DØ and CDF collaborations announced that they found excesses that might be interpreted as coming from a Higgs boson with a mass in the region of 115 to 135 GeV/c2 in the full sample of data from Tevatron. The significance of the excesses is quantified as 2.2 standard deviations, corresponding to a 1 in 250 probability of being due to a statistical fluctuation. This is a lower significance, but consistent with and independent of the ATLAS and CMS data at the LHC. This new result also extends the range of Higgs-mass values excluded by the Tevatron experiments at 95% CL, which becomes 147-179 GeV/c2.
+2 July 2012 – the ATLAS collaboration further analysed their 2011 data, excluding Higgs mass ranges of 111.4 GeV to 116.6 GeV, 119.4 GeV to 122.1 GeV, and 129.2 GeV to 541 GeV. Higgs bosons are probably located at 126 GeV with significance of 2.9 sigma. On the same day, the DØ and CDF collaborations also announced further analysis, increasing their confidence that the data between 115 and 140 GeV is corresponding to a Higgs boson to 2.9 sigma, excluding mass ranges at 100–103 and 147–180 GeV.
+4 July 2012 – the CMS collaboration announced the discovery of a boson with mass 125.3 ± 0.6 GeV/c2 within 4.9 σ (sigma) (up to 5 sigma depending on the analysed channel), and the ATLAS collaboration a boson with mass of ~126.5 GeV/c2.
+31 July 2012  – the ATLAS collaboration further improved their analysis and announced the discovery of a boson with mass 126 ± 0.4 (stat.) ± 0.4 (sys) GeV/c2. Also CMS improved the significance to 5 sigma with the boson's mass at 125.3 ± 0.4 (stat) ± 0.5 (sys) GeV/c2.
+
+== Statistical analysis ==
+In 2012, the "5-sigma" criterion required by the scientists at the LHC, and its underlying frequentist interpretation of probability, triggered the interest of some statisticians, especially Bayesians: "five standard deviations, assuming normality, means a p-value of around 0.0000005 [...] Are the particle physics community completely wedded to frequentist analysis?". However, the research at LHC being already too advanced, the discussion didn't seem to have led to a Bayesian re-analysis of the data.
+
+== Notes ==
+
+== References ==
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+title: "Speed of gravity"
+chunk: 1/5
+source: "https://en.wikipedia.org/wiki/Speed_of_gravity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:26.680281+00:00"
+instance: "kb-cron"
+---
+
+In classical theories of gravitation, the changes in a gravitational field propagate. A change in the distribution of energy and momentum of matter results in subsequent alteration, at a distance, of the gravitational field which it produces. In the relativistic sense, the "speed of gravity" refers to the speed of a gravitational wave, which, as predicted by general relativity and confirmed by observation of the GW170817 neutron star merger, is equal to the  speed of light (c).
+
+== Introduction ==
+The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, c. Within the theory of special relativity, the constant c is not only about light; instead it is the highest possible speed for any interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and / or gravity. Thus, the speed of "light" is also the speed of gravitational waves, and further the speed of any massless particle. Such particles include the gluon (carrier of the strong force), the photons that make up light (hence carrier of electromagnetic force), and the hypothetical gravitons (which are the presumptive field particles associated with gravity; however, an understanding of the graviton, if it exists, requires an as-yet unavailable theory of quantum gravity).
+
+== Static fields ==
+The speed of physical changes in a gravitational or electromagnetic field should not be confused with "changes" in the behavior of static fields that are due to pure observer-effects. These changes in direction of a static field are, because of relativistic considerations, the same for an observer when a distant charge is moving, as when an observer (instead) decides to move with respect to a distant charge. Thus, constant motion of an observer with regard to a static charge and its extended static field (either a gravitational or electric field) does not change the field. For static fields, such as the electrostatic field connected with electric charge, or the gravitational field connected to a massive object, the field extends to infinity, and does not propagate. Motion of an observer does not cause the direction of such a field to change, and by symmetrical considerations, changing the observer frame so that the charge appears to be moving at a constant rate, also does not cause the direction of its field to change, but requires that it continues to "point" in the direction of the charge, at all distances from the charge.
+The consequence of this is that static fields (either electric or gravitational) always point directly to the actual position of the bodies that they are connected to, without any delay that is due to any "signal" traveling (or propagating) from the charge, over a distance to an observer. This remains true if the charged bodies and their observers are made to "move" (or not), by simply changing reference frames. This fact sometimes causes confusion about the "speed" of such static fields, which sometimes appear to change infinitely quickly when the changes in the field are mere artifacts of the motion of the observer, or of observation.
+In such cases, nothing actually changes infinitely quickly, save the point of view of an observer of the field. For example, when an observer begins to move with respect to a static field that already extends over light years, it appears as though "immediately" the entire field, along with its source, has begun moving at the speed of the observer. This, of course, includes the extended parts of the field. However, this "change" in the apparent behavior of the field source, along with its distant field, does not represent any sort of propagation that is faster than light.
+
+== Newtonian gravitation ==
+Isaac Newton's formulation of a gravitational force law requires that each particle with mass respond instantaneously to every other particle with mass irrespective of the distance between them.  In modern terms, Newtonian gravitation is described by the Poisson equation, according to which, when the mass distribution of a system changes, its gravitational field instantaneously adjusts.  Therefore, the theory assumes the speed of gravity to be infinite.  This assumption was adequate to account for all phenomena with the observational accuracy of that time.  It was not until the 19th century that an anomaly in astronomical observations which could not be reconciled with the Newtonian gravitational model of instantaneous action was noted: the French astronomer Urbain Le Verrier determined in 1859 that the elliptical orbit of Mercury precesses at a significantly different rate from that predicted by Newtonian theory.
+
+== Laplace ==
+The first attempt to combine a finite gravitational speed with Newton's theory was made by Laplace in 1805. Based on Newton's force law he considered a model in which the gravitational field is defined as a radiation field or fluid. Changes in the motion of the attracting body are transmitted by some sort of waves. Therefore, the movements of the celestial bodies should be modified in the order v/c, where v is the relative speed between the bodies and c is the speed of gravity. The effect of a finite speed of gravity goes to zero as c goes to infinity, but not as 1/c2 as it does in modern theories. This led Laplace to conclude that the speed of gravitational interactions is at least 7×106 times the speed of light. This velocity was used by many in the 19th century to criticize any model based on a finite speed of gravity, like electrical or mechanical explanations of gravitation.
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+title: "Speed of gravity"
+chunk: 2/5
+source: "https://en.wikipedia.org/wiki/Speed_of_gravity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:26.680281+00:00"
+instance: "kb-cron"
+---
+
+From a modern point of view, Laplace's analysis is incorrect. Not knowing about Lorentz invariance of static fields, Laplace assumed that when an object like the Earth is moving around the Sun, the attraction of the Earth would not be toward the instantaneous position of the Sun, but toward where the Sun had been if its position was retarded using the relative velocity (this retardation actually does happen with the optical position of the Sun, and is called annual solar aberration). Putting the Sun immobile at the origin, when the Earth is moving in an orbit of radius R with velocity v presuming that the gravitational influence moves with velocity c, moves the Sun's true position ahead of its optical position, by an amount equal to vR/c, which is the travel time of gravity from the sun to the Earth times the relative velocity of the sun and the Earth. As seen in Fig. 1, the pull of gravity (if it behaved like a wave, such as light) would then always be displaced in the direction of the Earth's velocity, so that the Earth would always be pulled toward the optical position of the Sun, rather than its actual position. This would cause a pull ahead of the Earth, which would cause the orbit of the Earth to spiral outward. Such an outspiral would be suppressed by an amount v/c compared to the force which keeps the Earth in orbit; and since the Earth's orbit is observed to be stable, Laplace's c must be very large. As is now known, it may be considered to be infinite in the limit of straight-line motion, since as a static influence it is instantaneous at distance when seen by observers at constant transverse velocity. For orbits in which velocity (direction of speed) changes slowly, it is almost infinite.
+The attraction toward an object moving with a steady velocity is towards its instantaneous position with no delay, for both gravity and electric charge. In a field equation consistent with special relativity (i.e., a Lorentz invariant equation), the attraction between static charges moving with constant relative velocity is always toward the instantaneous position of the charge (in this case, the "gravitational charge" of the Sun), not the time-retarded position of the Sun. When an object is moving in orbit at a steady speed but changing velocity v, the effect on the orbit is order v2/c2, and the effect preserves energy and angular momentum, so that orbits do not decay.
+
+== Electrodynamical analogies ==
+
+=== Early theories ===
+At the end of the 19th century, many tried to combine Newton's force law with the established laws of electrodynamics, like those of Wilhelm Eduard Weber, Carl Friedrich Gauss, Bernhard Riemann and James Clerk Maxwell. Those theories are not invalidated by Laplace's critique, because although they are based on finite propagation speeds, they contain additional terms which maintain the stability of the planetary system. Those models were used to explain the perihelion advance of Mercury, but they could not provide exact values. One exception was Maurice Lévy in 1890, who succeeded in doing so by combining the laws of Weber and Riemann, whereby the speed of gravity is equal to the speed of light. However, those hypotheses were rejected.
+However, a more important variation of those attempts was the theory of Paul Gerber, who derived in 1898 the identical formula, which was also derived later by Einstein for the perihelion advance. Based on that formula, Gerber calculated a propagation speed for gravity of 305000 km/s, i.e. practically the speed of light. But Gerber's derivation of the formula was faulty, i.e., his conclusions did not follow from his premises, and therefore many (including Einstein) did not consider it to be a meaningful theoretical effort. Additionally, the value it predicted for the deflection of light in the gravitational field of the sun was too high by the factor 3/2.
+
+=== Lorentz ===
+In 1900, Hendrik Lorentz tried to explain gravity on the basis of his ether theory and the Maxwell's equations. After proposing (and rejecting) a Le Sage type model, he assumed like Ottaviano-Fabrizio Mossotti and Johann Karl Friedrich Zöllner that the attraction of opposite charged particles is stronger than the repulsion of equal charged particles. The resulting net force is exactly what is known as universal gravitation, in which the speed of gravity is that of light. This leads to a conflict with the law of gravitation by Isaac Newton, in which it was shown by Pierre-Simon Laplace that a finite speed of gravity leads to some sort of aberration and therefore makes the orbits unstable. However, Lorentz showed that the theory is not concerned by Laplace's critique, because due to the structure of the Maxwell equations only effects in the order v2/c2 arise. But Lorentz calculated that the value for the perihelion advance of Mercury was much too low. He wrote:
+
+The special form of these terms may perhaps be modified. Yet, what has been said is sufficient to show that gravitation may be attributed to actions which are propagated with no greater velocity than that of light.
+In 1908, Henri Poincaré examined the gravitational theory of Lorentz and classified it as compatible with the relativity principle, but (like Lorentz) he criticized the inaccurate indication of the perihelion advance of Mercury.
+
+== Lorentz covariant models ==
+Henri Poincaré argued in 1904 that a propagation speed of gravity which is greater than c would contradict the concept of local time (based on synchronization by light signals) and the principle of relativity. He wrote:
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+title: "Speed of gravity"
+chunk: 3/5
+source: "https://en.wikipedia.org/wiki/Speed_of_gravity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:26.680281+00:00"
+instance: "kb-cron"
+---
+
+What would happen if we could communicate by signals other than those of light, the velocity of propagation of which differed from that of light? If, after having regulated our watches by the optimal method, we wished to verify the result by means of these new signals, we should observe discrepancies due to the common translatory motion of the two stations. And are such signals inconceivable, if we take the view of Laplace, that universal gravitation is transmitted with a velocity a million times as great as that of light?
+However, in 1905 Poincaré calculated that changes in the gravitational field can propagate with the speed of light if it is presupposed that such a theory is based on the Lorentz transformation. He wrote:
+
+Laplace showed in effect that the propagation is either instantaneous or much faster than that of light. However, Laplace examined the hypothesis of finite propagation velocity ceteris non mutatis [all other things being unchanged]; here, on the contrary, this hypothesis is conjoined with many others, and it may be that between them a more or less perfect compensation takes place. The application of the Lorentz transformation has already provided us with numerous examples of this.
+Similar models were also proposed by Hermann Minkowski (1907) and Arnold Sommerfeld (1910). However, those attempts were quickly superseded by Einstein's theory of general relativity. Whitehead's theory of gravitation (1922) explains  gravitational red shift, light bending, perihelion shift and Shapiro delay.
+
+== General relativity ==
+
+=== Background ===
+General relativity predicts that gravitational radiation should exist and propagate as a wave at lightspeed: a slowly evolving and weak gravitational field will produce, according to general relativity (GR), effects like those of Newtonian gravitation (it does not depend on the existence of gravitons, mentioned above, or any similar force-carrying particles).
+Suddenly displacing one of two gravitoelectrically interacting particles would, after a delay corresponding to lightspeed, cause the other to feel the displaced particle's absence: accelerations due to the change in quadrupole moment of star systems, like the Hulse–Taylor binary, have removed much energy (almost 2% of the energy of our own Sun's output) as gravitational waves, which would theoretically travel at the speed of light.
+In GR, gravity is described by a tensor of degree two, which, in the weak gravity limit, can be described by the gravitoelectromagnetism approximation. In the following discussion the diagonal components of the tensor would be termed gravitoelectric components, and the other components will be termed gravitomagnetic.
+Two gravitoelectrically interacting particle ensembles, e.g., two planets or stars moving at constant velocity with respect to each other, each feel a force toward the instantaneous position of the other body without a speed-of-light delay because Lorentz invariance demands that what a moving body in a static field sees and what a moving body that emits that field sees be symmetrical.
+A moving body's seeing no aberration in a static field emanating from a "motionless body" therefore means Lorentz invariance requires that in the previously moving body's reference frame the (now moving) emitting body's field lines must not at a distance be retarded or aberred.  Moving charged bodies (including bodies that emit static gravitational fields) exhibit static field lines that do not bend with distance and show no speed of light delay effects, as seen from bodies moving relative to them.
+In other words, since the gravitoelectric field is, by definition, static and continuous, it does not propagate. If such a source of a static field is accelerated (for example stopped) with regard to its formerly constant velocity frame, its distant field continues to be updated as though the charged body continued with constant velocity. This effect causes the distant fields of unaccelerated moving charges to appear to be "updated" instantly for their constant velocity motion, as seen from distant positions, in the frame where the source-object is moving at constant velocity. However, as discussed, this is an effect which can be removed at any time, by transitioning to a new reference frame in which the distant charged body is now at rest.
+The static and continuous gravitoelectric component of a gravitational field is not a gravitomagnetic component (gravitational radiation); see Petrov classification.  The gravitoelectric field is a static field and therefore cannot superluminally transmit quantized (discrete) information, i.e., it could not constitute a well-ordered series of impulses carrying a well-defined meaning (this is the same for gravity and electromagnetism).
+
+=== Aberration of field direction in general relativity, for a weakly accelerated observer ===
+
+The finite speed of gravitational interaction in general relativity does not lead to the sorts of problems with the aberration of gravity that Newton was originally concerned with, because there is no such aberration in static field effects. Because the acceleration of the Earth with regard to the Sun is small (meaning, to a good approximation, the two bodies can be regarded as traveling in straight lines past each other with unchanging velocity), the orbital results calculated by general relativity are the same as those of Newtonian gravity with instantaneous action at a distance, because they are modelled by the behavior of a static field with constant-velocity relative motion, and no aberration for the forces involved. Although the calculations are considerably more complicated, one can show that a static field in general relativity does not suffer from aberration problems as seen by an unaccelerated observer (or a weakly accelerated observer, such as the Earth). Analogously, the "static term" in the electromagnetic Liénard–Wiechert potential theory of the fields from a moving charge does not suffer from either aberration or positional-retardation. Only the term corresponding to acceleration and electromagnetic emission in the Liénard–Wiechert potential shows a direction toward the time-retarded position of the emitter.
+It is in fact not very easy to construct a self-consistent gravity theory in which gravitational interaction propagates at a speed other than the speed of light, which complicates discussion of this possibility.
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+title: "Speed of gravity"
+chunk: 4/5
+source: "https://en.wikipedia.org/wiki/Speed_of_gravity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:26.680281+00:00"
+instance: "kb-cron"
+---
+
+=== Formulaic conventions ===
+In general relativity the metric tensor symbolizes the gravitational potential, and Christoffel symbols of the spacetime manifold symbolize the gravitational force field. The tidal gravitational field is associated with the curvature of spacetime.
+
+=== Measurements ===
+For the reader who desires a deeper background, a comprehensive review of the definition of the speed of gravity and its measurement with high-precision astrometric and other techniques appears in the textbook Relativistic Celestial Mechanics in the Solar System.
+
+==== PSR 1913+16 orbital decay ====
+The speed of gravity (more correctly, the speed of gravitational waves) can be calculated from observations of the orbital decay rate of binary pulsars  PSR 1913+16 (the Hulse–Taylor binary system noted above) and PSR B1534+12.  The orbits of these binary pulsars are decaying due to loss of energy in the form of gravitational radiation.  The rate of this energy loss ("gravitational damping") can be measured, and since it depends on the speed of gravity, comparing the measured values to theory shows that the speed of gravity is equal to the speed of light to within 1%. However, according to parameterized post-Newtonian formalism setting, measuring the speed of gravity by comparing theoretical results with experimental results will depend on the theory; use of a theory other than that of general relativity could in principle show a different speed, although the existence of gravitational damping at all implies that the speed cannot be infinite.
+
+==== Jovian occultation of QSO J0842+1835 (contested) ====
+In September 2002, Sergei Kopeikin and Edward Fomalont announced that they had measured the speed of gravity indirectly, using their data from very-long-baseline interferometry measurement of the retarded position of Jupiter on its orbit during Jupiter's transit across the line-of-sight of the bright radio source quasar QSO J0842+1835. Kopeikin and Fomalont concluded that the speed of gravity is between 0.8 and 1.2 times the speed of light, which would be fully consistent with the theoretical prediction of general relativity that the speed of gravity is exactly the same as the speed of light.
+Several physicists, including Clifford M. Will and Steve Carlip, have criticized these claims on the grounds that they have allegedly misinterpreted the results of their measurements. Notably, prior to the actual transit, Hideki Asada in a paper to the Astrophysical Journal Letters theorized that the proposed experiment was essentially a roundabout confirmation of the speed of light instead of the speed of gravity.
+It is important to keep in mind that none of the debaters in this controversy are claiming that general relativity is "wrong". Rather, the debated issue is whether or not Kopeikin and Fomalont have really provided yet another verification of one of its fundamental predictions.
+Kopeikin and Fomalont, however, continue to vigorously argue their case and the means of presenting their result at the press conference of the American Astronomical Society (AAS) that was offered after the results of the Jovian experiment had been peer-reviewed by the experts of the AAS scientific organizing committee. In a later publication by Kopeikin and Fomalont, which uses a bi-metric formalism that splits the space-time null cone in two — one for gravity and another one for light — the authors claimed that Asada's claim was theoretically unsound. The two null cones overlap in general relativity, which makes tracking the speed-of-gravity effects difficult and requires a special mathematical technique of gravitational retarded potentials, which was worked out by Kopeikin and co-authors but was never properly employed by Asada and/or the other critics.
+Stuart Samuel also showed that the experiment did not actually measure the speed of gravity because the effects were too small to have been measured. A response by Kopeikin and Fomalont challenges this opinion.
+
+==== GW170817 and the demise of two neutron stars ====
+The detection of GW170817 in 2017, the finale of a neutron star inspiral observed through both gravitational waves and gamma rays, at a distance of 130 million light years, currently provides by far the best limit on the difference between the speed of light and that of gravity. Photons were detected 1.7 seconds after peak gravitational wave emission; assuming a delay of zero to 10 seconds, the difference between the speeds of gravitational and electromagnetic waves, vGW − vEM, is constrained to between −3×10−15 and +7×10−16 times the speed of light. However, this conclusion has been challenged by independent research suggesting that astronomical observations of supernova SN 1987A and distant galaxies JADES are inconsistent with the assumption that the speed of gravity equals the speed of light. 
+This also excluded some alternatives to general relativity, including variants of scalar–tensor theory, instances of Horndeski's theory, and Hořava–Lifshitz gravity.
+
+== Notes ==
+
+== References ==
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+title: "Speed of gravity"
+chunk: 5/5
+source: "https://en.wikipedia.org/wiki/Speed_of_gravity"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:26.680281+00:00"
+instance: "kb-cron"
+---
+
+== Further reading ==
+Kopeikin, Sergei M. (2001). "Testing Relativistic Effect of Propagation of Gravity by Very-Long Baseline Interferometry". Astrophys. J. 556 (1): L1–L6. arXiv:gr-qc/0105060. Bibcode:2001ApJ...556L...1K. doi:10.1086/322872. S2CID 2121856.
+Asada, Hidecki (2002). "The Light-cone Effect on the Shapiro Time Delay". Astrophys. J. 574 (1): L69–L70. arXiv:astro-ph/0206266. Bibcode:2002ApJ...574L..69A. doi:10.1086/342369. S2CID 14589086.
+Will, Clifford M. (2003). "Propagation Speed of Gravity and the Relativistic Time Delay". Astrophys. J. 590 (2): 683–690. arXiv:astro-ph/0301145. Bibcode:2003ApJ...590..683W. doi:10.1086/375164. S2CID 16402202.
+Fomalont, E. B. & Kopeikin, Sergei M. (2003). "The Measurement of the Light Deflection from Jupiter: Experimental Results". Astrophys. J. 598 (1): 704–711. arXiv:astro-ph/0302294. Bibcode:2003ApJ...598..704F. doi:10.1086/378785. S2CID 14002701.
+Kopeikin, Sergei M. (Feb 21, 2003). "The Measurement of the Light Deflection from Jupiter: Theoretical Interpretation". arXiv:astro-ph/0302462.
+Kopeikin, Sergei M. (2003). "The Post-Newtonian Treatment of the VLBI Experiment on September 8, 2002". Phys. Lett. A. 312 (3–4): 147–157. arXiv:gr-qc/0212121. Bibcode:2003PhLA..312..147K. doi:10.1016/S0375-9601(03)00613-3. S2CID 11664954.
+Faber, Joshua A. (Mar 14, 2003). "The speed of gravity has not been measured from time delays". arXiv:astro-ph/0303346.
+Kopeikin, Sergei M. (2004). "The Speed of Gravity in General Relativity and Theoretical Interpretation of the Jovian Deflection Experiment". Classical and Quantum Gravity. 21 (13): 3251–3286. arXiv:gr-qc/0310059. Bibcode:2004CQGra..21.3251K. doi:10.1088/0264-9381/21/13/010. S2CID 250893542.
+Samuel, Stuart (2003). "On the Speed of Gravity and the v/c Corrections to the Shapiro Time Delay". Phys. Rev. Lett. 90 (23) 231101. arXiv:astro-ph/0304006. Bibcode:2003PhRvL..90w1101S. doi:10.1103/PhysRevLett.90.231101. PMID 12857246. S2CID 15905017.
+Kopeikin, Sergei & Fomalont, Edward (2006). "On the speed of gravity and relativistic v/c corrections to the Shapiro time delay". Physics Letters A. 355 (3): 163–166. arXiv:gr-qc/0310065. Bibcode:2006PhLA..355..163K. doi:10.1016/j.physleta.2006.02.028. S2CID 12121566.
+Hideki, Asada (Aug 20, 2003). "Comments on "Measuring the Gravity Speed by VLBI"". arXiv:astro-ph/0308343.
+Kopeikin, Sergei & Fomalont, Edward (2006). "Aberration and the Fundamental Speed of Gravity in the Jovian Deflection Experiment". Foundations of Physics. 36 (8): 1244–1285. arXiv:astro-ph/0311063. Bibcode:2006FoPh...36.1244K. doi:10.1007/s10701-006-9059-7. S2CID 53514468.
+Carlip, Steven (2004). "Model-Dependence of Shapiro Time Delay and the "Speed of Gravity/Speed of Light" Controversy". Class. Quantum Grav. 21 (15): 3803–3812. arXiv:gr-qc/0403060. Bibcode:2004CQGra..21.3803C. doi:10.1088/0264-9381/21/15/011. S2CID 250863503.
+Kopeikin, Sergei M. (2005). "Comment on 'Model-dependence of Shapiro time delay and the "speed of gravity/speed of light" controversy". Class. Quantum Grav. 22 (23): 5181–5186. arXiv:gr-qc/0510048. Bibcode:2005CQGra..22.5181K. doi:10.1088/0264-9381/22/23/N01. S2CID 17222421.
+Pascual-Sánchez, J.-F. (2004). "Speed of gravity and gravitomagnetism". Int. J. Mod. Phys. D. 13 (10): 2345–2350. arXiv:gr-qc/0405123. Bibcode:2004IJMPD..13.2345P. doi:10.1142/S0218271804006425. S2CID 2402650.
+Kopeikin, Sergei (2006). "Gravitomagnetism and the speed of gravity". Int. J. Mod. Phys. D. 15 (3): 305–320. arXiv:gr-qc/0507001. Bibcode:2006IJMPD..15..305K. doi:10.1142/S0218271806007663. S2CID 18790529.
+Samuel, Stuart (2004). "On the Speed of Gravity and the Jupiter/Quasar Measurement". Int. J. Mod. Phys. D. 13 (9): 1753–1770. arXiv:astro-ph/0412401. Bibcode:2004IJMPD..13.1753S. doi:10.1142/S0218271804005900. S2CID 2908984.
+Kopeikin, Sergei (2006). "Comments on the paper by S. Samuel "On the speed of gravity and the Jupiter/Quasar measurement"". Int. J. Mod. Phys. D. 15 (2): 273–288. arXiv:gr-qc/0501001. Bibcode:2006IJMPD..15..273K. doi:10.1142/S021827180600853X.
+Kopeikin, Sergei & Fomalont, Edward (2007). "Gravimagnetism, Causality, and Aberration of Gravity in the Gravitational Light-Ray Deflection Experiments". General Relativity and Gravitation. 39 (10): 1583–1624. arXiv:gr-qc/0510077. Bibcode:2007GReGr..39.1583K. doi:10.1007/s10714-007-0483-6. S2CID 15412146.
+Kopeikin, Sergei & Fomalont, Edward (2008). "Radio interferometric tests of general relativity". Proceedings of the International Astronomical Union. 3 (S248, A Giant Step: From Milli- to Micro-arcsecond Astrometry): 383–386. arXiv:0912.4038. Bibcode:2008IAUS..248..383F. doi:10.1017/S1743921308019613. S2CID 53363773.
+Zhu, Yin (2011). "Measurement of the Speed of Gravity". Chinese Physics Letters. 28 (7) 070401. arXiv:1108.3761. Bibcode:2011ChPhL..28g0401Z. doi:10.1088/0256-307X/28/7/070401. S2CID 250811249.
+
+== External links ==
+Does Gravity Travel at the Speed of Light? in The Physics FAQ (also here).
+Measuring the Speed of Gravity at MathPages
+Hazel Muir, First speed of gravity measurement revealed, a New Scientist article on Kopeikin's original announcement.
+Clifford M. Will, Has the Speed of Gravity Been Measured?.
+Kevin Carlson, MU physicist defends Einstein's theory and 'speed of gravity' measurement.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Spherical_wave_transformation-0.md b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-0.md
new file mode 100644
index 000000000..e017fbd90
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-0.md
@@ -0,0 +1,492 @@
+---
+title: "Spherical wave transformation"
+chunk: 1/8
+source: "https://en.wikipedia.org/wiki/Spherical_wave_transformation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:27.922869+00:00"
+instance: "kb-cron"
+---
+
+Spherical wave transformations leave the form of spherical waves as well as the laws of optics and electrodynamics invariant in all inertial frames. They were defined between 1908 and 1909 by Harry Bateman and Ebenezer Cunningham, with Bateman giving the transformation its name. They correspond to the conformal group of "transformations by reciprocal radii" in relation to the framework of Lie sphere geometry, which were already known in the 19th century.
+Time is used as fourth dimension as in Minkowski space, so spherical wave transformations are connected to the Lorentz transformation of special relativity, and it turns out that the conformal group of spacetime includes the Lorentz group and the Poincaré group as subgroups. However, only the Lorentz/Poincaré groups represent symmetries of all laws of nature including mechanics, whereas the conformal group is related to certain areas such as electrodynamics. In addition, it can be shown that the conformal group of the plane (corresponding to the Möbius group of the extended complex plane) is isomorphic to the Lorentz group.
+A special case of Lie sphere geometry is the transformation by reciprocal directions or Laguerre inversion, being a generator of the Laguerre group. It transforms not only spheres into spheres but also planes into planes. If time is used as fourth dimension, a close analogy to the Lorentz transformation as well as isomorphism to the Lorentz group was pointed out by several authors such as Bateman, Cartan or Poincaré.
+
+== Transformation by reciprocal radii ==
+
+=== Development in the 19th century ===
+Inversions preserving angles between circles were first discussed by Durrande (1820), with Quetelet (1827) and Plücker (1828) writing down the corresponding transformation formula, 
+  
+    
+      
+        k
+      
+    
+    {\displaystyle k}
+  
+ being the radius of inversion:
+
+  
+    
+      
+        
+          x
+          
+            ′
+          
+        
+        =
+        
+          
+            
+              
+                k
+                
+                  2
+                
+              
+              x
+            
+            
+              
+                x
+                
+                  2
+                
+              
+              +
+              
+                y
+                
+                  2
+                
+              
+            
+          
+        
+        ,
+        
+        
+          y
+          
+            ′
+          
+        
+        =
+        
+          
+            
+              
+                k
+                
+                  2
+                
+              
+              y
+            
+            
+              
+                x
+                
+                  2
+                
+              
+              +
+              
+                y
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle x^{\prime }={\frac {k^{2}x}{x^{2}+y^{2}}},\quad y^{\prime }={\frac {k^{2}y}{x^{2}+y^{2}}}}
+  
+.
+These inversions were later called "transformations by reciprocal radii", and became better known when Thomson (1845, 1847) applied them on spheres with coordinates 
+  
+    
+      
+        x
+        ,
+        y
+        ,
+        z
+      
+    
+    {\displaystyle x,y,z}
+  
+ in the course of developing the method of inversion in electrostatics. Joseph Liouville (1847) demonstrated its mathematical meaning by showing that it belongs to the conformal transformations producing the following quadratic form:
+
+  
+    
+      
+        δ
+        
+          x
+          
+            ′
+            2
+          
+        
+        +
+        δ
+        
+          y
+          
+            ′
+            2
+          
+        
+        +
+        δ
+        
+          z
+          
+            ′
+            2
+          
+        
+        =
+        λ
+        
+          (
+          
+            δ
+            
+              x
+              
+                2
+              
+            
+            +
+            δ
+            
+              y
+              
+                2
+              
+            
+            +
+            δ
+            
+              z
+              
+                2
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle \delta x^{\prime 2}+\delta y^{\prime 2}+\delta z^{\prime 2}=\lambda \left(\delta x^{2}+\delta y^{2}+\delta z^{2}\right)}
+  
+.
+Liouville himself and more extensively Sophus Lie (1871) showed that the related conformal group can be differentiated (Liouville's theorem): For instance, 
+  
+    
+      
+        λ
+        =
+        1
+      
+    
+    {\displaystyle \lambda =1}
+  
+ includes the Euclidean group of ordinary motions; 
+  
+    
+      
+        λ
+        ≠
+        1
+      
+    
+    {\displaystyle \lambda \neq 1}
+  
+ scale or similarity transformations in which the coordinates of the previous transformations are multiplied by 
+  
+    
+      
+        
+          
+            λ
+          
+        
+      
+    
+    {\displaystyle {\sqrt {\lambda }}}
+  
+; and 
+  
+    
+      
+        λ
+        =
+        
+          k
+          
+            4
+          
+        
+        
+          /
+        
+        
+          
+            (
+            
+              
+                x
+                
+                  2
+                
+              
+              +
+              
+                y
+                
+                  2
+                
+              
+              +
+              
+                z
+                
+                  2
+                
+              
+            
+            )
+          
+          
+            2
+          
+        
+      
+    
+    {\displaystyle \lambda =k^{4}/\left(x^{2}+y^{2}+z^{2}\right)^{2}}
+  
+ gives Thomson's transformation by reciprocal radii (inversions):
+
+  
+    
+      
+        
+          x
+          
+            ′
+          
+        
+        =
+        
+          
+            
+              
+                k
+                
+                  2
+                
+              
+              x
+            
+            
+              
+                x
+                
+                  2
+                
+              
+              +
+              
+                y
+                
+                  2
+                
+              
+              +
+              
+                z
+                
+                  2
+                
+              
+            
+          
+        
+        ,
+        
+        
+          y
+          
+            ′
+          
+        
+        =
+        
+          
+            
+              
+                k
+                
+                  2
+                
+              
+              y
+            
+            
+              
+                x
+                
+                  2
+                
+              
+              +
+              
+                y
+                
+                  2
+                
+              
+              +
+              
+                z
+                
+                  2
+                
+              
+            
+          
+        
+        ,
+        
+        
+          z
+          
+            ′
+          
+        
+        =
+        
+          
+            
+              
+                k
+                
+                  2
+                
+              
+              z
+            
+            
+              
+                x
+                
+                  2
+                
+              
+              +
+              
+                y
+                
+                  2
+                
+              
+              +
+              
+                z
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle x^{\prime }={\frac {k^{2}x}{x^{2}+y^{2}+z^{2}}},\quad y^{\prime }={\frac {k^{2}y}{x^{2}+y^{2}+z^{2}}},\quad z^{\prime }={\frac {k^{2}z}{x^{2}+y^{2}+z^{2}}}}
+  
+.
+Subsequently, Liouville's theorem was extended to 
+  
+    
+      
+        n
+      
+    
+    {\displaystyle n}
+  
+ dimensions by Lie (1871) and others such as Darboux (1878):
+
+  
+    
+      
+        δ
+        
+          x
+          
+            1
+          
+          
+            ′
+            2
+          
+        
+        +
+        ⋯
+        +
+        δ
+        
+          x
+          
+            n
+          
+          
+            ′
+            2
+          
+        
+        =
+        λ
+        
+          (
+          
+            δ
+            
+              x
+              
+                1
+              
+              
+                2
+              
+            
+            +
+            ⋯
+            +
+            δ
+            
+              x
+              
+                n
+              
+              
+                2
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle \delta x_{1}^{\prime 2}+\dots +\delta x_{n}^{\prime 2}=\lambda \left(\delta x_{1}^{2}+\dots +\delta x_{n}^{2}\right)}
+  
+.
+This group of conformal transformations by reciprocal radii preserves angles and transforms spheres into spheres or hyperspheres (see Möbius transformation, conformal symmetry, special conformal transformation). It is a 6-parameter group in the plane R2 which corresponds to the Möbius group of the extended complex plane, a 10-parameter group in space R3, and a 15-parameter group in R4. In R2 it represents only a small subset of all conformal transformations therein, whereas in R2+n it is identical to the group of all conformal transformations (corresponding to the Möbius transformations in higher dimensions) therein, in accordance with Liouville's theorem. Conformal transformations in R3 were often applied to what Darboux (1873) called "pentaspherical coordinates" by relating the points to homogeneous coordinates based on five spheres.
+
+=== Oriented spheres ===
+Another method for solving such sphere problems was to write down the coordinates together with the sphere's radius. This was employed by Lie (1871) in the context of Lie sphere geometry which represents a general framework of sphere-transformations (being a special case of contact transformations) conserving lines of curvature and transforming spheres into spheres. The previously mentioned 10-parameter group in R3 related to pentaspherical coordinates is extended to the 15-parameter group of Lie sphere transformations related to "hexaspherical coordinates" (named by Klein in 1893) by adding a sixth homogeneous coordinate related to the radius. Since the radius of a sphere can have a positive or negative sign, one sphere always corresponds to two transformed spheres. It is advantageous to remove this ambiguity by attributing a definite sign to the radius, consequently giving the spheres a definite orientation too, so that one oriented sphere corresponds to one transformed oriented sphere. This method was occasionally and implicitly employed by Lie (1871) himself and explicitly introduced by Laguerre (1880). In addition, Darboux (1887) brought the transformations by reciprocal radii into a form by which the radius r of a sphere can be determined if the radius of the other one is known:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Spherical_wave_transformation-1.md b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-1.md
new file mode 100644
index 000000000..671ebf2f8
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-1.md
@@ -0,0 +1,753 @@
+---
+title: "Spherical wave transformation"
+chunk: 2/8
+source: "https://en.wikipedia.org/wiki/Spherical_wave_transformation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:27.922869+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  x
+                  
+                    ′
+                  
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      
+                        k
+                        
+                          2
+                        
+                      
+                      x
+                    
+                    
+                      
+                        x
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        y
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        z
+                        
+                          2
+                        
+                      
+                      −
+                      
+                        r
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+                
+              
+              
+                
+                  z
+                  
+                    ′
+                  
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      
+                        k
+                        
+                          2
+                        
+                      
+                      z
+                    
+                    
+                      
+                        x
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        y
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        z
+                        
+                          2
+                        
+                      
+                      −
+                      
+                        r
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+              
+            
+            
+              
+                
+                  y
+                  ′
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      
+                        k
+                        
+                          2
+                        
+                      
+                      y
+                    
+                    
+                      
+                        x
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        y
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        z
+                        
+                          2
+                        
+                      
+                      −
+                      
+                        r
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+              
+              
+                
+                  r
+                  
+                    ′
+                  
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      ±
+                      
+                        k
+                        
+                          2
+                        
+                      
+                      r
+                    
+                    
+                      
+                        x
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        y
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        z
+                        
+                          2
+                        
+                      
+                      −
+                      
+                        r
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                .
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}x^{\prime }&={\frac {k^{2}x}{x^{2}+y^{2}+z^{2}-r^{2}}},\quad &z^{\prime }&={\frac {k^{2}z}{x^{2}+y^{2}+z^{2}-r^{2}}},\\y'&={\frac {k^{2}y}{x^{2}+y^{2}+z^{2}-r^{2}}},&r^{\prime }&={\frac {\pm k^{2}r}{x^{2}+y^{2}+z^{2}-r^{2}}}.\end{aligned}}}
+  
+
+Using coordinates together with the radius was often connected to a method called "minimal projection" by Klein (1893), which was later called "isotropy projection" by Blaschke (1926) emphasizing the relation to oriented circles and spheres. For instance, a circle with rectangular coordinates 
+  
+    
+      
+        x
+        ,
+        y
+      
+    
+    {\displaystyle x,y}
+  
+ and radius 
+  
+    
+      
+        r
+      
+    
+    {\displaystyle r}
+  
+ in R2 corresponds to a point in R3 with coordinates 
+  
+    
+      
+        x
+        ,
+        y
+        ,
+        z
+      
+    
+    {\displaystyle x,y,z}
+  
+. This method was known for some time in circle geometry (though without using the concept of orientation) and can be further differentiated depending on whether the additional coordinate is treated as imaginary or real: 
+  
+    
+      
+        z
+        =
+        i
+        r
+      
+    
+    {\displaystyle z=ir}
+  
+  was used by Chasles (1852), Möbius (1857), Cayley (1867), and Darboux (1872); 
+  
+    
+      
+        z
+        =
+        r
+      
+    
+    {\displaystyle z=r}
+  
+ was used by Cousinery (1826), Druckenmüller (1842), and in the "cyclography" of Fiedler (1882), therefore the latter method was also called "cyclographic projection" – see E. Müller (1910) for a summary. This method was also applied to spheres by Darboux (1872), Lie (1871), or Klein (1893). Let 
+  
+    
+      
+        x
+        ,
+        y
+        ,
+        z
+        ,
+        r
+      
+    
+    {\displaystyle x,y,z,r}
+  
+ and 
+  
+    
+      
+        
+          x
+          ′
+        
+        ,
+        
+          y
+          ′
+        
+        ,
+        
+          z
+          ′
+        
+        ,
+        
+          r
+          ′
+        
+      
+    
+    {\displaystyle x',y',z',r'}
+  
+ be the center coordinates and radii of two spheres in three-dimensional space R3. If the spheres are touching each other with same orientation, their equation is given
+
+  
+    
+      
+        (
+        x
+        −
+        
+          x
+          ′
+        
+        
+          )
+          
+            2
+          
+        
+        +
+        (
+        y
+        −
+        
+          y
+          ′
+        
+        
+          )
+          
+            2
+          
+        
+        +
+        (
+        z
+        −
+        
+          z
+          ′
+        
+        
+          )
+          
+            2
+          
+        
+        −
+        (
+        r
+        −
+        
+          r
+          ′
+        
+        
+          )
+          
+            2
+          
+        
+        =
+        0
+      
+    
+    {\displaystyle (x-x')^{2}+(y-y')^{2}+(z-z')^{2}-(r-r')^{2}=0}
+  
+.
+Setting 
+  
+    
+      
+        t
+        =
+        i
+        r
+      
+    
+    {\displaystyle t=ir}
+  
+, these coordinates correspond to rectangular coordinates in four-dimensional space R4:
+
+  
+    
+      
+        (
+        x
+        −
+        
+          x
+          ′
+        
+        
+          )
+          
+            2
+          
+        
+        +
+        (
+        y
+        −
+        
+          y
+          ′
+        
+        
+          )
+          
+            2
+          
+        
+        +
+        (
+        z
+        −
+        
+          z
+          ′
+        
+        
+          )
+          
+            2
+          
+        
+        +
+        (
+        t
+        −
+        
+          t
+          ′
+        
+        
+          )
+          
+            2
+          
+        
+        =
+        0
+      
+    
+    {\displaystyle (x-x')^{2}+(y-y')^{2}+(z-z')^{2}+(t-t')^{2}=0}
+  
+.
+In general, Lie (1871) showed that the conformal point transformations in Rn (composed of motions, similarities, and transformations by reciprocal radii) correspond in Rn-1 to those sphere transformations which are contact transformations. Klein (1893) pointed out that by using minimal projection on hexaspherical coordinates, the 15-parameter Lie sphere transformations in R3 are simply the projections of the 15-parameter conformal point transformations in R4, whereas the points in R4 can be seen as the stereographic projection of the points of a sphere in R5.
+
+=== Relation to electrodynamics ===
+Harry Bateman and Ebenezer Cunningham (1909) showed that the electromagnetic equations are not only Lorentz invariant, but also scale and conformal invariant. They are invariant under the 15-parameter group of conformal transformations 
+  
+    
+      
+        
+          G
+          
+            15
+          
+        
+      
+    
+    {\displaystyle G_{15}}
+  
+ (transformations by reciprocal radii) in R4 producing the relation
+
+  
+    
+      
+        δ
+        
+          x
+          
+            ′
+            2
+          
+        
+        +
+        δ
+        
+          y
+          
+            ′
+            2
+          
+        
+        +
+        δ
+        
+          z
+          
+            ′
+            2
+          
+        
+        +
+        δ
+        
+          u
+          
+            ′
+            2
+          
+        
+        =
+        λ
+        
+          (
+          
+            δ
+            
+              x
+              
+                2
+              
+            
+            +
+            δ
+            
+              y
+              
+                2
+              
+            
+            +
+            δ
+            
+              z
+              
+                2
+              
+            
+            +
+            δ
+            
+              u
+              
+                2
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle \delta x^{\prime 2}+\delta y^{\prime 2}+\delta z^{\prime 2}+\delta u^{\prime 2}=\lambda \left(\delta x^{2}+\delta y^{2}+\delta z^{2}+\delta u^{2}\right)}
+  
+,
+where 
+  
+    
+      
+        u
+        =
+        i
+        c
+        t
+      
+    
+    {\displaystyle u=ict}
+  
+ includes 
+  
+    
+      
+        t
+      
+    
+    {\displaystyle t}
+  
+ as time component and 
+  
+    
+      
+        c
+      
+    
+    {\displaystyle c}
+  
+ as the speed of light. Bateman (1909) also noticed the equivalence to the previously mentioned Lie sphere transformations in R3, because the radius 
+  
+    
+      
+        r
+      
+    
+    {\displaystyle r}
+  
+ used in them can be interpreted as the radius 
+  
+    
+      
+        c
+        t
+      
+    
+    {\displaystyle ct}
+  
+ of a spherical wave contracting or expanding with 
+  
+    
+      
+        c
+      
+    
+    {\displaystyle c}
+  
+, therefore he called them "spherical wave transformations". He wrote:
+
+When we use Darboux's representation of a point in 
+  
+    
+      
+        
+          S
+          
+            4
+          
+        
+      
+    
+    {\displaystyle S_{4}}
+  
+ by a spherical wave in 
+  
+    
+      
+        
+          S
+          
+            3
+          
+        
+      
+    
+    {\displaystyle S_{3}}
+  
+, the group 
+  
+    
+      
+        
+          G
+          
+            15
+          
+        
+      
+    
+    {\displaystyle G_{15}}
+  
+ becomes the group of spherical wave transformations which transform a spherical wave into a spherical wave. This group of transformations has been discussed by S. Lie; it is the group of transformations which transform lines of curvature on a surface enveloped by spherical waves into lines of curvature on the surface enveloped by the corresponding spherical waves.
+Depending on 
+  
+    
+      
+        λ
+      
+    
+    {\displaystyle \lambda }
+  
+ they can be differentiated into subgroups:
+(a) 
+  
+    
+      
+        λ
+        =
+        1
+      
+    
+    {\displaystyle \lambda =1}
+  
+ correspond to mappings which transform not only spheres into spheres but also planes into planes. These are called Laguerre transformations/inversions forming the Laguerre group, which in physics correspond to the Lorentz transformations forming the 6-parameter Lorentz group or 10-parameter Poincaré group with translations.
+(b) 
+  
+    
+      
+        λ
+        ≠
+        1
+      
+    
+    {\displaystyle \lambda \neq 1}
+  
+ represents scale or similarity transformations by multiplication of the space-time variables of the Lorentz transformations by a constant factor depending on 
+  
+    
+      
+        λ
+      
+    
+    {\displaystyle \lambda }
+  
+. For instance, if 
+  
+    
+      
+        l
+        =
+        
+          
+            λ
+          
+        
+      
+    
+    {\displaystyle l={\sqrt {\lambda }}}
+  
+ is used, then the transformation given by Poincaré in 1905 follows:
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Spherical_wave_transformation-2.md b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-2.md
new file mode 100644
index 000000000..add205b18
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-2.md
@@ -0,0 +1,954 @@
+---
+title: "Spherical wave transformation"
+chunk: 3/8
+source: "https://en.wikipedia.org/wiki/Spherical_wave_transformation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:27.922869+00:00"
+instance: "kb-cron"
+---
+
+  
+    
+      
+        
+          x
+          
+            ′
+          
+        
+        =
+        γ
+        l
+        
+          (
+          
+            x
+            −
+            v
+            t
+          
+          )
+        
+        ,
+        
+        
+          y
+          
+            ′
+          
+        
+        =
+        l
+        y
+        ,
+        
+        
+          z
+          
+            ′
+          
+        
+        =
+        l
+        z
+        ,
+        
+        
+          t
+          
+            ′
+          
+        
+        =
+        γ
+        l
+        
+          (
+          
+            t
+            −
+            x
+            
+              
+                v
+                
+                  c
+                  
+                    2
+                  
+                
+              
+            
+          
+          )
+        
+      
+    
+    {\displaystyle x^{\prime }=\gamma l\left(x-vt\right),\quad y^{\prime }=ly,\quad z^{\prime }=lz,\quad t^{\prime }=\gamma l\left(t-x{\frac {v}{c^{2}}}\right)}
+  
+.
+However, it was shown by Poincaré and Einstein that only 
+  
+    
+      
+        l
+        =
+        1
+      
+    
+    {\displaystyle l=1}
+  
+ produces a group that is a symmetry of all laws of nature as required by the principle of relativity (the Lorentz group), while the group of scale transformations is only a symmetry of optics and electrodynamics.
+(c) Setting 
+  
+    
+      
+        λ
+        =
+        
+          r
+          
+            4
+          
+        
+        
+          /
+        
+        
+          
+            (
+            
+              
+                x
+                
+                  2
+                
+              
+              +
+              
+                y
+                
+                  2
+                
+              
+              +
+              
+                z
+                
+                  2
+                
+              
+              +
+              
+                u
+                
+                  2
+                
+              
+            
+            )
+          
+          
+            2
+          
+        
+      
+    
+    {\displaystyle \lambda =r^{4}/\left(x^{2}+y^{2}+z^{2}+u^{2}\right)^{2}}
+  
+ particularly relates to the wide conformal group of transformations by reciprocal radii. It consists of elementary transformations that represent a generalized inversion into a four-dimensional hypersphere:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  x
+                  ′
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      
+                        k
+                        
+                          2
+                        
+                      
+                      x
+                    
+                    
+                      
+                        x
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        y
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        z
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        u
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+                
+              
+              
+                
+                  z
+                  ′
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      
+                        k
+                        
+                          2
+                        
+                      
+                      z
+                    
+                    
+                      
+                        x
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        y
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        z
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        u
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+              
+            
+            
+              
+                
+                  y
+                  ′
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      
+                        k
+                        
+                          2
+                        
+                      
+                      y
+                    
+                    
+                      
+                        x
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        y
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        z
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        u
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+              
+              
+                
+                  u
+                  ′
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      
+                        k
+                        
+                          2
+                        
+                      
+                      u
+                    
+                    
+                      
+                        x
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        y
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        z
+                        
+                          2
+                        
+                      
+                      +
+                      
+                        u
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}x'&={\frac {k^{2}x}{x^{2}+y^{2}+z^{2}+u^{2}}},\quad &z'&={\frac {k^{2}z}{x^{2}+y^{2}+z^{2}+u^{2}}},\\y'&={\frac {k^{2}y}{x^{2}+y^{2}+z^{2}+u^{2}}},&u'&={\frac {k^{2}u}{x^{2}+y^{2}+z^{2}+u^{2}}},\end{aligned}}}
+  
+
+which become real spherical wave transformations in terms of Lie sphere geometry if the real radius 
+  
+    
+      
+        c
+        t
+      
+    
+    {\displaystyle ct}
+  
+ is used instead of 
+  
+    
+      
+        u
+        =
+        i
+        c
+        t
+      
+    
+    {\displaystyle u=ict}
+  
+, thus 
+  
+    
+      
+        
+          x
+          
+            2
+          
+        
+        +
+        
+          y
+          
+            2
+          
+        
+        +
+        
+          z
+          
+            2
+          
+        
+        −
+        
+          c
+          
+            2
+          
+        
+        
+          t
+          
+            2
+          
+        
+      
+    
+    {\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}}
+  
+ is given in the denominator.
+Felix Klein (1921) pointed out the similarity of these relations to Lie's and his own researches of 1871, adding that the conformal group doesn't have the same meaning as the Lorentz group, because the former applies to electrodynamics whereas the latter is a symmetry of all laws of nature including mechanics. The possibility was discussed for some time, whether conformal transformations allow for the transformation into uniformly accelerated frames. Later, conformal invariance became important again in certain areas such as conformal field theory.
+
+=== Lorentz group isomorphic to Möbius group ===
+
+It turns out that also the 6-parameter conformal group of R2 (i.e. the Möbius group composed of automorphisms of the Riemann sphere), which in turn is isomorphic to the 6-parameter group of hyperbolic motions (i.e. isometric automorphisms of a hyperbolic space) in R3, can be physically interpreted: It is isomorphic to the Lorentz group.
+For instance, Fricke and Klein (1897) started by defining an "absolute" Cayley metric in terms of a one-part curvilinear surface of second degree, which can be represented by a sphere whose interior represents hyperbolic space with the equation
+
+  
+    
+      
+        
+          z
+          
+            1
+          
+          
+            2
+          
+        
+        +
+        
+          z
+          
+            2
+          
+          
+            2
+          
+        
+        +
+        
+          z
+          
+            3
+          
+          
+            2
+          
+        
+        −
+        
+          z
+          
+            4
+          
+          
+            2
+          
+        
+        =
+        0
+      
+    
+    {\displaystyle z_{1}^{2}+z_{2}^{2}+z_{3}^{2}-z_{4}^{2}=0}
+  
+,
+where 
+  
+    
+      
+        
+          z
+          
+            1
+          
+        
+        ,
+         
+        
+          z
+          
+            2
+          
+        
+        ,
+         
+        
+          z
+          
+            3
+          
+        
+        ,
+         
+        
+          z
+          
+            4
+          
+        
+      
+    
+    {\displaystyle z_{1},\ z_{2},\ z_{3},\ z_{4}}
+  
+ are homogeneous coordinates. They pointed out that motions of hyperbolic space into itself also transform this sphere into itself. They developed the corresponding transformation by defining a complex parameter 
+  
+    
+      
+        ξ
+      
+    
+    {\displaystyle \xi }
+  
+ of the sphere
+
+  
+    
+      
+        ξ
+        =
+        
+          
+            
+              
+                z
+                
+                  1
+                
+              
+              +
+              i
+              
+                z
+                
+                  2
+                
+              
+            
+            
+              
+                z
+                
+                  4
+                
+              
+              −
+              
+                z
+                
+                  3
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle \xi ={\frac {z_{1}+iz_{2}}{z_{4}-z_{3}}}}
+  
+
+which is connected to another parameter 
+  
+    
+      
+        
+          ξ
+          ′
+        
+      
+    
+    {\displaystyle \xi '}
+  
+ by the substitution
+
+  
+    
+      
+        
+          ξ
+          ′
+        
+        =
+        
+          
+            
+              α
+              ξ
+              +
+              β
+            
+            
+              γ
+              ξ
+              +
+              δ
+            
+          
+        
+      
+    
+    {\displaystyle \xi '={\frac {\alpha \xi +\beta }{\gamma \xi +\delta }}}
+  
+
+where 
+  
+    
+      
+        α
+        ,
+        β
+        ,
+        γ
+        ,
+        δ
+      
+    
+    {\displaystyle \alpha ,\beta ,\gamma ,\delta }
+  
+ are complex coefficients. They furthermore showed that by setting 
+  
+    
+      
+        
+          z
+          
+            1
+          
+        
+        :
+        
+          z
+          
+            2
+          
+        
+        :
+        
+          z
+          
+            3
+          
+        
+        :
+        
+          z
+          
+            4
+          
+        
+        =
+        X
+        :
+        Y
+        :
+        Z
+        :
+        1
+      
+    
+    {\displaystyle z_{1}:z_{2}:z_{3}:z_{4}=X:Y:Z:1}
+  
+, the above relations assume the form in terms of the unit sphere in R3:
+
+  
+    
+      
+        
+          X
+          
+            2
+          
+        
+        +
+        
+          Y
+          
+            2
+          
+        
+        +
+        
+          Z
+          
+            2
+          
+        
+        =
+        1
+        ,
+        
+        ξ
+        =
+        
+          
+            
+              X
+              +
+              i
+              Y
+            
+            
+              1
+              −
+              Z
+            
+          
+        
+      
+    
+    {\displaystyle X^{2}+Y^{2}+Z^{2}=1,\quad \xi ={\frac {X+iY}{1-Z}}}
+  
+.
+which is identical to the stereographic projection of the 
+  
+    
+      
+        ξ
+      
+    
+    {\displaystyle \xi }
+  
+-plane on a spherical surface already given by Klein in 1884. Since the substitutions 
+  
+    
+      
+        ξ
+        ,
+        
+          ξ
+          ′
+        
+      
+    
+    {\displaystyle \xi ,\xi '}
+  
+ are Möbius transformations (German: Kreisverwandtschaften) in the 
+  
+    
+      
+        ξ
+      
+    
+    {\displaystyle \xi }
+  
+-plane or upon the 
+  
+    
+      
+        ξ
+      
+    
+    {\displaystyle \xi }
+  
+-sphere, they concluded that by carrying out an arbitrary motion of hyperbolic space in itself, the 
+  
+    
+      
+        ξ
+      
+    
+    {\displaystyle \xi }
+  
+-sphere undergoes a Möbius transformation, that the entire group of hyperbolic motions gives all direct Möbius transformations, and finally that any direct Möbius transformation corresponds to a motion of hyperbolic space.
+Based on the work of Fricke & Klein, the isomorphism of that group of hyperbolic motions (and consequently of the Möbius group) to the Lorentz group  was demonstrated by Gustav Herglotz (1909). Namely, the Minkowski metric corresponds to the above Cayley metric (based on a real conic section), if the spacetime coordinates are identified with the above homogeneous coordinates
+
+  
+    
+      
+        
+          z
+          
+            1
+          
+        
+        =
+        x
+        ,
+        
+        
+          z
+          
+            2
+          
+        
+        =
+        y
+        ,
+        
+        
+          z
+          
+            3
+          
+        
+        =
+        z
+        ,
+        
+        
+          z
+          
+            4
+          
+        
+        =
+        t
+      
+    
+    {\displaystyle z_{1}=x,\quad z_{2}=y,\quad z_{3}=z,\quad z_{4}=t}
+  
+,
+by which the above parameter become
+
+  
+    
+      
+        
+          
+            ξ
+          
+        
+        =
+        
+          
+            
+              x
+              +
+              i
+              y
+            
+            
+              t
+              −
+              z
+            
+          
+        
+        ,
+        
+        
+          ξ
+          ′
+        
+        =
+        
+          
+            
+              
+                x
+                ′
+              
+              +
+              i
+              
+                y
+                ′
+              
+            
+            
+              
+                t
+                ′
+              
+              −
+              
+                z
+                ′
+              
+            
+          
+        
+        ,
+      
+    
+    {\displaystyle {\mathsf {\xi }}={\frac {x+iy}{t-z}},\quad \xi '={\frac {x'+iy'}{t'-z'}},}
+  
+ again connected by the substitution 
+  
+    
+      
+        
+          ξ
+          ′
+        
+        =
+        
+          
+            
+              α
+              ξ
+              +
+              β
+            
+            
+              γ
+              ξ
+              +
+              δ
+            
+          
+        
+      
+    
+    {\displaystyle \xi '={\frac {\alpha \xi +\beta }{\gamma \xi +\delta }}}
+  
+.
+Herglotz concluded, that any such substitution corresponds to a Lorentz transformation, establishing a one-to-one correspondence to hyperbolic motions in R3. The relation between the Lorentz group and the Cayley metric in hyperbolic space was also pointed out by Klein (1910) as well as Pauli (1921). The corresponding isomorphism of the Möbius group to the Lorentz group was employed, among others, by Roger Penrose.
+
+== Transformation by reciprocal directions ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Spherical_wave_transformation-3.md b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-3.md
new file mode 100644
index 000000000..9c5be65b2
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-3.md
@@ -0,0 +1,839 @@
+---
+title: "Spherical wave transformation"
+chunk: 4/8
+source: "https://en.wikipedia.org/wiki/Spherical_wave_transformation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:27.922869+00:00"
+instance: "kb-cron"
+---
+
+=== Development in the 19th century ===
+Above, the connection of conformal transformations with coordinates including the radius of spheres within Lie sphere geometry was mentioned. The special case 
+  
+    
+      
+        λ
+        =
+        1
+      
+    
+    {\displaystyle \lambda =1}
+  
+ corresponds to a sphere transformation given by Edmond Laguerre (1880–1885), who called it the "transformation by reciprocal directions" and who laid down the foundation of a geometry of oriented spheres and planes. According to Darboux and Bateman, similar relations were discussed before by Albert Ribaucour (1870) and by Lie himself (1871).  Stephanos (1881) pointed out that Laguerre's geometry is indeed a special case of Lie's sphere geometry. He also represented Laguerre's oriented spheres by quaternions (1883).
+Lines, circles, planes, or spheres with radii of certain orientation are called by Laguerre half-lines, half-circles (cycles), half-planes, half-spheres, etc. A tangent is a half-line cutting a cycle at a point where both have the same direction. The transformation by reciprocal directions transforms oriented spheres into oriented spheres and oriented planes into oriented planes, leaving invariant the "tangential distance" of two cycles (the distance between the points of each one of their common tangents), and also conserves the lines of curvature. Laguerre (1882) applied the transformation to two cycles under the following conditions: Their radical axis is the axis of transformation, and their common tangents are parallel to two fixed directions of the half-lines that are transformed into themselves (Laguerre called this specific method the "transformation by reciprocal half-lines", which was later called "Laguerre inversion"). Setting 
+  
+    
+      
+        R
+      
+    
+    {\displaystyle R}
+  
+ and 
+  
+    
+      
+        
+          R
+          ′
+        
+      
+    
+    {\displaystyle R'}
+  
+ as the radii of the cycles, and 
+  
+    
+      
+        D
+      
+    
+    {\displaystyle D}
+  
+ and 
+  
+    
+      
+        
+          D
+          ′
+        
+      
+    
+    {\displaystyle D'}
+  
+ as the distances of their centers to the axis, he obtained:
+
+  
+    
+      
+        
+          D
+          
+            2
+          
+        
+        −
+        
+          D
+          
+            ′
+            2
+          
+        
+        =
+        
+          R
+          
+            2
+          
+        
+        −
+        
+          R
+          
+            ′
+            2
+          
+        
+        ,
+        
+        D
+        −
+        
+          D
+          ′
+        
+        =
+        α
+        (
+        R
+        −
+        
+          R
+          ′
+        
+        )
+        ,
+        
+        D
+        +
+        
+          D
+          ′
+        
+        =
+        
+          
+            1
+            α
+          
+        
+        (
+        R
+        +
+        
+          R
+          ′
+        
+        )
+        ,
+      
+    
+    {\displaystyle D^{2}-D^{\prime 2}=R^{2}-R^{\prime 2},\quad D-D'=\alpha (R-R'),\quad D+D'={\frac {1}{\alpha }}(R+R'),}
+  
+
+with the transformation:
+
+  
+    
+      
+        
+          D
+          ′
+        
+        =
+        
+          
+            
+              D
+              
+                (
+                
+                  1
+                  +
+                  
+                    α
+                    
+                      2
+                    
+                  
+                
+                )
+              
+              −
+              2
+              α
+              R
+            
+            
+              1
+              −
+              
+                α
+                
+                  2
+                
+              
+            
+          
+        
+        ,
+        
+        
+          R
+          ′
+        
+        =
+        
+          
+            
+              2
+              α
+              D
+              −
+              R
+              
+                (
+                
+                  1
+                  +
+                  
+                    α
+                    
+                      2
+                    
+                  
+                
+                )
+              
+            
+            
+              1
+              −
+              
+                α
+                
+                  2
+                
+              
+            
+          
+        
+        .
+      
+    
+    {\displaystyle D'={\frac {D\left(1+\alpha ^{2}\right)-2\alpha R}{1-\alpha ^{2}}},\quad R'={\frac {2\alpha D-R\left(1+\alpha ^{2}\right)}{1-\alpha ^{2}}}.}
+  
+
+Darboux (1887) obtained the same formulas in different notation (with 
+  
+    
+      
+        z
+        =
+        D
+      
+    
+    {\displaystyle z=D}
+  
+ and 
+  
+    
+      
+        k
+        =
+        α
+      
+    
+    {\displaystyle k=\alpha }
+  
+) in his treatment of the "transformation by reciprocal directions", though he included the 
+  
+    
+      
+        x
+      
+    
+    {\displaystyle x}
+  
+ and 
+  
+    
+      
+        y
+      
+    
+    {\displaystyle y}
+  
+ coordinates as well:
+
+  
+    
+      
+        
+          
+            
+              
+                
+                  x
+                  ′
+                
+              
+              
+                
+                =
+                x
+                ,
+                
+              
+              
+                
+                  z
+                  ′
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      1
+                      +
+                      
+                        k
+                        
+                          2
+                        
+                      
+                    
+                    
+                      1
+                      −
+                      
+                        k
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                z
+                −
+                
+                  
+                    
+                      2
+                      k
+                      R
+                    
+                    
+                      1
+                      −
+                      
+                        k
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                ,
+              
+            
+            
+              
+                
+                  y
+                  ′
+                
+              
+              
+                
+                =
+                y
+                ,
+              
+              
+                
+                  R
+                  ′
+                
+              
+              
+                
+                =
+                
+                  
+                    
+                      2
+                      k
+                      z
+                    
+                    
+                      1
+                      −
+                      
+                        k
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                −
+                
+                  
+                    
+                      1
+                      +
+                      
+                        k
+                        
+                          2
+                        
+                      
+                    
+                    
+                      1
+                      −
+                      
+                        k
+                        
+                          2
+                        
+                      
+                    
+                  
+                
+                R
+                ,
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}x'&=x,\quad &z'&={\frac {1+k^{2}}{1-k^{2}}}z-{\frac {2kR}{1-k^{2}}},\\y'&=y,&R'&={\frac {2kz}{1-k^{2}}}-{\frac {1+k^{2}}{1-k^{2}}}R,\end{aligned}}}
+  
+
+with
+
+  
+    
+      
+        
+          z
+          ′
+        
+        +
+        
+          R
+          ′
+        
+        =
+        
+          
+            
+              1
+              +
+              k
+            
+            
+              1
+              −
+              k
+            
+          
+        
+        (
+        z
+        −
+        R
+        )
+        ,
+        
+        
+          z
+          ′
+        
+        −
+        
+          R
+          ′
+        
+        =
+        
+          
+            
+              1
+              −
+              k
+            
+            
+              1
+              +
+              k
+            
+          
+        
+        (
+        z
+        +
+        R
+        )
+        ,
+      
+    
+    {\displaystyle z'+R'={\frac {1+k}{1-k}}(z-R),\quad z'-R'={\frac {1-k}{1+k}}(z+R),}
+  
+
+consequently he obtained the relation
+
+  
+    
+      
+        
+          x
+          
+            ′
+            2
+          
+        
+        +
+        
+          y
+          
+            ′
+            2
+          
+        
+        +
+        
+          z
+          
+            ′
+            2
+          
+        
+        −
+        
+          R
+          
+            ′
+            2
+          
+        
+        =
+        
+          x
+          
+            2
+          
+        
+        +
+        
+          y
+          
+            2
+          
+        
+        +
+        
+          z
+          
+            2
+          
+        
+        −
+        
+          R
+          
+            2
+          
+        
+      
+    
+    {\displaystyle x^{\prime 2}+y^{\prime 2}+z^{\prime 2}-R^{\prime 2}=x^{2}+y^{2}+z^{2}-R^{2}}
+  
+.
+As mentioned above, oriented spheres in R3 can be represented by points of four-dimensional space R4 using minimal (isotropy) projection, which became particularly important in Laguerre's geometry. For instance, E. Müller (1898) based his discussion of oriented spheres on the fact that they can be mapped upon the points of a plane manifold of four dimensions (which he likened to Fiedler's "cyclography" from 1882). He systematically compared the transformations by reciprocal radii (calling it "inversion at a sphere") with the transformations by reciprocal directions (calling it "inversion at a plane sphere complex"). Following Müller's paper, Smith (1900) discussed Laguerre's transformation and the related "group of the geometry of reciprocal directions". Alluding to Klein's (1893) treatment of minimal projection, he pointed out that this group "is simply isomorphic with the group of all displacements and symmetry transformations in space of four dimensions". Smith obtained the same transformation as Laguerre and Darboux in different notation, calling it "inversion into a spherical complex":
+
+  
+    
+      
+        
+          p
+          ′
+        
+        =
+        
+          
+            
+              
+                κ
+                
+                  2
+                
+              
+              +
+              1
+            
+            
+              
+                κ
+                
+                  2
+                
+              
+              −
+              1
+            
+          
+        
+        p
+        −
+        
+          
+            
+              2
+              κ
+            
+            
+              
+                κ
+                
+                  2
+                
+              
+              −
+              1
+            
+          
+        
+        R
+        ,
+        
+        
+          R
+          ′
+        
+        =
+        
+          
+            
+              2
+              κ
+            
+            
+              
+                κ
+                
+                  2
+                
+              
+              −
+              1
+            
+          
+        
+        p
+        −
+        
+          
+            
+              
+                κ
+                
+                  2
+                
+              
+              +
+              1
+            
+            
+              
+                κ
+                
+                  2
+                
+              
+              −
+              1
+            
+          
+        
+        R
+      
+    
+    {\displaystyle p'={\frac {\kappa ^{2}+1}{\kappa ^{2}-1}}p-{\frac {2\kappa }{\kappa ^{2}-1}}R,\quad R'={\frac {2\kappa }{\kappa ^{2}-1}}p-{\frac {\kappa ^{2}+1}{\kappa ^{2}-1}}R}
+  
+
+with the relations
+
+  
+    
+      
+        κ
+        =
+        
+          
+            
+              
+                R
+                ′
+              
+              −
+              R
+            
+            
+              
+                p
+                ′
+              
+              −
+              p
+            
+          
+        
+        ,
+        
+        
+          p
+          
+            ′
+            2
+          
+        
+        −
+        
+          p
+          
+            2
+          
+        
+        =
+        
+          R
+          
+            ′
+            2
+          
+        
+        −
+        
+          R
+          
+            2
+          
+        
+        .
+      
+    
+    {\displaystyle \kappa ={\frac {R'-R}{p'-p}},\quad p^{\prime 2}-p^{2}=R^{\prime 2}-R^{2}.}
+  
+
+=== Laguerre inversion and Lorentz transformation ===
+In 1905 both Poincaré and Einstein pointed out that the Lorentz transformation of special relativity (setting 
+  
+    
+      
+        c
+        =
+        1
+      
+    
+    {\displaystyle c=1}
+  
+)
+
+  
+    
+      
+        
+          x
+          ′
+        
+        =
+        
+          
+            
+              x
+              −
+              v
+              t
+            
+            
+              1
+              −
+              
+                v
+                
+                  2
+                
+              
+            
+          
+        
+        ,
+        
+        
+          y
+          ′
+        
+        =
+        y
+        ,
+        
+        
+          z
+          ′
+        
+        =
+        z
+        ,
+        
+        
+          t
+          ′
+        
+        =
+        
+          
+            
+              t
+              −
+              v
+              x
+            
+            
+              1
+              −
+              
+                v
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle x'={\frac {x-vt}{\sqrt {1-v^{2}}}},\quad y'=y,\quad z'=z,\quad t'={\frac {t-vx}{\sqrt {1-v^{2}}}}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Spherical_wave_transformation-4.md b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-4.md
new file mode 100644
index 000000000..60f146cbe
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-4.md
@@ -0,0 +1,946 @@
+---
+title: "Spherical wave transformation"
+chunk: 5/8
+source: "https://en.wikipedia.org/wiki/Spherical_wave_transformation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:27.922869+00:00"
+instance: "kb-cron"
+---
+
+leaves the relation 
+  
+    
+      
+        
+          x
+          
+            2
+          
+        
+        +
+        
+          y
+          
+            2
+          
+        
+        +
+        
+          z
+          
+            2
+          
+        
+        −
+        
+          t
+          
+            2
+          
+        
+      
+    
+    {\displaystyle x^{2}+y^{2}+z^{2}-t^{2}}
+  
+ invariant. Einstein stressed the point that by this transformation a spherical light wave in one frame is transformed into a spherical light wave in another one. Poincaré showed that the Lorentz transformation can be seen as a rotation in four-dimensional space with time as fourth coordinate, with Minkowski deepening this insight much further (see History of special relativity).
+As shown above, also Laguerre's transformation by reciprocal directions or half-lines – later called Laguerre inversion – in the form given by Darboux (1887) leaves the expression 
+  
+    
+      
+        
+          x
+          
+            2
+          
+        
+        +
+        
+          y
+          
+            2
+          
+        
+        +
+        
+          z
+          
+            2
+          
+        
+        −
+        
+          R
+          
+            2
+          
+        
+      
+    
+    {\displaystyle x^{2}+y^{2}+z^{2}-R^{2}}
+  
+ invariant. Subsequently, the relation to the Lorentz transformation was noted by several authors. For instance, Bateman (1910) argued that this transformation (which he attributed to Ribaucour) is "identical" to the Lorentz transformation. In particular, he argued (1912) that the variant given by Darboux (1887) corresponds to the Lorentz transformation in 
+  
+    
+      
+        z
+      
+    
+    {\displaystyle z}
+  
+ direction, if 
+  
+    
+      
+        R
+        =
+        c
+        t
+      
+    
+    {\displaystyle R=ct}
+  
+, 
+  
+    
+      
+        
+          R
+          ′
+        
+        =
+        c
+        
+          t
+          ′
+        
+      
+    
+    {\displaystyle R'=ct'}
+  
+, and the 
+  
+    
+      
+        k
+      
+    
+    {\displaystyle k}
+  
+ terms are replaced by velocities. Bateman (1910) also sketched geometric representations of relativistic light spheres using such spherical systems. However, Kubota (1925) responded to Bateman by arguing that the Laguerre inversion is involutory whereas the Lorentz transformation is not. He concluded that in order to make them equivalent, the Laguerre inversion has to be combined with a reversal of direction of the cycles.
+The specific relation between the Lorentz transformation and the Laguerre inversion can also be demonstrated as follows (see H.R. Müller (1948) for analogous formulas in different notation). Laguerre's inversion formulas from 1882 (equivalent to those of Darboux in 1887) read:
+
+  
+    
+      
+        
+          D
+          ′
+        
+        =
+        
+          
+            
+              D
+              
+                (
+                
+                  1
+                  +
+                  
+                    α
+                    
+                      2
+                    
+                  
+                
+                )
+              
+              −
+              2
+              α
+              R
+            
+            
+              1
+              −
+              
+                α
+                
+                  2
+                
+              
+            
+          
+        
+        ,
+        
+        
+          R
+          ′
+        
+        =
+        
+          
+            
+              2
+              α
+              D
+              −
+              R
+              
+                (
+                
+                  1
+                  +
+                  
+                    α
+                    
+                      2
+                    
+                  
+                
+                )
+              
+            
+            
+              1
+              −
+              
+                α
+                
+                  2
+                
+              
+            
+          
+        
+        .
+      
+    
+    {\displaystyle D'={\frac {D\left(1+\alpha ^{2}\right)-2\alpha R}{1-\alpha ^{2}}},\quad R'={\frac {2\alpha D-R\left(1+\alpha ^{2}\right)}{1-\alpha ^{2}}}.}
+  
+
+by setting
+
+  
+    
+      
+        
+          
+            
+              2
+              α
+            
+            
+              1
+              +
+              
+                α
+                
+                  2
+                
+              
+            
+          
+        
+        =
+        w
+      
+    
+    {\displaystyle {\frac {2\alpha }{1+\alpha ^{2}}}=w}
+  
+
+it follows
+
+  
+    
+      
+        
+          
+            
+              1
+              −
+              
+                α
+                
+                  2
+                
+              
+            
+            
+              1
+              +
+              
+                α
+                
+                  2
+                
+              
+            
+          
+        
+        =
+        
+          
+            1
+            −
+            
+              w
+              
+                2
+              
+            
+          
+        
+        ,
+        
+        
+          
+            
+              2
+              α
+            
+            
+              1
+              −
+              
+                α
+                
+                  2
+                
+              
+            
+          
+        
+        =
+        
+          
+            w
+            
+              1
+              −
+              
+                w
+                
+                  2
+                
+              
+            
+          
+        
+        ,
+      
+    
+    {\displaystyle {\frac {1-\alpha ^{2}}{1+\alpha ^{2}}}={\sqrt {1-w^{2}}},\quad {\frac {2\alpha }{1-\alpha ^{2}}}={\frac {w}{\sqrt {1-w^{2}}}},}
+  
+
+finally by setting 
+  
+    
+      
+        D
+        =
+        x
+        ,
+        
+          D
+          ′
+        
+        =
+        
+          x
+          ′
+        
+        ,
+        R
+        =
+        t
+        ,
+        
+          R
+          ′
+        
+        =
+        
+          t
+          ′
+        
+      
+    
+    {\displaystyle D=x,D'=x',R=t,R'=t'}
+  
+ the Laguerre inversion becomes very similar to the Lorentz transformation except that the expression 
+  
+    
+      
+        t
+        −
+        v
+        x
+      
+    
+    {\displaystyle t-vx}
+  
+ is reversed into 
+  
+    
+      
+        w
+        x
+        −
+        t
+      
+    
+    {\displaystyle wx-t}
+  
+:
+
+  
+    
+      
+        
+          x
+          ′
+        
+        =
+        
+          
+            
+              x
+              −
+              w
+              t
+            
+            
+              1
+              −
+              
+                w
+                
+                  2
+                
+              
+            
+          
+        
+        ,
+        
+        
+          t
+          ′
+        
+        =
+        
+          
+            
+              w
+              x
+              −
+              t
+            
+            
+              1
+              −
+              
+                w
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle x'={\frac {x-wt}{\sqrt {1-w^{2}}}},\quad t'={\frac {wx-t}{\sqrt {1-w^{2}}}}}
+  
+.
+According to Müller, the Lorentz transformation can be seen as the product of an even number of such Laguerre inversions that change the sign. First an inversion is conducted into plane 
+  
+    
+      
+        
+          π
+          
+            1
+          
+        
+      
+    
+    {\displaystyle \pi _{1}}
+  
+ which is inclined with respect to plane 
+  
+    
+      
+        π
+      
+    
+    {\displaystyle \pi }
+  
+ under a certain angle, followed by another inversion back to 
+  
+    
+      
+        π
+      
+    
+    {\displaystyle \pi }
+  
+. See section #Laguerre group isomorphic to Lorentz group for more details of the connection between the Laguerre inversion to other variants of Laguerre transformations.
+
+=== Lorentz transformation within Laguerre geometry ===
+Timerding (1911) used Laguerre's concept of oriented spheres in order to represent and derive the Lorentz transformation. Given a sphere of radius 
+  
+    
+      
+        r
+      
+    
+    {\displaystyle r}
+  
+, with 
+  
+    
+      
+        x
+      
+    
+    {\displaystyle x}
+  
+ as the distance between its center and the central plane, he obtained the relations to a corresponding sphere
+
+  
+    
+      
+        
+          x
+          ′
+        
+        +
+        
+          r
+          ′
+        
+        =
+        
+          
+            
+              
+                1
+                +
+                
+                  λ
+                  
+                    2
+                  
+                
+              
+              
+                1
+                −
+                
+                  λ
+                  
+                    2
+                  
+                
+              
+            
+          
+        
+        (
+        x
+        +
+        r
+        )
+        ,
+        
+        
+          
+            
+              
+                x
+                ′
+              
+              −
+              
+                r
+                ′
+              
+            
+            
+              
+                x
+                ′
+              
+              +
+              
+                r
+                ′
+              
+            
+          
+        
+        =
+        
+          
+            
+              1
+              −
+              λ
+            
+            
+              1
+              +
+              λ
+            
+          
+        
+        ⋅
+        
+          
+            
+              x
+              −
+              r
+            
+            
+              x
+              +
+              r
+            
+          
+        
+        ,
+      
+    
+    {\displaystyle x'+r'={\sqrt {\frac {1+\lambda ^{2}}{1-\lambda ^{2}}}}(x+r),\quad {\frac {x'-r'}{x'+r'}}={\frac {1-\lambda }{1+\lambda }}\cdot {\frac {x-r}{x+r}},}
+  
+
+resulting in the transformation
+
+  
+    
+      
+        
+          
+            1
+            −
+            
+              λ
+              
+                2
+              
+            
+          
+        
+        ⋅
+        
+          x
+          ′
+        
+        =
+        x
+        −
+        λ
+        r
+        ,
+        
+        
+          
+            1
+            −
+            
+              λ
+              
+                2
+              
+            
+          
+        
+        ⋅
+        
+          r
+          ′
+        
+        =
+        r
+        −
+        λ
+        x
+        .
+      
+    
+    {\displaystyle {\sqrt {1-\lambda ^{2}}}\cdot x'=x-\lambda r,\quad {\sqrt {1-\lambda ^{2}}}\cdot r'=r-\lambda x.}
+  
+
+By setting 
+  
+    
+      
+        λ
+        =
+        v
+        
+          /
+        
+        c
+      
+    
+    {\displaystyle \lambda =v/c}
+  
+ and 
+  
+    
+      
+        r
+        =
+        c
+        t
+      
+    
+    {\displaystyle r=ct}
+  
+, it becomes the Lorentz transformation.
+Following Timerding and Bateman, Ogura (1913) analyzed a Laguerre transformation of the form
+
+  
+    
+      
+        
+          α
+          ′
+        
+        =
+        α
+        
+          
+            1
+            
+              1
+              −
+              
+                λ
+                
+                  2
+                
+              
+            
+          
+        
+        −
+        R
+        
+          
+            λ
+            
+              1
+              −
+              
+                λ
+                
+                  2
+                
+              
+            
+          
+        
+        ,
+        
+        
+          β
+          ′
+        
+        =
+        β
+        ,
+        
+        
+          γ
+          ′
+        
+        =
+        γ
+        ,
+        
+        
+          R
+          ′
+        
+        =
+        α
+        
+          
+            
+              −
+              λ
+            
+            
+              1
+              −
+              
+                λ
+                
+                  2
+                
+              
+            
+          
+        
+        +
+        R
+        
+          
+            1
+            
+              1
+              −
+              
+                λ
+                
+                  2
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle \alpha '=\alpha {\frac {1}{\sqrt {1-\lambda ^{2}}}}-R{\frac {\lambda }{\sqrt {1-\lambda ^{2}}}},\quad \beta '=\beta ,\quad \gamma '=\gamma ,\quad R'=\alpha {\frac {-\lambda }{\sqrt {1-\lambda ^{2}}}}+R{\frac {1}{\sqrt {1-\lambda ^{2}}}}}
+  
+,
+which become the Lorentz transformation with
+
+  
+    
+      
+        
+          
+            
+              
+                x
+              
+              
+                
+                =
+                α
+                ,
+              
+              
+                y
+              
+              
+                
+                =
+                β
+                ,
+              
+              
+                z
+              
+              
+                
+                =
+                γ
+                ,
+              
+              
+                R
+              
+              
+                
+                =
+                c
+                t
+                ,
+              
+            
+            
+              
+                
+                  x
+                  ′
+                
+              
+              
+                
+                =
+                
+                  α
+                  ′
+                
+                ,
+              
+              
+                
+                  y
+                  ′
+                
+              
+              
+                
+                =
+                
+                  β
+                  ′
+                
+                ,
+              
+              
+                
+                  z
+                  ′
+                
+              
+              
+                
+                =
+                
+                  γ
+                  ′
+                
+                ,
+              
+              
+                
+                  R
+                  ′
+                
+              
+              
+                
+                =
+                c
+                
+                  t
+                  ′
+                
+                ,
+              
+            
+          
+        
+      
+    
+    {\displaystyle {\begin{aligned}x&=\alpha ,&y&=\beta ,&z&=\gamma ,&R&=ct,\\x'&=\alpha ',&y'&=\beta ',&z'&=\gamma ',&R'&=ct',\end{aligned}}}
+  
+    
+  
+    
+      
+        λ
+        =
+        
+          
+            v
+            c
+          
+        
+      
+    
+    {\displaystyle \lambda ={\frac {v}{c}}}
+  
+.
+He stated that "the Laguerre transformation in sphere manifoldness is equivalent to the Lorentz transformation in spacetime manifoldness".
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Spherical_wave_transformation-5.md b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-5.md
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-5.md
@@ -0,0 +1,344 @@
+---
+title: "Spherical wave transformation"
+chunk: 6/8
+source: "https://en.wikipedia.org/wiki/Spherical_wave_transformation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:27.922869+00:00"
+instance: "kb-cron"
+---
+
+=== Laguerre group isomorphic to Lorentz group ===
+As shown above, the group of conformal point transformations in Rn (composed of motions, similarities, and inversions) can be related by minimal projection to the group of contact transformations in Rn-1 transforming circles or spheres into other circles or spheres. In addition, Lie (1871, 1896) pointed out that in R3 there is a 7-parameter subgroup of point transformations composed of motions and similarities, which by using minimal projection corresponds to a 7-parameter subgroup of contact transformations in R2 transforming circles into circles. These relations were further studied by Smith (1900), Blaschke (1910), Coolidge (1916) and others, who pointed out the connection to Laguerre's geometry of reciprocal directions related to oriented lines, circles, planes and spheres. Therefore, Smith (1900) called it the "group of the geometry of reciprocal directions", and Blaschke (1910) used the expression "Laguerre group". The "extended Laguerre group" consists of motions and similarities, having 7 parameters in R2 transforming oriented lines and circles, or 11 parameters in R3 transforming oriented planes and spheres. If similarities are excluded, it becomes the "restricted Laguerre group" having 6 parameters in R2 and 10 parameters in R3, consisting of orientation-preserving or orientation-reversing motions, and preserving the tangential distance between oriented circles or spheres. Subsequently, it became common that the term Laguerre group only refers to the restricted Laguerre group. It was also noted that the Laguerre group is part of a wider group conserving tangential distances, called the "equilong group" by Scheffers (1905).
+In R2 the Laguerre group leaves invariant the relation 
+  
+    
+      
+        d
+        
+          x
+          
+            2
+          
+        
+        +
+        d
+        
+          y
+          
+            2
+          
+        
+        −
+        d
+        
+          r
+          
+            2
+          
+        
+      
+    
+    {\displaystyle dx^{2}+dy^{2}-dr^{2}}
+  
+, which can be extended to arbitrary Rn as well. For instance, in R3 it leaves invariant the relation 
+  
+    
+      
+        d
+        
+          x
+          
+            2
+          
+        
+        +
+        d
+        
+          y
+          
+            2
+          
+        
+        +
+        d
+        
+          z
+          
+            2
+          
+        
+        −
+        d
+        
+          r
+          
+            2
+          
+        
+      
+    
+    {\displaystyle dx^{2}+dy^{2}+dz^{2}-dr^{2}}
+  
+. This is equivalent to relation 
+  
+    
+      
+        d
+        
+          x
+          
+            2
+          
+        
+        +
+        d
+        
+          y
+          
+            2
+          
+        
+        +
+        d
+        
+          z
+          
+            2
+          
+        
+        +
+        d
+        
+          r
+          
+            2
+          
+        
+      
+    
+    {\displaystyle dx^{2}+dy^{2}+dz^{2}+dr^{2}}
+  
+ in R4 by using minimal (isotropy) projection with imaginary radius coordinate, or cyclographic projection (in descriptive geometry) with real radius coordinate. The transformations forming the Laguerre group can be further differentiated into "direct Laguerre transformations" which are related to motions preserving both the tangential distance as well as the sign; or "indirect Laguerre transformations" which are related to orientation-reversing motions, preserving the tangential distance with the sign reversed. The Laguerre inversion first given by Laguerre in 1882 is involutory, thus it belongs to the indirect Laguerre transformations. Laguerre himself did not discuss the group related to his inversion, but it turned out that every Laguerre transformation can be generated by at most four Laguerre inversions and every direct Laguerre transformation is the product of two involutory transformations, thus Laguerre inversions are of special importance because they are generating operators of the entire Laguerre group.
+It was noted that the Laguerre group is indeed isomorphic to the Lorentz group (or the Poincaré group if translations are included), as both groups leave invariant the form 
+  
+    
+      
+        d
+        
+          x
+          
+            1
+          
+          
+            2
+          
+        
+        +
+        d
+        
+          x
+          
+            2
+          
+          
+            2
+          
+        
+        +
+        d
+        
+          x
+          
+            3
+          
+          
+            2
+          
+        
+        −
+        d
+        
+          x
+          
+            4
+          
+          
+            2
+          
+        
+      
+    
+    {\displaystyle dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-dx_{4}^{2}}
+  
+. After the first comparison of the Lorentz transformation and the Laguerre inversion by Bateman (1910) as mentioned above, the equivalence of both groups was pointed out by Cartan in 1912 and 1914, and he expanded upon it in 1915 (published 1955) in the French version of Klein's encyclopedia. Also Poincaré (1912, published 1921) wrote:
+
+Mr. Cartan has recently given a curious example. We know the importance in mathematical physics of what has been called the Lorentz group; it is this group upon which our new ideas on the principle of relativity and the dynamics of the electron are based. On the other hand, Laguerre once introduced into geometry a group of transformations that change the spheres into spheres. These two groups are isomorphic, so that mathematically these two theories, one physical, the other one geometric, show no essential difference.
+Others who noticed this connection include Coolidge (1916), Klein & Blaschke (1926), Blaschke (1929), H.R. Müller, Kunle & Fladt (1970), Benz (1992). It was recently pointed out:
+
+A Laguerre transformation (L-transform) is a mapping which is bijective on the sets of oriented planes and oriented spheres, respectively, and preserves tangency between plane and sphere. L-transforms are more easily understood if we use the so-called cyclographic model of Laguerre geometry. There, an oriented sphere 
+  
+    
+      
+        S
+      
+    
+    {\displaystyle S}
+  
+ is represented as point 
+  
+    
+      
+        
+          S
+        
+        
+          :=
+        
+        ⁡
+        (
+        
+          m
+        
+        ,
+        R
+        )
+        ∈
+        
+          
+            R
+          
+          
+            4
+          
+        
+      
+    
+    {\displaystyle \mathbf {S} \operatorname {\text{:=}} (\mathbf {m} ,R)\in \mathbb {R} ^{4}}
+  
+. An oriented plane 
+  
+    
+      
+        P
+      
+    
+    {\displaystyle P}
+  
+ in 
+  
+    
+      
+        
+          E
+          
+            3
+          
+        
+      
+    
+    {\displaystyle E^{3}}
+  
+ may be interpreted as the set of all oriented spheres which are tangent to 
+  
+    
+      
+        P
+      
+    
+    {\displaystyle P}
+  
+. Mapping 
+  
+    
+      
+        P
+      
+    
+    {\displaystyle P}
+  
+ via this set of spheres into 
+  
+    
+      
+        
+          
+            R
+          
+          
+            4
+          
+        
+      
+    
+    {\displaystyle \mathbb {R} ^{4}}
+  
+, one finds a hyperplane in 
+  
+    
+      
+        
+          
+            R
+          
+          
+            4
+          
+        
+      
+    
+    {\displaystyle \mathbb {R} ^{4}}
+  
+ which is parallel to a tangent hyperplane of the cone 
+  
+    
+      
+        
+          x
+          
+            1
+          
+          
+            2
+          
+        
+        +
+        
+          x
+          
+            2
+          
+          
+            2
+          
+        
+        +
+        
+          x
+          
+            3
+          
+          
+            2
+          
+        
+        −
+        
+          x
+          
+            4
+          
+          
+            2
+          
+        
+        =
+        0
+      
+    
+    {\displaystyle x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-x_{4}^{2}=0}
+  
+. In the cyclographic model, an L-transform is seen as a special affine map (Lorentz transformation),...
+
+== See also ==
+History of Lorentz transformations
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Spherical_wave_transformation-6.md b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-6.md
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+---
+title: "Spherical wave transformation"
+chunk: 7/8
+source: "https://en.wikipedia.org/wiki/Spherical_wave_transformation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:27.922869+00:00"
+instance: "kb-cron"
+---
+
+== Primary sources ==
+Bateman, Harry (1909) [1908]. "The conformal transformations of a space of four dimensions and their applications to geometrical optics" . Proceedings of the London Mathematical Society. 7: 70–89. doi:10.1112/plms/s2-7.1.70.
+Bateman, Harry (1910) [1909]. "The Transformation of the Electrodynamical Equations" . Proceedings of the London Mathematical Society. 8: 223–264. doi:10.1112/plms/s2-8.1.223.
+Bateman, Harry (1910a). "The Physical Aspect of Time" . Manchester Memoirs. 54 (14): 1–13.
+Bateman, Harry (1910b). "The Relation between Electromagnetism and Geometry". Philosophical Magazine. 20 (118): 623–628. doi:10.1080/14786441008636944.
+Bateman, Harry (1912) [1910]. "Some geometrical theorems connected with Laplace's equation and the equation of wave motion". American Journal of Mathematics. 34 (3): 325–360. doi:10.2307/2370223. JSTOR 2370223.
+Blaschke, Wilhelm (1910). "Untersuchungen über die Geometrie der Speere in der Euklidischen Geometrie". Monatshefte für Mathematik und Physik. 21 (1): 3–60. doi:10.1007/bf01693218. S2CID 120182503.
+Cartan, Élie (1912). "Sur les groupes de transformation de contact et la Cinématique nouvelle". Société de Mathématique the France - Comptes Rendus des Séances: 23.
+Cartan, Élie (1914). "La théorie des groupes". Revue du Mois: 452–457.
+Cunningham, Ebenezer (1910) [1909]. "The principle of Relativity in Electrodynamics and an Extension Thereof". Proceedings of the London Mathematical Society. 8: 77–98. doi:10.1112/plms/s2-8.1.77.
+Darboux, Gaston (1872). "Sur les relations entre les groupes de points, de cercles et de sphères". Annales Scientifiques de l'École Normale Supérieure. 1: 323–392. doi:10.24033/asens.87.
+Darboux, Gaston (1878). "Mémoire sur la théorie des coordonnées curvilignes et des systèmes orthogonaux. Troisième partie". Annales Scientifiques de l'École Normale Supérieure. 7: 275–348. doi:10.24033/asens.164.
+Darboux, Gaston (1887). Leçons sur la théorie générale des surfaces. Première partie. Paris: Gauthier-Villars.
+Herglotz, Gustav (1910) [1909], "Über den vom Standpunkt des Relativitätsprinzips aus als starr zu bezeichnenden Körper" [Wikisource translation: On bodies that are to be designated as "rigid" from the standpoint of the relativity principle], Annalen der Physik, 336 (2): 393–415, Bibcode:1910AnP...336..393H, doi:10.1002/andp.19103360208
+Felix Klein (1884), Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, Teubner, Leipzig; English translation: Lectures on the ikosahedron and the solution of equations of the fifth degree (1888)
+Klein, Felix (1921). "Über die geometrischen Grundlagen der Lorentzgruppe". Gesammelte Mathematische Abhandlungen . Vol. 19. pp. 533–552. doi:10.1007/978-3-642-51960-4_31 (inactive 12 July 2025). ISBN 978-3-642-51898-0. {{cite book}}: ISBN / Date incompatibility (help); |journal= ignored (help)CS1 maint: DOI inactive as of July 2025 (link) Reprinted in Klein, Felix (1921). "Über die geometrischen Grundlagen der Lorentzgruppe". Gesammelte Mathematische Abhandlungen. Vol. 1. pp. 533–552. doi:10.1007/978-3-642-51960-4_31 (inactive 12 July 2025). ISBN 978-3-642-51898-0. {{cite book}}: ISBN / Date incompatibility (help)CS1 maint: DOI inactive as of July 2025 (link) English translation by David Delphenich: On the geometric foundations of the Lorentz group
+Kubota, Tadahiko (1925). "Über die (2-2)-deutigen quadratischen Verwandtschaften V". Science Reports of the Tôhoku Imperial University. 14: 155–164..
+Laguerre, Edmond (1881). "Sur la transformation par directions réciproques" . Comptes Rendus. 92: 71–73.
+Laguerre, Edmond (1882). "Transformations par semi-droites réciproques" . Nouvelles annales de mathématiques. 1: 542–556.
+Laguerre, Edmond (1905). "Collection of papers published between 1880 and 1885". Œuvres de Laguerre, vol. 2. Paris: Gauthier-Villars. pp. 592–684.
+Lie, Sophus (1871). "Ueber diejenige Theorie eines Raumes mit beliebig vielen Dimensionen, die der Krümmungs-Theorie des gewöhnlichen Raumes entspricht". Göttinger Nachrichten: 191–209.
+Lie, Sophus (1872). "Ueber Complexe, insbesondere Linien- und Kugel-Complexe, mit Anwendung auf die Theorie partieller Differentialgleichungen". Mathematische Annalen. 5: 145–256. doi:10.1007/bf01446331. S2CID 122317672. English translation by David Delphenich: On complexes - in particular, line and sphere complexes - with applications to the theory of partial differential equations
+Lie, Sophus; Scheffers, Georg (1896). Geometrie der Berührungstransformationen. Leipzig: B.G. Teubner.
+Liouville, Joseph (1847). "Note au sujet de l'article précédent". Journal de Mathématiques Pures et Appliquées. 12: 265–290.
+Liouville, Joseph (1850a). "Théorème sur l'équation dx²+dy²+dz²=λ(dα²+dβ²+dγ²)". Journal de Mathématiques Pures et Appliquées. 15: 103.
+Liouville, Joseph (1850b). "Extension au cas des trois dimensions de la question du tracé géographique". In Gaspard Monge (ed.). Application de l'analyse à la Géométrie. Paris: Bachelier. pp. 609–616.
+Müller, Emil (1898). "Die Geometrie orientierter Kugeln nach Grassmann'schen Methoden". Monatshefte für Mathematik und Physik. 9 (1): 269–315. doi:10.1007/bf01707874. S2CID 121786469.
+Müller, Hans Robert (1948). "Zyklographische Betrachtung der Kinematik der speziellen Relativitätstheorie". Monatshefte für Mathematik und Physik. 52 (4): 337–353. doi:10.1007/bf01525338. S2CID 120150204.{{cite journal}}:  CS1 maint: deprecated archival service (link)
+Ogura, Kinnosuke (1913). "On the Lorentz Transformation with some Geometrical Interpretations". Science Reports of the Tôhuku University. 2: 95–116.
+Poincaré, Henri (1906) [1905], "Sur la dynamique de l'électron"  [Wikisource translation: On the Dynamics of the Electron], Rendiconti del Circolo Matematico di Palermo, 21: 129–176, Bibcode:1906RCMP...21..129P, doi:10.1007/BF03013466, S2CID 120211823
+Poincaré, Henri (1921) [1912]. "Rapport sur les travaux de M. Cartan (fait à la Faculté des sciences de l'Université de Paris)". Acta Mathematica. 38 (1): 137–145. doi:10.1007/bf02392064. S2CID 122517182.. Written by Poincaré in 1912, printed in Acta Mathematica in 1914 though belatedly published in 1921.
+Ribaucour, Albert (1870). "Sur la déformation des surfaces" . Comptes Rendus. 70: 330–333.
+Smith, Percey F. (1900). "On a Transformation of Laguerre". Annals of Mathematics. 1 (1/4): 153–172. doi:10.2307/1967282. JSTOR 1967282.
+Stephanos, C. (1881). "Sur la géométrie des sphères". Comptes Rendus. 92: 1195–1197.
+Stephanos, C. (1883). "Sur la théorie des quaternions". Mathematische Annalen. 7 (4): 589–592. doi:10.1007/bf01443267. S2CID 179178015.
+Timerding, H. E. (1912). "Über ein einfaches geometrisches Bild der Raumzeitwelt Minkowskis". Jahresbericht der Deutschen Mathematiker-Vereinigung. 21: 274–285.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Spherical_wave_transformation-7.md b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-7.md
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Spherical_wave_transformation-7.md
@@ -0,0 +1,31 @@
+---
+title: "Spherical wave transformation"
+chunk: 8/8
+source: "https://en.wikipedia.org/wiki/Spherical_wave_transformation"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:27.922869+00:00"
+instance: "kb-cron"
+---
+
+== Secondary sources ==
+Textbooks, encyclopaedic entries, historical surveys:
+Bateman, Harry (1915). The mathematical analysis of electrical and optical wave motion on the basis of Maxwell's equations. Cambridge: University Press.
+Benz, Walter (2005) [1992]. Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces Third Edition. Springer. pp. 133–175. ISBN 978-3034804202.
+Blaschke, Wilhelm (1929). Thomsen, Gerhard (ed.). Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie Bd. 3. Berlin: Springer. doi:10.1007/978-3-642-50823-3. hdl:2027/mdp.39015017405492. ISBN 978-3-642-50513-3. {{cite book}}: ISBN / Date incompatibility (help)
+Cartan, Élie; Fano, Gino (1915). "La théorie des groupes continus et la géométrie". Encyclopédie des Sciences Mathématiques Pures et Appliquées. Vol. 3. pp. 39–43. (Only pages 1–21 were published in 1915, the entire article including pp. 39–43 concerning the groups of Laguerre and Lorentz was posthumously published in 1955 in Cartan's collected papers, and was reprinted in the Encyclopédie in 1991.)
+Cecil, Thomas E. (2008) [1992], "Laguerre geometry", Lie sphere geometry, Springer, pp. 37–46, ISBN 978-0387746555
+Coolidge, Julian (1916). A treatise on the circle and the sphere. Oxford: Clarendon Press.
+Cunningham, Ebenezer (1914). The principle of relativity. Cambridge: University Press.
+Fano, Gino (1910). "Kontinuierliche Geometrische Gruppen. Die Gruppentheorie als Geometrisches Einteilungsprinzip". Encyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Vol. 3.1.1. pp. 289–388. doi:10.1007/978-3-663-16027-4_5. ISBN 978-3-663-15456-3. {{cite book}}: ISBN / Date incompatibility (help)
+Robert Fricke & Felix Klein (1897), Vorlesungen über die Theorie der autormorphen Functionen - Erster Band: Die gruppentheoretischen Grundlagen, Teubner, Leipzig
+Kastrup, H. A. (2008). "On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics". Annalen der Physik. 520 (9–10): 631–690. arXiv:0808.2730. Bibcode:2008AnP...520..631K. doi:10.1002/andp.200810324. S2CID 12020510.
+Klein, Felix (1893). Einleitung in die höhere Geometrie I. Göttingen: Göttingen.
+Klein, Felix; Blaschke, Wilhelm (1926). Vorlesungen über höhere Geometrie. Berlin: Springer. (Klein's lectures from 1893 updated and edited by Blaschke in 1926.)
+Kunle H.; Fladt K. (1926). "Erlangen program and higher geometry – Laguerre geometry". In Heinrich Behnke (ed.). Fundamentals of Mathematics: Geometry. MIT Press. pp. 460–516.{{cite book}}:  CS1 maint: multiple names: authors list (link)
+Müller, Emil (1910). "Die Verschiedenen Koordinatensysteme". Encyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Vol. 3.1.1. pp. 596–770. doi:10.1007/978-3-663-16027-4_9. ISBN 978-3-663-15456-3. {{cite book}}: ISBN / Date incompatibility (help)
+Pedoe, Daniel (1972). "A forgotten geometrical transformation". L'Enseignement Mathématique. 18: 255–267. doi:10.5169/seals-45376.
+Rougé, André (2008). Relativité restreinte: la contribution d'Henri Poincaré. Editions Ecole Polytechnique. ISBN 978-2730215251.
+Walter, Scott A. (2018). "Figures of light in the early history of relativity (1905-1914)". In Rowe, David; et al. (eds.). Beyond Einstein. Einstein Studies. Vol. 14. Basel: Birkhäuser. pp. 1–50. doi:10.1007/978-1-4939-7708-6_1. ISBN 978-1-4939-7706-2.
+Warwick, Andrew (1992). "Cambridge mathematics and Cavendish physics: Cunningham, Campbell and Einstein's relativity 1905–1911 Part I: The uses of theory". Studies in History and Philosophy of Science Part A. 23 (4): 625–656. Bibcode:1992SHPSA..23..625W. doi:10.1016/0039-3681(92)90015-X.
+Warwick, Andrew (2003). Masters of Theory: Cambridge and the Rise of Mathematical Physics. Chicago: University of Chicago Press. ISBN 978-0-226-87375-6.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Sticky_bead_argument-0.md b/data/en.wikipedia.org/wiki/Sticky_bead_argument-0.md
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index 000000000..033be2e92
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Sticky_bead_argument-0.md
@@ -0,0 +1,35 @@
+---
+title: "Sticky bead argument"
+chunk: 1/2
+source: "https://en.wikipedia.org/wiki/Sticky_bead_argument"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:29.159313+00:00"
+instance: "kb-cron"
+---
+
+In general relativity, the sticky bead argument is a simple thought experiment designed to show that gravitational radiation is indeed predicted by general relativity and can have physical effects. These claims were not widely accepted prior to about 1955, but after the introduction of the bead argument, any remaining doubts soon disappeared from the research literature.
+The argument is often credited to Hermann Bondi, who popularized it, but it was originally proposed by Richard Feynman.
+
+== Description ==
+The thought experiment was first described by Feynman at the 1957 Chapel Hill Conference, and later addressed in his private letter to Victor Weisskopf: 
+
+Feynman’s gravitational wave detector: It is simply two beads sliding freely (but with a small amount of friction) on a rigid rod. As the wave passes over the rod, atomic forces hold the length of the rod fixed, but the proper distance between the two beads oscillates. Thus, the beads rub against the rod, dissipating heat.
+As the gravitational waves are mainly transverse, the rod has to be oriented perpendicular to the propagation direction of the wave.
+
+== History of arguments on the properties of gravitational waves ==
+
+=== Einstein's double reversal ===
+The creator of the theory of general relativity, Albert Einstein, argued in 1916 that gravitational radiation should be produced, according to his theory, by any mass-energy configuration that has a time-varying quadrupole moment (or higher multipole moment). Using a linearized field equation (appropriate for the study of weak gravitational fields), he derived the famous quadrupole formula quantifying the rate at which such radiation should carry away energy. Examples of systems with time varying quadrupole moments include vibrating strings, bars rotating about an axis perpendicular to the symmetry axis of the bar, and binary star systems, but not rotating disks.
+In 1922, Arthur Stanley Eddington wrote a paper expressing (apparently for the first time) the view that gravitational waves are in essence ripples in coordinates, and have no physical meaning. He did not appreciate Einstein's arguments that the waves are real.
+In 1936, together with Nathan Rosen, Einstein rediscovered the Beck vacuums, a family of exact gravitational wave solutions with cylindrical symmetry (sometimes also called Einstein–Rosen waves). While investigating the motion of test particles in these solutions, Einstein and Rosen became convinced that gravitational waves were unstable to collapse. Einstein reversed himself and declared that gravitational radiation was not after all a prediction of his theory. Einstein wrote to his friend Max Born
+
+Together with a young collaborator, I arrived at the interesting result that gravitational waves do not exist, though they had been assumed a certainty to the first approximation. This shows that the nonlinear field equations can show us more, or rather limit us more, than we have believed up till now.
+
+In other words, Einstein believed that he and Rosen had established that their new argument showed that the prediction of gravitational radiation was a mathematical artifact of the linear approximation he had employed in 1916. Einstein believed these plane waves would gravitationally collapse into points; he had long hoped something like this would explain quantum mechanical wave-particle duality.
+Einstein and Rosen accordingly submitted a paper entitled Do gravitational waves exist? to a leading physics journal, Physical Review, in which they described their wave solutions and concluded that the "radiation" that seemed to appear in general relativity was not genuine radiation capable of transporting energy or having (in principle) measurable physical effects. The anonymous referee, who—as the current editor of Physical Review recently confirmed, all parties now being deceased—was the combative cosmologist, Howard Percy Robertson, pointed out the error described below, and the manuscript was returned to the authors with a note from the editor asking them to revise the paper to address these concerns. Quite uncharacteristically, Einstein took this criticism very badly, angrily replying "I see no reason to address the, in any case erroneous, opinion expressed by your referee." He vowed never again to submit a paper to Physical Review. Instead, Einstein and Rosen resubmitted the paper without change to another and much less well known journal, The Journal of the Franklin Institute. He kept his vow regarding Physical Review.
+Leopold Infeld, who arrived at Princeton University at this time, later remembered his utter astonishment on hearing of this development, since radiation is such an essential element for any classical field theory worthy of the name. Infeld expressed his doubts to a leading expert on general relativity: H. P. Robertson, who had just returned from a visit to Caltech. Going over the argument as Infeld remembered it, Robertson was able to show Infeld the mistake: locally, the Einstein–Rosen waves are gravitational plane waves. Einstein and Rosen had correctly shown that a cloud of test particles would, in sinusoidal plane waves, form caustics, but changing to another chart (essentially the Brinkmann coordinates) shows that the formation of the caustic is not a contradiction at all, but in fact just what one would expect in this situation. Infeld then approached Einstein, who concurred with Robertson's analysis (still not knowing it was he who reviewed the Physical Review submission).
+Since Rosen had recently departed for the Soviet Union, Einstein acted alone in promptly and thoroughly revising their joint paper. This third version was retitled On gravitational waves, and, following Robertson's suggestion of a transformation to cylindrical coordinates, presented what are now called Einstein–Rosen cylindrical waves (these are locally isometric to plane waves). This is the version that eventually appeared. However, Rosen was unhappy with this revision and eventually published his own version, which retained the erroneous "disproof" of the prediction of gravitational radiation.
+In a letter to the editor of Physical Review, Robertson wryly reported that in the end, Einstein had fully accepted the objections that had initially so upset him.
+
+=== Bern and Chapel Hill conferences ===
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Sticky_bead_argument-1.md b/data/en.wikipedia.org/wiki/Sticky_bead_argument-1.md
new file mode 100644
index 000000000..2ca69454c
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Sticky_bead_argument-1.md
@@ -0,0 +1,42 @@
+---
+title: "Sticky bead argument"
+chunk: 2/2
+source: "https://en.wikipedia.org/wiki/Sticky_bead_argument"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:29.159313+00:00"
+instance: "kb-cron"
+---
+
+In 1955, an important conference honoring the semi-centennial of special relativity was held in Bern, the Swiss capital city where Einstein was working in the famous patent office during the Annus mirabilis.  Rosen attended and gave a talk in which he computed the Einstein pseudotensor and Landau–Lifshitz pseudotensor (two alternative, non-covariant, descriptions of the energy carried by a gravitational field, a notion that is notoriously difficult to pin down in general relativity). These turn out to be zero for the Einstein–Rosen waves, and Rosen argued that this reaffirmed the negative conclusion he had reached with Einstein in 1936.
+However, by this time a few physicists, such as Felix Pirani and Ivor Robinson, had come to appreciate the role played by curvature in producing tidal accelerations, and were able to convince many peers that gravitational radiation would indeed be produced, at least in cases such as a vibrating spring where different pieces of the system were clearly not in inertial motion. Nonetheless, some physicists continued to doubt whether radiation would be produced by a binary star system, where the world lines of the centers of mass of the two stars should, according to the EIH approximation (dating from 1938 and due to Einstein, Infeld, and Banesh Hoffmann), follow timelike geodesics.
+Inspired by conversations by Felix Pirani, Hermann Bondi took up the study of gravitational radiation, in particular the question of quantifying the energy and momentum carried off 'to infinity' by a radiating system. During the next few years, Bondi developed the Bondi radiating chart and the notion of Bondi energy to rigorously study this question in maximal generality.
+In 1957, at a conference at Chapel Hill, North Carolina, appealing to various mathematical tools developed by John Lighton Synge, A. Z. Petrov and André Lichnerowicz, Pirani explained more clearly than had previously been possible the central role played by the Riemann tensor and in particular the tidal tensor in general relativity. He gave the first correct description of the relative (tidal) acceleration of initially mutually static test particles that encounter a sinusoidal gravitational plane wave.
+
+=== Feynman's argument ===
+Later in the Chapel Hill conference, Richard Feynman used Pirani's description to point out that a passing gravitational wave should, in principle, cause a bead on a stick (oriented transversely to the direction of propagation of the wave) to slide back and forth, thus heating the bead and the stick by friction. This heating, said Feynman, showed that the wave did indeed impart energy to the bead and stick system, so it must indeed transport energy, contrary to the view expressed in 1955 by Rosen.
+In two 1957 papers, Bondi and (separately) Joseph Weber and John Archibald Wheeler used this bead argument to present detailed refutations of Rosen's argument.
+
+=== Rosen's final views ===
+Nathan Rosen continued to argue as late as the 1970s, on the basis of a supposed paradox involving the radiation reaction, that gravitational radiation is not in fact predicted by general relativity. His arguments were generally regarded as invalid, but in any case the sticky bead argument had by then long since convinced other physicists of the reality of the prediction of gravitational radiation.
+
+== See also ==
+Dashpot, of which the sticky-bead device is a variant.
+Monochromatic electromagnetic plane wave and monochromatic gravitational plane wave, for a modern account of two exact solutions, which should clarify the point that confused Einstein and Rosen in 1936.
+pp-wave spacetime, for the Brinkmann gravitational wave solutions.
+Gravitational plane wave, for the Baldwin–Jeffery gravitational plane wave solutions.
+Brinkmann coordinates and Rosen coordinates for the two coordinate charts.
+Beck vacuums, for the Beck or Einstein–Rosen family of vacuum solutions.
+
+== Notes ==
+
+== References ==
+Kennefick, Daniel (2005). "Einstein versus the Physical Review". Physics Today. 48 (9): 43–48. Bibcode:2005PhT....58i..43K. doi:10.1063/1.2117822. See also the on-line version
+Kennefick, Daniel, Controversies in the History of the Radiation Reaction problem in General Relativity
+Rosen, Nathan (1937). "Plane polarized waves in the general theory of relativity". Phys. Z. Sowjetunion. 12: 366–372.
+Einstein, Albert & Rosen, Nathan (1937). "On gravitational waves". J. Franklin Inst. 223: 43–54. Bibcode:1937FrInJ.223...43E. doi:10.1016/S0016-0032(37)90583-0.
+Baldwin, O. R. & Jeffery, G. B. (1926). "The relativity theory of plane waves". Proc. R. Soc. Lond. A. 111 (757): 95–104. Bibcode:1926RSPSA.111...95B. doi:10.1098/rspa.1926.0051.
+Beck, Guido (1925). "Zur Theorie binärer Gravitationsfelder". Z. Phys. 33 (1): 713–738. Bibcode:1925ZPhy...33..713B. doi:10.1007/BF01328358. S2CID 125868491.
+H. W. Brinkmann (1925). "Einstein spaces which are mapped conformally on each other". Math. Ann. 18: 119–145. doi:10.1007/BF01208647. S2CID 121619009.
+Eddington, Arthur Stanley (1922). "The propagation of gravitational waves". Proc. R. Soc. Lond. A. 102 (716): 268–282. Bibcode:1922RSPSA.102..268E. doi:10.1098/rspa.1922.0085.
+Einstein, Albert (1918). "Über Gravitationswellen". Königlich Preussische Akademie der Wissenschaften Berlin Sitzungberichte: 154–167. Bibcode:1918SPAW.......154E.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Strangelet-0.md b/data/en.wikipedia.org/wiki/Strangelet-0.md
index 30fe3b421..b2be26b7b 100644
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+++ b/data/en.wikipedia.org/wiki/Strangelet-0.md
@@ -4,7 +4,7 @@ chunk: 1/3
 source: "https://en.wikipedia.org/wiki/Strangelet"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T16:11:32.116101+00:00"
+date_saved: "2026-05-05T16:30:30.615733+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Strangelet-1.md b/data/en.wikipedia.org/wiki/Strangelet-1.md
index 2f319bb73..881485b6a 100644
--- a/data/en.wikipedia.org/wiki/Strangelet-1.md
+++ b/data/en.wikipedia.org/wiki/Strangelet-1.md
@@ -4,7 +4,7 @@ chunk: 2/3
 source: "https://en.wikipedia.org/wiki/Strangelet"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T16:11:32.116101+00:00"
+date_saved: "2026-05-05T16:30:30.615733+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Strangelet-2.md b/data/en.wikipedia.org/wiki/Strangelet-2.md
index d1e1d46ae..fb2ae39f1 100644
--- a/data/en.wikipedia.org/wiki/Strangelet-2.md
+++ b/data/en.wikipedia.org/wiki/Strangelet-2.md
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 source: "https://en.wikipedia.org/wiki/Strangelet"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T16:11:32.116101+00:00"
+date_saved: "2026-05-05T16:30:30.615733+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Teleparallelism-0.md b/data/en.wikipedia.org/wiki/Teleparallelism-0.md
new file mode 100644
index 000000000..2ff6ea0b0
--- /dev/null
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@@ -0,0 +1,314 @@
+---
+title: "Teleparallelism"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Teleparallelism"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:34.335957+00:00"
+instance: "kb-cron"
+---
+
+Teleparallelism (also called teleparallel gravity), was an attempt by Albert Einstein to base a unified theory of electromagnetism and gravity on the mathematical structure of distant parallelism, also referred to as absolute or teleparallelism. In this theory, a spacetime is characterized by a curvature-free linear connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field.
+
+== Teleparallel spacetimes ==
+The crucial new idea, for Einstein, was the introduction of a tetrad field, i.e., a set {X1, X2, X3, X4} of four vector fields defined on all of M such that for every p ∈ M the set {X1(p), X2(p), X3(p), X4(p)} is a basis of TpM, where TpM denotes the fiber over p of the tangent vector bundle TM. Hence, the four-dimensional spacetime manifold M must be a parallelizable manifold. The tetrad field was introduced to allow the distant comparison of the direction of tangent vectors at different points of the manifold, hence the name distant parallelism. His attempt failed because there was no Schwarzschild solution in his simplified field equation.
+In fact, one can define the connection of the parallelization (also called the Weitzenböck connection) {Xi} to be the linear connection ∇ on M such that
+
+  
+    
+      
+        
+          ∇
+          
+            v
+          
+        
+        
+          (
+          
+            
+              f
+              
+                i
+              
+            
+            
+              
+                X
+              
+              
+                i
+              
+            
+          
+          )
+        
+        =
+        
+          (
+          
+            v
+            
+              f
+              
+                i
+              
+            
+          
+          )
+        
+        
+          
+            X
+          
+          
+            i
+          
+        
+        (
+        p
+        )
+        ,
+      
+    
+    {\displaystyle \nabla _{v}\left(f^{i}\mathrm {X} _{i}\right)=\left(vf^{i}\right)\mathrm {X} _{i}(p),}
+  
+
+where v ∈ TpM and fi are (global) functions on M; thus fiXi is a global vector field on M. In other words, the coefficients of Weitzenböck connection ∇ with respect to {Xi} are all identically zero, implicitly defined by:
+
+  
+    
+      
+        
+          ∇
+          
+            
+              
+                X
+              
+              
+                i
+              
+            
+          
+        
+        
+          
+            X
+          
+          
+            j
+          
+        
+        =
+        0
+        ,
+      
+    
+    {\displaystyle \nabla _{\mathrm {X} _{i}}\mathrm {X} _{j}=0,}
+  
+
+hence
+
+  
+    
+      
+        
+          
+            
+              W
+              
+                k
+              
+            
+          
+          
+            i
+            j
+          
+        
+        =
+        
+          ω
+          
+            k
+          
+        
+        
+          (
+          
+            
+              ∇
+              
+                
+                  
+                    X
+                  
+                  
+                    i
+                  
+                
+              
+            
+            
+              
+                X
+              
+              
+                j
+              
+            
+          
+          )
+        
+        ≡
+        0
+        ,
+      
+    
+    {\displaystyle {W^{k}}_{ij}=\omega ^{k}\left(\nabla _{\mathrm {X} _{i}}\mathrm {X} _{j}\right)\equiv 0,}
+  
+
+for the connection coefficients (also called Weitzenböck coefficients) in this global basis. Here ωk is the dual global basis (or coframe) defined by ωi(Xj) = δij.
+This is what usually happens in Rn, in any affine space or Lie group (for example the 'curved' sphere S3 but 'Weitzenböck flat' manifold).
+Using the transformation law of a connection, or equivalently the ∇ properties, we have the following result.
+
+Proposition. In a natural basis, associated with local coordinates (U, xμ), i.e., in the holonomic frame ∂μ, the (local) connection coefficients of the Weitzenböck connection are given by:
+
+  
+    
+      
+        
+          
+            
+              Γ
+              
+                β
+              
+            
+          
+          
+            μ
+            ν
+          
+        
+        =
+        
+          h
+          
+            i
+          
+          
+            β
+          
+        
+        
+          ∂
+          
+            ν
+          
+        
+        
+          h
+          
+            μ
+          
+          
+            i
+          
+        
+        ,
+      
+    
+    {\displaystyle {\Gamma ^{\beta }}_{\mu \nu }=h_{i}^{\beta }\partial _{\nu }h_{\mu }^{i},}
+  
+
+where Xi = hμi∂μ for i, μ = 1, 2,… n are the local expressions of a global object, that is, the given tetrad.
+The Weitzenböck connection has vanishing curvature, but – in general – non-vanishing torsion.
+Given the frame field {Xi}, one can also define a metric by conceiving of the frame field as an orthonormal vector field. One would then obtain a pseudo-Riemannian metric tensor field g of signature (3,1) by
+
+  
+    
+      
+        g
+        
+          (
+          
+            
+              
+                X
+              
+              
+                i
+              
+            
+            ,
+            
+              
+                X
+              
+              
+                j
+              
+            
+          
+          )
+        
+        =
+        
+          η
+          
+            i
+            j
+          
+        
+        ,
+      
+    
+    {\displaystyle g\left(\mathrm {X} _{i},\mathrm {X} _{j}\right)=\eta _{ij},}
+  
+
+where
+
+  
+    
+      
+        
+          η
+          
+            i
+            j
+          
+        
+        =
+        diag
+        ⁡
+        (
+        −
+        1
+        ,
+        −
+        1
+        ,
+        −
+        1
+        ,
+        1
+        )
+        .
+      
+    
+    {\displaystyle \eta _{ij}=\operatorname {diag} (-1,-1,-1,1).}
+  
+
+The corresponding underlying spacetime is called, in this case, a Weitzenböck spacetime.
+These 'parallel vector fields' give rise to the metric tensor as a byproduct.
+
+== New teleparallel gravity theory ==
+New teleparallel gravity theory (or new general relativity) is a theory of gravitation on Weitzenböck spacetime, and attributes gravitation to the torsion tensor formed of the parallel vector fields.
+In the new teleparallel gravity theory the fundamental assumptions are as follows:
+
+In 1961 Christian Møller revived Einstein's idea, and Pellegrini and Plebanski found a Lagrangian formulation for absolute parallelism.
+
+=== Møller tetrad theory of gravitation ===
+In 1961, Møller showed that a tetrad description of gravitational fields allows a more rational treatment of the energy-momentum complex than in a theory based on the metric tensor alone. The advantage of using tetrads as gravitational variables was connected with the fact that this allowed to construct expressions for the energy-momentum complex which had more satisfactory transformation properties than in a purely metric formulation. In 2015, it was shown that the total energy of matter and gravitation is proportional to the Ricci scalar of three-space up to the linear order of perturbation.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Teleparallelism-1.md b/data/en.wikipedia.org/wiki/Teleparallelism-1.md
new file mode 100644
index 000000000..1e10667fa
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Teleparallelism-1.md
@@ -0,0 +1,438 @@
+---
+title: "Teleparallelism"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Teleparallelism"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:34.335957+00:00"
+instance: "kb-cron"
+---
+
+== New translation teleparallel gauge theory of gravity ==
+Independently in 1967, Hayashi and Nakano revived Einstein's idea, and Pellegrini and Plebanski started to formulate the gauge theory of the spacetime translation group. Hayashi pointed out the connection between the gauge theory of the spacetime translation group and absolute parallelism. The first fiber bundle formulation was provided by Cho. This model was later studied by Schweizer et al., Nitsch and Hehl, Meyer; more recent advances can be found in Aldrovandi and Pereira, Gronwald, Itin, Maluf and da Rocha Neto, Münch, Obukhov and Pereira, and Schucking and Surowitz.
+Nowadays, teleparallelism is studied purely as a theory of gravity without trying to unify it with electromagnetism. In this theory, the gravitational field turns out to be fully represented by the translational gauge potential Baμ, as it should be for a gauge theory for the translation group.
+If this choice is made, then there is no longer any Lorentz gauge symmetry because the internal Minkowski space fiber—over each point of the spacetime manifold—belongs to a fiber bundle with the Abelian group R4 as structure group. However, a translational gauge symmetry may be introduced thus: Instead of seeing tetrads as fundamental, we introduce a fundamental R4 translational gauge symmetry instead (which acts upon the internal Minkowski space fibers affinely so that this fiber is once again made local) with a connection B and a "coordinate field" x taking on values in the Minkowski space fiber.
+More precisely, let π : M → M be the Minkowski fiber bundle over the spacetime manifold M. For each point p ∈ M, the fiber Mp is an affine space. In a fiber chart (V, ψ), coordinates are usually denoted by ψ = (xμ, xa), where xμ are coordinates on spacetime manifold M, and xa are coordinates in the fiber Mp.
+Using the abstract index notation, let a, b, c,… refer to Mp and μ, ν,… refer to the tangent bundle TM. In any particular gauge, the value of xa at the point p is given by the section
+
+  
+    
+      
+        
+          x
+          
+            μ
+          
+        
+        →
+        
+          (
+          
+            
+              x
+              
+                μ
+              
+            
+            ,
+            
+              x
+              
+                a
+              
+            
+            =
+            
+              ξ
+              
+                a
+              
+            
+            (
+            p
+            )
+          
+          )
+        
+        .
+      
+    
+    {\displaystyle x^{\mu }\to \left(x^{\mu },x^{a}=\xi ^{a}(p)\right).}
+  
+
+The covariant derivative
+
+  
+    
+      
+        
+          D
+          
+            μ
+          
+        
+        
+          ξ
+          
+            a
+          
+        
+        ≡
+        
+          
+            (
+            
+              d
+              
+                ξ
+                
+                  a
+                
+              
+            
+            )
+          
+          
+            μ
+          
+        
+        +
+        
+          
+            
+              B
+              
+                a
+              
+            
+          
+          
+            μ
+          
+        
+        =
+        
+          ∂
+          
+            μ
+          
+        
+        
+          ξ
+          
+            a
+          
+        
+        +
+        
+          
+            
+              B
+              
+                a
+              
+            
+          
+          
+            μ
+          
+        
+      
+    
+    {\displaystyle D_{\mu }\xi ^{a}\equiv \left(d\xi ^{a}\right)_{\mu }+{B^{a}}_{\mu }=\partial _{\mu }\xi ^{a}+{B^{a}}_{\mu }}
+  
+
+is defined with respect to the connection form B, a 1-form assuming values in the Lie algebra of the translational abelian group R4. Here, d is the exterior derivative of the ath component of x, which is a scalar field (so this isn't a pure abstract index notation). Under a gauge transformation by the translation field αa,
+
+  
+    
+      
+        
+          x
+          
+            a
+          
+        
+        →
+        
+          x
+          
+            a
+          
+        
+        +
+        
+          α
+          
+            a
+          
+        
+      
+    
+    {\displaystyle x^{a}\to x^{a}+\alpha ^{a}}
+  
+
+and
+
+  
+    
+      
+        
+          
+            
+              B
+              
+                a
+              
+            
+          
+          
+            μ
+          
+        
+        →
+        
+          
+            
+              B
+              
+                a
+              
+            
+          
+          
+            μ
+          
+        
+        −
+        
+          ∂
+          
+            μ
+          
+        
+        
+          α
+          
+            a
+          
+        
+      
+    
+    {\displaystyle {B^{a}}_{\mu }\to {B^{a}}_{\mu }-\partial _{\mu }\alpha ^{a}}
+  
+
+and so, the covariant derivative of xa = ξa(p) is gauge invariant. This is identified with the translational (co-)tetrad
+
+  
+    
+      
+        
+          
+            
+              h
+              
+                a
+              
+            
+          
+          
+            μ
+          
+        
+        =
+        
+          ∂
+          
+            μ
+          
+        
+        
+          ξ
+          
+            a
+          
+        
+        +
+        
+          
+            
+              B
+              
+                a
+              
+            
+          
+          
+            μ
+          
+        
+      
+    
+    {\displaystyle {h^{a}}_{\mu }=\partial _{\mu }\xi ^{a}+{B^{a}}_{\mu }}
+  
+
+which is a one-form which takes on values in the Lie algebra of the translational Abelian group R4, whence it is gauge invariant. But what does this mean? xa = ξa(p) is a local section of the (pure translational) affine internal bundle M → M, another important structure in addition to the translational gauge field Baμ. Geometrically, this field determines the origin of the affine spaces; it is known as Cartan's radius vector. In the gauge-theoretic framework, the one-form
+
+  
+    
+      
+        
+          h
+          
+            a
+          
+        
+        =
+        
+          
+            
+              h
+              
+                a
+              
+            
+          
+          
+            μ
+          
+        
+        d
+        
+          x
+          
+            μ
+          
+        
+        =
+        
+          (
+          
+            
+              ∂
+              
+                μ
+              
+            
+            
+              ξ
+              
+                a
+              
+            
+            +
+            
+              
+                
+                  B
+                  
+                    a
+                  
+                
+              
+              
+                μ
+              
+            
+          
+          )
+        
+        d
+        
+          x
+          
+            μ
+          
+        
+      
+    
+    {\displaystyle h^{a}={h^{a}}_{\mu }dx^{\mu }=\left(\partial _{\mu }\xi ^{a}+{B^{a}}_{\mu }\right)dx^{\mu }}
+  
+
+arises as the nonlinear translational gauge field with ξa interpreted as the Goldstone field describing the spontaneous breaking of the translational symmetry.
+A crude analogy: Think of Mp as the computer screen and the internal displacement as the position of the mouse pointer. Think of a curved mousepad as spacetime and the position of the mouse as the position. Keeping the orientation of the mouse fixed, if we move the mouse about the curved mousepad, the position of the mouse pointer (internal displacement) also changes and this change is path dependent; i.e., it does not depend only upon the initial and final position of the mouse. The change in the internal displacement as we move the mouse about a closed path on the mousepad is the torsion.
+Another crude analogy: Think of a crystal with line defects (edge dislocations and screw dislocations but not disclinations). The parallel transport of a point of M along a path is given by counting the number of (up/down, forward/backwards and left/right) crystal bonds transversed. The Burgers vector corresponds to the torsion. Disinclinations correspond to curvature, which is why they are neglected.
+The torsion—that is, the translational field strength of Teleparallel Gravity (or the translational "curvature")—
+
+  
+    
+      
+        
+          
+            
+              T
+              
+                a
+              
+            
+          
+          
+            μ
+            ν
+          
+        
+        ≡
+        
+          
+            (
+            
+              D
+              
+                B
+                
+                  a
+                
+              
+            
+            )
+          
+          
+            μ
+            ν
+          
+        
+        =
+        
+          D
+          
+            μ
+          
+        
+        
+          
+            
+              B
+              
+                a
+              
+            
+          
+          
+            ν
+          
+        
+        −
+        
+          D
+          
+            ν
+          
+        
+        
+          
+            
+              B
+              
+                a
+              
+            
+          
+          
+            μ
+          
+        
+        ,
+      
+    
+    {\displaystyle {T^{a}}_{\mu \nu }\equiv \left(DB^{a}\right)_{\mu \nu }=D_{\mu }{B^{a}}_{\nu }-D_{\nu }{B^{a}}_{\mu },}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Teleparallelism-2.md b/data/en.wikipedia.org/wiki/Teleparallelism-2.md
new file mode 100644
index 000000000..722845c57
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+++ b/data/en.wikipedia.org/wiki/Teleparallelism-2.md
@@ -0,0 +1,36 @@
+---
+title: "Teleparallelism"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Teleparallelism"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:34.335957+00:00"
+instance: "kb-cron"
+---
+
+is gauge invariant.
+We can always choose the gauge where xa is zero everywhere, although Mp is an affine space and also a fiber; thus the origin must be defined on a point-by-point basis, which can be done arbitrarily. This leads us back to the theory where the tetrad is fundamental.
+Teleparallelism refers to any theory of gravitation based upon this framework. There is a particular choice of the action that makes it exactly equivalent to general relativity, but there are also other choices of the action which are not equivalent to general relativity. In some of these theories, there is no equivalence between inertial and gravitational masses.
+Unlike in general relativity, gravity is due not to the curvature of spacetime but to the torsion thereof.
+
+== Non-gravitational contexts ==
+There exists a close analogy of geometry of spacetime with the structure of defects in crystals. Dislocations are represented by torsion, disclinations by curvature. These defects are not independent of each other. A dislocation is equivalent to a disclination-antidisclination pair, a disclination is equivalent to a string of dislocations. This is the basic reason why Einstein's theory based purely on curvature can be rewritten as a teleparallel theory based only on torsion. There exists, moreover, infinitely many ways of rewriting Einstein's theory, depending on how much of the curvature one wants to reexpress in terms of torsion, the teleparallel theory being merely one specific version of these.
+A further application of teleparallelism occurs in quantum field theory, namely, two-dimensional non-linear sigma models with target space on simple geometric manifolds, whose renormalization behavior is controlled by a Ricci flow, which includes torsion. This torsion modifies the Ricci tensor and hence leads to an infrared fixed point for the coupling, on account of teleparallelism ("geometrostasis").
+
+== See also ==
+Classical theories of gravitation
+Gauge gravitation theory
+Geometrodynamics
+Kaluza–Klein theory
+
+== References ==
+
+== Further reading ==
+Aldrovandi, R.; Pereira, J. G. (2012). Teleparallel Gravity: An Introduction. Springer: Dordrecht. ISBN 978-94-007-5142-2.{{cite book}}:  CS1 maint: publisher location (link)
+Bishop, R. L.; Goldberg, S. I. (1968). Tensor Analysis on Manifolds (First Dover 1980 ed.). Macmillan. ISBN 978-0-486-64039-6.
+Weitzenböck, R. (1923). Invariantentheorie. Groningen: Noordhoff.{{cite book}}:  CS1 maint: publisher location (link)
+
+== External links ==
+Selected Papers on Teleparallelism, translated and edited by D. H. Delphenich
+Teleparallel gravity at the nLab
+Teleparallel Structures and Gravity Theories by Luca Bombelli
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Teylers_Instrument_Room-0.md b/data/en.wikipedia.org/wiki/Teylers_Instrument_Room-0.md
new file mode 100644
index 000000000..3ec218e82
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Teylers_Instrument_Room-0.md
@@ -0,0 +1,32 @@
+---
+title: "Teylers Instrument Room"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Teylers_Instrument_Room"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:35.585978+00:00"
+instance: "kb-cron"
+---
+
+The Instrument Room is a room in Teylers Museum which houses a part of the museum's Cabinet of Physics: a collection of scientific instruments from the 18th and 19th centuries. The instruments in the collection were used for research as well as for educational public demonstrations. Most of them are demonstration models that illustrate various aspects of electricity, acoustics, light, magnetism, thermodynamics, and weights and measures. The rest are high-quality precision instruments that were used for research.
+
+
+== History of the room ==
+Originally all of the museum's collections were housed in the Oval Room from 1784. The electricity instrument demonstrations tended to make a lot of noise and distracted the readers of the books in the gallery, and after the mineralogical cabinet was built for the center of the room, demonstrations there became more difficult and a new demonstration and lecture room was built on the north side (today the Print room). This new room shared its purpose with the art gallery but as the number of instrument cabinets increased, was felt to be too dark, leading to the creation of a separate painting gallery in 1838. The current instrument room was built as part of an 1880-1885 extension of the museum, designed to have daylight from both sides for better viewing of the experiments. It is located between the Fossil Room II and the Oval Room.
+
+
+== History of the collection ==
+Though Pieter Teyler van der Hulst was a patron of the arts and sciences, he was not a member of the Natuur- en Sterrekundig Collegie, a science society in Haarlem that was founded in the Patientiestraat in 1775. The popularity of the study of science and the ideals of the Dutch enlightenment were such that after his death however, when Martin van Marum joined the young Teylers Stichting, this proved quickly to become the emphasis of the society in the years to come. Teylers Museum was not alone. The society Oefening door Wetenschappen was also started in Haarlem in 1798 and lasted until 1892. It was Haarlem's reputation for the study of science that attracted Van Marum to settle there. When he became director of the collection of the Koninklijke Hollandsche Maatschappij der Wetenschappen in 1778 and later, also of Teylers in 1784, he used the funds of both institutions to purchase expensive instruments and even whole scientific collections from personal estates. He started before he even worked there with a proposal to build his large elektriseermachine that forms the center attraction of the instrument room. Van Marum was not only the curator of the cabinet, he gave public laboratorium lectures from 1777 to 1803 on physics and geology. The number of demonstration models in the collection is directly related to his and his successors' need for demonstration models in Teylers lectures. Van Marum collected 350 demonstration models and set a precedent as lecturer-demonstrator for curators who came after him. Today there are over a thousand in the collection altogether.
+
+
+== Instruments on display ==
+The centerpiece of the Instrument Room is the large electrostatic generator built by John Cuthbertson in 1784. This apparatus is the largest flat-plate electrostatic generator of the world and the oldest piece in the room itself, which is filled mostly with items from the 19th century. Surrounding this centerpiece are 10 numbered cabinets filled with instruments accompanied by numbered cards that can be cross-referenced to a guide located in the room.
+
+
+== References ==
+Teyler 1778-1978:studies en bijdragen over Teylers Stichting naar aanleiding van het tweede eeuwfeest, by J. H. van Borssum Buisman, H. Enno van Gelder, Pieter Teyler van der Hulst, Schuyt, 1978, ISBN 90-6097-091-8
+
+
+== External links ==
+
+The Cabinet of Physics of the Teylers Museum, a thematic website describing the Teylers Museum's Physical Cabinet collection in 3D.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/The_Internet_Pilot_to_Physics-0.md b/data/en.wikipedia.org/wiki/The_Internet_Pilot_to_Physics-0.md
index 59d52169f..062168b88 100644
--- a/data/en.wikipedia.org/wiki/The_Internet_Pilot_to_Physics-0.md
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@@ -4,7 +4,7 @@ chunk: 1/1
 source: "https://en.wikipedia.org/wiki/The_Internet_Pilot_to_Physics"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T06:35:30.495366+00:00"
+date_saved: "2026-05-05T16:29:29.233425+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_chemical_element_discoveries-0.md b/data/en.wikipedia.org/wiki/Timeline_of_chemical_element_discoveries-0.md
index bf8f5d1d9..172812ad3 100644
--- a/data/en.wikipedia.org/wiki/Timeline_of_chemical_element_discoveries-0.md
+++ b/data/en.wikipedia.org/wiki/Timeline_of_chemical_element_discoveries-0.md
@@ -4,7 +4,7 @@ chunk: 1/1
 source: "https://en.wikipedia.org/wiki/Timeline_of_chemical_element_discoveries"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T16:16:37.371965+00:00"
+date_saved: "2026-05-05T16:30:36.884170+00:00"
 instance: "kb-cron"
 ---
 
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_computational_physics-0.md b/data/en.wikipedia.org/wiki/Timeline_of_computational_physics-0.md
new file mode 100644
index 000000000..34df100b9
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Timeline_of_computational_physics-0.md
@@ -0,0 +1,71 @@
+---
+title: "Timeline of computational physics"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Timeline_of_computational_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:38.161295+00:00"
+instance: "kb-cron"
+---
+
+The following timeline starts with the invention of the modern computer in the late interwar period.
+
+
+== 1930s ==
+John Vincent Atanasoff  and Clifford Berry create the first electronic non-programmable, digital computing device, the Atanasoff–Berry Computer, that lasted from 1937 to 1942.
+
+
+== 1940s ==
+Nuclear bomb and ballistics simulations at Los Alamos National Laboratory and Ballistic Research Laboratory (BRL), respectively.
+Monte Carlo simulation (voted one of the top 10 algorithms of the 20th century by Jack Dongarra and Francis Sullivan in the 2000 issue of Computing in Science and Engineering) is invented at  Los Alamos National Laboratory by John von Neumann, Stanislaw Ulam and Nicholas Metropolis.
+First hydrodynamic simulations performed at Los Alamos National Laboratory.
+Ulam and von Neumann introduce the notion of cellular automata.
+
+
+== 1950s ==
+Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm. Also, important earlier independent work by Berni Alder and Stan Frankel.
+Enrico Fermi, Ulam and John Pasta with help from Mary Tsingou, discover the Fermi–Pasta–Ulam-Tsingou problem.
+Research initiated into percolation theory.
+Molecular dynamics is formulated by Alder and Tom E. Wainwright.
+
+
+== 1960s ==
+Using computational investigations of the 3-body problem, Michael Minovitch formulates the gravity assist method.
+Glauber dynamics is invented for the Ising model by Roy J. Glauber.
+Edward Lorenz discovers the butterfly effect on a computer, attracting interest in chaos theory.
+Molecular dynamics is independently invented by Aneesur Rahman.
+Walter Kohn instigates the development of density functional theory (with L.J. Sham and Pierre Hohenberg), for which he shared the Nobel Chemistry Prize (1998).
+Martin Kruskal and Norman Zabusky follow up the Fermi–Pasta–Ulam problem with further numerical experiments, and coin the term "soliton".
+Kawasaki dynamics is invented for the Ising model.
+Loup Verlet (re)discovers a numerical integration algorithm, (first used in 1791 by Jean Baptiste Delambre, by P. H. Cowell and A. C. C. Crommelin in 1909, and by Carl Fredrik Störmer in 1907, hence the alternative names Störmer's method or the Verlet-Störmer method) for dynamics, and the Verlet list.
+
+
+== 1970s ==
+Computer algebra replicates the work of Boris Delaunay in Lunar theory.
+Martinus Veltman's calculations at CERN lead him and Gerard 't Hooft to valuable insights into renormalizability of electroweak theory. The computation has been cited as a key reason for the award of the Nobel Physics Prize that has been given to both.
+Jean Hardy, Yves Pomeau and Olivier de Pazzis introduce the first lattice gas model, abbreviated as the HPP model after its authors. These later evolved into lattice Boltzmann models.
+Kenneth G. Wilson shows that continuum quantum chromodynamics (QCD) is recovered for an infinitely large lattice with its sites infinitesimally close to one another, thereby beginning lattice QCD.
+
+
+== 1980s ==
+Italian physicists Roberto Car and Michele Parrinello invent the Car–Parrinello method.
+Swendsen–Wang algorithm is invented in the field of Monte Carlo simulations.
+Fast multipole method is invented by Vladimir Rokhlin and Leslie Greengard (voted one of the top 10 algorithms of the 20th century).
+Ullli Wolff invents the Wolff algorithm for statistical physics and Monte Carlo simulation.
+
+
+== See also ==
+Timeline of scientific computing
+Computational physics
+Important publications in computational physics
+
+
+== Notes ==
+
+
+== References ==
+
+
+== External links ==
+The Monte Carlo Method: Classic Papers
+Monte Carlo Landmark Papers
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-0.md b/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-0.md
new file mode 100644
index 000000000..f1c09423e
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-0.md
@@ -0,0 +1,43 @@
+---
+title: "Timeline of condensed matter physics"
+chunk: 1/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:39.481309+00:00"
+instance: "kb-cron"
+---
+
+This article lists the main historical events in the history of condensed matter physics. This branch of physics focuses on understanding and studying the physical properties and transitions between phases of matter. Condensed matter refers to materials where particles (atoms, molecules, or ions) are closely packed together or under interaction, such as solids and liquids. This field explores a wide range of phenomena, including the electronic, magnetic, thermal, and mechanical properties of matter.
+This timeline includes developments in subfields of condensed matter physics such as theoretical crystallography, solid-state physics, soft matter physics, mesoscopic physics, material physics, low-temperature physics, microscopic theories of magnetism in matter and optical properties of matter and metamaterials.
+Even if material properties were modeled before 1900, condensed matter topics were considered as part of physics since the development of quantum mechanics and microscopic theories of matter. According to Philip W. Anderson, the term "condensed matter" appeared about 1965.
+For history of fluid mechanics, see timeline of fluid and continuum mechanics.
+
+== Before quantum mechanics ==
+
+=== Prehistory ===
+28,000–12,000 BP – Upper Paleolithic: earliest evidence of ceramic objects made for ritual purposes.
+10,000–3300 BC – Neolithic: development of pottery, as well as early evidence of glass production and metalworking.
+3300–1200 BC – Bronze Age: development of metallurgy, with copper and tin being combined to create bronze.
+1200–300 BC – Iron Age: development of ferrous metallurgy, allowing iron and steel to largely replace bronze.
+
+=== Antiquity ===
+
+8th century BC: first writings on the magnetic properties of lodestone in Ancient Greece.
+6th century BC – Thales of Miletus observes that rubbing fur on various substances, such as amber, would cause an attraction between the two, which is now known to be caused by static electricity.
+5th century BC – Leucippus and Democritus postulate the philosophy of atomism.
+4th century BC – Aristotle describes the composition of matter in terms of the four classical elements, founding Aristotelian physics.
+1st century AD – Pliny the Elder in his Natural History records the story of Magnes the shepherd who discovered the magnetic properties of some iron stones.
+160 AD – Claudius Ptolemy writes his book Optics on reflection and refraction of light, and tabulated angles of refraction for several media. He found a refraction law valid for small angles.
+
+=== Classical theories before the 19th century ===
+1611 – Johannes Kepler first states the Kepler conjecture about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements.
+1621 – Willebrord Snellius reformulates the laws of refraction and reflection of light into Snell's law.
+1660 – Robert Hooke postulates the simplest equation of linear elasticity known as Hooke's law.
+1687 – Isaac Newton postulates the Newton's laws of motion.
+1701 – Newton studies heat, leading to Newton's law of cooling.
+1729 – Scientist Stephen Gray discovers the electrical conduction of metals.
+1778 – Diamagnetism was first discovered when Anton Brugmans observed in 1778 that bismuth was repelled by magnetic fields.
+1781 – René Just Haüy (often termed the "Father of Modern Crystallography") discovers that crystals always cleave along crystallographic planes. Based on this observation, and the fact that the inter-facial angles in each crystal species always have the same value, Haüy concluded that crystals must be periodic and composed of regularly arranged rows of tiny polyhedra (molécules intégrantes). This theory explained why all crystal planes are related by small rational numbers (the law of rational indices).
+
+=== 19th century ===
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-1.md b/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-1.md
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-1.md
@@ -0,0 +1,49 @@
+---
+title: "Timeline of condensed matter physics"
+chunk: 2/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:39.481309+00:00"
+instance: "kb-cron"
+---
+
+1800 – The Voltaic pile, the first electric battery is developed by Alessandro Volta.
+1803–1808 – John Dalton reconsiders the atomic theory of matter in order to understand chemistry.
+1816 – David Brewster discovers stress birefringence in diamond.
+1819 – Experimentally Pierre Louis Dulong and Alexis Thérèse Petit find that the specific heat capacity of solids was close to a constant value given by Dulong–Petit law.
+1821 – Thomas Johann Seebeck discovers the thermoelectric effect, related by the Seebeck coefficient.
+1822 – Joseph Fourier proposes Fourier's law of thermal conduction and the heat equation.
+1826 – Moritz Ludwig Frankenheim derives the 32 crystal classes by using the crystallographic restriction, consistent with Haüy's laws, that only 2, 3, 4 and 6-fold rotational axes are permitted.
+1827 – Georg Ohm, publishes the proportional relation between electric current and voltage in metals, known as Ohm's law.
+1834 – Jean-Charles Peltier discovers the Peltier effect: heating by an electric current at the junction of two different metals.
+1839 – William Hallowes Miller invents zonal relations by projecting the faces of a crystal upon the surface of a circumscribed sphere. Miller indices are defined which form a notation system in crystallography for planes in crystal (Bravais) lattices.
+1840 – James Prescott Joule formulates the equation for Joule heating quantifying the amount of heat produced in a circuit as proportional to the product of the time duration, the resistance, and the square of the current passing through it.
+1845 – Michael Faraday studies the interaction of light and magnetic fields with matter (Faraday rotation).
+1848 – Louis Pasteur discovers that sodium ammonium tartrate can crystallize in left- and right-handed forms and showed that the two forms can rotate polarized light in opposite directions. This was the first demonstration of molecular chirality, and also the first explanation of isomerism.
+1850 – Auguste Bravais develops the concept of Bravais lattices to describe periodicity in crystals. He derives the 14 space lattices.
+1853 – Discovery of Wiedemann–Franz law relating thermal and electrical conductivities, by Gustav Wiedemann and Rudolph Franz.
+1854 – Lord Kelvin discovers the thermoelectric Thomson effect.
+1859 – Gustav Kirchhoff introduces the concept of a blackbody and proves that its emission spectrum depends only on its temperature.
+1861–1865 – James Clerk Maxwell summarizes the fundamental equations of electromagnetism into an early version of Maxwell's equations and relates electromagnetism to light in his publications On Physical Lines of Force and A Dynamical Theory of the Electromagnetic Field.
+1867 – Dmitry Chernov establishes the critical temperatures of steel.
+1872 – The Boltzmann transport equation, describing the statistical behaviour of a thermodynamic system not in a state of equilibrium, is devised by Ludwig Boltzmann.
+1872 – Ludvig Lorenz finds the Lorenz number, the constant of the Wiedemann–Franz law.
+1874 – Karl Ferdinand Braun discovered current rectification using a point-contact metal–semiconductor junction.
+1875 – John Kerr discovers the double refraction of solid and liquids, now known as the Kerr effect.
+1876 – Josiah Willard Gibbs introduces the concept of phase transition.
+1879 – Edwin Hall discovers the Hall effect.
+1879 – Leonhard Sohncke lists the 65 crystallographic point systems using rotations and reflections in addition to translations.
+1880 – The first demonstration of the direct piezoelectric effect by the brothers Pierre Curie and Jacques Curie.
+1883 – Thomas Edison discovers thermionic emission or the Edison effect.
+1887 – Floris Osmond names the phases of steel.
+1887 – Heinrich Hertz discovers the photoelectric effect.
+1888–1889 – Crystalline optical properties of liquid crystals and their ability to flow are first described by Friedrich Reinitzer and confirmed by Otto Lehmann.
+1891 – Derivation of the 230 space groups (by adding mirror-image symmetry to Sohncke's work) by a collaborative effort of Evgraf Fedorov and Arthur Schoenflies.
+1895 – Wilhelm Conrad Röntgen discovers X-rays in experiments with electron beams in plasma.
+1895 – Hendrik Lorentz derives the Lorentz force for charged particles in electric and magnetic fields.
+1895 – Pierre Curie discovers empirically that the magnetic susceptibility of many materials is inversely proportional to temperature according to Curie's law. He also found that permanent magnetism was lost after a certain Curie temperature.
+1896–1897 – Pieter Zeeman first observes the Zeeman splitting effect by applying a magnetic field to light sources.
+1897 – J. J. Thomson's experimentation with cathode rays led him to suggest a fundamental unit more than a 1000 times smaller than an atom, based on the high charge-to-mass ratio. He called the particle a "corpuscle", but later scientists preferred the term electron.
+
+== 20th century ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-2.md b/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-2.md
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--- /dev/null
+++ b/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-2.md
@@ -0,0 +1,27 @@
+---
+title: "Timeline of condensed matter physics"
+chunk: 3/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:39.481309+00:00"
+instance: "kb-cron"
+---
+
+=== Early 1900s ===
+1900 – Max Planck uses for the first time quantum theory to explain black-body radiation. 1900 – Paul Drude proposes the Drude model to explain thermal and electric properties of metals. 1901 – Thermionic emission is first theoretically modeled by Owen Willans Richardson
+1905 – Albert Einstein's Annus mirabilis papers postulating special relativity, the theory for Brownian motion and explaining the photoelectric effect using quantum mechanics. 1905 – Paul Langevin derives the classical theory for diamagnetism. 1907:
+Einstein solid model predicts the deviations for the specific heat of solids from Dulong–Petit law. The first theory describing crystallographic defects is developed by Vito Volterra. Pierre Weiss introduces the magnetic domain theory of ferromagnetism. 1909 – Lorentz develops the classical Lorentz oscillator model to describe the optical response of materials. 1911:
+Heike Kamerlingh Onnes and Gilles Holst discover superconductivity in mercury. The electron hole concept is pioneered by Karl Baedeker to understand semiconductors. 1912:
+Max von Laue discovers diffraction of X-rays by crystals. Peter Debye develops a model for the specific heat of solids in terms of phonons, known as Debye model. Geertruida Lorentz, applies Einstein's Brownian motion equations to noise in electrical circuits. 1913 – William Henry Bragg and Lawrence Bragg use X-rays to analyze crystals. 1917 – Weiss and Auguste Piccard first observe the magnetocaloric effect. 1919 – Walter H. Schottky introduces the concept of shot noise while studying vacuum tubes. 1919 – Hendrika Johanna van Leeuwen rediscovers the Bohr–Van Leeuwen theorem, showing that magnetic properties of matter are due to quantum mechanics. 1920:
+Ferroelectricity gets discovered in Rochelle salt by Joseph Valasek. Hermann Staudinger, suggest that small molecules can be link together through covalent bonds to form polymer. Wilhelm Lenz describes for the first time the Ising model as a model for magnetism in matter. 1923 – Pierre Auger discovers the Auger effect, where filling the inner-shell vacancy of an atom is accompanied by the emission of an electron from the same atom. 1923 – Louis de Broglie extends wave–particle duality to particles, postulating that electrons in motion are associated with waves. He predicts that the wavelengths are given by the Planck constant h divided by the momentum of the mv = p of the electron: λ = h / mv = h / p. 1923–1927 Electron wave diffraction is demonstrated experimentally independently by Davisson–Germer experiments and the experiments by George Paget Thomson and Alexander Reid. 1924 – Satyendra Nath Bose explains Planck's law using a new statistical law that governs bosons, and Einstein generalizes it to predict Bose–Einstein condensate. The theory becomes known as Bose–Einstein statistics. 1924 – Wolfgang Pauli outlines the Pauli exclusion principle which states that no two identical fermions may occupy the same quantum state simultaneously, a fact that explains many features of the periodic table. 1925 – Werner Heisenberg, Max Born, and Pascual Jordan develop the matrix mechanics formulation of quantum mechanics. 1925 – Ernst Ising finds the analytical solution to the 1D Ising model. 1926:
+Enrico Fermi discovers the spin-statistics theorem connection. Paul Dirac introduces Fermi–Dirac statistics. Erwin Schrödinger uses de Broglie's electron wave postulate (1924) to develop a Schrödinger equation; also introduces the Hamiltonian operator in quantum mechanics. Johnson–Nyquist noise is first measured by John B. Johnson at Bell Labs. He described his findings to Harry Nyquist, also at Bell Labs, who was able to explain the results. 1927:
+Max Born and J. Robert Oppenheimer introduce the Born–Oppenheimer approximation, which allows the quick approximation of the energy and wavefunctions of smaller molecules. Pauli models the paramagnetic contribution of itinerant electrons due to spins (Pauli paramagnetism). Walter Heitler and Fritz London introduce the concepts of valence bond theory and apply it to the hydrogen molecule. Llewellyn Thomas and Fermi develop the Thomas–Fermi model for a gas in a box. Chandrasekhara Venkata Raman studies optical photon scattering by electrons, now known as Raman spectroscopy. Walter Heitler uses Schrödinger's wave equation to show how two hydrogen atom wavefunctions join, with plus, minus, and exchange terms, to form a covalent bond. Robert S. Mulliken works, in coordination with Hund, to develop a molecular orbital theory where electrons are assigned to states that extend over an entire molecule and, in 1932, introduces many new molecular orbital terminologies, such as σ bond, π bond, and δ bond. Eugene Wigner relates degeneracies of quantum states to irreducible representations of symmetry groups. Arnold Sommerfeld, extends Drude's model using Fermi–Dirac statistics leading to the free electron model. Douglas Hartree introduced the Hartree equation for atoms. 1928–1930 – John Hasbrouck Van Vleck formalizes the quantum theory of magnetism and formulates Van Vleck paramagnetism. 1928 – Linus Pauling outlines the quantum nature of the chemical bonds. 1928 – Friedrich Hund and Robert S. Mulliken introduce the concept of molecular orbitals. 1929:
+Felix Bloch demonstrates Bloch's theorem. John Lennard-Jones introduces the linear combination of atomic orbitals (LCAO) approximation for the calculation of molecular orbitals. Peierls coins the term Umklapp scattering. First observation of plasma oscillations by Irving Langmuir and Lewi Tonks. Egil Hylleraas finds an approximate solution to the helium atom. 1930:
+Léon Brillouin develops the concept of Brillouin zone. Bloch introduces the theory of spin waves and magnons,
+Erich Hückel introduces the Hückel molecular orbital method, which expands on orbital theory to determine the energies of orbitals of pi electrons in conjugated hydrocarbon systems. Fritz London explains van der Waals forces as due to the interacting fluctuating dipole moments between molecules. Landau formulates the concept of Landau quantization, explaining the diamagnetic contribution of a free electron gas (Landau diamagnetism) and predicting the De Haas–Van Alphen effect. This effect was measured a few months after by Wander Johannes de Haas and his student Pieter M. van Alphen. 1931:
+Onsager reciprocal relations are first proposed by Lars Onsager
+Ralph Kronig and William Penney solve the infinite periodic array of rectangular potential barriers (Kronig–Penney model). Alan Herries Wilson develops the theory of electronic band structure to describe the conduction properties of solids. He also distinguished between intrinsic and extrinsic semiconductors. The concept of excitons is proposed by Yakov Frenkel. John Lennard-Jones proposes the Lennard-Jones interatomic potential. Ernst Ruska creates the first electron microscope. 1932 – Werner Heisenberg applies perturbation theory to the two-electron problem to show how resonance arising from electron exchange can explain exchange forces. 1933:
+Walther Meissner and Robert Ochsenfeld discover the Meissner effect by measuring the magnetic field distribution outside superconducting tin and lead samples. Landau models antiferromagnetism for the first time. Landau introduces the concept of electron-phonon quasiparticle, termed polaron. Erich Mollwo, working with Robert Wichard Pohl concludes that color in alkali metal halides is due to the existence of F-centers (color centers). 1935:
+J.N. Rjabinin and Lev Shubnikov experimentally discover type-II superconductivity. The London equations get developed by brothers Fritz and Heinz London. Hartree introduces Hartree–Fock method. 1937:
+Landau introduces Landau theory of phase transitions. Jan Hendrik de Boer and Evert Verwey, and independently Peierls, and Nevill Francis Mott introduce the problem of the metal–insulator transition. Other developments include the discovery of the Verwey transition and the theory of the Mott insulator. Wannier functions are introduced by Gregory Wannier. Conyers Herring theorizes the possibility of Weyl semimetals.
\ No newline at end of file
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+---
+title: "Timeline of condensed matter physics"
+chunk: 4/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:39.481309+00:00"
+instance: "kb-cron"
+---
+
+1938 – Superfluidity is discovered by the team of Pyotr Kapitsa. 1941 – Landau introduces the concept of second sound. 1944 – Lars Onsager find an analytical solution for the 2D Ising model. 1947 – The first transistor is developed by William Shockley, John Bardeen and Walter Houser Brattain. 1947 – The theory of single layer graphite (graphene) is first published by P. R. Wallace. 1948 – Louis Néel discovers ferrimagnetism
+1945–1946 – First neutron diffraction experiments are carried out by Ernest O. Wollan and independently by Clifford Shull. 1947–1948 – Hendrik Casimir and Dirk Polder at Philips Research Labs propose the existence of Casimir–Polder effect between two polarizable atoms and between such an atom and a conducting plate. After a conversation with Niels Bohr, who suggested it had something to do with zero-point energy. 1947–1948 – The formal development of quantum field theory by Richard Feynman, Julian Schwinger, Shin'ichirō Tomonaga and Freeman Dyson. 1949 – Werner Ehrenberg and Raymond E. Siday first predict Aharonov–Bohm effect.
\ No newline at end of file
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+---
+title: "Timeline of condensed matter physics"
+chunk: 5/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:39.481309+00:00"
+instance: "kb-cron"
+---
+
+=== Second half of the 20th century ===
+
+1950 – The Ginzburg–Landau theory phenomenological theory of superconductors is formulated by Vitaly Ginzburg and Landau.
+1950 – Tomonaga introduces the Luttinger liquid model for electrons in 1D.
+1952 – The plasmon (quantum of plasma oscillation in metals) is proposed by David Pines and David Bohm.
+1952 – Friedel oscillations are first described by Jacques Friedel.
+1953 – The occurrence of Van Hove singularities is first analyzed by Léon Van Hove for the case of phonon densities of states.
+1953 – Charles H. Townes, James P. Gordon, and Herbert Zeiger demonstrate the first maser.
+1954:
+Lindhard theory for electric-field screening is published by Jens Lindhard.
+The tight-binding method is conceived by John Clarke Slater and George Fred Koster.
+Bernd T. Matthias comes up with the empirical Matthias rules for finding superconductors.
+Herbert Fröhlich introduces the Frölich Hamiltonian for polarons.
+Publication of Dynamical Theory of Crystal Lattices by Max Born and Huang Kun, introducing Born–Huang approximation and Cauchy–Born rule.
+1954–1957 – Malvin Ruderman and Charles Kittel develop the theory of indirect exchange interaction, later expanded by Tadao Kasuya and Kei Yosida into the RKKY theory.
+1955 – Dresselhaus spin–orbit coupling is discovered by Gene Dresselhaus.
+1955 – Takeo Matsubara introduces his many-body Green's function based on Matsubara frequency formalism.
+1956 – Theory of interacting electrons in solids, Fermi liquid theory is developed by Landau
+1957:
+BCS theory by Bardeen, Leon Cooper and John Robert Schrieffer.
+Rolf Landauer, who first suggested a version the Landauer formula.
+Ryogo Kubo who first presents the Kubo formula, to express the linear response of an observable quantity due to a time-dependent perturbation using quantum mechanics.
+Jack Kilby proposes the first integrated circuit.
+1957–1959 – Kubo, Paul C. Martin and Schwinger introduced the KMS condition used it in 1959 to define thermodynamic Green's functions.
+1958:
+Philip W. Anderson starts developing the theory of metal-insulator transitions and Anderson localization.
+John Hopfield coins the polariton in theory of Hopfield dielectric.
+John Clarke, Michel Devoret and John M. Martinis demonstrate macroscopic quantum tunneling and energy quantization in a Josephson junction.
+1958–1960 – The first laser is built by Theodore Maiman at Hughes Aircraft Company, based on a patent from Townes and Arthur Leonard Schawlow.
+1959 – Rashba spin-orbit coupling is discovered by Emmanuel Rashba and Valentin I. Sheka.
+1961–1964 – Schwinger, O. V. Konstantinov and Vladimir I. Perel, Leo Kadanoff and Gordon Baym, and Leonid Keldysh independently develop Keldysh formalism.
+1962:
+Jeffrey Goldstone, Yoichiro Nambu, Abdus Salam, and Steven Weinberg develop what is now known as Goldstone's Theorem: if there is a continuous symmetry transformation under which the Lagrangian is invariant, then either the vacuum state is also invariant under the transformation, or there must be spinless particles of zero mass, thereafter called Nambu-Goldstone bosons.
+Philip W. Anderson proposes a spontaneous symmetry breaking mechanism (later called Higgs mechanism) for superconductors.
+Josephson effect of electron tunneling in superconductors is predicted by Brian Josephson.
+The Little–Parks effect is discovered by William A. Little and Ronald D. Parks.
+1963 – John Hubbard, Martin Gutzwiller and Junjiro Kanamori each independently propose the Hubbard model.
+1964 – Jun Kondō models the resistance minimum in metals leading to the Kondo model and the prediction of the Kondo effect. The development of the density functional theory starts with the theorems of Walter Kohn and Pierre Hohenberg.
+1966–1967: Mermin–Wagner theorem is proved by N. David Mermin, Herbert Wagner and independently by Pierre Hohenberg.
+1966–1968 – Zhores Alferov and independently Herbert Kroemer created the first lasers based on heterostructures.
+1967 – Volker Heine coins the term ''condensed matter''.
+1967 – Negative-index materials are first described theoretically by Victor Veselago.
+1970 – French scientist Madeleine Veyssié, coins the term soft matter (French: matière molle).
+1971:
+The spin Hall effect is predicted by Mikhail I. Dyakonov and Vladimir I. Perel.
+Pierre-Gilles de Gennes introduces the reptation model for polymer physics.
+Polder and Michael Van Hove derive the theory for near-field radiative heat transfer between arbitrary non-magnetic media.
+1971–75 – Michael Fisher, Kenneth G. Wilson, and Leo Kadanoff come up with the renormalization group.
+1972 – David Lee, Douglas Osheroff and Robert Coleman Richardson discovered two phase transitions of helium-3 along the melting curve, which were soon realized to be the two superfluid phases.
+1972 – The concept of Berezinskii–Kosterlitz–Thouless phase transition in the XY model is developed by Vadim Berezinskii, J. Michael Kosterlitz and David J. Thouless.
+1973 – Peter Mansfield formulates the physical theory of nuclear magnetic resonance imaging (NMRI)
+1979:
+Giorgio Parisi finds a solution to Sherrington–Kirkpatrick model for spin glasses.
+Su–Schrieffer–Heeger model is devised by Wu-Pei Su, John Robert Schrieffer, and Alan J. Heeger to describe the increase of electrical conductivity of polyacetylene polymer chain when doped.
+Alexey Ekimov creates the first quantum dots and their quantum size effects.
+1980 – The integer quantum Hall effect is discovered by Klaus von Klitzing
+1980 – Richard Feynman proposes quantum computing.
+1981 – The scanning tunneling microscope (STM), an instrument for imaging surfaces at the atomic level, was developed by Gerd Binnig and Heinrich Rohrer.
+1982 – The fractional quantum Hall effect is discovered by Robert Laughlin, Horst Störmer, and Daniel Tsui.
+1982 – First observation of a quasicrystal by Dan Shechtman.
+1982 – Frank Wilczek explores the fractional statistics of quasiparticles in two dimensions and coins the term "anyon".
+1985 – Fullerene C60 discovered by Richard Smalley, Robert Curl, and Harry Kroto.
+1985 – Patrick A. Lee and A. Douglas Stone coin the term universal conductance fluctuations.
+1986 – Binnig, Calvin Quate and Christoph Gerber invent the first atomic force microscope (AFM).
+1986 – Discovery of high-temperature superconductivity by K. Alex Müller and Georg Bednorz.
+1987 – Karl Alexander Müller and Georg Bednorz discover high-temperature superconductivity in ceramics.
+1988 – Giant magnetoresistance is discovered by Albert Fert and Peter Grünberg.
+1988 – The conductance quantum are first demonstrated in quantum point contacts.
+1989 – Jainendra K. Jain proposes the concept of composite fermions.
+1991 – Carbon nanotubes are discovered by Sumio Iijima
+1995 – Experimental Bose–Einstein condensate is first demonstrated by Eric Cornell, Carl Wieman and Wolfgang Ketterle.
+1997 – Experiment discovery of rare-earth oxides that behave as spin ice by Steven T. Bramwell, Mark Harris and collaborators, who also coined the term.
+1998 – Thomas Callister Hales proves Kepler's conjecture.
+1998 – Lene Hau produces slow light with a speed of 17 m/s.
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-5.md b/data/en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics-5.md
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@@ -0,0 +1,33 @@
+---
+title: "Timeline of condensed matter physics"
+chunk: 6/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_condensed_matter_physics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:39.481309+00:00"
+instance: "kb-cron"
+---
+
+== 21st century ==
+2000 – The thermal conductance quantum is first measured.
+2000 Alexei Kitaev introduces the theory of the Kitaev chain.
+2001 – Attosecond pulsed sources are developed independently by Pierre Agostini and Ferenc Krausz, leading to the development of attosecond physics.
+2003 – Deborah S. Jin and her collaboration produce the first fermionic condensate.
+2004 – Single-layer graphene was first unambiguously produced and identified by the group of Andre Geim and Konstantin Novoselov.
+2005 –  Charles Kane and Gene Mele propose the quantum spin Hall effect.
+2008-2010 – Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki and Andreas W. W. Ludwig; and well as Alexei Kitaev, develop the periodic table of topological matter.
+2013 – The quantum anomalous Hall effect is first observed by the team of Xue Qikun.
+2012 – Wilczek proposes the idea of time crystals.
+2015 – M. Zahid Hasan's team demonstrates the existence of Weyl semimetals.
+2018 – Twisted graphene superconductivity is demonstrated by Pablo Jarillo-Herrero.
+2024 – Altermagnetism is discovered in experiment.
+
+== See also ==
+History of metamaterials
+Physical crystallography before X-rays
+Timeline of crystallography
+Timeline of materials technology
+Timeline of states of matter and phase transitions
+Timeline of quantum computing and communication
+
+== References ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics-0.md b/data/en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics-0.md
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+++ b/data/en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics-0.md
@@ -0,0 +1,64 @@
+---
+title: "Timeline of fluid and continuum mechanics"
+chunk: 1/4
+source: "https://en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:40.789795+00:00"
+instance: "kb-cron"
+---
+
+This timeline describes the major developments, both experimental and theoretical understanding of fluid mechanics and continuum mechanics. This timeline includes developments in:
+
+Theoretical models of hydrostatics, hydrodynamics and aerodynamics.
+Hydraulics
+Elasticity
+Mechanical waves and acoustics
+Valves and fluidics
+Gas laws
+Turbulence modeling
+Plasticity and rheology
+Quantum fluids like Bose–Einstein condensates and superfluidity
+Microfluidics
+
+== Prehistory and antiquity ==
+
+Before 3000 BC – Civilization starts by settling around rivers, coast and lakes.
+3000 BC – Irrigation techniques develop in Mesopotamia and Ancient Egypt. Indus Valley Civilisation develops city-wide drainage systems and toilet systems. Egyptians develop reed boats.
+2300 BC – Construction of the Nahrawan Canal.
+2000–1500 BC – First dams constructed in India to control water.
+1700 BC – Windmill are used in Babylonia to pump water.
+14th century BC – Water clock are developed in Egypt under the reign of Amenhotep III.  Clepsydra water clock design is developed in ancient Greece.
+6th century BC – Theodorus of Samos invents the water level. Ancient Rome's drainage system is designed during the reign of Tarquinius Priscus. Rome's Cloaca Maxima is constructed by lining a river bed with stone. Tunnel of Eupalinos is constructed in Samos.
+4th century BC – Mencius describes how to measure an elephant using displacement of water. Development of rain gauges in India. Aqua Appia first Roman aqueduct is built in Rome.
+3rd century BC – Archimedes published On Floating Bodies describing the general principle for buoyancy and hydrostatics. Archimedes develops Archimedes' screw for water extraction.
+2nd century BC – The aqueduct Aqua Tepula and Aqua Marcia aqueducts are completed in Rome. Zhang Heng of Han dynasty designs the first known seismoscope.
+1st century BC – Frontinus publishes his treatise De aquaeductu on Roman water engineering. Hero of Alexandria makes a series of experiments and devices with fluids, including the aeolipile steam device and wind harnessing devices.
+
+== Middle ages ==
+8th–13th century – Arab Agricultural Revolution
+725 – Northumbrian monk Bede publishes The Reckoning of Time, which includes a quantitative description of the influence of the moon and the sun over the tides.
+c. 850– Abu Ma'shar al-Balkhi (Albumasar) publishes his Kitab al-madkhal al-kabir recording the Moon position and tides, he recognizes that there are two tides in day.
+850 – The Book of Ingenious Devices is published by the Banū Mūsā brothers, describing a number of early automatic controls using fluid mechanics.
+1206 – Ismail al-Jazari invented water-powered programmable automata/robots and water music devices.
+
+== Renaissance ==
+1432 – Portuguese develop caravels for long-distance ocean travel.
+1450 –Nicholas of Cusa publishes his experiments with fluids in Idiota de staticis experimentis, including the first proposal to measure air moisture using wool.
+1480-1510 – Leonardo da Vinci develops the first sophisticated parachute,  the first descriptions of capillary action, and the first turbine water wheels designs.
+1586 – Simon Stevin publishes De Beghinselen des Waterwichts ("Principles on the weight of water") on hydrostatics. He first details the hydrostatic paradox.
+1596 – Galileo Galilei produces the first (Galileo) thermometer.
+
+== 17th century ==
+1619 – Benedetto Castelli published Della Misura dell'Acque Correnti ("On the Measurement of Running Waters"), one of the foundations of modern hydrodynamics.
+1619 – William Harvey provides first model of the human circulatory system.
+1624 – Jan Baptist van Helmont coins the term "gas".
+1631 – René Descartes first describes the principle of the mercury barometer.
+1643 – Evangelista Torricelli provides a relation between the speed of fluid flowing from an orifice to the height of fluid above the opening, given by Torricelli's law. He also builds a mercury barometer and does a series of experiments on vacuum.
+1650 – Otto von Guericke invents the first vacuum pump.
+1653–1663 Blaise Pascal establishes Pascal's law of hydrostatics.
+1662-1678 – Robert Boyle and Edme Mariotte independently discover a gas law that describes the relationship between pressure and volume given by Boyle's law (or Boyle-Mariotte's law).
+1678 – Robert Hooke publishes Hooke's law describing linear deformation of a spring.
+1687 – Isaac Newton publishes Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), introducing the Newton's laws of motion of classical mechanics. He also introduces the concept of Newtonian fluid.
+
+== 18th century ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics-1.md b/data/en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics-1.md
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@@ -0,0 +1,37 @@
+---
+title: "Timeline of fluid and continuum mechanics"
+chunk: 2/4
+source: "https://en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:40.789795+00:00"
+instance: "kb-cron"
+---
+
+1713 – Antoine Parent introduces the concept of shear stress.
+1714 – Daniel Gabriel Fahrenheit develops the mercury-in-glass thermometer along the Fahrenheit temperature scale.
+1718–1719 – James Jurin writes the law of capillary action, known as Jurin's law.
+1727 – Leonhard Euler introduces linear elasticity and the Young's modulus.
+1732 – Henri Pitot discovers how to measure the pressure from the speed of a fluid using a Pitot tube.
+1738 – Daniel Bernoulli publishes Hydrodynamica discussing the mathematical relation between pressure and velocity of fluids according to Bernoulli's principle.
+1742 – Anders Celsius designs a thermometer with the Celsius scale.
+1744 – Euler introduces the concept of deformation and strain.
+1747 – Jean le Rond d'Alembert's formula for the solutions of the wave equation in a string gets published.
+1752 –  D'Alembert show an inconsistency of treating fluids as inviscid incompressible fluids, known as d'Alembert's paradox.
+1757 – Euler introduces the Euler equations of fluid dynamics for incompressible and non-viscous flow. He also introduces the mathematical model for buckling.
+1764 – James Watt develops his steam water condenser leading to efficient steam engines.
+1765 – Jean-Charles de Borda experiments with whirling arm experiments. He corrects the available theories of air friction.
+1766 – de Borda publishes "Mémoire sur l'Écoulement des Fluides par les Orifices des Vases" on hydraulics and resistance of fluid through orifices. He comes up with Borda–Carnot equation.
+1768 – Antoine de Chézy provides a semi-empirical formula for resistance of open channel flow, described by Chézy formula.
+1775 – Pierre-Simon Girard invents the water turbine.
+1776 – Charles Bossut, supervised by the Marquis de Condorcet and d'Alembert, publishes Nouvelles expériences sur la resistance de fluides, a report on a series experiments to test currents theories of hydraulics.
+1775-76 – Pierre-Simon Laplace introduces the mathematical theory for tidal forces on oceans.
+1779 – Pierre-Louis-Georges du Buat publishes Principes de l'hydraulique ("Principles of hydraulics"), with semiempirical equations for the flow of water through pipes and open channels.
+1780 – Jacques Charles discover a gas law that describes the relationship between temperature and volume, given by Charles's law.
+1782 – The Montgolfier brothers invent the hot air balloon.
+1785 – First theories of friction are introduced by Charles-Augustin de Coulomb.
+1787 – Ernst Chladni, publishes his experiments on vibrational modes of thin solid surfaces, describing the Chladni patterns created using a violin bow, based on previous experiments by Hooke.
+1797 – Giovanni Battista Venturi discovers the Venturi effect.
+1799 – George Cayley introduces modern fixed wing-machines and identifies three important factors for flying machines: thrust, lift, drag, and weight.
+
+== 19th century ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics-2.md b/data/en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics-2.md
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@@ -0,0 +1,58 @@
+---
+title: "Timeline of fluid and continuum mechanics"
+chunk: 3/4
+source: "https://en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:40.789795+00:00"
+instance: "kb-cron"
+---
+
+1801 – Robert Fulton develops the first submarine.
+1805-1806 – The development of Young–Laplace equation by Thomas Young and improved by Laplace.
+1808-1809 – Joseph Louis Gay-Lussac describes the law of combining gases.
+1811–1812 – Amedeo Avogadro and André-Marie Ampère independently discover a gas law relating volume and quantity of gas, given by Avogadro's law (or Avogadro-Ampère's law).
+1821 – Claude-Louis Navier introduces viscosity in to Euler equations of fluids.
+1821 – Sophie Germain wins a contest of the French Academy of Sciences for providing a partial theory for the vibration of an elastic surfaces.
+1827 – Augustin-Louis Cauchy introduces the Cauchy stress tensor and the concept of stress in elasticity.
+1827 – Robert Brown (botanist, born 1773), identifies the Brownian motion of pollen grains suspended in water.
+1831– Michael Faraday first describes vibrational modes in liquids, known as Faraday waves.
+1831-1833– Thomas Graham first studies the diffusion in gases.
+1834 – Benoît Paul Émile Clapeyron unifies many of the empirical gas laws into the ideal gas law.
+1834 – John Scott Russell first describes the observation of solitary waves.
+1837 – George Green find the minimal number of elastic moduli.
+1838-40 – Gotthilf Hagen and Jean Léonard Marie Poiseuille study laminar flow, independently establishing Hagen–Poiseuille equation.
+1841 – George Biddell Airy publishes the first correct formulation of Airy wave theory of water waves.
+1842 – Christian Doppler introduces the Doppler effect.
+1842 – James Prescott Joule discovers magnetostriction, the first magnetomechanical effect.
+1842-1850 – Stokes completes the equations of motions of fluids, now referred as Navier–Stokes equations. He also extends Airy wave theory to non-linear Stokes wave theory.
+1852 – Heinrich Gustav Magnus describes the Magnus effect.
+1855 – Lord Kelvin calculates the thermodynamics work and energy due to elastic deformation.
+1855 – Adolf Eugen Fick publishes Fick's laws of diffusion.
+1857 – Henry Darcy studies flow through porous media, leading to the discovery of Darcy's law.
+1857 – Rudolf Clausius introduces the first model for the kinetic theory of gases.
+1859 – W. H. Besant introduces an equation for the dynamics of bubbles in an incompressible fluid.
+1860 – James Clerk Maxwell introduces the Maxwell distribution of velocity of classical gas molecules.
+1863 –Hermann von Helmholtz publishes Sensations of Tone on the physics of sound perception.
+1864 – August Toepler invents Schlieren photography.
+1865 – Lord Kelvin introduces the Kelvin material model for viscoelasticity.
+1856 – Carlo Marangoni studies the tears of wine, now explained by the Marangoni effect.
+1867 – Helmholtz works on Helmholtz's theorems for vortex dynamics.
+1867 – James Clerk Maxwell introduces the Maxwell material model for viscoelasticity.
+1868–1871 – Helmholtz and Kelvin study and develop the theory of the Kelvin–Helmholtz instability.
+1870 – William Rankine develops an equation for the study of shock waves.
+1871 – Francis Herbert Wenham designs and builds the first wind tunnel.
+1872-1877 – Joseph Valentin Boussinesq introduces the concept of turbulence in forms of eddy viscosity, as well as Boussinesq approximation for water waves and Boussinesq approximation for buoyancy.
+1873 – Johannes Diderik van der Waals introduces the Van der Waals equation.
+1883 – Osborne Reynolds demonstrates the transition and differences between laminar and turbulent pipe flow.
+1885 – Lord Rayleigh predicts the existence of Rayleigh surface waves.
+1885 – Helmholtz describes the concept of Helmholtz resonance.
+1887 – Pierre Henri Hugoniot based on the work of Rankine, introduces the Rankine–Hugoniot conditions to model shock waves.
+1887 – First models of supersonic waves by Ernst Mach. He introduces the concept of Mach number.
+1888 – First commercial Venturi tube by Clemens Herschel.
+1888-1890 – Independently, Henry R. A. Mallock and Maurice Couette find the mathematical solution for the Couette flow.
+1889 – Robert Manning produces Manning's formula for open channel flow.
+1893 – Carl Barus develops the theory of the die swell in complex fluids.
+1895 – Diederik Korteweg and Gustav de Vries (1895) rediscover the Korteweg–De Vries equation first treated by Boussinesq and introduce the idea of soliton solutions.
+
+== 20th century ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics-3.md b/data/en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics-3.md
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+---
+title: "Timeline of fluid and continuum mechanics"
+chunk: 4/4
+source: "https://en.wikipedia.org/wiki/Timeline_of_fluid_and_continuum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:40.789795+00:00"
+instance: "kb-cron"
+---
+
+1902 – Martin Kutta discusses the air flow through an airfoil using the Kutta condition.
+1903 – The Wright brothers carry the first successful manned airplane flight.
+1903 – Walther Ritz introduces the Ritz method to study beam theory and Chladni figures.
+1905 – First theory of dislocations by Vito Volterra.
+1905-1906 – First successful theories of Brownian motion by Albert Einstein and Marian Smoluchowski, supporting the atomic theory of matter.
+1906 – Richard Dixon Oldham identifies the separate arrival of p-waves, s-waves and surface waves on seismograms and found the first clear evidence that the Earth has a central core.
+1908 – Paul Richard Heinrich Blasius introduces the concept of boundary layer.
+1908 – Experimental confirmation of the theories of Brownian motion by Jean Baptiste Perrin.
+1910:
+Harry Fielding Reid put forward the elastic rebound theory for earthquakes.
+Lord Rayleigh introduces the concept of Rayleigh flow.
+Nikolay Zhukovsky introduces the Joukowsky transform and the Kutta–Joukowski theorem based on the work of Kutta.
+Carl Wilhelm Oseen solves the Stokes' paradox by introducing Oseen's approximation.
+1911 – Augustus Edward Hough Love predicts the existence of Love surface waves.
+1915–1916 – Frederick W. Lanchester comes up with the Lanchester's laws, a set of differential equations that were practical for flying combat.
+1915-1917 – George Barker Jeffery and Georg Hamel introduce the equations of Jeffery–Hamel flow.
+1916 – Horace Lamb coins the term "vorticity".
+1916 – Eugene C. Bingham studies Bingham plastics
+1916-1923 – Lord Rayleigh, and later G. I. Taylor describe Rayleigh–Taylor instability.
+1917 – Lamb introduces Lamb waves, generalizing Rayleigh's wave theory for thin metal plates.
+1918 – Ludwig Prandtl develops theory of flow over airplane wings.
+1919 – Jacob Bjerknes established the bases the Norwegian cyclone model.
+1920 – Nikola Tesla patents the Tesla valve, opening the field of fluidics.
+1920 – Bingham coins the term rheology from a suggestion by a colleague, Markus Reiner.
+1921 – Theodore von Kármán introduces the turbulence model of Von Kármán swirling flow, and phenomena like Kármán vortex street.
+1921 – Alan Arnold Griffith develops his theory of fracture mechanics.
+1922 – Supersonic wind tunnel is invented in National Physical Laboratory (United Kingdom).
+1926 – Einstein solves the tea leaf paradox.
+1925 – Jakob Ackeret publishes the theory of supersonic airfoils.
+1926 – Erwin Madelung relates quantum mechanics with hydrodynamics through his quantum hydrodynamics equations, known as Madelung equations.
+1931 – Sylvia Skan and Victor Montague Falkner introduce the equations for the Falkner–Skan boundary layer.
+1932 – The concept of quantum of sound (phonons) is introduced by Igor Tamm.
+1937 – Superfluidity is discovered in helium-4 by Pyotr Kapitsa and independently by John F. Allen and Don Misener.
+1938 – Philip Saffman and G. I. Taylor publish on Saffman–Taylor instability.
+1937 – Lev Landau introduces Landau theory of phase transitions.
+1940-1941 – László Tisza and Landau introduce the two-fluid model for helium.
+1941 – Landau introduces the concept of second sound in condensed matter.
+1942 – First magnetohydrodynamics descriptions of plasma by Hannes Alfvén. He also introduced the idea of Alfvén waves.
+1948 – Milton S. Plesset improves on Rayleigh and Bessant equations for the dynamics of bubbles by including surface tension according to Rayleigh–Plesset equation.
+1941 – Andrey Kolmogorov introduces his detailed theory of turbulence.
+1947– Karl Weissenberg introduces the Weissenberg effect in non-Newtonian fluids.
+1950 – James G. Oldroyd introduces the Oldroyd-B model of viscoelasticity.
+1944 – Lewis Ferry Moody plots Darcy–Weisbach friction factor against Reynolds number for various values of relative roughness, leading to the first Moody chart.
+1961 – Eugene P. Gross and Lev Pitaevskii introduce Gross–Pitaevskii equation for the condensation of bosons.
+1963 – Alex Kaye describes the Kaye effect in viscoelastic liquids.
+1972 – David Lee, Douglas Osheroff and Robert Coleman Richardson discovered two phase transitions of helium-3 along the melting curve, which were soon realized to be the two superfluid phases.
+1990 – first micro total analysis system (μTAS) for microfluidics by Andreas Manz.
+1995 – The first Bose–Einstein condensate is produced by Eric Cornell and Carl Wieman at the University of Colorado at Boulder NIST–JILA lab, in a gas of rubidium atoms cooled to 170 nanokelvins (nK). Shortly thereafter, Wolfgang Ketterle at MIT produced a Bose–Einstein condensate in a gas of sodium atoms.
+
+== 21st century ==
+c. 2000 – Development of droplet-based microfluidics.
+2003 – Deborah S. Jin and her collaboration produce the first fermionic condensate.
+
+== See also ==
+History of aviation
+
+== References ==
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/Timeline_of_nuclear_power-0.md b/data/en.wikipedia.org/wiki/Timeline_of_nuclear_power-0.md
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+---
+title: "Timeline of nuclear power"
+chunk: 1/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_nuclear_power"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:42.001442+00:00"
+instance: "kb-cron"
+---
+
+This timeline of nuclear power is an incomplete chronological summary of significant events in the study and use of nuclear power. This is primarily limited to sustained fission and decay processes, and does not include detailed timelines of nuclear weapons development or fusion experiments.
+
+== 1920s ==
+1925
+On February 2, Patrick Blackett publishes experimental results of the first nuclear transmutation, by the bombardment of a nitrogen nucleus with an alpha particle, producing an oxygen-17 nucleus and a proton, at Cavendish Laboratory, Cambridge.
+
+== 1930s ==
+
+1931
+On January 2, Ernest Lawrence and M. Stanley Livingston complete the first cyclotron, a type of circular particle accelerator. This early design is only 4.5 inches in diameter and yields a maximum proton energy of 80 keV.
+1932
+On January 1, Harold Urey, Ferdinand Brickwedde, and George M Murphy publish the discovery of deuterium. It is spectroscopically identified following separation from a sample of cryogenic liquid hydrogen at Columbia University, New York. Like all nuclei, preceding the discovery of the neutron, it is assumed to be composed entirely of protons and hypothetical "nuclear electrons".
+On February 27, James Chadwick publishes the discovery of the neutron, identified as the "beryllium radiation" emitted under alpha-particle bombardment, previously observed by Irène Joliot-Curie and Frédéric Joliot-Curie.
+On April 30, John Cockcroft and Ernest Walton publish the first disintegration of an atomic nucleus, popularly described as splitting the atom. They report the production of two alpha particles from the bombardment of lithium-7 nuclei by protons, using a Cockcroft–Walton generator at the University of Cambridge's Cavendish Laboratory. While in lithium this reaction is exothermic, nucleus disintegration is distinct from the undiscovered process of fission, which induces a radioactive decay.
+1934
+On June 24, Leo Szilard files the first patent for a nuclear reactor. The design, which predates the discovery of fission, resembles an accelerator-driven subcritical reactor, suggesting deuteron beam fusion interacting with indium, beryllium, bromine, or uranium as neutron-rich core materials.
+Mikhail Alekseevich Eremeev completes the first cyclotron in the Soviet Union and in Europe, at the Leningrad Physico-Technical Institute. It is a small design based a prototype by Lawrence, with a 28 cm diameter capable of achieving 530 keV proton energies.
+1935
+In January, Vemork hydroelectric plant in Norway operates the first large-scale heavy water production site, pioneered by Leif Tronstad.
+1937
+In March, V. N. Rukavishnikov, Lev Mysovskii and Igor Kurchatov complete the first MeV cyclotron in the Soviet Union and in Europe, and outside the United States, at the V. G. Khlopin Radium Institute in Leningrad. It is a 100 cm (39 in) accelerator capable of achieving 3.2 MeV proton energies.
+On April 3, Yoshio Nishina, Tameichi Yasaki, and Sukeo Watanabe complete the first cyclotron in Japan and in Asia, at the Riken laboratory in Tokyo. It is a 26-inch accelerator capable of achieving 2.9 MeV deuteron energies.
+1938
+In August, Niels Bohr, George de Hevesy, and August Krogh complete the first cyclotron in Denmark, at the Institute for Theoretical Physics of the University of Copenhagen.
+1939
+On February 11, Lise Meitner and Otto Frisch publish the discovery of nuclear fission, collaborating with Otto Hahn and Fritz Strassmann who previously identified barium following neutron bombardment of uranium, at the Kaiser Wilhelm Institute for Chemistry, Berlin. Meitner and Frisch, both Jewish, had already fled Nazi Germany to Stockholm and Copenhagen respectively, and were barred from co-publishing with their German colleagues under Nazi anti-Jewish legislation.
+On March 8, Hans von Halban, Frédéric Joliot-Curie, Lew Kowarski, and Francis Perrin submit for publication the first net neutron production in an atomic pile. The experiment in Ivry-sur-Seine, Paris uses a 50-cm copper sphere filled with a uranyl nitrate water solution and a radium-beryllium neutron source.
+On March 16, Herbert L. Anderson, Enrico Fermi, and H B Hanstein submit for publication the first pile neutron production in the United States, from pile Columbia number 1 at Columbia University, New York. The pile submerges a 13-cm glass bulb filled with uranium oxide in water acting as a moderator and reflector.
+In March, Frédéric Joliot-Curie achieves a 7 MeV proton beam at the first cyclotron in France, at the Collège de France in Paris.
+
+== 1940s ==
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+---
+title: "Timeline of nuclear power"
+chunk: 2/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_nuclear_power"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:42.001442+00:00"
+instance: "kb-cron"
+---
+
+1940
+On May 27, Edwin McMillan and Philip Abelson publish the discovery of neptunium at the Berkeley Radiation Laboratory. They use the 60-inch cyclotron produce a small sample of neptunium-239 via neutron bombardment of uranium-238. They also correctly assume its beta decay to the alpha-emitting plutonium-239, but are unable to isolate it. On July 1, Georgy Flyorov and Konstantin Petrzhak publish the discovery of spontaneous fission, in uranium atoms insulated from cosmic rays 60 meters underground in the Dinamo station of the Moscow Metro. They also report no such reactions in protactinium or thorium. 1941
+In January, Walther Bothe and Peter Jensen conduct an neutronics experiment with a 55-cm radius graphite sphere. They erroneously conclude, possibly due to unaccounted boron and cadmium impurities of a few ppm, a neutron capture cross-section value for carbon over twice its accepted value. This hinders development of the Nazi German nuclear program. On February 24, Glenn T. Seaborg, Edwin McMillan, Emilio Segrè, Joseph W. Kennedy, and Arthur Wahl make the discovery of plutonium at the Berkeley Radiation Laboratory. They identify plutonium-238 from oxidation of a sample of beta-decaying neptunium-238, produced via deuteron bombardment of uranium in the 60-inch cyclotron. A paper is submitted to Physical Review in March but publication is delayed until 1946 due to World War II. 1942
+In May, the L-IV atomic pile at the University of Leipzig sees the first net neutron production of the Nazi German nuclear program. The design uses a uranium powder, a heavy water moderator and reflector, and a central radium-beryllium neutron source. On June 23, uranium powder in the L-IV atomic pile ignites on contact with air, causing a steam explosion and wider fire. This is the first nuclear-related accident, and leads the German program to use only solid uranium in future designs. On November 13, Alpha-I, the first calutron track, begins uranium enrichment operation at the Y-12 facility, the first electromagnetic separation plant. On December 2, Chicago Pile-1, the first artificial nuclear reactor, achieves criticality at the University of Chicago. The Manhattan Project's assembly uses blocks of natural uranium and graphite as a moderator to produce 0.5 watts of thermal power. 1943
+On February 28, in the early hours of the morning, a Special Operations Executive-trained team of Norwegian commandos detonate explosive charges on the heavy-water electrolysis chambers at the Vemork hydroelectric plant during Operation Gunnerside. On March 20, Chicago Pile-2, the world's second reactor, achieves criticality at Site A, Illinois. It is a rebuilt and slightly enlarged version of CP-1. On March 22, Igor Kurchatov, director of Laboratory No. 2 writes a letter to Mikhail Pervukhin suggesting that "eka-osmium-239" (plutonium-239) produced in a theoretical "uranium boiler" (reactor) will undergo fission as an alternative to uranium-235 in bomb designs. In March, the US approves a Soviet request for over 0.3 tons of uranium compounds under the Lend-Lease program. General Leslie Groves hopes to hide the extent of the Manhattan Project, and reveal the location of Laboratory No. 2. On July 31, Igor Kurchatov learns via atomic spies of the successful criticality and graphite moderator choice of Chicago Pile-1 eight months prior. On November 4, the X-10 Graphite Reactor achieves criticality at Oak Ridge National Laboratory, Tennessee. It is the world's third reactor, the first built for continuous operation, the first reactor for the production of plutonium-239. 1944
+On March 19, Takeuchi Masa of the Japanese nuclear weapons program's Riken laboratory constructs the country's first Clusius tube thermal diffusion design for uranium enrichment. In March, the 305 Test Pile begins operation at the Hanford Site, primarily to provide quality assurance of graphite for subsequent reactors. Via atomic spies, this design would be replicated as the USSR's first F-1 reactor. On May 9, LOPO (low-power), the first aqueous homogeneous reactor, the first reactor to use enriched uranium, and the first water-cooled and water-moderated reactor, achieves criticality at Los Alamos National Laboratory, using a solution of uranyl sulfate at 14.7% enrichment. On May 15, Chicago Pile-3, the first heavy-water reactor, achieves criticality at Site A, Illinois. It uses deuterium oxide i.e. heavy water as a moderator instead of graphite, as well as a coolant. In July, the X-10 Graphite Reactor becomes the first reactor to exceed 1 MWth power output, reading 4 MWth due to the addition of two large fans. On September 16, S-50, the first and only full-scale liquid thermal diffusion plant, begins operation at Clinton Engineer Works, Tennessee. On September 26, the B Reactor is started at Hanford Site, Washington. At 250 MWth, it is the first reactor to exceed 10 and 100 MWth and is considered the first large-scale reactor. The site is primarily built for weapons-grade plutonium production, but also produces weapons-usable tritium, polonium-210, and uranium-233, as well as non-military plutonium, thulium-170, and iridium-192. On September 27, the first instance of xenon poisoning occurs in the Hanford B reactor. Water contamination of graphite, boron impurities in the Columbia River water coolant, and nitrogen in the air are all suggested as the neutron poisoning cause. John Archibald Wheeler and Enrico Fermi calculate the cause and the problem is solved by loading additional fuel slugs into extra tubes. In December, HYPO (high-power), the second aqueous homogenous reactor, achieves criticality at Los Alamos National Laboratory, using a uranyl nitrate solution at 14.5% enrichment. In December, the D Reactor is started at Hanford Site, Washington. It is largely identical to the B Reactor with the same primary purpose of weapons-grade plutonium production. 1945
+On January 20, a team led by Otto Robert Frisch achieves the first criticality burst in the Dragon Critical Assembly at Los Alamos National Laboratory, the first fast neutron reactor and first prompt criticality. The device uses a uranium hydride slug and hollow cylinder both enriched at 71-75%, with the former dropped through the latter. In February, the F Reactor is started at Hanford Site, Washington. It is largely identical to the B Reactor with the same primary purpose of weapons-grade plutonium production. On March 12, K-25, the first gaseous diffusion plant becomes fully operational at Oak Ridge National Laboratory, Tennessee. It is the world's largest building, and had an electrical consumption almost triple that of the entire city of Detroit. On March 15, 612 Boeing B-17 Flying Fortress bomb the Auergesellschaft plant of the Nazi German nuclear program, in Oranienburg. It is an attempt to deny its uranium to the advancing Soviet Army on the recommendation of General Leslie Groves. Over 100 tons are still ultimately recovered by Russian Alsos for the F-1 reactor. On April 23, the Allied Alsos Mission dismantles and recovers uranium and heavy water from the B-VIII atomic pile at Haigerloch, the final pile of the Nazi German nuclear program. On September 5, ZEEP, the first reactor in Canada and outside the United States, achieves criticality at Chalk River Laboratories, on the Ontario side of the Ottawa River. 1946
+On November 19, Clementine, the first continuous fast neutron reactor, the first liquid metal cooled reactor, and the first reactor to use plutonium fuel achieves criticality at Los Alamos National Laboratory, using a mercury coolant abandoned by all later designs.
\ No newline at end of file
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+---
+title: "Timeline of nuclear power"
+chunk: 3/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_nuclear_power"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:42.001442+00:00"
+instance: "kb-cron"
+---
+
+On December 25, F-1, the first reactor in the Soviet Union and in Europe, and outside North America, achieves criticality at the Kurchatov Institute in Moscow. It is fuelled with uranium recovered by "Russian Alsos" from the Nazi German nuclear program including the Auergesellschaft Oranienburg plant. 1947
+On July 22, NRX, the second reactor in Canada, achieves criticality at Chalk River Laboratories. On August 15, GLEEP, the first reactor in the United Kingdom, achieves criticality at the Atomic Energy Research Establishment in Oxfordshire. 1948
+On June 10, Reactor A, the second reactor and the first plutonium production reactor in the Soviet Union, achieves criticality at Mayak Production Association, Chelyabinsk Oblast. In August, the X-10 Graphite Reactor becomes the first reactor to generate electricity. The experiment uses a steam generator and engine to power a single flashlight bulb. This could be considered the first boiling water reactor. On December 15, Zoé aka EL-1, the first reactor in France, and the first heavy water reactor in Europe, begins experimental operation at Fort de Châtillon. 1949
+On February 1, Georgy Flyorov uses the Physical Boiler on Fast Neutrons, the first Soviet pulsed fast reactor, at Design Bureau 11, Sarov, to measure the critical mass of plutonium, ahead of the RDS-1 test. In April, TVR, the third reactor and first heavy water reactor in the Soviet Union, achieves criticality.
\ No newline at end of file
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+---
+title: "Timeline of nuclear power"
+chunk: 4/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_nuclear_power"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:42.001442+00:00"
+instance: "kb-cron"
+---
+
+== 1950s ==
+
+1951
+On August 24, EBR-I, the first breeder reactor, producing more fuel than it consumes, begins power operation.
+1952
+On October 27, EL-2, the first gas-cooled reactor, achieves criticality at the Saclay Nuclear Research Centre, France. While many early reactors were air-cooled, it is an experimental 2 MW design testing the first closed circuit nitrogen and carbon dioxide cooling.
+On December 2, NRX, Canada's second reactor, constructed at Chalk River Laboratories, experiences the first core meltdown in a nuclear facility. Future president Jimmy Carter is among the US Navy crew sent to assist clean-up.
+The AI reactor (Industrial Association Mayak) begins production of tritium at the Mayak plant in Ozyorsk, USSR.
+1953
+On March 30, the S1W, the first pressurized water reactor, achieves criticality at Idaho National Laboratory. It is designed to power submarines 
+On December 8, US president Dwight D. Eisenhower delivers the Atoms for Peace speech to the United Nations General Assembly in New York City. It promotes education resources and empowers companies such as American Machine and Foundry to supply research reactors to Mexico, Colombia, Brazil, Peru, Chile, Argentina, Portugal, Israel, Iran, Pakistan, Thailand, South Korea, Japan, the Philippines, Indonesia, and Yugoslavia.
+On December 28, the R reactor, the first production reactor at Savannah River Site, is started. It uses natural uranium and a heavy water moderator, and is intended to produce both plutonium and tritium for weapons.
+BORAX-I, the first full-scale boiling water reactor, achieves criticality at Argonne National Laboratory.
+1954
+On January 21, the USS Nautilus, the first vessel to use nuclear propulsion and the first nuclear submarine, powered by the S2W reactor is launched from General Dynamics Electric Boat shipyard, Groton, Connecticut, and in 1958 completes the first journey under the North Pole.
+On June 27, AM-1 becomes the first grid-connected reactor at Obninsk Nuclear Power Plant, southwest of Moscow. It is a predecessor to the RBMK design.
+On November 3, the Aircraft Reactor Experiment, the first molten-salt reactor, achieves criticality at Oak Ridge National Laboratory.
+1955
+On July 17, BORAX-III becomes the first reactor to fully power a town, during a demonstration in Arco, Idaho.
+On September 17, the Aircraft Shield Test Reactor, the first reactor operated during aircraft flight, begins test flights in the Convair NB-36H.
+1956
+On August 4, Apsara, the first reactor in India and in Asia, achieves criticality at Bhabha Atomic Research Centre, in Trombay, Mumbai.
+On December 3, BORAX-IV, the first reactor to use thorium fuel, achieves criticality at Argonne National Laboratory.
+1957
+On October 31, FRM I, the first reactor in West Germany, achieves criticality at Technical University of Munich.
+On November 2, the first gas centrifuge enrichment plant begins operation, in Leningrad, under a team led by Evgeni Kamenev.
+On December 5, the Lenin, the first nuclear-powered surface vessel, a Soviet icebreaker, is launched from the Admiralty Shipyards in Leningrad.
+The OMRE, the first complete organic nuclear reactor, cooled and moderated by hydrocarbons, in this case terphenyls, achieves criticality at the Idaho National Laboratory.
+1958
+On September 27, HWRR, a Soviet-supplied 7 MW heavy water research reactor, the first reactor in China, begins operation in Beijing. Nuclear power is developed primarily for weapons production until the Qinshan I reactor begins development in 1985.
+1959
+On June 16, TRICO-I, the first reactor in the Belgian Congo and in Africa, achieves criticality at Lovanium University, Kinshasa.
+On July 1, Kiwi A, the first nuclear thermal rocket, begins testing at Area 25, Nevada, under Los Alamos Scientific Laboratory's Project Rover. It produces 70 MW for five minutes and achieves a core temperature of 2,900 K, using liquid hydrogen as the coolant, moderator, and propellant.
+On July 14, the USS Long Beach, the first nuclear-powered surface combat ship, is launched from Fore River Shipyard, Massachusetts.
\ No newline at end of file
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+---
+title: "Timeline of nuclear power"
+chunk: 5/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_nuclear_power"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:42.001442+00:00"
+instance: "kb-cron"
+---
+
+== 1960s ==
+1960
+In June, IRR-1, a HEU-fueled research reactor, the first reactor in Israel, achieves criticality at the Soreq Nuclear Research Center near Yavne. It is under US inspection.
+On September 24, the USS Enterprise, the first nuclear-powered aircraft carrier, is launched from Newport News Shipbuilding, Virginia.
+1961
+On January 3, the Army Nuclear Power Program's SL-1 experiences a prompt critical accident, killing three workers, the first and only fatal nuclear power accident in the United States.
+On November 11, UTR-KINKI, the first reactor in Japan, achieves criticality at Kinki University.
+1962
+On March 3, PM-3A, the first and only reactor to operate in Antarctica, achieves criticality at McMurdo Station.
+In March, KRR-1, the first reactor in South Korea, achieves criticality at Korea Atomic Energy Research Institute.
+On September 16, Indian Point Unit 1, the first commercial reactor to use thorium fuel, begins commercial operation in New York.
+1963
+On December 26, IRR-2, a plutonium production reactor, the second reactor in Israel, achieves criticality at Shimon Peres Negev Nuclear Research Center near Dimona. It is a heavy water-moderated design sold by France and not under IAEA monitoring.
+In December, the N reactor, the ninth at the Hanford Site, Washington, begins operation. At 4000 MWth it is one of the largest plutonium production reactors ever. Additionally, until the DR reactor's shutdown in December 1964, the Hanford Site operates at 25,870 MWth, the largest nuclear plant ever by thermal power.
+1964
+In August, the Dragon reactor, the first helium-cooled reactor, achieves criticality under UKAEA operation at Winfrith, England.
+The AMB-100, the first reactor to use supercritical water, begins operation at Beloyarsk Nuclear Power Station in the Soviet Union. Alongside the AMB-200 they are the only two such reactors ever, but the design has re-emerged as a Generation IV reactor concept.
+1965
+On April 3, NASA launches into orbit the Snapshot satellite carrying SNAP-10A, the first reactor operated in space and via its cesium ion thruster also the first use of nuclear electric propulsion. It uses a uranium zirconium hydride fuel-moderator hybrid, and a liquid sodium–potassium alloy (NaK) coolant.
+A Soviet-supplied IR-2000 pool-type research reactor begins operation as the first reactor in North Korea, at the Nyongbyon Nuclear Scientific Research Center.
+1966
+On August 28, the AVR, the first pebble-bed reactor, achieves criticality at Julich Research Center, West Germany. It was an early pioneer of helium-cooled high temperature designs.
+On November 8, Alexander Vinogradov and colleagues at the USSR Academy of Sciences publishes the detection by Luna 10's gamma ray spectrometer of radiation from uranium, thorium, and potassium on the Moon's surface.
+1967
+On January 24, MH-1A, the first floating nuclear power plant, achieves criticality. It was developed by the Army Nuclear Power Program at Gunston Cove, Virginia.
+1968
+On June 8, the Phoebus-2A nuclear thermal rocket engine undergoes its second test and first at full power. It achieves a maximum power output of 4082 MWth.
+On October 2, the Molten-Salt Reactor Experiment achieves criticality as the first uranium-233 reactor, at Oak Ridge National Laboratory, Tennessee.
+1969
+On March 28, the Ultra-High Temperature Reactor Experiment achieves criticality at Los Alamos National Laboratory. Unlike other HTGRs, the helium coolant directly contacts the fuel and removes fission products, allowing outlet temperatures up to 1300 °C.
+
+== 1970s ==
+1973
+On June 11, Alexander Vinogradov and colleagues at the USSR Academy of Sciences publishes the detection by Venera 8's gamma ray spectrometer of radiation from uranium, thorium, and potassium on Venus' surface.
+1975
+In July, Kraftwerk Union AG begins work on the Bushehr Nuclear Power Plant in Iran. It is the first commercial nuclear project in the Middle East. Work is paused following the 1979 Iranian revolution and completed in collaboration with Russia in 2011.
+1976
+On October 28, US president Gerald Ford indefinitely suspends nuclear spent fuel reprocessing, and encourages other nations to do the same. The decision is based on the plutonium proliferation risk, especially the 1974 first Indian nuclear weapons test, Smiling Buddha.
+1978
+On November 5, voters in Austria reject a referendum to allow the startup of its first nuclear power plant, Zwentendorf, by 50.47% to 49.53%. A subsequent law makes Austria the first country to ban nuclear power.
+1979
+On March 28, Three Mile Island Nuclear Generating Station's Unit 2 reactor experiences a partial core meltdown, in Pennsylvania, US. It is the worst nuclear accident in US history based on radioactive material released. It is classed as a Level 5 nuclear accident out of seven on the International Nuclear Event Scale.
+
+== 1980s ==
+1981
+On June 7, the Israeli Air Force carries out Operation Opera, bombing an unfinished secret Iraqi nuclear reactor. Ten Iraqi soldiers and one French civilian engineer were killed. France sold Iraq the Osiris-class research reactor which claimed it was for peaceful use.
+1983
+On December 31, Unit 1 at Ignalina Nuclear Power Plant comes online in the Lithuanian SSR. The first RBMK-1500 unit, at 4800 MWth, it is the largest nuclear reactor unit by thermal power ever. Alongside Unit 2 they are the only RBMK-1500 units completed. During testing the "positive scram" power excursion flaw in the RBMK design during graphite moderator-tipped control rod insertion is discovered. Other RBMK plants are alerted but changes are not made to prevent it triggering the 1986 Chernobyl disaster.
+1985
+In September, Superphénix, the largest fast reactor and breeder reactor ever, at 1,242 MWe, achieves criticality at Creys-Malville in France.
+1986
+On April 26, in the Ukrainian SSR, Chernobyl Nuclear Power Plant Unit 4 experiences a core meltdown during a test, the first Level 7 nuclear accident on the International Nuclear Event Scale. It destroys its containment building and spreads radioactive material across Europe.
+1987
+On January 7, the N reactor, the last US plutonium production reactor, is shut down at the Hanford Site, Washington. Modifications are begun to improve safety due to the water-cooled graphite-moderated design being shared by Chernobyl Unit 4, but the plant never reopens.
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+---
+title: "Timeline of nuclear power"
+chunk: 6/6
+source: "https://en.wikipedia.org/wiki/Timeline_of_nuclear_power"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:42.001442+00:00"
+instance: "kb-cron"
+---
+
+== 1990s ==
+1991
+On December 15, Qinshan I, the first commercial reactor in China, is connected to the grid.
+1993
+On February 18, the United States and Russia sign the Megatons to Megawatts Program agreement. Russia agrees to dilute 500 metric tons of its excess weapons-grade highly enriched uranium to low-enriched uranium, using US-supplied natural uranium, for sale on the global market, over the course of 20 years. The deal is signed by William J. Burns and Viktor Mikhaylov in Washington D.C.
+1994
+On October 21, the United States and North Korea sign the Agreed Framework. The DPRK agrees to freeze its operational 5 MWe and under construction 50 MWe and 200 MWe Magnox-style reactors at Nyongbyon and Taechon, seen as a plutonium production risk. The US assures the construction of two 1000 MWe light water reactors, likely OPR-1000s, by the formation of the Korean Peninsula Energy Development Organization (KEDO). KEDO's director later comments the agreement is "a political orphan within two weeks of its signature" as the Republican Revolution ends Congressional funding for the organization.
+1995
+On January 8, Russia's Minatom and Iran's Atomic Energy Organization sign an agreement to complete the Bushehr Nuclear Power Plant with two VVER-1000 PWR units.
+1997
+On July 2, Unit 7 begins commercial operation at Kashiwazaki-Kariwa Nuclear Power Plant, Japan, making it the largest nuclear power plant ever by net electrical power at 7,965 MWe.
+
+== 2000s ==
+2000
+On December 21, the HTR-10 prototype high-temperature helium-cooled pebble-bed reactor achieves criticality at Tsinghua University, China.
+2001
+On June 26, the United States Department of Energy classifies the SILEX process of uranium laser enrichment, originally developed by the Australian company Silex Systems.
+2007
+On September 6, the Israeli Air Force carries out Operation Outside the Box, bombing an unfinished secret Syrian nuclear reactor in Deir ez-Zor Governorate. Allegedly 10 North Korean scientists are killed, and Syria initially considers a chemical weapons response. Iran reportedly provided $1 billion in funding to North Korea for its construction, which is the same gas-cooled graphite-moderated design as the Nyongbyon reactor and intended it as a backup to their enrichment facilities. The IAEA confirms the reactor in 2011 and Israel confirms the attack in 2018.
+
+== 2010s ==
+2011
+On March 11, during electrical outage from the Tōhoku earthquake and tsunami, Fukushima Daiichi reactor units 1, 2, and 3 experience partial core meltdowns, and release radioactive material into the environment. It is the second Level 7 nuclear accident on the International Nuclear Event Scale, making it the worst accident since Chernobyl, and influences divestment from nuclear power in Germany, Italy, Belgium, Spain, and Switzerland.
+On September 3, Bushehr Nuclear Power Plant in Iran, the first commercial nuclear reactor in the Middle East, begins supplying grid electricity.
+2013
+On May 22, the Australian company Silex Systems, working with a consortium of General Electric, Hitachi, and Cameco, completes the first demonstration of a laser enrichment facility at a test loop in Wilmington, North Carolina.
+On October 11, the Dongfang Electric generator stator of the Taishan 1 EPR is installed in Guangdong, China. At 1750 MWe it is said to be the largest single-piece electrical generator in the world.
+In December, the 20-year Megatons to Megawatts Program successfully concludes with the final Russian delivery of low-enriched uranium to the US. Critics later say that it led to Rosatom's dominance over the global enriched uranium market.
+2016
+On
+2017
+In November, Russia completes the first test of the 9M730 Burevestnik, the first nuclear-powered cruise missile and the first nuclear-powered aircraft of any kind.
+2018
+In December, the Taishan 1 EPR begins operation in Guangdong, China. At 1660 MWe it is the largest nuclear reactor unit by electrical power ever.
+2019
+On August 8, a Russian explosion and radiation accident kills five military and civilian specialists off the coast of Nyonoksa, on the White Sea floor. Russia claimed the accident was related to an "isotope power source for a liquid-fuelled rocket engine". A US delegate tells the United Nations General Assembly First Committee that a nuclear reaction occurred. CNBC and Reuters report it occurred during recovery of a previously tested 9M730 Burevestnik nuclear-powered cruise missile left on the seabed to cool the fission core's decay heat.
+On December 8, the US NRC grants a 20-year extension to Turkey Point Nuclear Generating Station Units 3 and 4, the first US reactors licensed for an 80-year lifetime.
+On December 19, Akademik Lomonosov, the first commercial floating nuclear power plant, begins operation in Chukotka, Russia.
+
+== 2020s ==
+2022
+On February 24, during their invasion of Ukraine, Russian Armed Forces capture the Chernobyl exclusion zone including the power plant.
+On March 4, Russian Armed Forces capture Zaporizhzhia Nuclear Power Plant and thermal plant, the first military attack and capture of operational commercial nuclear reactors. The largest nuclear plant in Europe, it previously provided 23% of Ukraine's electricity. Rosatom claims control while the plant continues to be operated by Ukrainian Energoatom staff under Russian orders. The six reactors are placed in various levels of shutdown.
+On April 1, Russian Armed Forces withdraw from the Chernobyl exclusion zone. Armed Forces of Ukraine re-enter two days later.
+On September 11, Unit 6 at Zaporizhzhia Nuclear Power Plant, the last operating reactor, is disconnected from the grid.
+
+== See also ==
+History of nuclear power
+History of nuclear fusion
+Timeline of nuclear fusion
+Timeline of nuclear weapons development
+Lists of nuclear reactors
+Lists of nuclear disasters and radioactive incidents
+
+== References ==
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+---
+title: "Timeline of quantum mechanics"
+chunk: 1/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+The timeline of quantum mechanics is a list of key events in the history of quantum mechanics, quantum field theories and quantum chemistry.
+The initiation of quantum science occurred in 1900, originating from the problem of the oscillator beginning during the mid-19th century.
+
+== 19th century ==
+
+1801 – Thomas Young establishes the wave nature of light with his double-slit experiment. 
+1859 – Gustav Kirchhoff introduces the concept of a blackbody and proves that its emission spectrum depends only on its temperature.
+1860–1900 – Ludwig Eduard Boltzmann, James Clerk Maxwell and others develop the theory of statistical mechanics. Boltzmann argues that entropy is a measure of disorder.
+1877 – Boltzmann suggests that the energy levels of a physical system could be discrete based on statistical mechanics and mathematical arguments; also produces the first circle diagram representation, or atomic model of a molecule (such as an iodine gas molecule) in terms of the overlapping terms α and β, later (in 1928) called molecular orbitals, of the constituting atoms.
+1885 – Johann Jakob Balmer discovers a numerical relationship between visible spectral lines of hydrogen, the Balmer series.
+1887 – Heinrich Hertz discovers the photoelectric effect, shown by Einstein in 1905 to involve quanta of light.
+1888 – Hertz demonstrates experimentally that electromagnetic waves exist, as predicted by Maxwell.
+1888 – Johannes Rydberg modifies the Balmer formula to include all spectral series of lines for the hydrogen atom, producing the Rydberg formula that is employed later by Niels Bohr and others to verify Bohr's first quantum model of the atom.
+1895 – Wilhelm Conrad Röntgen discovers X-rays in experiments with electron beams in plasma.
+1896 – Antoine Henri Becquerel accidentally discovers radioactivity while investigating the work of Wilhelm Conrad Röntgen; he finds that uranium salts emit radiation that resembled Röntgen's X-rays in their penetrating power. In one experiment, Becquerel wraps a sample of a phosphorescent substance, potassium uranyl sulfate, in photographic plates surrounded by very thick black paper in preparation for an experiment with bright sunlight; then, to his surprise, the photographic plates are already exposed before the experiment starts, showing a projected image of his sample.
+1896–1897 – Pieter Zeeman first observes the Zeeman splitting effect by applying a magnetic field to light sources.
+1896–1897 – Marie Curie (née Skłodowska, Becquerel's doctoral student) investigates uranium salt samples using a very sensitive electrometer device that was invented 15 years before by her husband and his brother Jacques Curie to measure electrical charge. She discovers that rays emitted by the uranium salt samples make the surrounding air electrically conductive, and measures the emitted rays' intensity. In April 1898, through a systematic search of substances, she finds that thorium compounds, like those of uranium, emitted "Becquerel rays", thus preceding the work of Frederick Soddy and Ernest Rutherford on the nuclear decay of thorium to radium by three years.
+1897:
+Ivan Borgman demonstrates that X-rays and radioactive materials induce thermoluminescence.
+J. J. Thomson's experimentation with cathode rays led him to suggest a fundamental unit more than a 1,000 times smaller than an atom, based on the high charge-to-mass ratio. He called the particle a "corpuscle", but later scientists preferred the term electron.
+Joseph Larmor explained the splitting of the spectral lines in a magnetic field by the oscillation of electrons.
+Larmor, created the first solar system model of the atom in 1897. He also postulated the proton, calling it a "positive electron". He said the destruction of this type of atom making up matter "is an occurrence of infinitely small probability".
+1899–1903 – Ernest Rutherford investigates radioactivity. He coins the terms alpha and beta rays in 1899 to describe the two distinct types of radiation emitted by thorium and uranium salts. Rutherford is joined at McGill University in 1900 by Frederick Soddy and together they discover nuclear transmutation when they find in 1902 that radioactive thorium is converting itself into radium through a process of nuclear decay and a gas (later found to be 42He); they report their interpretation of radioactivity in 1903. Rutherford becomes known as the "father of nuclear physics" with his nuclear atom model of 1911.
+
+== 20th century ==
+
+=== 1900–1909 ===
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+---
+title: "Timeline of quantum mechanics"
+chunk: 2/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+1900 – To explain black-body radiation (1862), Max Planck suggests that electromagnetic energy could only be emitted in quantized form, i.e. the energy could only be a multiple of an elementary unit E = hν, where h is the Planck constant and ν is the frequency of the radiation.
+1902 – To explain the octet rule (1893), Gilbert N. Lewis develops the "cubical atom" theory in which electrons in the form of dots are positioned at the corner of a cube. Predicts that single, double, or triple "bonds" result when two atoms are held together by multiple pairs of electrons (one pair for each bond) located between the two atoms.
+1903 – Antoine Becquerel, Pierre Curie and Marie Curie share the 1903 Nobel Prize in Physics for their work on spontaneous radioactivity.
+1904 – Richard Abegg notes the pattern that the numerical difference between the maximum positive valence, such as +6 for H2SO4, and the maximum negative valence, such as −2 for H2S, of an element tends to be eight (Abegg's rule).
+1905 :
+Albert Einstein explains the photoelectric effect (reported in 1887 by Heinrich Hertz), i.e. that shining light on certain materials can function to eject electrons from the material. He postulates, as based on Planck's quantum hypothesis (1900), that light itself consists of individual quantum particles (photons).
+Einstein explains the effects of Brownian motion as caused by the kinetic energy (i.e., movement) of atoms, which was subsequently, experimentally verified by Jean Baptiste Perrin, thereby settling the century-long dispute about the validity of John Dalton's atomic theory.
+Einstein publishes his special theory of relativity
+Einstein theoretically derives the equivalence of matter and energy.
+1907 to 1917 – Ernest Rutherford: To test his planetary model of 1904, later known as the Rutherford model, he sent a beam of positively charged alpha particles onto a gold foil and noticed that some bounced back, thus showing that an atom has a small-sized positively charged atomic nucleus at its center. However, he received in 1908 the Nobel Prize in Chemistry "for his investigations into the disintegration of the elements, and the chemistry of radioactive substances", which followed on the work of Marie Curie, not for his planetary model of the atom; he is also widely credited with first "splitting the atom" in 1917. In 1911 Ernest Rutherford explained the Geiger–Marsden experiment by invoking a nuclear atom model and derived the Rutherford cross section.
+1909 – Geoffrey Ingram Taylor demonstrates that interference patterns of light were generated even when the light energy introduced consisted of only one photon. This discovery of the wave–particle duality of matter and energy is fundamental to the later development of quantum field theory.
+1909 and 1916 – Einstein shows that, if Planck's law of black-body radiation is accepted, the energy quanta must also carry momentum p = h / λ, making them full-fledged particles.
+
+=== 1910–1919 ===
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+---
+title: "Timeline of quantum mechanics"
+chunk: 3/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+1911:
+Lise Meitner and Otto Hahn perform an experiment that shows that the energies of electrons emitted by beta decay had a continuous rather than discrete spectrum. This is in apparent contradiction to the law of conservation of energy, as it appeared that energy was lost in the beta decay process. A second problem is that the spin of the nitrogen-14 atom was 1, in contradiction to the Rutherford prediction of 1⁄2. These anomalies are later explained by the discoveries of the neutrino and the neutron.
+Ștefan Procopiu performs experiments in which he determines the correct value of electron's magnetic dipole moment, μB = 9.27×10−21 erg·Oe−1 (in 1913 he is also able to calculate a theoretical value of the Bohr magneton based on Planck's quantum theory).
+John William Nicholson is noted as the first to create an atomic model that quantized angular momentum as h/2π. Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.
+1912 – Victor Hess discovers the existence of cosmic radiation.
+1912 – Henri Poincaré publishes an influential mathematical argument in support of the essential nature of energy quanta.
+1913:
+Robert Andrews Millikan publishes the results of his "oil drop" experiment, in which he precisely determines the electric charge of the electron. Determination of the fundamental unit of electric charge makes it possible to calculate the Avogadro constant (which is the number of atoms or molecules in one mole of any substance) and thereby to determine the atomic weight of the atoms of each element.
+Niels Bohr publishes his 1913 paper of the Bohr model of the atom.
+Ștefan Procopiu publishes a theoretical paper with the correct value of the electron's magnetic dipole moment μB.
+Niels Bohr obtains theoretically the value of the electron's magnetic dipole moment μB as a consequence of his atom model
+Johannes Stark and Antonino Lo Surdo independently discover the shifting and splitting of the spectral lines of atoms and molecules due to the presence of the light source in an external static electric field.
+To explain the Rydberg formula (1888), which correctly modeled the light emission spectra of atomic hydrogen, Bohr hypothesizes that negatively charged electrons revolve around a positively charged nucleus at certain fixed "quantum" distances and that each of these "spherical orbits" has a specific energy associated with it such that electron movements between orbits requires "quantum" emissions or absorptions of energy.
+1914 – James Franck and Gustav Hertz report their experiment on electron collisions with mercury atoms, which provides a new test of Bohr's quantized model of atomic energy levels.
+1915 – Einstein first presents to the Prussian Academy of Science what are now known as the Einstein field equations. These equations specify how the geometry of space and time is influenced by whatever matter is present, and form the core of Einstein's General Theory of Relativity. Although this theory is not directly applicable to quantum mechanics, theorists of quantum gravity seek to reconcile them.
+1916 – Paul Epstein and Karl Schwarzschild, working independently, derive equations for the linear and quadratic Stark effect in hydrogen.
+1916 – Gilbert N. Lewis conceives the theoretical basis of Lewis dot formulas, diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule.
+1916 – To account for the Zeeman effect (1896), i.e. that atomic absorption or emission spectral lines change when the light source is subjected to a magnetic field, Arnold Sommerfeld suggests there might be "elliptical orbits" in atoms in addition to spherical orbits.
+1918 – Sir Ernest Rutherford notices that, when alpha particles are shot into nitrogen gas, his scintillation detectors shows the signatures of hydrogen nuclei. Rutherford determines that the only place this hydrogen could have come from was the nitrogen, and therefore nitrogen must contain hydrogen nuclei. He thus suggests that the hydrogen nucleus, which is known to have an atomic number of 1, is an elementary particle, which he decides must be the protons hypothesized by Eugen Goldstein.
+1919 – Building on the work of Lewis (1916), Irving Langmuir coins the term "covalence" and postulates that coordinate covalent bonds occur when two electrons of a pair of atoms come from both atoms and are equally shared by them, thus explaining the fundamental nature of chemical bonding and molecular chemistry.
+
+=== 1920–1929 ===
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+---
+title: "Timeline of quantum mechanics"
+chunk: 4/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+1920 – Hendrik Kramers uses Bohr–Sommerfeld quantization to derive formulas for intensities of spectral transitions of the Stark effect. Kramers also includes the effect of fine structure, including corrections for relativistic kinetic energy and coupling between electron spin and orbit. 1921–1922 – Frederick Soddy receives the Nobel Prize for 1921 in Chemistry one year later, in 1922, "for his contributions to our knowledge of the chemistry of radioactive substances, and his investigations into the origin and nature of isotopes"; he writes in his Nobel Lecture of 1922: "The interpretation of radioactivity which was published in 1903 by Sir Ernest Rutherford and myself ascribed the phenomena to the spontaneous disintegration of the atoms of the radio-element, whereby a part of the original atom was violently ejected as a radiant particle, and the remainder formed a totally new kind of atom with a distinct chemical and physical character."
+1922:
+Arthur Compton finds that X-ray wavelengths increase due to scattering of the radiant energy by free electrons. The scattered quanta have less energy than the quanta of the original ray. This discovery, known as the Compton effect or Compton scattering, demonstrates the particle concept of electromagnetic radiation. Otto Stern and Walther Gerlach perform the Stern–Gerlach experiment, which detects discrete values of angular momentum for atoms in the ground state passing through an inhomogeneous magnetic field leading to the discovery of the spin of the electron. Bohr updates his model of the atom to better explain the properties of the periodic table by assuming that certain numbers of electrons (for example 2, 8 and 18) corresponded to stable "closed shells", presaging orbital theory. 1923:
+Pierre Auger discovers the Auger effect, where filling the inner-shell vacancy of an atom is accompanied by the emission of an electron from the same atom. Louis de Broglie extends wave–particle duality to particles, postulating that electrons in motion are associated with waves. He predicts that the wavelengths are given by the Planck constant h divided by the momentum of the mv = p of the electron: λ = h / mv = h / p. Gilbert N. Lewis creates the theory of Lewis acids and bases based on the properties of electrons in molecules, defining an acid as accepting an electron lone pair from a base. 1924 – Satyendra Nath Bose explains Planck's law using a new statistical law that governs bosons, and Einstein generalizes it to predict Bose–Einstein condensate. The theory becomes known as Bose–Einstein statistics. 1924 – Wolfgang Pauli outlines the "Pauli exclusion principle", which states that no two identical fermions may occupy the same quantum state simultaneously, a fact that explains many features of the periodic table. 1925:
+George Uhlenbeck and Samuel Goudsmit postulate the existence of electron spin. Friedrich Hund outlines Hund's rule of Maximum Multiplicity, which states that when electrons are added successively to an atom as many levels or orbits are singly occupied as possible before any pairing of electrons with opposite spin occurs and made the distinction that the inner electrons in molecules remained in atomic orbitals and only the valence electrons needed to be in molecular orbitals involving both nuclei. Werner Heisenberg published his Umdeutung paper, reinterpreting quantum mechanics using non-commutative algebra. Heisenberg, Max Born, and Pascual Jordan develop the matrix mechanics formulation of quantum Mechanics. 1926:
+Lewis coins the term photon in a letter to the scientific journal Nature, which he derives from the Greek word for light, φως (transliterated phôs). Oskar Klein and Walter Gordon state their relativistic quantum wave equation, later called the Klein–Gordon equation. Enrico Fermi discovers the spin–statistics theorem connection. Paul Dirac introduces Fermi–Dirac statistics. Erwin Schrödinger uses De Broglie's electron wave postulate (1924) to develop a "wave equation" that represents mathematically the distribution of a charge of an electron distributed through space, being spherically symmetric or prominent in certain directions, i.e. directed valence bonds, which gives the correct values for spectral lines of the hydrogen atom; also introduces the Hamiltonian operator in quantum mechanics. Max Born postulates the statistical interpretation of the quantum mechanical wave function (Born rule)
+Paul Epstein reconsiders the linear and quadratic Stark effect from the point of view of the new quantum theory, using the equations of Schrödinger and others. The derived equations for the line intensities are a decided improvement over previous results obtained by Hans Kramers. 1926 to 1932 – John von Neumann published the Mathematical Foundations of Quantum Mechanics in terms of Hermitian operators on Hilbert spaces, subsequently published in 1932 as a basic textbook on the mathematical formulation of quantum mechanics. 1927:
+Werner Heisenberg formulates the quantum uncertainty principle. Niels Bohr and Werner Heisenberg develop the Copenhagen interpretation of the probabilistic nature of wavefunctions. Born and J. Robert Oppenheimer introduce the Born–Oppenheimer approximation, which allows the quick approximation of the energy and wavefunctions of smaller molecules. Walter Heitler and Fritz London introduce the concepts of valence bond theory and apply it to the hydrogen molecule. Llewellyn Thomas and Fermi develop the Thomas–Fermi model for a gas in a box. Chandrasekhara Venkata Raman studies optical photon scattering by electrons. Dirac states his relativistic electron quantum wave equation, the Dirac equation. Charles Galton Darwin and Walter Gordon solve the Dirac equation for a Coulomb potential. Charles Drummond Ellis (along with James Chadwick and colleagues) finally establish clearly that the beta decay spectrum is in fact continuous and not discrete, posing a problem that will later be solved by theorizing (and later discovering) the existence of the neutrino. Walter Heitler uses Schrödinger's wave equation to show how two hydrogen atom wavefunctions join, with plus, minus, and exchange terms, to form a covalent bond. Robert Mulliken works, in coordination with Hund, to develop a molecular orbital theory where electrons are assigned to states that extend over an entire molecule and, in 1932, introduces many new molecular orbital terminologies, such as σ bond, π bond, and δ bond. Eugene Wigner relates degeneracies of quantum states to irreducible representations of symmetry groups. Hermann Klaus Hugo Weyl proves in collaboration with his student Fritz Peter a fundamental theorem in harmonic analysis—the Peter–Weyl theorem—relevant to group representations in quantum theory (including the complete reducibility of unitary representations of a compact topological group); introduces the Weyl quantization, and earlier, in 1918, introduces the concept of gauge and a gauge theory; later in 1935 he introduces and characterizes with Richard Bauer the concept of spinor in n dimensions. 1928:
+Linus Pauling outlines the nature of the chemical bond: uses Heitler's quantum mechanical covalent bond model to outline the quantum mechanical basis for all types of molecular structure and bonding and suggests that different types of bonds in molecules can become equalized by rapid shifting of electrons, a process called "resonance" (1931), such that resonance hybrids contain contributions from the different possible electronic configurations. Friedrich Hund and Robert S. Mulliken introduce the concept of molecular orbitals. Born and Vladimir Fock formulate and prove the adiabatic theorem, which states that a physical system shall remain in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum.
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+---
+title: "Timeline of quantum mechanics"
+chunk: 5/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+1929:
+Oskar Klein discovers the Klein paradox
+Oskar Klein and Yoshio Nishina derive the Klein–Nishina cross section for high energy photon scattering by electrons. Sir Nevill Mott derives the Mott cross section for the Coulomb scattering of relativistic electrons. John Lennard-Jones introduces the linear combination of atomic orbitals approximation for the calculation of molecular orbitals. Fritz Houtermans and Robert d'Escourt Atkinson propose that stars release energy by nuclear fusion.
\ No newline at end of file
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+---
+title: "Timeline of quantum mechanics"
+chunk: 6/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+=== 1930–1939 ===
+
+1930
+Dirac hypothesizes the existence of the positron.
+Dirac's textbook The Principles of Quantum Mechanics is published, becoming a standard reference book that is still used today.
+Erich Hückel introduces the Hückel molecular orbital method, which expands on orbital theory to determine the energies of orbitals of pi electrons in conjugated hydrocarbon systems.
+Fritz London explains van der Waals forces as due to the interacting fluctuating dipole moments between molecules
+Pauli suggests in a famous letter that, in addition to electrons and protons, atoms also contain an extremely light neutral particle that he calls the "neutron". He suggests that this "neutron" is also emitted during beta decay and has simply not yet been observed. Later it is determined that this particle is actually the almost massless neutrino.
+1931:
+John Lennard-Jones proposes the Lennard-Jones inter-atomic potential.
+Walther Bothe and Herbert Becker find that if the very energetic alpha particles emitted from polonium fall on certain light elements, specifically beryllium, boron, or lithium, an unusually penetrating radiation is produced. At first this radiation is thought to be gamma radiation, although it is more penetrating than any gamma rays known, and the details of experimental results are very difficult to interpret on this basis. Some scientists begin to hypothesize the possible existence of another fundamental particle.
+Erich Hückel redefines the property of aromaticity in a quantum mechanical context by introducing the 4n+2 rule, or Hückel's rule, which predicts whether an organic planar ring molecule will have aromatic properties.
+Ernst Ruska creates the first electron microscope.
+Ernest Lawrence creates the first cyclotron and founds the Radiation Laboratory, later the Lawrence Berkeley National Laboratory; in 1939 he was awarded the Nobel Prize in Physics for his work on the cyclotron.
+1932:
+Irène Joliot-Curie and Frédéric Joliot show that if the unknown radiation generated by alpha particles falls on paraffin or any other hydrogen-containing compound, it ejects protons of very high energy. This is not in itself inconsistent with the proposed gamma ray nature of the new radiation, but detailed quantitative analysis of the data become increasingly difficult to reconcile with such a hypothesis.
+James Chadwick performs a series of experiments showing that the gamma ray hypothesis for the unknown radiation produced by alpha particles is untenable, and that the new particles must be the neutrons hypothesized by Fermi.
+Werner Heisenberg applies perturbation theory to the two-electron problem to show how resonance arising from electron exchange can explain Force carriers.
+Mark Oliphant: Building upon the nuclear transmutation experiments of Ernest Rutherford done a few years earlier, observes fusion of light nuclei (hydrogen isotopes). The steps of the main cycle of nuclear fusion in stars are subsequently worked out by Hans Bethe over the next decade.
+Carl D. Anderson experimentally proves the existence of the positron.
+1933 – Following Chadwick's experiments, Fermi renames Pauli's "neutron" to neutrino to distinguish it from Chadwick's theory of the much more massive neutron.
+1933 – Leó Szilárd first theorizes the concept of a nuclear chain reaction. He files a patent for his idea of a simple nuclear reactor the following year.
+1934:
+Fermi publishes a very successful model of beta decay in which neutrinos are produced.
+Fermi studies the effects of bombarding uranium isotopes with neutrons.
+N. N. Semyonov develops the total quantitative chain chemical reaction theory, later the basis of various high technologies using the incineration of gas mixtures. The idea is also used for the description of the nuclear reaction.
+Irène Joliot-Curie and Frédéric Joliot-Curie discover artificial radioactivity and are jointly awarded the 1935 Nobel Prize in Chemistry
+1935:
+Einstein, Boris Podolsky, and Nathan Rosen describe the EPR paradox, which challenges the completeness of quantum mechanics as it was theorized up to that time. Assuming that local realism is valid, they demonstrated that there would need to be hidden parameters to explain how measuring the quantum state of one particle could influence the quantum state of another particle without apparent contact between them.
+Schrödinger develops the Schrödinger's cat thought experiment. It illustrates what he saw as the problems of the Copenhagen interpretation of quantum mechanics if subatomic particles can be in two contradictory quantum states at once.
+Hideki Yukawa predicts the existence of the pion, stating that such a potential arises from the exchange of a massive scalar field, as it would be found in the field of the pion. Prior to Yukawa's paper, it was believed that the scalar fields of the fundamental forces necessitated massless particles.
+1936 – Alexandru Proca publishes prior to Hideki Yukawa his relativistic quantum field equations for a massive vector meson of spin-1 as a basis for nuclear forces.
+1936 – Garrett Birkhoff and John von Neumann introduce Quantum Logic in an attempt to reconcile the apparent inconsistency of classical, Boolean logic with the Heisenberg Uncertainty Principle of quantum mechanics as applied, for example, to the measurement of complementary (noncommuting) observables in quantum mechanics, such as position and momentum; current approaches to quantum logic involve noncommutative and non-associative many-valued logic.
+1936 – Carl D. Anderson discovers muons while he is studying cosmic radiation.
+1937 – Hermann Arthur Jahn and Edward Teller prove, using group theory, that non-linear degenerate molecules are unstable. The Jahn–Teller theorem essentially states that any non-linear molecule with a degenerate electronic ground state will undergo a geometrical distortion that removes that degeneracy, because the distortion lowers the overall energy of the complex. The latter process is called the Jahn–Teller effect; this effect was recently considered also in relation to the superconductivity mechanism in YBCO and other high temperature superconductors. The details of the Jahn–Teller effect are presented with several examples and EPR data in the basic textbook by Abragam and Bleaney (1970).
+1938 – Charles Coulson makes the first accurate calculation of a molecular orbital wavefunction with the hydrogen molecule.
+1938 – Otto Hahn and his assistant Fritz Strassmann send a manuscript to Naturwissenschaften reporting they have detected the element barium after bombarding uranium with neutrons. Hahn calls this new phenomenon a 'bursting' of the uranium nucleus. Simultaneously, Hahn communicates these results to Lise Meitner. Meitner, and her nephew Otto Robert Frisch, correctly interpret these results as being a nuclear fission. Frisch confirms this experimentally on 13 January 1939.
+1939 – Leó Szilárd and Fermi discover neutron multiplication in uranium, proving that a chain reaction is indeed possible.
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+---
+title: "Timeline of quantum mechanics"
+chunk: 7/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+=== 1940–1949 ===
+
+1942 – A team led by Enrico Fermi creates the first artificial self-sustaining nuclear chain reaction, called Chicago Pile-1, in a racquets court below the bleachers of Stagg Field at the University of Chicago on December 2, 1942.
+1942 to 1946 – J. Robert Oppenheimer successfully leads the Manhattan Project, predicts quantum tunneling and proposes the Oppenheimer–Phillips process in nuclear fusion
+1945 – the Manhattan Project produces the first nuclear fission explosion on July 16, 1945, in the Trinity test in New Mexico.
+1945 – John Archibald Wheeler and Richard Feynman originate Wheeler–Feynman absorber theory, an interpretation of electrodynamics that supposes that elementary particles are not self-interacting.
+1946 – Theodor V. Ionescu and Vasile Mihu report the construction of the first hydrogen maser by stimulated emission of radiation in molecular hydrogen.
+1947 – Willis Lamb and Robert Retherford measure a small difference in energy between the energy levels 2S1/2 and 2P1/2 of the hydrogen atom, known as the Lamb shift.
+1947 – George Rochester and Clifford Charles Butler publish two cloud chamber photographs of cosmic ray-induced events, one showing what appears to be a neutral particle decaying into two charged pions, and one that appears to be a charged particle decaying into a charged pion and something neutral. The estimated mass of the new particles is very rough, about half a proton's mass. More examples of these "V-particles" were slow in coming, and they are soon given the name kaons.
+1948 – Sin-Itiro Tomonaga and Julian Schwinger independently introduce perturbative renormalization as a method of correcting the original Lagrangian of a quantum field theory so as to eliminate a series of infinite terms that would otherwise result.
+1948 – Richard Feynman states the path integral formulation of quantum mechanics.
+1949 – Freeman Dyson determines the equivalence of two formulations of quantum electrodynamics: Feynman's diagrammatic path integral formulation and the operator method developed by Julian Schwinger and Tomonaga. A by-product of that demonstration is the invention of the Dyson series.
+
+=== 1950–1959 ===
+1951:
+Clemens C. J. Roothaan and George G. Hall derive the Roothaan–Hall equations, putting rigorous molecular orbital methods on a firm basis.
+Edward Teller, physicist and "father of the hydrogen bomb", and Stanislaw Ulam, mathematician, are reported to have written jointly in March 1951 a classified report on "Hydrodynamic Lenses and Radiation Mirrors" that results in the next step in the Manhattan Project.
+1951 and 1952 – at the Manhattan Project, the first planned fusion thermonuclear reaction experiment is carried out successfully in the Spring of 1951 at Eniwetok, based on the work of Edward Teller and Dr. Hans A. Bethe. The Los Alamos Laboratory proposes a date in November 1952 for a hydrogen bomb, full-scale test that is apparently carried out.
+Felix Bloch and Edward Mills Purcell receive a shared Nobel Prize in Physics for their first observations of the quantum phenomenon of nuclear magnetic resonance previously reported in 1949. Purcell reports his contribution as Research in Nuclear Magnetism, and gives credit to his coworkers such as Herbert S. Gutowsky for their NMR contributions, as well as theoretical researchers of nuclear magnetism such as John Hasbrouck Van Vleck.
+1952 – Albert W. Overhauser formulates a theory of dynamic nuclear polarization, also known as the Overhauser Effect; other contenders are the subsequent theory of Ionel Solomon reported in 1955 that includes the Solomon equations for the dynamics of coupled spins, and that of R. Kaiser in 1963. The general Overhauser effect is first demonstrated experimentally by T. R. Carver and Charles P. Slichter in 1953.
+1952 – Donald A. Glaser creates the bubble chamber, which allows detection of electrically charged particles by surrounding them by a bubble. Properties of the particles such as momentum can be determined by studying their helical paths. Glaser receives a Nobel prize in 1960 for his invention.
+1953 – Charles H. Townes, collaborating with James P. Gordon, and Herbert J. Zeiger, builds the first ammonia maser; receives a Nobel prize in 1964 for his experimental success in producing coherent radiation by atoms and molecules.
+1954 – Chen Ning Yang and Robert Mills derive a gauge theory for nonabelian groups, leading to the successful formulation of both electroweak unification and quantum chromodynamics.
+1955 – Ionel Solomon develops the first nuclear magnetic resonance theory of magnetic dipole coupled nuclear spins and of the Nuclear Overhauser effect.
+1956 – P. Kuroda predicts that self-sustaining nuclear chain reactions should occur in natural uranium deposits.
+1956 – Chien-Shiung Wu carries out the Wu Experiment, which observes parity violation in cobalt-60 decay, showing that parity violation is present in the weak interaction.
+1956 – Clyde L. Cowan and Frederick Reines experimentally prove the existence of the neutrino.
+1957 – John Bardeen, Leon Cooper and John Robert Schrieffer propose their quantum BCS theory of low temperature superconductivity, for which they receive a Nobel prize in 1972. The theory represents superconductivity as a macroscopic quantum coherence phenomenon involving phonon coupled electron pairs with opposite spin
+1957 – William Alfred Fowler, Margaret Burbidge, Geoffrey Burbidge, and Fred Hoyle, in their 1957 paper Synthesis of the Elements in Stars, show that the abundances of essentially all but the lightest chemical elements can be explained by the process of nucleosynthesis in stars.
+1957 – Hugh Everett formulates the many-worlds interpretation of quantum mechanics, which states that every possible quantum outcome is realized in divergent, non-communicating parallel universes in quantum superposition.
+1958–1959 – magic angle spinning described by Edward Raymond Andrew, A. Bradbury, and R. G. Eades, and independently in 1959 by I. J. Lowe.
+
+=== 1960–1969 ===
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+---
+title: "Timeline of quantum mechanics"
+chunk: 8/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+1961 – Claus Jönsson performs Young's double-slit experiment (1909) for the first time with particles other than photons by using electrons and with similar results, confirming that massive particles also behaved according to the wave–particle duality that is a fundamental principle of quantum field theory.
+1961 – Anatole Abragam publishes the fundamental textbook on the quantum theory of Nuclear Magnetic Resonance entitled The Principles of Nuclear Magnetism;
+1961 – Sheldon Glashow extends the electroweak interaction models developed by Julian Schwinger by including a short range neutral current, the Zo. The resulting symmetry structure that Glashow proposes, SU(2) × U(1), forms the basis of the accepted theory of the electroweak interactions.
+1962 – Leon M. Lederman, Melvin Schwartz and Jack Steinberger show that more than one type of neutrino exists by detecting interactions of the muon neutrino (already hypothesised with the name "neutretto")
+1962 – Jeffrey Goldstone, Yoichiro Nambu, Abdus Salam, and Steven Weinberg develop what is now known as Goldstone's Theorem: if there is a continuous symmetry transformation under which the Lagrangian is invariant, then either the vacuum state is also invariant under the transformation, or there must be spinless particles of zero mass, thereafter called Nambu–Goldstone bosons.
+1962 to 1973 – Brian David Josephson, predicts correctly the quantum tunneling effect involving superconducting currents while he is a PhD student under the supervision of Professor Brian Pippard at the Royal Society Mond Laboratory in Cambridge, UK; subsequently, in 1964, he applies his theory to coupled superconductors. The effect is later demonstrated experimentally at Bell Labs in the USA. For his important quantum discovery he is awarded the Nobel Prize in Physics in 1973.
+1963 – Eugene P. Wigner lays the foundation for the theory of symmetries in quantum mechanics as well as for basic research into the structure of the atomic nucleus; makes important "contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles"; he shares half of his Nobel prize in Physics with Maria Goeppert-Mayer and J. Hans D. Jensen.
+1963 – Maria Goeppert Mayer and J. Hans D. Jensen share with Eugene P. Wigner half of the Nobel Prize in Physics in 1963 "for their discoveries concerning nuclear shell structure theory".
+1964 – John Stewart Bell puts forth Bell's theorem, which used testable inequality relations to show the flaws in the earlier Einstein–Podolsky–Rosen paradox and prove that no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. This inaugurated the study of quantum entanglement, the phenomenon in which separate particles share the same quantum state despite being at a distance from each other.
+1964 – Nikolai G. Basov and Aleksandr M. Prokhorov share the Nobel Prize in Physics in 1964 for, respectively, semiconductor lasers and Quantum Electronics; they also share the prize with Charles Hard Townes, the inventor of the ammonium maser.
+1969 to 1977 – Sir Nevill Mott and Philip Warren Anderson publish quantum theories for electrons in non-crystalline solids, such as glasses and amorphous semiconductors; receive in 1977 a Nobel prize in Physics for their investigations into the electronic structure of magnetic and disordered systems, which allow for the development of electronic switching and memory devices in computers. The prize is shared with John Hasbrouck Van Vleck for his contributions to the understanding of the behavior of electrons in magnetic solids; he established the fundamentals of the quantum mechanical theory of magnetism and the crystal field theory (chemical bonding in metal complexes) and is regarded as the Father of modern Magnetism.
+1969 and 1970 – Theodor V. Ionescu, Radu Pârvan and I.C. Baianu observe and report quantum amplified stimulation of electromagnetic radiation in hot deuterium plasmas in a longitudinal magnetic field; publish a quantum theory of the amplified coherent emission of radiowaves and microwaves by focused electron beams coupled to ions in hot plasmas.
+
+=== 1971–1979 ===
+1971 – Martinus J. G. Veltman and Gerardus 't Hooft show that, if the symmetries of Yang–Mills theory are broken according to the method suggested by Peter Higgs, then Yang–Mills theory can be renormalized. The renormalization of Yang–Mills Theory predicts the existence of a massless particle, called the gluon, which could explain the nuclear strong force. It also explains how the particles of the weak interaction, the W and Z bosons, obtain their mass via spontaneous symmetry breaking and the Yukawa interaction.
+1972 – Francis Perrin discovers "natural nuclear fission reactors" in uranium deposits in Oklo, Gabon, where analysis of isotope ratios demonstrate that self-sustaining, nuclear chain reactions have occurred. The conditions under which a natural nuclear reactor could exist were predicted in 1956 by P. Kuroda.
+1973 – Peter Mansfield formulates the physical theory of nuclear magnetic resonance imaging (NMRI) aka magnetic resonance imaging (MRI).
+1974 – Pier Giorgio Merli performs Young's double-slit experiment (1909) using a single electron with similar results, confirming the existence of quantum fields for massive particles.
+1977 – Ilya Prigogine develops non-equilibrium, irreversible thermodynamics and quantum operator theory, especially the time superoperator theory; he is awarded the Nobel Prize in Chemistry in 1977 "for his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures".
+1978 – Pyotr Kapitsa observes new phenomena in hot deuterium plasmas excited by very high power microwaves in attempts to obtain controlled thermonuclear fusion reactions in such plasmas placed in longitudinal magnetic fields, using a novel and low-cost design of thermonuclear reactor, similar in concept to that reported by Theodor V. Ionescu et al. in 1969. Receives a Nobel prize for early low temperature physics experiments on helium superfluidity carried out in 1937 at the Cavendish Laboratory in Cambridge, UK, and discusses his 1977 thermonuclear reactor results in his Nobel lecture on December 8, 1978.
+1979 – Kenneth A. Rubinson and coworkers, at the Cavendish Laboratory, observe ferromagnetic spin wave resonant excitations in metallic glasses and interpret the observations in terms of two-magnon dispersion and a spin exchange Hamiltonian, similar in form to that of a Heisenberg ferromagnet.
\ No newline at end of file
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+---
+title: "Timeline of quantum mechanics"
+chunk: 9/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+=== 1980–1999 ===
+1980 to 1982 – Alain Aspect verifies experimentally the quantum entanglement hypothesis; his Bell test experiments provide strong evidence that a quantum event at one location can affect an event at another location without any obvious mechanism for communication between the two locations. This remarkable result confirmed the experimental verification of quantum entanglement by John F. Clauser. and. Stuart Freedman in 1972. Aspect later shared the 2022 Nobel Prize in Physics with Clauser and Anton Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science".
+1982 to 1997 – Tokamak Fusion Test Reactor (TFTR) at PPPL, Princeton, USA: Operated since 1982, produces 10.7 MW of controlled fusion power for only 0.21 s in 1994 by using T–D nuclear fusion in a tokamak reactor with "a toroidal 6T magnetic field for plasma confinement, a 3 MA plasma current and an electron density of 1.0×1020 m−3 of 13.5 keV"
+1983 – Carlo Rubbia and Simon van der Meer, at the Super Proton Synchrotron, see unambiguous signals of W particles in January. The actual experiments are called UA1 (led by Rubbia) and UA2 (led by Peter Jenni), and are the collaborative effort of many people. Simon van der Meer is the driving force on the use of the accelerator. UA1 and UA2 find the Z particle a few months later, in May 1983.
+1983 to 2011 – The largest and most powerful experimental nuclear fusion tokamak reactor in the world, Joint European Torus (JET) begins operation at Culham Facility in UK; operates with T-D plasma pulses and has a reported gain factor Q of 0.7 in 2009, with an input of 40MW for plasma heating, and a 2800-ton iron magnet for confinement; in 1997 in a tritium-deuterium experiment JET produces 16 MW of fusion power, a total of 22 MJ of fusion, energy and a steady fusion power of 4 MW, which is maintained for 4 seconds.
+1985 to 2010 – The JT-60 (Japan Torus) begins operation in 1985 with an experimental D–D nuclear fusion tokamak similar to the JET; in 2010 JT-60 holds the record for the highest value of the fusion triple product achieved: 1.77×1028 K·s·m−3 = 1.53×1021 keV·s·m−3. JT-60 claims it would have an equivalent energy gain factor, Q of 1.25 if it were operated with a T–D plasma instead of the D–D plasma, and on May 9, 2006, attains a fusion hold time of 28.6 s in full operation; moreover, a high-power microwave gyrotron construction is completed that is capable of 1.5 MW output for 1 s, thus meeting the conditions for the planned ITER, large-scale nuclear fusion reactor. JT-60 is disassembled in 2010 to be upgraded to a more powerful nuclear fusion reactor—the JT-60SA—by using niobium–titanium superconducting coils for the magnet confining the ultra-hot D–D plasma.
+1986 – Johannes Georg Bednorz and Karl Alexander Müller produce unambiguous experimental proof of high temperature superconductivity involving Jahn–Teller polarons in orthorhombic La2CuO4, YBCO and other perovskite-type oxides; promptly receive a Nobel prize in 1987 and deliver their Nobel lecture on December 8, 1987.
+1986 – Vladimir Gershonovich Drinfeld introduces the concept of quantum groups as Hopf algebras in his seminal address on quantum theory at the International Congress of Mathematicians, and also connects them to the study of the Yang–Baxter equation, which is a necessary condition for the solvability of statistical mechanics models; he also generalizes Hopf algebras to quasi-Hopf algebras, and introduces the study of Drinfeld twists, which can be used to factorize the R-matrix corresponding to the solution of the Yang–Baxter equation associated with a quasitriangular Hopf algebra.
+1988 to 1998 – Mihai Gavrilă discovers in 1988 the new quantum phenomenon of atomic dichotomy in hydrogen and subsequently publishes a book on the atomic structure and decay in high-frequency fields of hydrogen atoms placed in ultra-intense laser fields.
+1991 – Richard R. Ernst develops two-dimensional nuclear magnetic resonance spectroscopy (2D-FT NMRS) for small molecules in solution and is awarded the Nobel Prize in Chemistry in 1991 "for his contributions to the development of the methodology of high resolution nuclear magnetic resonance (NMR) spectroscopy".
+1995 – Eric Cornell, Carl Wieman and Wolfgang Ketterle and co-workers at JILA create the first "pure" Bose–Einstein condensate. They do this by cooling a dilute vapor consisting of approximately two thousand rubidium-87 atoms to below 170 nK using a combination of laser cooling and magnetic evaporative cooling. About four months later, an independent effort led by Wolfgang Ketterle at MIT creates a condensate made of sodium-23. Ketterle's condensate has about a hundred times more atoms, allowing him to obtain several important results such as the observation of quantum mechanical interference between two different condensates.
+1997 – Peter Shor publishes Shor's algorithm, a quantum computing algorithm for finding prime factors of integers. The algorithm is one of the few known quantum algorithms with immediate potential applications, which likely leads to a superpolynomial improvement over known non-quantum algorithms.
+1999 to 2013 – NSTX—The National Spherical Torus Experiment at PPPL, Princeton, USA launches a nuclear fusion project on February 12, 1999, for "an innovative magnetic fusion device that was constructed by the Princeton Plasma Physics Laboratory (PPPL) in collaboration with the Oak Ridge National Laboratory, Columbia University, and the University of Washington at Seattle"; NSTX is being used to study the physics principles of spherically shaped plasmas.
+
+== 21st century ==
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+---
+title: "Timeline of quantum mechanics"
+chunk: 10/10
+source: "https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:43.361745+00:00"
+instance: "kb-cron"
+---
+
+2001 – Researchers at IBM physically implement Shor's algorithm with an NMR setup, factoring 15 into 3 times 5 using seven qubits.
+2002 – Leonid I. Vainerman organizes a meeting at Strasbourg of theoretical physicists and mathematicians focused on quantum group and quantum groupoid applications in quantum theories; the proceedings of the meeting are published in 2003 in a book edited by the meeting organizer.
+2009 – Aaron D. O'Connell invents the first quantum machine, applying quantum mechanics to a macroscopic object just large enough to be seen by the naked eye, which is able to vibrate a small amount and large amount simultaneously.
+2011 – Zachary Dutton demonstrates how photons can co-exist in superconductors. "Direct Observation of Coherent Population Trapping in a Superconducting Artificial Atom",
+2012 – The existence of Higgs boson was confirmed by the ATLAS and CMS collaborations based on proton-proton collisions in the Large Hadron Collider at CERN. Peter Higgs and François Englert were awarded the 2013 Nobel Prize in Physics for their theoretical predictions.
+2015 – The first loophole-free Bell tests are performed by three independent teams, led by Ronald Hanson and Bas Hensen at TU Delft, by Sae Woo Nam and Krister Shalm at NIST, and by Anton Zeilinger and Marissa Giustina at the University of Vienna, confirming precisely the predictions of quantum mechanics and ruling out any local-realistic description of nature. These experiments are the culmination of a series of experiments started by John Clauser in the 1970s and significantly advanced by Alain Aspect in the 1980s among others. Clauser, Aspect, and Zeilinger share the Nobel Prize in Physics 2022 for their results.
+
+== See also ==
+
+History of quantum mechanics
+Timeline of atomic and subatomic physics
+Timeline of particle physics
+Timeline of physical chemistry
+List of scientific publications by Albert Einstein
+
+== References ==
+
+== Bibliography ==
+Peacock, Kent A. (2008). The Quantum Revolution: A Historical Perspective. Westport, Conn.: Greenwood Press. ISBN 9780313334481.
+Ben-Menahem, A. (2009). "Historical timeline of quantum mechanics 1925–1989". Historical Encyclopedia of Natural and Mathematical Sciences (1st ed.). Berlin: Springer. pp. 4342–4349. ISBN 9783540688310.
+
+== Notes ==
+
+== External links ==
+ Learning materials related to the history of Quantum Mechanics at Wikiversity
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diff --git a/data/en.wikipedia.org/wiki/Unmoved_mover-0.md b/data/en.wikipedia.org/wiki/Unmoved_mover-0.md
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+---
+title: "Unmoved mover"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Unmoved_mover"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:48.803622+00:00"
+instance: "kb-cron"
+---
+
+The unmoved mover (Ancient Greek: ὃ οὐ κινούμενον κινεῖ, romanized: ho ou kinoúmenon kineî, lit. 'that which moves without being moved'), or prime mover (Latin: primum movens), is a concept advanced by Aristotle as a primary cause, or first uncaused cause, or "mover" of all the motion in the universe. As is implicit in the name, the unmoved mover moves other things, but is not itself moved by any prior action. In Book 12 (Ancient Greek: Λ) of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: self-contemplation. He also equates this concept with the active intellect. This Aristotelian concept had its roots in cosmological speculations of the earliest Greek pre-Socratic philosophers, and became highly influential and widely drawn upon in medieval philosophy and theology. For example, St. Thomas Aquinas elaborated on the unmoved mover in the Five Ways.
+
+== First philosophy ==
+Aristotle argues, in Book 8 of the Physics and Book 12 of the Metaphysics, "that there must be an immortal, unchanging being, ultimately responsible for all wholeness and orderliness in the sensible world." In the Physics (VIII 4–6) Aristotle finds "surprising difficulties" explaining even commonplace change, and in support of his approach of explanation by four causes, he required "a fair bit of technical machinery". This "machinery" includes potentiality and actuality, hylomorphism, the theory of categories, and "an audacious and intriguing argument, that the bare existence of change requires the postulation of a first cause, an unmoved mover whose necessary existence underpins the ceaseless activity of the world of motion". Aristotle's "first philosophy", or Metaphysics ("after the Physics"), develops his peculiar theology of the prime mover, as πρῶτον κινοῦν ἀκίνητον: an independent divine eternal unchanging immaterial substance.
+
+=== Celestial spheres ===
+Aristotle adopted the geometrical model of Eudoxus of Cnidus to provide a general explanation of the apparent wandering of the classical planets arising from uniform circular motions of celestial spheres. While the number of spheres in the model itself was subject to change (47 or 55), Aristotle's account of aether, and of potentiality and actuality, required an individual unmoved mover for each sphere.
+
+=== Final cause and efficient cause ===
+Simplicius argues that the first unmoved mover is a cause not only in the sense of being a final cause—which everyone in his day, as in ours, would accept—but also in the sense of being an efficient cause (1360. 24ff.), and his master Ammonius wrote a whole book defending the thesis (ibid. 1363. 8–10). Simplicius's arguments include citations of Plato's views in the Timaeus—evidence not relevant to the debate unless one happens to believe in the essential harmony of Plato and Aristotle—and inferences from approving remarks which Aristotle makes about the role of Nous in Anaxagoras, which require a good deal of reading between the lines. But he does point out rightly that the unmoved mover fits the definition of an efficient cause—"whence the first source of change or rest" (Phys. II. 3, 194b29–30; Simpl. 1361. 12ff.). The examples which Aristotle adduces do not obviously suggest an application to the first unmoved mover, and it is at least possible that Aristotle originated his fourfold distinction without reference to such an entity. But the real question is whether his definition of the efficient cause includes the unmoved mover willy-nilly. One curious fact remains: that Aristotle never acknowledges the alleged fact that the unmoved mover is an efficient cause (a problem of which Simplicius is well aware: 1363. 12–14)...
+Despite their apparent function in the celestial model, the unmoved movers were a final cause, not an efficient cause for the movement of the spheres; they were solely a constant inspiration, and even if taken for an efficient cause precisely due to being a final cause, the nature of the explanation is purely teleological.
+
+=== Aristotle's theology ===
+The unmoved mover, if they were anywhere, were said to fill the outer void beyond the sphere of fixed stars:
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+---
+title: "Unmoved mover"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Unmoved_mover"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:48.803622+00:00"
+instance: "kb-cron"
+---
+
+It is clear then that there is neither place, nor void, nor time, outside the heaven. Hence whatever is there, is of such a nature as not to occupy any place, nor does time age it; nor is there any change in any of the things which lie beyond the outermost motion; they continue through their entire duration unalterable and unmodified, living the best and most self sufficient of lives… From [the fulfilment of the whole heaven] derive the being and life which other things, some more or less articulately but other feebly, enjoy.
+The unmoved mover is an immaterial substance (separate and individual beings), having neither parts nor magnitude. As such, it would be physically impossible for them to move material objects of any size by pushing, pulling, or collision. Because matter is, for Aristotle, a substratum in which a potential to change can be actualized, any potentiality must be actualized in an eternal being, but it must not be still because continuous activity is essential for all forms of life. This immaterial form of activity must be intellectual and cannot be contingent upon sensory perception if it is to remain uniform; therefore, eternal substance must think only of thinking itself and exist outside the starry sphere, where even the notion of place is undefined for Aristotle. Their influence on lesser beings is purely the result of an "aspiration or desire," and each aetheric celestial sphere emulates one of the unmoved movers, as best it can, by uniform circular motion. The first heaven, the outmost sphere of fixed stars, is moved by a desire to emulate the prime mover (first cause), about whom, the subordinate movers suffer an accidental dependency.
+Many of Aristotle's contemporaries complained that oblivious, powerless gods are unsatisfactory. Nonetheless, it was a life which Aristotle enthusiastically endorsed as one most enviable and perfect, the unembellished basis of theology. As the whole of nature depends on the inspiration of the eternal unmoved movers, Aristotle was concerned with establishing the metaphysical necessity of the perpetual motions of the heavens. Through the Sun's seasonal action upon the terrestrial spheres, the cycles of generation and corruption give rise to all natural motion as efficient cause.
+The intellect, nous, "or whatever else it be that is thought to rule and lead us by nature, and to have cognizance of what is noble and divine" is the highest activity, according to Aristotle (contemplation or speculative thinking, theōríā). It is also the most sustainable, pleasant, self-sufficient activity; something which is aimed at for its own sake. Unlike politics and warfare, it does not involve doing things we'd rather not do, but rather something we do at our leisure. This aim is not strictly human: to achieve it means to live following not mortal thoughts but something immortal and divine within humans. According to Aristotle, contemplation is the only type of happy activity that it would not be ridiculous to imagine the gods having. In Aristotle's psychology and biology, the intellect is the soul (see also eudaimonia). According to Giovanni Reale, the first Unmoved Mover is a living, thinking, and personal God who "possesses the theoretical knowledge alone or in the highest degree...knows not only Himself, but all things in their causes and first principles."
+
+=== First cause ===
+In Book VIII of his Physics, Aristotle examines the notions of change or motion, and attempts to show by a challenging argument, that the mere supposition of a 'before' and an 'after', requires a first principle. He argues that in the beginning, if the cosmos had come to be, its first motion would lack an antecedent state; and, as Parmenides said, "nothing comes from nothing". The cosmological argument, later attributed to Aristotle, thereby concludes that God exists. However, if the cosmos had a beginning, Aristotle argued, it would require an efficient first cause, a notion that Aristotle took to demonstrate a critical flaw.
+
+But it is a wrong assumption to suppose universally that we have an adequate first principle in virtue of the fact that something always is so ... Thus Democritus reduces the causes that explain nature to the fact that things happened in the past in the same way as they happen now: but he does not think fit to seek for a first principle to explain this 'always' ... Let this conclude what we have to say in support of our contention that there never was a time when there was not motion, and never will be a time when there will not be motion.
+The purpose of Aristotle's cosmological argument that at least one eternal unmoved mover must exist is to support everyday change.
+
+Of things that exist, substances are the first. But if substances can, then all things can perish... and yet, time and change cannot. Now, the only continuous change is that of place, and the only continuous change of place is circular motion. Therefore, there must be an eternal circular motion and this is confirmed by the fixed stars which are moved by the eternal actual substance that's purely actual.
+In Aristotle's estimation, an explanation without the temporal actuality and potentiality of an infinite locomotive chain is required for an eternal cosmos with neither beginning nor end: an unmoved eternal substance for whom the Primum Mobile turns diurnally, whereby all terrestrial cycles are driven by day and night, the seasons of the year, the transformation of the elements, and the nature of plants and animals.
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+title: "Unmoved mover"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Unmoved_mover"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:48.803622+00:00"
+instance: "kb-cron"
+---
+
+== Substance and change ==
+Aristotle begins by describing substance, of which he says there are three types: the sensible, subdivided into the perishable, which belongs to physics, and the eternal, which belongs to "another science." He notes that sensible substance is changeable and that there are several types of change, including quality and quantity, generation and destruction, increase and diminution, alteration, and motion. Change occurs when one given state becomes something contrary to it: that is to say, what exists potentially comes to exist actually (see potentiality and actuality). Therefore, "a thing [can come to be], incidentally, out of that which is not, [and] also all things come to be out of that which is, but is potentially, and is not actually." That by which something is changed is the mover, that which is changed is the matter, and that into which it is changed is the form. Substance is necessarily composed of different elements. The proof for this is that there are things that are different from each other and that all things are composed of elements. Since elements combine to form composite substances, and because these substances differ from each other, there must be different elements: in other words, "b or a cannot be the same as ba."
+
+== Number of movers ==
+Near the end of Metaphysics, Book Λ, Aristotle introduces a surprising question, asking "whether we have to suppose one such [mover] or more than one, and if the latter, how many." Aristotle concludes that the number of all the movers equals the number of separate movements, and we can determine these by considering the mathematical science most akin to philosophy, i.e., astronomy. Although the mathematicians differ on the number of movements, Aristotle considers that the number of celestial spheres would be 47 or 55. Nonetheless, he concludes his Metaphysics, Book Λ, with a quotation from the Iliad: "The rule of many is not good; one ruler let there be."
+
+== Influence ==
+
+In 1892, John Burnet wrote:
+
+The Neoplatonists were quite justified in regarding themselves as the spiritual heirs of Pythagoras; and, in their hands, philosophy ceased to exist as such, and became theology. And this tendency was at work all along; hardly a single Greek philosopher was wholly uninfluenced by it. Perhaps Aristotle might seem to be an exception; but it is probable that, if we still possessed a few such "exoteric" works as the Protreptikos in their entirety, we should find that the enthusiastic words in which he speaks of the "blessed life" in the Metaphysics and in the Ethics (Nicomachean Ethics) were less isolated outbursts of feeling than they appear now. In later days, Apollonios of Tyana showed in practice what this sort of thing must ultimately lead to. The theurgy and thaumaturgy of the late Greek schools were only the fruit of the seed sown by the generation which immediately preceded the Persian War.
+Aristotle's principles of being influenced Anselm's view of God, whom he called "that than which nothing greater can be conceived." Anselm thought God did not feel emotions such as anger or love but appeared to do so through our imperfect understanding. The incongruity of judging "being" against something that might not exist may have led Anselm to his famous ontological argument for God's existence. Many medieval philosophers used the idea of approaching a knowledge of God through negative attributes. For example, we should not say that God exists in the usual sense of the term; all we can safely say is that God is not nonexistent. We should not say that God is wise, but we can say that God is not ignorant (i.e., in some way, God has some properties of knowledge). We should not say that God is One, but we can state that there is no multiplicity in God's being.
+Many later Jewish, Islamic, and Christian philosophers accepted Aristotelian theological concepts. Key Jewish philosophers included ibn Tibbon, Maimonides, and Gersonides, among many others. Their views of God are considered mainstream by many Jews of all denominations, even today. Preeminent among Islamic philosophers who were influenced by Aristotelian theology are Avicenna and Averroes. In Christian theology, the key philosopher influenced by Aristotle was undoubtedly Thomas Aquinas. There had been earlier Aristotelian influences within Christianity (notably Anselm), but Aquinas (who, incidentally, found his Aristotelian influence via Avicenna, Averroes, and Maimonides) incorporated extensive Aristotelian ideas throughout his theology. Through Aquinas and the Scholastic Christian theology of which he was a significant part, Aristotle became "academic theology's great authority in the thirteenth century", and also influenced Christian theology that became widespread and deeply embedded. However, notable Christian theologians rejected Aristotelian theological influence, especially the first generation of Christian Reformers, most notably Martin Luther. In subsequent Protestant theology, Aristotelian thought quickly reemerged in Protestant scholasticism.
+
+== See also ==
+
+== Notes ==
+
+== References ==
+
+== Sources ==
+
+The Theology of Aristotle in the Stanford Encyclopedia of Philosophy
+John W. Watt (2019). The Aristotelian Tradition in Syriac. Routledge. ISBN 9780429817489.
+Gilles Emery; Matthew Levering (2015). Aristotle in Aquinas's Theology. Oxford University Press. ISBN 9780198749639.
+Richard Bodeus (2000). Aristotle and the Theology of the Living Immortals. SUNY Press. ISBN 9780791447284.
+Otfried Hoffe (2003). Aristotle. SUNY Press. ISBN 9780791456347.
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+---
+title: "Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Vorlesungen_über_die_Entwicklung_der_Mathematik_im_19._Jahrhundert"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:51.435568+00:00"
+instance: "kb-cron"
+---
+
+Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert (German for 'Lectures on the Development of Mathematics in the 19th Century') is a book by Felix Klein that was published posthumously in two volumes (volumes 24 and 25 of Grundlehren der mathematischen Wissenschaften) in 1926 and 1927. 
+Felix Klein had lectured on the development of mathematics in the 19th century and then on relativity during World War I. The books were created from the notes of these lectures and edited by Richard Courant and Otto Neugebauer for the first volume and Courant and Stefan Cohn-Vossen for the second. Some content that Klein had originally envisioned as part of the text is missing. 
+The book has been enthusiastically received and widely praised. The first volume has been translated into Russian in 1937 and into English in 1979; in 1989, a second Russian translation appeared, followed in 2003 by a translation of the second volume. Both volumes have also been translated into Chinese. 
+
+== Background and publication ==
+
+Felix Klein (1849–1925) was a German mathematician best known for his Erlangen program, which emphasised the use of groups in geometry. From 1886 to 1913 he was professor at the University of Göttingen, which became one of the leading centres of mathematical research under his leadership. 
+Klein was interested in the history of mathematics and bought relevant books for the Göttingen library. One of his students, Conrad Müller, studied for a PhD in history of mathematics under Klein and was later awarded the first habilitation degree in Göttingen in this topic area. Klein was responsible for the mathematical content in an encyclopaedic project called Die Kultur der Gegenwart  ('The Culture of the Present') published by B. G. Teubner Verlag in Leipzig, a publishing house he had longstanding ties with. The history of mathematics was supposed to be covered in three volumes; H. G. Zeuthen was responsible for the period up to the middle ages and Paul Stäckel for the time from 1500 to 1800. For covering 19th century applied mathematics, Klein tried to convince Heinrich Weber and Carl Runge, but he eventually accepted he had to do it himself. 
+Klein planned to lecture on the development of mathematics in the 19th century in the winter semester of 1910/11 and again in the winter semester of 1912/13, but both times was unable to do so. The classes were then taught privately during World War I. The winter 1914/15 courses were not announced in the Vorlesungsverzeichnis  (list of lectures), while the summer 1915 and winter 1915/16 courses were announced as "privatissime and free of charge". The first semester of lectures was attended by 24 people, including 13 male students, 9 faculty and 2 women. The women were Iris Runge and Klein's daughter Elisabeth Staiger. The first two semesters of lecture notes were edited and typed by the recently widowed Staiger, while the third course was worked on by Käthe Heinemann and Helene Stähelin. Stähelin's part, completed in Basel in 1918, included figures drawn by Erwin Voellmy. For a few years, the lecture notes were only available as these typescripts. After Klein's death, Richard Courant and Otto Neugebauer edited the notes and published the first volume in 1926 in the Springer Verlag's "yellow series", Grundlehren der mathematischen Wissenschaften . In their preface, they explained that they had changed as little as possible in the original text and admitted it was closer to a draft than to a thorough and balanced presentation of the history. While they thanked several other mathematicians for their help, they did not mention the three women who had prepared the typescripts from the original lectures anywhere in the book.
+Possibly because the Kultur der Gegenwart project was running into financial difficulties caused by the war, or because of his personal interests, Klein's lectures from 1916 onwards were concerned with relativity, and he postponed working on content regarding the works of Poincaré and Sophus Lie. Starting in 1916, Klein taught his lectures in his own house to avoid having to walk to the university. The notes were taken by Klein's assistant Walter Baade. Klein's lectures on "selected aspects of newer mathematics" were concerned with Einstein, the special theory of relativity on an invariant basis, and the foundations of general relativity. In 1916, his audience of 14 included the professors Runge and Carathéodory and the Swiss student Paul Finsler. Hilbert's assistant Emmy Noether and Käthe Heinemann were among the five women in attendance, and there were two blind students, Willi Windau and Friedrich Mittelsten Scheid. In winter 1916/17, there were seven attendees: Baade, Richard Bär, Josef Engel, Vsevolod Frederiks, Heinemann, Rudolf Jakob Humm and Windau. Klein sent a version of his summer 1917 lectures on general relativity to Albert Einstein, who dismissed the approach as overemphasising the formal over the heuristic point of view. In 1927, the lectures were published as the second volume of Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, with the additional subtitle Die Grundbegriffe der Invariantentheorie und ihr Eindringen in die mathematische Physik ('The Fundamental Concepts of Invariant Theory and Their Infiltration into Mathematical Physics'). The editors were Courant and especially Stefan Cohn-Vossen, who admitted the fragmentary character of the book in their introduction.
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+title: "Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Vorlesungen_über_die_Entwicklung_der_Mathematik_im_19._Jahrhundert"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:51.435568+00:00"
+instance: "kb-cron"
+---
+
+== Content ==
+The first volume is organised in eight chapters; the first chapter, simply titled "Gauß", is concerned with the life and work of Carl Friedrich Gauss and split into a section on applied and one on pure mathematics. The second chapter, "France and the École Polytechnique in the First Decades of the Nineteenth Century", contains sections on mechanics and mathematical physics (including the work of Poisson, Fourier and Cauchy), geometry (Monge and his followers), analysis and algebra (focusing on Cauchy and Galois). The third chapter "The Founding of Crelle's Journal and the Rise of Pure Mathematics in Germany" is concerned with mathematicians connected to Crelle's Journal (the analysts Dirichlet, Abel and Jacobi and the geometers Moebius, Plücker and Steiner), is followed by a chapter on "The Development of Algebraic Geometry after Moebius, Plücker and Steiner", with sections on projective geometry, invariant theory and n-dimensional spaces and general complex numbers, including content on Graßmann and Hamilton. In the fifth chapter, "Mechanics and Mathematical Physics in Germany and England until about 1880", Klein discusses Hamilton's and Jacobi's works on mechanics and works of English mathematicians including Green, Stokes and Maxwell. Chapter 6, "The General Theory of Functions of Complex Variables according to Riemann and Weierstraß" contrasts Riemann's approach to complex analysis with that of Weierstraß, and is followed by Chapter 7, "Deeper Insight into the Nature of Algebraic Varieties and Structures", which discusses algebraic geometry (including contributions by Clebsch and Noether) and algebraic number theory (Kummer, Dedekind and Hilbert, among others). In the final chapter, "Group Theory and Function Theory; Automorphic Functions", Klein discusses first group theory in connection with the works of Lagrange, Galois and C. Jordan. In the section on automorphic forms, he treats hypergeometric functions, conformal mappings, the icosahedron and elliptic functions, including a few pages on Poincaré. Originally, Klein had also planned to include full chapters on Poincaré and Sophus Lie in the book, but these are missing. Additionally, he planned to discuss set theory, the 1900 International Congress of Mathematicians and Hilbert's problems.
+The second volume is organised in three chapters. The first chapter, "Elementary Content regarding the Fundamentals of Linear Invariant Theory", is split into part A about general linear invariant theory and a "freer" part B about linear invariant theory including comments on the Erlangen Program and the development of vector and tensor analysis. The second chapter, "The Special Theory of Relativity in Mechanics and Mathematical Physics", has three parts: Part A is concerned with classical celestial mechanics, part B with Maxwell's electrodynamics and the Lorentz group, while part C treats the adaptation of mechanics to the relativity theory of the Lorentz group. The third chapter, "Transformation Groups on the Basis of a Quadratic Differential Form", has five parts. Part A treats Lagrangian mechanics, part B the intrinsic differential geometry of surfaces following Gauß. The remaining parts are concerned with Riemannian geometry: part C contains the formal background of Riemannian manifolds, part D normal coordinates and geometric interpretations, and part E reports on the further development after the time of Riemann, including the work of Beltrami, Lipschitz and Christoffel. A planned fourth chapter on the general theory of relativity and Hamiltonian mechanics with a focus on contact transformations and Lie groups was not finished; the editors stated that none of the existing drafts could have been turned into a printable form without adding an additional author's thoughts to Klein's approach. In contrast to the first volume, the second volume has a more systematic and factual focus and has fewer biographical and historical remarks.
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+---
+title: "Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Vorlesungen_über_die_Entwicklung_der_Mathematik_im_19._Jahrhundert"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T16:30:51.435568+00:00"
+instance: "kb-cron"
+---
+
+== Reception and legacy ==
+The books were received enthusiastically and especially the first volume has been widely celebrated. G. A. Miller, reviewing the first volume in Science, sees Klein as the most eminent mathematician to write a general history and finds the "extremely difficult task ... well begun", and praises Klein's personal acquaintance with most leading mathematicians. Josef Lense's review praises the editors and finds Klein the most suited person to the task. David Eugene Smith, writing for the Bulletin of the American Mathematical Society, calls Klein a "master" and emphasises the lack of national prejudice in the work. F. P. White's admiring review in The Mathematical Gazette calls the book "fascinating" and mentions several "curious and entertaining" episodes. The historian of mathematics Heinrich Wieleitner reviewed both volumes for Isis. His review of the first volume warmly welcomes its publication and the information coming from Klein's personal involvement, but criticises some of Klein's methods as not up to the standards of scientific historiography. The overall verdict is that the book is eine sehr wertvolle Vorarbeit zu einer wirklichen Geschichte der Mathematik des 19. Jahrh. ('a very valuable preliminary work for a true history of 19th century mathematics'). The second volume is described as incomplete but admirable. Although the reviewer notes a near-total lack of the personal touch of the first volume, he praises a few beautiful passages.
+The books had a great influence on Dirk Jan Struik, who had helped the editors in preparing the original manuscripts. In his later book A Concise History of Mathematics, Struik calls them "the best history of nineteenth century mathematics". The Soviet mathematician Vladimir Arnold deeply valued the books, and remarked in an interview that much of what he had learned about mathematics ("One-half of the mathematics I know", in his own words) came through their study. He often recommended them to his students.
+Reviewing the English edition of the book, the French mathematician Jean Dieudonné praises the idea of a new edition and notes that Klein's book has long been the only one on its topic, and still among the best. Nevertheless, he gives a long list of omissions and laments the lack of an index. In another French review of the German reprint of both volumes, Pierre Dugac calls the book "irreplaceable" and praises Klein's expressions of the "mood" of 19th century mathematics, but criticises the lack of a modern introduction putting the book in context of newer historical works. Welcoming the reprint, the East German historian of mathematics Hans Wußing calls the book a part of the fundamental mathematical-historical literature, while noting that some of Klein's opinions are subjective and have been superseded.
+In his book about Klein and Sophus Lie, the Soviet mathematician Isaak Yaglom defends Klein against accusations of chauvinism brought forward by Jacques Hadamard in 1943. While admitting that Klein ignored the contributions of Russian and Italian mathematicians and some fields like probability theory, Yaglom writes, "the book's import lies in the concept of joint work by scientists of all races and nationalities, contributing perhaps in different ways, but with equal merit, to the construction of the mathematical edifice." The mathematician and historian Detlef Laugwitz quotes Klein's Vorlesungen in his book about Bernhard Riemann, calling Klein "important as a witness of the effect of Riemann's ideas in the last decades of the 19th century". The historian of mathematics David E. Rowe describes them as "a highly personalized account of this period", and notes that the original lecture notes "were sometimes even more opinionated, expressing his misgivings about recent modernist trends toward abstraction and axiomatics".
+
+== Translations ==
+The book was translated into Russian twice, both times as Лекции о развитии математики в XIX столетии. The 1937 edition was translated by B. Livshits, A. Lopshits, Y. Rabinovich and L. Tumerman and had a preface by the Soviet historian of mathematics Mark Vygodskii. It contained some errors. For example, it mistranslated Jacobi dying from Blattern (smallpox) as dying in a place called Blattern. The second version appeared in 1989, translated by N. M. Nagorny and edited by M. M. Postnikov. In the preface, which builds on Vygodskii's, they noted that their main focus was to be as faithful as possible to Klein's thought and the spirit of his work. In 2003, also the second volume appeared, translated by V. A. Antonov and edited by B. P. Kondratyev. 
+The book was translated into English by M. Ackerman as Development of Mathematics in The 19th Century (1979), edited by Robert Hermann, who provided a lengthy appendix on "Kleinian Mathematics from an Advanced Standpoint".
+It was translated into Chinese as 数学在19世纪的发展 as part of the 数学翻译丛书 (Mathematical Translations series) edited by Shing-Tung Yau for Higher Education Press. The first volume appeared in 2010, translated by Qi Minyou; the second in 2011, translated by Li Peilian (李培廉). The first volume includes a translation into Chinese of Hermann's preface to the English translation.
+
+=== List of translations ===
+Klein, Felix (1937). Lekcii o razvitii matematiki v XIX stoletii (in Russian). Moscow; Leningrad: Ob'edinennoye nauchno-tekhnicheskoye izdatelstvo NKTP SSSR.
+Klein, Felix (1989). Lekcii o razvitii matematiki v XIX stoletii. 1. Moscow: Nauka. ISBN 978-5-02-013920-6.
+Klein, Felix (2003). Lekcii o razvitii matematiki v XIX stoletii. 2. Moscow; Izhevsk: Institut Komp'yuternykh Issledovaniy. ISBN 5-93972-208-3.
+Klein, Felix (2010). 数学在19世纪的发展 (第一卷) (in Chinese). 高等教育出版社. ISBN 978-7-04-028886-5.
+Klein, Felix (2011). 数学在19世纪的发展 (第二卷) (in Chinese). 高等教育出版社. ISBN 978-7-04-032284-2.
+Klein, Felix (1979a). Development of mathematics in the 19th century. Translated by Ackerman, M. Brookline, Mass: Math Sci Press. ISBN 0-915692-28-7.
+
+== References ==
+
+=== Citations ===
+
+=== Sources ===
+
+== External links ==
+Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert at Göttinger Digitalisierungszentrum: http://resolver.sub.uni-goettingen.de/purl?PPN375425993
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+title: "Woodstock of physics"
+chunk: 1/1
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+tags: "science, encyclopedia"
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+
+The Woodstock of physics was the popular name given by physicists to the marathon session of the American Physical Society’s meeting on March 18, 1987, which featured 51 presentations of recent discoveries in the science of high-temperature superconductors. Various presenters anticipated that these new materials would soon result in revolutionary technological applications, but in the three subsequent decades, this proved to be overly optimistic. The name is a reference to the 1969 Woodstock Music and Art Festival.
+
+
+== Leading up to the meeting ==
+Before a series of breakthroughs in the mid-1980s, most scientists believed that the extremely low temperature requirements of superconductors rendered them impractical for everyday use. However, in June 1986, K. Alex Muller and Georg Bednorz working in IBM Zurich broke the record of critical temperature superconductivity in lanthanum barium copper oxide (LBCO) to 35 K above absolute zero, which had remained unbroken at 23 K for 17 years. Their discovery stimulated a great deal of additional research in high-temperature superconductivity.
+By March 1987, a flurry of recent research on ceramic superconductors had succeeded in creating ever-higher superconducting temperatures, including the discovery of Maw-Kue Wu and Jim Ashburn at the University of Alabama, who found a critical temperature of 77 K in yttrium barium copper oxide (YBCO). This result was followed by Paul C. W. Chu at the University of Houston's of a superconductor that operated at 93 K (−180 °C; −292 °F) – a temperature that could be achieved by cooling with liquid nitrogen. The scientific community was abuzz with excitement.
+
+
+== Events ==
+The discoveries were so recent that no papers on them had been submitted by the deadline. However, the Society added a last-minute session to their annual meeting to discuss the new research. The session was chaired by physicist M. Brian Maple, a superconductor researcher himself, who was one of the meeting's organizers. It was scheduled to start at 7:30 pm in the Sutton ballroom of the New York Hilton, but excited scientists started lining up at 5:30. Key researchers such as Chu and Müller were given 10 minutes to describe their research; other physicists were given five minutes. Nearly 2,000 scientists tried to squeeze into the ballroom. Those who could not find a seat filled the aisles or watched outside the room on television monitors. The session ended at 3:15 am, but many lingered until dawn to discuss the presentations. The meeting caused a surge in mainstream media interest in superconductors, and laboratories around the world raced to pursue breakthroughs in the field.
+In October of the same year, Bednorz and Muller were awarded the Nobel Prize in Physics "for their important break-through in the discovery of superconductivity in ceramic materials", setting a record for the shortest time between the discovery and the prize award for any scientific Nobel Prize category.
+
+
+== Sequels ==
+
+
+=== Woodstock of physics II ===
+By the following year (1988) two new families of copper-oxide superconductors – the bismuth based or so-called BSCCO and the thallium based or TBCCO materials – had been discovered. Both of these have superconducting transitions above 110 K (−163 °C; −262 °F). So in the follow-up March APS meeting at New Orleans a special evening session called Woodstock of Physics-II was hastily organized to highlight the synthesis and properties of these new, first-ever 'triple digit superconductors'. The format of the session was the same as in New York. Some of the panelists were repeats from the original "Woodstock" session. Additional researchers including Allen M. Hermann (at that time at the University of Arkansas), the co-discoverer of the thallium system, and Laura H. Greene (then with AT&T Labs) were panelists. The 1988 session was chaired by Timir Datta from the University of South Carolina.
+
+
+=== 20 year anniversary ===
+On March 5, 2007, many of the original participants reconvened in Denver to recognize and review the session on its 20-year anniversary; the "reunion" was again chaired by Maple.
+
+
+== See also ==
+List of physics conferences
+
+
+== Notes ==
+
+
+== References ==
+Fishlock, David (April 3, 1987). "A Ceramic Goldmine At The Electronics Frontier; Superconductivity". The Financial Times.
+Fishlock, David (March 17, 1989). "Superconductivity Hits A Quieter Note Since The 'Woodstock Of Physics'". The Financial Times.
+Dahl, Per Fridtjof (February 1992). Superconductivity: Its Historical Roots and Development from Mercury to the Ceramic Oxides. American Inst. of Physics. ISBN 9780883188484.
+Poole, Charles P.; Datta, Timir; Farach, Horacio A. (1988). Copper oxide superconductors. Wiley. ISBN 9780471623427.
+
+
+== External links ==
+Video recordings (published in 2016 by the American Physical Society, announcement: Experience the 1987 "Woodstock of Physics" Online)
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