diff --git a/_index.db b/_index.db index 7083b09a7..8c52be70e 100644 Binary files a/_index.db and b/_index.db differ diff --git a/data/en.wikipedia.org/wiki/1821_in_archaeology-0.md b/data/en.wikipedia.org/wiki/1821_in_archaeology-0.md new file mode 100644 index 000000000..fa5269819 --- /dev/null +++ b/data/en.wikipedia.org/wiki/1821_in_archaeology-0.md @@ -0,0 +1,36 @@ +--- +title: "1821 in archaeology" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/1821_in_archaeology" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:35.523905+00:00" +instance: "kb-cron" +--- + +The year 1821 in archaeology involved some significant events. + + +== Explorations == +October - John Gardner Wilkinson begins a twelve-year stay in Egypt, surveying historical sites. + + +== Finds == +'Gallagh Man', an Iron Age bog body, is found in County Galway, Ireland. + + +== Miscellaneous == +"Egyptian Hall" in London displays artifacts from Ancient Egypt brought to the United Kingdom by Giovanni Battista Belzoni. The Philae obelisk is landed in England in December. +While not specifically the year 1821, this time period is when one of the most significant categorical discoveries of archaeology was named. Christian Thomsen, a Danish archaeologist, developed the three age system to date objects in museums. These three ages were the "Stone Age," "Bronze Age," and "Iron Age." +While not specifically the year 1821, this time period is when one of the most significant findings regarding time and dating archaeological findings was discovered. Boucher de Perthes established a much deeper sense of time than what James Usher had previously established. Perthes determined that the world was significantly older than 4004 BC and thus gave archaeology a deeper, more realistic time frame to work with. + + +== Births == +June 21, 1821- The birth of Ephraim George Squier, co-author of "Ancient Monuments of the Mississippi Valley" along with Edwin Hamilton Davis. + + +== See also == +Ancient Egypt / Egyptology + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/3rd_Stone-0.md b/data/en.wikipedia.org/wiki/3rd_Stone-0.md new file mode 100644 index 000000000..c854d94a5 --- /dev/null +++ b/data/en.wikipedia.org/wiki/3rd_Stone-0.md @@ -0,0 +1,29 @@ +--- +title: "3rd Stone" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/3rd_Stone" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:32.007406+00:00" +instance: "kb-cron" +--- + +3rd Stone is a defunct British magazine devoted to "archaeology, folklore and myth" and dealing with Earth mysteries. + + +== History and profile == +The magazine was originally published under the title of Gloucestershire Earth Mysteries (G.E.M.) magazine, founded by Danny Sullivan in the mid-1980s, and the name was changed to 3rd Stone magazine in 1986. The magazine was based in Cheltenham. Neil Mortimer took over as editor in 1995, and edited the magazine until its closure in 2003. +3rd Stone absorbed At the Edge magazine in 1998 before itself ceasing publication in 2003. Aubrey Burl, Ed Krupp, John Michell, Paul Devereux, Jeremy Harte, Rodney Castleden and Stan Beckensall are among the authors who contributed to the magazine. +Timothy Darvill, in reviewing The Modern Antiquarian, mentioned that The 3rd Stone followed "much the same path [as that book], and [had] a rapidly increasing subscription base and considerable public following" and that it carried "articles by a wide range of authors and gives each equal weight." +3rd Stone ceased publication with issue 47 published in 2003. + + +== See also == +List of magazines of anomalous phenomena + + +== References == + + +== External links == +Many issues of 3rd Stone are available for free PDF download here \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/4Q119-0.md b/data/en.wikipedia.org/wiki/4Q119-0.md new file mode 100644 index 000000000..8f3603d73 --- /dev/null +++ b/data/en.wikipedia.org/wiki/4Q119-0.md @@ -0,0 +1,19 @@ +--- +title: "4Q119" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/4Q119" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:33.209702+00:00" +instance: "kb-cron" +--- + +4Q119 (also 4QLXXLeva; TM 62293; LDAB 3454) designates the remnants of a Greek manuscript of the Book of Leviticus written on parchment. It was found at Qumran cave 4 and is dated to the 1st century BCE or 1st century CE. It got the no. 801 according to the system of Alfred Rahlfs. The manuscript is stored in Rockefeller Museum at Jerusalem (Mus. Inv. Gr. 1004). + + +== Bibliography == +Patrick Skehan, Eugene C. Ulrich, Judith E. Sanderson: 119. 4QLXXLeviticusa. Qumran Cave 4.IV (Discoveries in the Judaean Desert 9). Clarendon Press, Oxford 1992. ISBN 0-19-826328-7, pp. 161–165, plate XXXVIII. + + +== External links == +"Skehan e.a., Qumran cave 4.4 (Discoveries in the Judaean desert 9)". Trismegistos. Retrieved 2012-12-14. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/4Q240-0.md b/data/en.wikipedia.org/wiki/4Q240-0.md new file mode 100644 index 000000000..ae520b54c --- /dev/null +++ b/data/en.wikipedia.org/wiki/4Q240-0.md @@ -0,0 +1,33 @@ +--- +title: "4Q240" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/4Q240" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:34.401772+00:00" +instance: "kb-cron" +--- + +4Q240 ( or 4QCanta) is believed to be a commentary (or pesher) on the Song of Songs, also known as 'Canticles'. Written in Hebrew, it was found in Cave 4 at Qumran in the Judean Desert and comprises part of the Dead Sea Scrolls. From its palaeography (script) it has been identified as being early-Herodian. + + +== Location == +Included in Milik's original list, but this fragment has never been located. + + +== See also == +List of Hebrew Bible manuscripts +Dead Sea Scrolls +4Q106 +4Q107 +4Q108 +4QMMT +6Q6 +Tanakh at Qumran + + +== References == + + +== External links == +"The Dead Sea Scrolls and Why They Matter" – 4Q240 in Biblical Archaeology Review \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/AWM-SIAM_Sonia_Kovalevsky_Lecture-0.md b/data/en.wikipedia.org/wiki/AWM-SIAM_Sonia_Kovalevsky_Lecture-0.md new file mode 100644 index 000000000..3437f1307 --- /dev/null +++ b/data/en.wikipedia.org/wiki/AWM-SIAM_Sonia_Kovalevsky_Lecture-0.md @@ -0,0 +1,55 @@ +--- +title: "AWM-SIAM Sonia Kovalevsky Lecture" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/AWM-SIAM_Sonia_Kovalevsky_Lecture" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:25.025282+00:00" +instance: "kb-cron" +--- + +The AWM-SIAM Sonia Kovalevsky Lecture is an award and lecture series that "highlights significant contributions of women to applied or computational mathematics." The Association for Women in Mathematics (AWM) and the Society for Industrial and Applied Mathematics (SIAM) planned the award and lecture series in 2002 and first awarded it in 2003. The lecture is normally given each year at the SIAM Annual Meeting. Award winners receive a signed certificate from the AWM and SIAM presidents. +The lectures are named after Sonia Kovalevsky (1850–1891), a well-known Russian mathematician of the late 19th century. Karl Weierstrass regarded Kovalevsky as his most talented student. In 1874, she received her Doctor of Philosophy degree from the University of Göttingen under the supervision of Weierstrass. She was granted privatdozentin status and taught at the Stockholm University in 1883; she became an ordinary professor (the equivalent of full professor) at this institution in 1889. She was also an editor of the journal Acta Mathematica. Kovalevsky did her important work in the theory of partial differential equations and the rotation of a solid around a fixed point. + + +== Recipients == +The Kovalevky Lecturers have been: + +2003 Linda R. Petzold, University of California, Santa Barbara, “Towards the Multiscale Simulation of Biochemical Networks” +2004 Joyce R. McLaughlin, Rensselaer Polytechnic Institute, “Interior Elastodynamics Inverse Problems: Creating Shear Wave Speed Images of Tissue” +2005 Ingrid Daubechies, Princeton University, “Superfast and (Super)sparse Algorithms” +2006 Irene Fonseca, Carnegie Mellon University, “New Challenges in the Calculus of Variations” +2007 Lai-Sang Young, Courant Institute, “Shear-Induced Chaos” +2008 Dianne P. O'Leary, University of Maryland, “A Noisy Adiabatic Theorem: Wilkinson Meets Schrödinger’s Cat” +2009 Andrea Bertozzi, University of California, Los Angeles +2010 Suzanne Lenhart, University of Tennessee at Knoxville, “Mixing it up: Discrete and Continuous Optimal Control for Biological Models” +2011 Susanne C. Brenner, Louisiana State University, “A Cautionary Tale in Numerical PDEs” +2012 Barbara Keyfitz, Ohio State University, “The Role of Characteristics in Conservation Laws” +2013 Margaret Cheney, Colorado State University, “Introduction to Radar Imaging” +2014 Irene M. Gamba, University of Texas at Austin, “The evolution of complex interactions in non-linear kinetic systems” +2015 Linda J. S. Allen, Texas Tech University, “Predicting Population Extinction” +2016 Lisa J. Fauci, Tulane University, “Biofluids of Reproduction: Oscillators, Viscoelastic Networks and Sticky Situations” +2017 Liliana Borcea, University of Michigan, “Mitigating Uncertainty in Inverse Wave Scattering” +2018 Eva Tardos, Cornell University, “Learning and Efficiency of Outcomes in Games” +2019 Catherine Sulem, University of Toronto, “The Dynamics of Ocean Waves” +2020 Bonnie Berger, MIT, “Compressive genomics: leveraging the geometry of biological data” +2021 Vivette Girault, Université Pierre et Marie Curie, "From linear poroelasticity to nonlinear implicit elastic and related models" +2022 Anne Greenbaum, University of Washington, "Two of my Favorite Problems” +2023 Annalisa Buffa, Ecole Polytechnique Fédérale de Lausanne (EPFL), "Simulation of PDEs on Geometries Obtained via Boolean Operations" +2024 Sunčica Čanić, University of California at Berkeley, "Mathematics for Bioartificial Organ Design" +2025 Yongjie Jessica Zhang, Carnegie Mellon University, TBD +2026 Fioralba Cakoni, Rutgers University, TBD + + +== See also == +Falconer Lecture +Noether Lecture +List of mathematics awards + + +== References == + + +== External links == +"Kovalevsky Lectures – Association for Women in Mathematics (AWM)". awm-math.org. Retrieved 1 January 2021. +"Prizes, Awards, and Honors for Women Mathematicians". agnesscott.edu. Retrieved 1 January 2021. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/AWM–Microsoft_Research_Prize_in_Algebra_and_Number_Theory-0.md b/data/en.wikipedia.org/wiki/AWM–Microsoft_Research_Prize_in_Algebra_and_Number_Theory-0.md new file mode 100644 index 000000000..b1593e1ad --- /dev/null +++ b/data/en.wikipedia.org/wiki/AWM–Microsoft_Research_Prize_in_Algebra_and_Number_Theory-0.md @@ -0,0 +1,41 @@ +--- +title: "AWM–Microsoft Research Prize in Algebra and Number Theory" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/AWM–Microsoft_Research_Prize_in_Algebra_and_Number_Theory" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:23.832907+00:00" +instance: "kb-cron" +--- + +The AWM–Microsoft Research Prize in Algebra and Number Theory and is a prize given every other year by the Association for Women in Mathematics to an outstanding young female researcher in algebra or number theory. It was funded in 2012 by Microsoft Research and first issued in 2014. + + +== Winners == +Sophie Morel (2014), for her research in number theory, particularly her contributions to the Langlands program, an application of her results on weighted cohomology, and a new proof of Brenti's combinatorial formula for Kazhdan-Lusztig polynomials. +Lauren Williams (2016), for her research in algebraic combinatorics, particularly her contributions on the totally nonnegative Grassmannian, her work on cluster algebras, and her proof (with Musiker and Schiffler) of the famous Laurent positivity conjecture. +Melanie Wood (2018), for her research in number theory and algebraic geometry, particularly her contributions in arithmetic statistics and tropical geometry, as well as her work with Ravi Vakil on the limiting behavior of natural families of varieties. +Melody Chan (2020), in recognition of her advances at the interface between algebraic geometry and combinatorics. +Jennifer Balakrishnan (2022), in recognition of her advances in computing rational points on algebraic curves over number fields. +Yunqing Tang (2024), for "work in arithmetic geometry, including results on the Grothendieck–Katz + + + + p + + + {\displaystyle p} + +-curvature conjecture, a conjecture of Ogus on algebraicity of cycles, arithmetic intersection theory, and the unbounded denominators conjecture of Atkin and Swinnerton-Dyer" + + +== See also == +List of awards honoring women +List of mathematics awards + + +== References == + + +== External links == +AWM–Microsoft Research Prize, Association for Women in Mathematics \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Absolute_space_and_time-0.md b/data/en.wikipedia.org/wiki/Absolute_space_and_time-0.md index 6cf50fbf1..046306972 100644 --- a/data/en.wikipedia.org/wiki/Absolute_space_and_time-0.md +++ b/data/en.wikipedia.org/wiki/Absolute_space_and_time-0.md @@ -4,7 +4,7 @@ chunk: 1/2 source: "https://en.wikipedia.org/wiki/Absolute_space_and_time" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:13:41.731550+00:00" +date_saved: "2026-05-05T11:14:58.980985+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Absolute_space_and_time-1.md b/data/en.wikipedia.org/wiki/Absolute_space_and_time-1.md index c7e262a61..e8ea2dbf2 100644 --- a/data/en.wikipedia.org/wiki/Absolute_space_and_time-1.md +++ b/data/en.wikipedia.org/wiki/Absolute_space_and_time-1.md @@ -4,7 +4,7 @@ chunk: 2/2 source: "https://en.wikipedia.org/wiki/Absolute_space_and_time" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:13:41.731550+00:00" +date_saved: "2026-05-05T11:14:58.980985+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Ada_Byron_Award-0.md b/data/en.wikipedia.org/wiki/Ada_Byron_Award-0.md new file mode 100644 index 000000000..c87c5a0b2 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Ada_Byron_Award-0.md @@ -0,0 +1,60 @@ +--- +title: "Ada Byron Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Ada_Byron_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:20.303497+00:00" +instance: "kb-cron" +--- + +The Ada Byron Award for Women in Technology (Premio Ada Byron a la Mujer Tecnóloga) is an honor given annually by the University of Deusto to recognize the careers of women in technology. It seeks out women scientists and technologists who have contributed to various scientific disciplines, such as Ada Byron, for whom the award is named. + + +== History == +The Ada Byron Award for Women in Technology was established at the University of Deusto in October 2013. +Its first edition was presented on 11 April 2014, during the "Women and Technology" session at Forotech 2014, which was held as part of Deusto Engineering and Technology Week. The winner received a cash prize of €3,000. +In 2019 it expanded to Mexico, and in 2020 it reached Argentina through the Catholic University of Córdoba and the National Technological University. +In 2021 it arrived in Uruguay with the support of the Catholic University of Uruguay, and in Colombia with the Pontificia Universidad Javeriana. +Continuing with the internationalization of the award, in 2022, it was expanded to Chile, with the support of the Andrés Bello National University. +In 2023, the Ada Byron Award celebrated its tenth edition. To commemorate this milestone, a video was produced, featuring the winners from all previous editions. + + +== Goals == +The award aims to: + +Give visibility to women within the world of technology by recognizing their important work, which is insufficiently known in society as a whole +Enrich society with technology dissemination events, providing female role models for new generations +Promote technological vocations by making technological work accessible to teenagers, highlighting the positive aspects, especially in female vocations +Raise social awareness of the importance of technology for economic growth and as a future value for society +Contribute to the realization of the UN's Sustainable Development Goal 5: "Achieve gender equality and empower all women and girls" + + +== Administrators and jurors == +Nerea Aranguren – director of innovation at Danobat and manager at Ideko +Guillermo Dorronsoro – management board advisor, Zabala Innovation Consulting +Miren Elgarresta – director of Emakunde-Basque Institute for Women +Lorena Fernández Álvarez – director of digital communication at the University of Deusto +Cristina Giménez Elorriaga – member of the Scientific-Technological Committee at the University of Deusto +Sara Gómez Martín – director of the Women and Engineering Project at the Royal Academy of Engineering +Mari Luz Guenaga Gómez – member of the Scientific-Technological Committee at the University of Deusto +Teresa Laespada – deputy for employment, cohesion and equality in the General Assemblies of Biscay +Idoia Maguregui Villalain – advisory board member, CIOnet +Eva Ortega Paíno – Secretary General of Research at the Ministry of Science +Manuel Salaverria – president of Innobasque +María Cora Urdaneta Ponte – member of the Scientific-Technological Committee at the University of Deusto + + +== Winners == + + +== See also == +Ada Lovelace Award +BCS Lovelace Medal + + +== References == + + +== External links == +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Afghan_Liturgical_Quire-0.md b/data/en.wikipedia.org/wiki/Afghan_Liturgical_Quire-0.md new file mode 100644 index 000000000..7a5b64dfe --- /dev/null +++ b/data/en.wikipedia.org/wiki/Afghan_Liturgical_Quire-0.md @@ -0,0 +1,24 @@ +--- +title: "Afghan Liturgical Quire" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Afghan_Liturgical_Quire" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:37.902326+00:00" +instance: "kb-cron" +--- + +The Afghan Liturgical Quire (ALQ), also known as the Afghan Siddur, is a quire from the Afghan Geniza in Bamyan, Afghanistan. It is the oldest Hebrew codex ever discovered, and contains Hebrew liturgical texts, including prayers, blessings, and piyyuṭ. The manuscript was written in Hebrew, Aramaic and Judeo-Persian. The book is currently a part of the collection at the Museum of the Bible in Washington, D.C. +For an unknown reason, a portion of the Passover haggadah is upside-down in the book. + + +== History == +The manuscript was originally believed to have come from the Cairo Geniza in Egypt with an estimated origin from the 900s CE. In 2016, a photograph of the book in Afghanistan from 1997 was discovered, which led to radiometric dating tests on four parts of the manuscript. These parts of the manuscript were dated to c. 780 CE in 2019. +The book was found by a Hazara man, who gave it to a local Afghan leader. In 2013, the manuscript was purchased by Steve Green, president of Hobby Lobby and founder of the Museum of the Bible. It was later donated to the museum, which opened in 2017. + + +== See also == +Leningrad Codex + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/African_Union_Kwame_Nkrumah_Award_for_Scientific_Excellence-0.md b/data/en.wikipedia.org/wiki/African_Union_Kwame_Nkrumah_Award_for_Scientific_Excellence-0.md new file mode 100644 index 000000000..84328b884 --- /dev/null +++ b/data/en.wikipedia.org/wiki/African_Union_Kwame_Nkrumah_Award_for_Scientific_Excellence-0.md @@ -0,0 +1,84 @@ +--- +title: "African Union Kwame Nkrumah Award for Scientific Excellence" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/African_Union_Kwame_Nkrumah_Award_for_Scientific_Excellence" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:21.500559+00:00" +instance: "kb-cron" +--- + +The African Union Kwame Nkrumah Award for Scientific Excellence was established by the African Union (AU) to recognize and honor outstanding scientific achievements in Africa. These awards were named after Kwame Nkrumah, the first President of Ghana and a prominent Pan-Africanist, who strongly believed in the importance of science and technology for the development of Africa. It is the highest recognition for science in Africa. +The awards aim to recognize and celebrate scientific achievements, promote science and innovation in Africa and inspire the next generation of African scientists. They were established in September 2008. +The Kwame Nkrumah Awards are awarded in two categories: Life and Earth Sciences and Basic Science, Technology and Innovation. +Nominees are typically selected based on their achievements in advancing scientific knowledge, addressing African challenges, and their contributions to the scientific community at large. The awardees are often recognized during AU summits, where they are presented with both a monetary award and a certificate of recognition. +The awards aim to showcase the talent and intellectual contributions of African scientists and play a role in the continent's development by encouraging continued advancements in science and technology. +There are 3 types of awards: At the continental level for general scientists, at the regional level for women scientists and at the national level for young scientists. +The highest level is the Continental award which consists of a cash Prize of USD $100,000, a medal and a certificate. + + +== Award recipients at the continental level == + + +=== Basic Science, Technology and Innovation === +2011: Oluwole Daniel Makinde (Nigeria) +2012: Nabil A. Ibrahim (Egypt) +2014: Timoleon Crepin Kofane (Cameroon) +2015: Tebello Nyokong (South Africa) +2016: Ali Ali Hebeish (Egypt) +2017: Malik Maaza (Algeria) +2018: Obada Abdel Shafy (Egypt) +2019: Ahmed Mohammed Alsabagh (Egypt) +2020: Salah Obaya (Egypt) + + +=== Life and Earth Sciences === +2012: Michael John Wingfield (South Africa) +2014: Salim Abdool Karim (South Africa) +2015: Umezuruike Linus Opara (Nigeria) +2016: Felix Dapare Dakora (Ghana) +2017: Robert Peter Millar (South Africa) +2018: David Mark Richardson (South Africa) +2019: Chedly Abdelly (Tunisia) +2020: Abraham Aseffa (Ethiopia) + + +== Award recipients at the regional level == +This level is awarded to scientist women only. + + +=== Life and Earth Sciences category === +2010: Salimata Wade (Senegal) +2011: Mireille Dosso (Comoros / Ivory Coast) +2012: Matilda Steiner-Asiedu (Ghana) +2013: Adolé Glitho-Akueson (Togo) +2014: Isabella Akyinbah Quakyi (Ghana) +2015: Northern Region: Hafida Merzouk (Algeria) +2020: +Western Region: Philippa C. Ojimelukwe (Nigeria) +Eastern Region: Hulda Swai (Tanzania) +Northern Region: Elham Mahmoud (Egypt) + + +=== Basic Science, Technology and Innovation category === +2010: Geneviève Barro (Burkina Faso) +2011: Rita Kakou-Yao (Ivory Coast) +2013: +Quarraisha Abdool Karim (South Africa) +Yvonne Bonzi-Coulibaly (Burkina Faso) +2015: Eastern Region: Yalemtsehay Mekonnen (Ethiopia) +2020: +Northern Region: Fakiha Heakal (Egypt) +Western Region: Ibiyinka A. Fuwape (Nigeria) + + +== See also == + +List of general science and technology awards + + +== References == + + +== External links == +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Agnes_Fay_Morgan_Research_Award-0.md b/data/en.wikipedia.org/wiki/Agnes_Fay_Morgan_Research_Award-0.md new file mode 100644 index 000000000..f9757784f --- /dev/null +++ b/data/en.wikipedia.org/wiki/Agnes_Fay_Morgan_Research_Award-0.md @@ -0,0 +1,24 @@ +--- +title: "Agnes Fay Morgan Research Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Agnes_Fay_Morgan_Research_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:58.620407+00:00" +instance: "kb-cron" +--- + +The Agnes Fay Morgan Research Award was established in 1951 by the Iota Sigma Pi honorary society for women in chemistry. The award is given for research achievement in chemistry or biochemistry to a woman not over forty years of age at the time of her nomination. Individual chapters, Iota Sigma Pi members, chemists, and groups of chemists may nominate eligible chemists for the prize. +The award was named for Agnes Fay Morgan (1884–1968), biochemist and nutritionist, born in Peoria, Illinois, USA. She studied at the University of Chicago (BS, MS, PhD), and taught at the University of California, Berkeley (1915–54), where she helped organize (1919) what was to become a nationally outstanding home economics department. A founder of the science of nutrition, her research focused on the analysis of nutrients in foods, the stability of vitamins and proteins during food processing, and the physiological effects of vitamin deficiencies. Especially noteworthy was her discovery of the role of pantothenic acid in adrenal function and pigmentation. Her work for government and private agencies included the development of improved methods of dehydrating foods. + + +== Award recipients == +Source: Iota Sigma Pi Archived 2019-03-23 at the Wayback Machine + + +== See also == +List of chemistry awards +List of science and technology awards for women + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Al-Khawdh-0.md b/data/en.wikipedia.org/wiki/Al-Khawdh-0.md new file mode 100644 index 000000000..6f2fd49ea --- /dev/null +++ b/data/en.wikipedia.org/wiki/Al-Khawdh-0.md @@ -0,0 +1,26 @@ +--- +title: "Al-Khawdh" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Al-Khawdh" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:40.225824+00:00" +instance: "kb-cron" +--- + +Al-Khawdh (الخوض) (25°35'N; 58°10'E, altitude 40–50 m) contains several archaeological sites and lies in the Muscat Governorate, Oman, where Early Iron Age and Late Iron Age sites have been under study in recent years. +Major finds include a large cemetery of the Early Iron Age i.e. the Lizq-Rumaylah period. and a hoard of over 300 implements made of copper alloy This cemetery lies 2.5 kilometres (1.6 mi) south-east of the hoard site. + + +== See also == +Archaeology of Oman +Oman +Pre-Islamic recent period +List of archaeological sites by country + + +== Sources == +Paul Yule, Cross-roads – Early and Late Iron Age South-eastern Arabia, Abhandlungen Deutsche Orient-Gesellschaft, vol. 30, Wiesbaden, 2014, ISBN 978-3-447-10127-1; E-Book: ISBN 978-3-447-19287-3. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Alfoldean-0.md b/data/en.wikipedia.org/wiki/Alfoldean-0.md new file mode 100644 index 000000000..de4716904 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Alfoldean-0.md @@ -0,0 +1,14 @@ +--- +title: "Alfoldean" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Alfoldean" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:41.414734+00:00" +instance: "kb-cron" +--- + +Alfoldean was a Roman settlement founded in the Roman province of Britannia as a mansio on Stane Street where the road crosses the River Arun. Its remains are now near the village of Slinfold in West Sussex. They have been investigated by archaeologists including Samuel Edward Winbolt and Time Team. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Amarna_letter_EA_11-0.md b/data/en.wikipedia.org/wiki/Amarna_letter_EA_11-0.md new file mode 100644 index 000000000..a315abc56 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Amarna_letter_EA_11-0.md @@ -0,0 +1,22 @@ +--- +title: "Amarna letter EA 11" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Amarna_letter_EA_11" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:44.970354+00:00" +instance: "kb-cron" +--- + +Amarna letter EA11 is a letter of correspondence to Akhenaten of Egypt from the king of Babylon, Burna-Buriash II. +The tablet onto which letter EA11 is inscribed is badly damaged. +The letter content suggests of the place Amarna having experienced an epidemic of some kind of plague. +The letter (together with letter EA10) seems to undoubtedly indicate that Akhenaten married his daughters Meritaten and Ankhesenpaaten at a time when they were both 11 or 12 years of age. Meritaten is described as the mistress of the royal house within the text. +The letter is part of a series of correspondences from Babylonia to Egypt, which run from EA2 to EA4 and EA6 to EA14. EA1 and EA5 are from Egypt to Babylonia. + + +== See also == +Amarna letters: EA 1, EA 2, EA 3, EA 4, EA 5, EA 6, EA 7, EA 8, EA 9, EA 10 + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Amarna_letter_EA_12-0.md b/data/en.wikipedia.org/wiki/Amarna_letter_EA_12-0.md new file mode 100644 index 000000000..789f6fd6b --- /dev/null +++ b/data/en.wikipedia.org/wiki/Amarna_letter_EA_12-0.md @@ -0,0 +1,29 @@ +--- +title: "Amarna letter EA 12" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Amarna_letter_EA_12" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:46.166570+00:00" +instance: "kb-cron" +--- + +Amarna letter EA12 is a correspondence written to the King of Egypt by a princess of Babylonia. +A scribe named Kidin-Adad is mentioned within the letter. +This letter is part of a series of correspondences from Babylonia to Egypt, which run from EA2 to EA4 and EA6 to EA14. EA1 and EA5 are from Egypt to Babylonia. +During 1888 the Vorderasiatisches Museum received part of the tablet as part of a group of artifacts given to the museum by J.Simon. A second part of EA12 was given to the museum by Felix von Niemeyer. +The letter, translated by W.L. Moran, reads: + +(1–6) Speak to my lord; thus the princess: To you, your ch[ariot]s, the [m]en and [your house] may it be well. +(7–12) May the gods of Burraburiash go with you. Go safely and in peace go forward, see your house. +(12–22) In the pre[sence of my lord], thu[s,] I [prostrate myself], saying, “Since G[...] my envoy has brought colored cloth, to your cities and your house, may it be ‹w›ell. Do not murmur in your heart and impose darkness on me.” +Your servant, Kidin-Adad, is located with me(?), as the substitute of my lord, I would verily go. + + +== See also == +Amarna +Amarna letters: EA1, EA2, EA3, EA4, EA5, EA6, EA7, EA8, EA9, EA10, EA11 +Chronology of the ancient Near East + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Amarna_letter_EA_248-0.md b/data/en.wikipedia.org/wiki/Amarna_letter_EA_248-0.md new file mode 100644 index 000000000..b2fdc8a3d --- /dev/null +++ b/data/en.wikipedia.org/wiki/Amarna_letter_EA_248-0.md @@ -0,0 +1,48 @@ +--- +title: "Amarna letter EA 248" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Amarna_letter_EA_248" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:48.539019+00:00" +instance: "kb-cron" +--- + +In Ancient Egypt, the Amarna Period (c. 1350 BC) saw diplomatic correspondence sent to the city of Akhetaten (Amarna), providing valuable insights into the political situations at the time. +The Amarna Letter EA 248 (EA 248) is a fragmented letter by Yashdata, a displaced ruler, to the Pharaoh, also mentioning Biridiya of Megiddo. + + +== Translated Text == +Say [to] the king, my lord, Sun and god: Message of Ya(shd)ata, the loyal servant of the king and the dirt at the feet of the king. I fall at the feet of the king, my lord, Sun and god, 7 times and 7 times. +[9-22] May the king, my lord, know that everything the king, my [l]ord, gave to [his] servant, the men of Than[ak]a [have m]ade off with; they have slaughtered my oxen and driven me away. So I am now with Biridiya. May the King, my lord, take cognizance of his servant. + + +== Akkadian Text == +EA 248 +248:001 [a-na ]m.LUGAL-ri EN-ia +248:002 u d.UTU u DINGIR.MEß-ia +248:003 qí-bí-ma um-ma m.ya-a[$-d]a-ta +248:004 ÌR ki-it-ti LUGAL-ri +248:005 ù ip-ri GÌR.MEß LUGAL-ri +248:006 a-na GÌR.MEß LUGAL-ri +248:007 EN-ia u d.UTU u DINGIR.MEß-ia +248:008 7-$u u 7-ta-a-an am-qut +248:÷÷÷÷÷ +248:009 li-di-mi LUGAL-ru EN-ia +248:010 i-nu-ma gáb-bi mi-im-mì +248:$011 a yi-id-din LUGAL-[r]u +248:012 [E]N-ia a-[n]a ÌR[-$u] +248:013 n[a]m-$u-mi +248:014 L[Ú.M]Eß URU ta-ah-[na-k]a +248:015 [u] na-ak-$u-mì +248:016 GU4.MEß-ia ù +248:017 du-ub-bu-ru-ni +248:018 u a-nu-um-ma it-ti +248:019 m.bi-ri-di-ya +248:020 i-ba-a$-$a10-ku ù +248:021 li-di-mi LUGAL-ru +248:022 EN-ia a-na ÌR-$u +248:÷÷÷÷÷ + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Amarna_letter_EA_27-0.md b/data/en.wikipedia.org/wiki/Amarna_letter_EA_27-0.md new file mode 100644 index 000000000..1693c3d11 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Amarna_letter_EA_27-0.md @@ -0,0 +1,23 @@ +--- +title: "Amarna letter EA 27" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Amarna_letter_EA_27" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:47.378642+00:00" +instance: "kb-cron" +--- + +Amarna letter EA 27 is a letter addressed to Amenhotep IV and concerns "The Missing Gold Statues Again". + +The letter is dated to a period within the very beginning of the second regnal year of the pharaoh, and was written by Tushratta, who was living at Washukanni. At the time the pharaoh was located at Thebes. +The letter is thought to contain a reference to a royal funeral. + + +== See also == +List of Amarna letters by size +Amarna letter EA 5, EA 9, EA 15, EA 19, EA 26, EA 27, EA 35, EA 38 +EA 153, EA 161, EA 288, EA 364, EA 365, EA 367 + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Amarna_letter_EA_369-0.md b/data/en.wikipedia.org/wiki/Amarna_letter_EA_369-0.md new file mode 100644 index 000000000..8fb612ca3 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Amarna_letter_EA_369-0.md @@ -0,0 +1,32 @@ +--- +title: "Amarna letter EA 369" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Amarna_letter_EA_369" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:49.750582+00:00" +instance: "kb-cron" +--- + +Amarna letter EA 369 is a letter written on a clay tablet from the pharaoh to Milkilu of Gezer. The tablet is now housed in the Musées Royaux d'Art et d'Histoire, in Brussels. +The letter is one of a small number of the Amarna Letters that were written in Egypt, and sent out from the pharaoh to vassals. Other Amarna letters sent to vassals included EA 99, 162, 163, 190, 367, and 370. + + +== The letter == +The letter details the king sending female cupbearers, silver, linen garments, carnelian, precious stones, an ebony chair, with a total value of 160 deben. It also states that he is sending forty female cupbearers, which are recorded as 40 silver each. Some linguistic features of the letter indicate that the scribe also may have been of Gezer origin. + + +== Translation == +The letter has been translated by Dossin (1934), Rainey (2014) and Moran (1992). Moran's (1992) translation is below: + +To Milkilu, the ruler of Gazru: Thus the king. He herewith dispatches to you this tablet, saying to you, He herewith sends to you Hanya, the stable of the archers, along with everything for the acquisition of beautiful female cupbearers: +9—14 silver, gold, linen garments : ma-al-ba-si, carnelian, all sorts of (precious) stones, an ebony chair; all alike, fine things. Total (value): 160 diban. Total: 40 female cupbearers, 40 (shekels of) silver being the price of a female cupbearer. +15—23 Send extremely beautiful female cupbearers in whom there is no defect, so the king, your lord, will say to you, “This is excellent, in accordance with the order he sent to you.” + +24—32 And know that the king is hale like the Sun. For his troops, his ch[ariot]s, his horses, all goes very well. Aman has indeed put the Upper Land, the Lower Land, where the sun rises, where the sun sets, under the feet of the king. + + +== Notes == + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Amarna_letter_EA_5-0.md b/data/en.wikipedia.org/wiki/Amarna_letter_EA_5-0.md new file mode 100644 index 000000000..c79d242b6 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Amarna_letter_EA_5-0.md @@ -0,0 +1,46 @@ +--- +title: "Amarna letter EA 5" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Amarna_letter_EA_5" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:42.606197+00:00" +instance: "kb-cron" +--- + +Amarna Letter EA5, one of the Amarna letters (cited with the abbreviation EA, for "El Amarna"), is a correspondence between Kadašman-Enlil I and Amenhotep III. +The letter exists as two artifacts, one at the British Museum (BM29787) and one in the Cairo Museum (C12195). +The letter is part of a series of correspondences from Babylonia to Egypt, which run from EA2 to EA4 and EA6 to EA14. EA1 and EA5 are from Egypt to Babylonia. + + +== The letter == + + +=== EA 5: Gifts of Egyptian Furniture for the Babylonian Palace === +EA 5, letter five of five, Pharaoh to Kadashman-Enlil. (Not a linear, line-by-line translation.) +Obverse: (see British Museum) + +Paragraph 1 +(Lines 1-12)--[Thus Nibmuar]ey[a1 Great King, the king of Egypt. Say to] Kadašman-Enlil, the king of Karadunniyaš,2 my brother: For m]e all goes (well). For you may all go well. For you]r [household, your] wives, [your sons, yo]ur [magnates], yo[ur] troops, [yo]ur [horses], your [chariots], and i[n your countries, may all go] well. [For me al]l goes well. For my household, [my] wives, [my sons], my magnates, my ma[ny] troops, my [horses], my chariots, and in [m]y [countries] all goes very, very well. +Paragraph 2 +(Lines 13-33)--I have [just]3 heard that you have built some n[ew] quarters.4 I am sending herewith some furnishings for your house. Indeed I shall be preparing everything possible5 before the arrival of your messenger who is bringing your daughter. When6 your messenger returns, I will send (them) to [yo]u. I herewith send you, in the charge of Šutti, a greeting-gift of things for the new house: 1 bed7 of ebony, overlaid with ivory and gold; 3 beds of ebony, overlaid with gold; 1 uruššu of ebony, overlaid with gold; 1 lar[ge] chair [o]f ebo[ny], overlaid with gold.8 These things, the weight of all the gold: 7 minas, 9 shekels, of silver9 (In addition), 10 footrests of ebony; [ . . . ] of ebony, overlaid with gold; [ . . . ] footrests of ivory, overlaid with gold; [ . . . ] . . . of gold. [Total10 x] minas, 10 and 7 shekels, of gold.--(complete, lacunas throughout, lines 1-33) + + +== See also == +Chronology of the ancient Near East +Amarna letters: EA 1, EA 2, EA 3, EA 4, EA 6, EA 7, EA 8, EA 9, EA 10, EA 11 +List of Amarna letters by size +EA 5, EA 9, EA 15, EA 19, EA 26, EA 27, EA 35, EA 38 +EA 153, EA 161, EA 288, EA 364, EA 365, EA 367 + + +== References == + + +== External links == + +Photo EA 5, Obverse, (British Museum piece: BM 29787) +Photo EA 5, Reverse, (British Museum piece: BM 29787) (note: line 17 from Obverse extends across the entire Reverse (upside down cuneiform)) +British Museum page for Amarna letter EA 5 +CDLI entry of EA 5 ( Chicago Digital Library Initiative ) +CDLI listing of all EA Amarna letters, 1-382 \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Amarna_letter_EA_6-0.md b/data/en.wikipedia.org/wiki/Amarna_letter_EA_6-0.md new file mode 100644 index 000000000..c10c0dd0c --- /dev/null +++ b/data/en.wikipedia.org/wiki/Amarna_letter_EA_6-0.md @@ -0,0 +1,26 @@ +--- +title: "Amarna letter EA 6" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Amarna_letter_EA_6" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:43.764917+00:00" +instance: "kb-cron" +--- + +Amarna Letter EA6 is a correspondence from Burra-Buriyaš to Nimmuwarea(Amenhotep III) the king of Egypt. +According to one source, this letter concerns gifts between two kings. +The letter is part of a series of correspondences from Babylonia to Egypt, which run from EA2 to EA4 and EA6 to EA14. EA1 and EA5 are from Egypt to Babylonia. +The inscription is translated as follows: + +Say to Nimmuwarea the king of Egypt my brother Thus Burra-Buriyaš the king of Karaduniyaš your brother For me all goes well For you your household your wives your sons your country your magnates your horses your chariots may all go well. +Just as previously you and my father were friendly to one another you and I should be friendly to one another Between us anything else what-so-ever is not to be mentioned.Write to me for what you want from my country so that it may be taken to you and I will write to you of what I want from your country so that it may be taken to me...I will trust you...Write to me so that it may be taken to you, And as your greeting gift... and 1 ... I send you + + +== See also == +Amarna letters: EA 1, EA 2, EA 3, EA 4, EA 5, EA 7, EA 8, EA 9, EA 10, EA 11 +Bi (cuneiform) +De Beneficiis + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Amathus_sarcophagus-0.md b/data/en.wikipedia.org/wiki/Amathus_sarcophagus-0.md new file mode 100644 index 000000000..dd32a0eb1 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Amathus_sarcophagus-0.md @@ -0,0 +1,19 @@ +--- +title: "Amathus sarcophagus" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Amathus_sarcophagus" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:50.931128+00:00" +instance: "kb-cron" +--- + +The Amathus sarcophagus is a Cypriot sarcophagus that likely held a king of Amathus. Its sides show procession scenes and typify Cypriot, Greek and Phoenician-Near Eastern styles of the mid-fifth century BCE. The sarcophagus was excavated by Luigi Palma di Cesnola and is currently located at the Metropolitan Museum of Art. + + +== General references == + + +== External links == + Media related to Amathus sarcophagus at Wikimedia Commons +Amathus sarcophagus in the Metropolitan Museum of Art site \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Ancient_Egypt_(magazine)-0.md b/data/en.wikipedia.org/wiki/Ancient_Egypt_(magazine)-0.md new file mode 100644 index 000000000..3fb3906dd --- /dev/null +++ b/data/en.wikipedia.org/wiki/Ancient_Egypt_(magazine)-0.md @@ -0,0 +1,20 @@ +--- +title: "Ancient Egypt (magazine)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Ancient_Egypt_(magazine)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:52.094402+00:00" +instance: "kb-cron" +--- + +Ancient Egypt is a magazine that deals with the subject of Egyptology. It is published bi-monthly. Ancient Egypt magazine is pitched somewhere between an academic journal and a travel magazine – bringing the spectacular sights of the ancient world together with the latest archaeological discoveries and theories from the world's leading authorities on the subject, illustrated with numerous photographs. +The magazine has been published bi-monthly in the UK since April 2000. The contents concentrate mainly on a wide range of subjects related to ancient Egypt, though it does occasionally include items on Coptic or Islamic Egypt and also items of interest to visitors to Egypt. Edited by Peter Phillips, Ancient Egypt seeks to explain the mysteries of this ancient civilisation in a concise manner. One of the former editors was Robert Bernard Partridge who served in the post from 2004 to 2011. +The magazine does not just deal with the past, but has a correspondent in Cairo who provides updates on the latest travel information and assesses the impact Egyptology has on modern Egypt. + + +== References == + + +== External links == +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Ancient_Warfare_(magazine)-0.md b/data/en.wikipedia.org/wiki/Ancient_Warfare_(magazine)-0.md new file mode 100644 index 000000000..4a6f7ea9c --- /dev/null +++ b/data/en.wikipedia.org/wiki/Ancient_Warfare_(magazine)-0.md @@ -0,0 +1,26 @@ +--- +title: "Ancient Warfare (magazine)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Ancient_Warfare_(magazine)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:53.275823+00:00" +instance: "kb-cron" +--- + +Ancient Warfare is a glossy Dutch bi-monthly military history magazine. + + +== History and profile == +Ancient Warfare was started in 2007. It is published in Rotterdam by the Dutch publishing company Karwansaray. The magazine was founded by Jasper Oorthuys, who now serves as managing director and editor-in-chief. +Most of the magazine's feature articles focus on a central theme per issue. These include articles on a specific general, campaign or more abstract phenomenon such as sieges. Each issue usually starts off with a historical introduction to the theme. The introduction is usually followed by an article that delves into relevant sources for the theme, such as a historical narrative or an archaeological source. The theme is then fleshed out by articles on warriors, battles and generals that fit that issue's theme. Among the authors are well-known specialists like Bob Bennett, Duncan B. Campbell, Ross Cowan, Lukas de Blois, Stephen English, Adrian Murdoch, Joseph Pietrykowski, Jona Lendering, and Mike Roberts. +The magazine also includes news and letters from readers, as well as reviews of relevant books, games, models, and museums. The illustrations include original artwork, maps and photographs of artifacts. Online free features of the magazine include the editor's blog and a podcast which is published to coincide with the magazine themes. +Other spin-offs were specials on the Battle of the Teutoburg Forest and the nature of the Roman centuria. Since 2012, the yearly special is published in the form of a hardcover book. The first was Edge of Empire (2012), a reworked English translation of an originally Dutch book by Jona Lendering and Arjan Bosman on the Roman occupation of the Low Countries. The second was Henchmen of Ares: Warriors and Warfare in Early Greece (2013) written by then-editor Josho Brouwers and based on his PhD dissertation on Early Greek warfare. +The magazine is registered as ISSN 1874-7019. + + +== References == + + +== External links == +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Andriivka,_Sheptytskyi_Raion,_Lviv_Oblast-0.md b/data/en.wikipedia.org/wiki/Andriivka,_Sheptytskyi_Raion,_Lviv_Oblast-0.md new file mode 100644 index 000000000..5e09b1882 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Andriivka,_Sheptytskyi_Raion,_Lviv_Oblast-0.md @@ -0,0 +1,21 @@ +--- +title: "Andriivka, Sheptytskyi Raion, Lviv Oblast" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Andriivka,_Sheptytskyi_Raion,_Lviv_Oblast" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:54.475772+00:00" +instance: "kb-cron" +--- + +Andriivka (Ukrainian: Андрі́ївка) is a village in Sheptytskyi Raion, Lviv Oblast, Western Ukraine. It belongs to Radekhiv urban hromada, one of the hromadas of Ukraine. +Andriivka is the site of an ancient mega-settlement dating to 4000–3600 B.C. belonging to the Cucuteni-Trypillian culture. The settlement was for the time very large, covering an area of 80 hectares. This proto-city is just one of 2440 Cucuteni-Trypillia settlements discovered so far in Moldova and Ukraine. 194 (8%) of these settlements had an area of more than 10 hectares between 5000–2700 B.C. and more than 29 settlements had an area in the range 100–300–450 hectares. +Until 18 July 2020, Andriivka belonged to Radekhiv Raion. The raion was abolished in July 2020 as part of the administrative reform of Ukraine, which reduced the number of raions of Lviv Oblast to seven. The area of Radekhiv Raion was merged into Sheptytskyi Raion, which was then known as Chervonohrad Raion. + + +== See also == +Cucuteni-Trypillian culture +Danube civilization + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Angamuco-0.md b/data/en.wikipedia.org/wiki/Angamuco-0.md new file mode 100644 index 000000000..05e8c11d9 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Angamuco-0.md @@ -0,0 +1,16 @@ +--- +title: "Angamuco" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Angamuco" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:55.645287+00:00" +instance: "kb-cron" +--- + +Angamuco is the name given to a major urban settlement of the Purépecha civilization, (Tarascan) now in ruins hidden under vegetation, in the Lake Pátzcuaro Basin of Michoacán, Mexico, and discovered in 2007. In 2012, using LiDAR technology, archaeologist Christopher Fisher and team detected more than 40,000 foundations at the site, roughly the same as Manhattan, on a territory of approximately 25 square kilometres (9.7 sq mi) (less than half of Manhattan's 59 square kilometres (23 sq mi). +Analyzing architectural data Fisher found 60 distinctive, standardized, and recurrent architectural forms throughout the site, including commoner and elite buildings, altars, pyramids, storage facilities, ball courts, and a hierarchical road system. The most common types of structures are living spaces for both commoners and elites, including small platforms for houses and rectangular and circular walled rooms. The second most common features are structures for public or ritual activities, such as pyramids, plazas, and a ball court. Finally, a small part are structures associated with agriculture activities such as patios or terraces. The diverse range of structures at Angamuco suggests a large, active, and organized population embedded within an extensive human modified landscape. +Fisher believes the settlement was founded around 900 CE and reached peak importance from around 1000 to around 1350 CE with a population of over 100,000 – making it the most populous city in western Mexico at the time, and spanning a wider area than the Purépecha capital, Tzintzuntzan. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Anne_Bennett_Prize-0.md b/data/en.wikipedia.org/wiki/Anne_Bennett_Prize-0.md new file mode 100644 index 000000000..edd127507 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Anne_Bennett_Prize-0.md @@ -0,0 +1,44 @@ +--- +title: "Anne Bennett Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Anne_Bennett_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:22.666190+00:00" +instance: "kb-cron" +--- + +The Anne Bennett Prize and Senior Anne Bennett Prize are awards given by the London Mathematical Society. +In every third year, the society offers the Senior Anne Bennett prize to a mathematician normally based in the United Kingdom for work in, influence on or service to mathematics, particularly in relation to advancing the careers of women in mathematics. +In the two years out of three in which the Senior Anne Bennett Prize is not awarded, the society offers the Anne Bennett Prize to a mathematician within ten years of their doctorate for work in and influence on mathematics, particularly acting as an inspiration for women mathematicians. +Both prizes are awarded in memory of Anne Bennett, an administrator for the London Mathematical Society who died in 2012. The prize was established in 2013 and first given in 2014. +The Anne Bennett Prizes should be distinguished from the Anne Bennett Memorial Award for Distinguished Service of the Royal Society of Chemistry, for which Anne Bennett also worked. + + +== Anne Bennett Prize Winners == +The winners of the Anne Bennett Prize have been: + +2015 Apala Majumdar, in recognition of her outstanding contributions to the mathematics of liquid crystals and to the liquid crystal community. +2016 Julia Wolf, in recognition of her outstanding contributions to additive number theory, combinatorics and harmonic analysis and to the mathematical community. +2018 Lotte Hollands, in recognition of her outstanding research at the interface between quantum theory and geometry and of her leadership in mathematical outreach activities. +2019 Eva-Maria Graefe, in recognition of her outstanding research in quantum theory and the inspirational role she has played among female students and early career researchers in mathematics and physics. +2021 Viveka Erlandsson, "for her outstanding achievements in geometry and topology and her inspirational active role in promoting women mathematicians". +2022 Asma Hassannezhad, "for her outstanding work in spectral geometry and her substantial contributions toward the advancement of women in mathematics." +2024 Ana Ros Camacho, "for her ground-breaking work on categorical proofs of the Landau–Ginzburg/Conformal Field Theory correspondence and her tireless dedication to the advancement of women in mathematical physics" +2025 Henna Koivusalo, "for her work on cut-and-project sets, dynamical systems and fractals and her dedication to the advancement of women in mathematics." + + +== Senior Anne Bennett Prize Winners == +The winners of the Senior Anne Bennett Prize have been: + +2014 Caroline Series, in recognition of her leading contributions to hyperbolic geometry and symbolic dynamics, and of the major impact of her numerous initiatives towards the advancement of women in mathematics. +2017 Alison Etheridge, in recognition of her outstanding research on measure-valued stochastic processes and applications to population biology; and for her impressive leadership and service to the profession. +2020 Peter Clarkson, "in recognition of his tireless work to support gender equality in UK mathematics, and particularly for his leadership in developing good practice among departments of mathematical sciences". +2023 Eugénie Hunsicker, "for her outstanding work to improve equality and diversity in the mathematical community and for the depth of her mathematical achievements across an impressive range of areas, from L2 Hodge theory to data science." + + +== See also == +List of mathematics awards + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Annie_Jump_Cannon_Award_in_Astronomy-0.md b/data/en.wikipedia.org/wiki/Annie_Jump_Cannon_Award_in_Astronomy-0.md new file mode 100644 index 000000000..424366ebc --- /dev/null +++ b/data/en.wikipedia.org/wiki/Annie_Jump_Cannon_Award_in_Astronomy-0.md @@ -0,0 +1,26 @@ +--- +title: "Annie Jump Cannon Award in Astronomy" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Annie_Jump_Cannon_Award_in_Astronomy" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:28.559868+00:00" +instance: "kb-cron" +--- + +The Annie Jump Cannon Award in Astronomy is awarded annually by the American Astronomical Society (AAS) to a woman resident of North America, who is within five years of receipt of a PhD, for distinguished contributions to astronomy or for similar contributions in related sciences which have immediate application to astronomy. The awardee is invited to give a talk at an AAS meeting and is given a $1,500 honorarium. The award is named in honor of American astronomer Annie Jump Cannon. +Margaret Burbidge was due to be given the 1972 award, but she refused it on the grounds of gender discrimination, stating: "It is high time that discrimination in favor of, as well as against, women in professional life be removed". This prompted the AAS to set up its first committee on the status of women in astronomy and they ceased issuing the award directly. From 1973 to 2004 the American Association of University Women issued the awards, on advice from the AAS. The AAS resumed direct issuing of the award in 2005. + + +== List of winners == +Source: American Astronomical Society + + +== See also == +List of astronomy awards +List of women astronomers +List of prizes, medals, and awards for women in science +Prizes named after people + + +== Notes == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Antiquities_Trafficking_and_Heritage_Anthropology_Research_Project-0.md b/data/en.wikipedia.org/wiki/Antiquities_Trafficking_and_Heritage_Anthropology_Research_Project-0.md new file mode 100644 index 000000000..ba69413ae --- /dev/null +++ b/data/en.wikipedia.org/wiki/Antiquities_Trafficking_and_Heritage_Anthropology_Research_Project-0.md @@ -0,0 +1,19 @@ +--- +title: "Antiquities Trafficking and Heritage Anthropology Research Project" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Antiquities_Trafficking_and_Heritage_Anthropology_Research_Project" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:58.031946+00:00" +instance: "kb-cron" +--- + +The Antiquities Trafficking and Heritage Anthropology Research Project (ATHAR) consists of a group of experts that conduct research on the looting and trafficking of antiquities. +The Arab Spring and the ensuing wars created opportunities for traffickers in the Middle East to loot archeological sites with impunity. Social media allowed anyone with a smart phone to sell the looted antiquities. Much of the trade takes place on Facebook. + + +== References == + + +== External links == +ATHAR Project \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Archaeological_Recording_Kit-0.md b/data/en.wikipedia.org/wiki/Archaeological_Recording_Kit-0.md index 6058a2fc9..64dbf8b67 100644 --- a/data/en.wikipedia.org/wiki/Archaeological_Recording_Kit-0.md +++ b/data/en.wikipedia.org/wiki/Archaeological_Recording_Kit-0.md @@ -4,7 +4,7 @@ chunk: 1/1 source: "https://en.wikipedia.org/wiki/Archaeological_Recording_Kit" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T10:10:39.716591+00:00" +date_saved: "2026-05-05T11:16:59.288235+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Archaeological_Society_of_Alexandria-0.md b/data/en.wikipedia.org/wiki/Archaeological_Society_of_Alexandria-0.md new file mode 100644 index 000000000..92abed1db --- /dev/null +++ b/data/en.wikipedia.org/wiki/Archaeological_Society_of_Alexandria-0.md @@ -0,0 +1,39 @@ +--- +title: "Archaeological Society of Alexandria" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Archaeological_Society_of_Alexandria" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:01.828406+00:00" +instance: "kb-cron" +--- + +The Archaeological Society of Alexandria (formerly the Royal Archaeological Society of Alexandria) was established in 7 April 1893 in Alexandria, Egypt to ensure the archaeological monuments and remains of the old city of Alexandria were preserved and to raise awareness through high-quality research of the city's archaeological past. + + +== Founding == +Its first president was Ambrose Rally and the first general secretary was Georgios Gousios. Among its members were prominent Greeks like, Sir John Antoniades, Emmanouil Benakis, Michael Salvagos, Eustathios Glymenopoulos, Mikes Synadinos. + + +== Work == +In 1938 the Society supervised the second edition of E. M. Forster’s Alexandria: A History and a Guide. +The Archaeological Society of Alexandria with funds from the A. G. Leventis foundation and permission and supervision of the Egyptian Ministry of Tourism and Antiquities initiated the Alexandria Necropolis Project (2020–2023) that restored the Hellenistic necropolis at Shatby. + + +== Publications == +Bulletin de la Société Royale d'Archéologie d'Alexandrie + + +== See also == +Graeco-Roman Museum +Institut Français d'Archéologie Orientale +Egyptian Institute +Egypt Exploration Society + + +== References == + + +== External links == +Official website +The Archaeological Society of Alexandria, documentary on the history of the Archaeological Society of Alexandria, by CEAlex. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Archaeological_site_of_Shisr-0.md b/data/en.wikipedia.org/wiki/Archaeological_site_of_Shisr-0.md new file mode 100644 index 000000000..0e7dd2037 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Archaeological_site_of_Shisr-0.md @@ -0,0 +1,15 @@ +--- +title: "Archaeological site of Shisr" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Archaeological_site_of_Shisr" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:00.601518+00:00" +instance: "kb-cron" +--- + +The archaeological site of Shisr is located next to the village of Ash Shiṣr in Dhofar, Oman. The settlement was an inland trading post and has been a UNESCO World Heritage Site Land of Frankincense since 2000. It used to be an oasis. +Some considered it to be the legendary lost city of Ubar or Iram. This is not always accepted by scholars. There is a probability that it might have been in the land of Ubar which was a historical region rather than a city. The site might have inspired the legend of the lost city of Ubar when the spring dried up and the settlement was abandoned. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Archaeology_(magazine)-0.md b/data/en.wikipedia.org/wiki/Archaeology_(magazine)-0.md new file mode 100644 index 000000000..6dd6e88a8 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Archaeology_(magazine)-0.md @@ -0,0 +1,18 @@ +--- +title: "Archaeology (magazine)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Archaeology_(magazine)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:04.305606+00:00" +instance: "kb-cron" +--- + +Archaeology is a bimonthly magazine for the general public, published by the Archaeological Institute of America. The institute also publishes the professional American Journal of Archaeology. Its first issue was published in the spring of 1948. The editor-in-chief was Peter Young until 2011 when he was replaced by Claudia Valentino. Jarrett A. Lobell assumed the editorship from Valentino in November 2018. + + +== References == + + +== External links == +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Archaeopress-0.md b/data/en.wikipedia.org/wiki/Archaeopress-0.md new file mode 100644 index 000000000..36ea61b39 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Archaeopress-0.md @@ -0,0 +1,25 @@ +--- +title: "Archaeopress" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Archaeopress" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:05.466466+00:00" +instance: "kb-cron" +--- + +Archaeopress is an academic publisher specialising in archaeology, based in Bicester, Oxfordshire. The company publishes multiple series of books and academic journals, including Archaeopress Archaeology, Proceedings of the Seminar for Arabian Studies (PSAS), and Antiguo Oriente. + + +== History == +In the early 1990s, David Davison and Rajka Makjanic worked at Tempvs Reparatvm, involved with publishing archaeological titles. Archaeopress was founded in 1997, with Davison leading the editing process whilst Makjanic managed production of the books. +Archaeopress, with John and Erica Hedges, succeeded Tempvs Reparatvm as the publisher of the British Archaeological Reports series, though in 2015 began concentrating their own range of imprints. +In September 2024 Archaeopress relocated its headquarters north of Oxford to Bicester. + + +== References == +"About Us". archaeopress.com. Retrieved 9 October 2020. + + +== External links == +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Archaeoseismology-0.md b/data/en.wikipedia.org/wiki/Archaeoseismology-0.md new file mode 100644 index 000000000..132924a1a --- /dev/null +++ b/data/en.wikipedia.org/wiki/Archaeoseismology-0.md @@ -0,0 +1,42 @@ +--- +title: "Archaeoseismology" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Archaeoseismology" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:06.660442+00:00" +instance: "kb-cron" +--- + +Archaeoseismology is the study of ancient earthquakes by analysis of archaeological sites before Robert Mallet's protomodern seismology in the mid-19th century. Such analyses reveal information about seismic events that was not historically recorded before the advent of seismometers in the late 19th century. Such data can also help to document seismic risk in areas subject to brutally destructive earthquakes. In 1991, an international conference in Athens marked the beginning of modern research in the field of archaeoseismology, described as a "study of ancient earthquakes, and their social, cultural, historical and natural effects". + + +== The main idea == +Earthquakes in the distant past may provide important information for a regional seismic risk assessment. We have quantitative data concerning past earthquakes only from the beginning of the 20th century (as the seismograph was invented only at the end of the 19th century), but humanity has had to deal with earthquakes throughout its existence. Thus we have extremely limited historical information about seismic risks. A methodology for reconstruction of historical earthquakes was held during the 20th century, but with very limited results, especially for archaic earthquakes. Thus research in archaeological sites is needed to try to identify damage and destruction from ancient earthquakes. + + +== Archaeological record == +The archaeological record can carry three different types of evidence of seismic activity: + +The archaeological remains are displaced due to the movement of an active fault. +The remains and artefacts contained in destruction deposits, associated with the decline of soil or seismic vibration, can be used in the dating of earthquake damage. Other archaeological evidence, such as repairs, abandonment of an archaeological site or architectural changes, can help in identifying ancient earthquakes. +Αncient buildings and other man-made structures can be studied for signs of ancient seismic disaster, often associated with soil vibration. + + +== Notable events == +A key example of an ancient earthquake is the 226 BC Rhodes earthquake, which toppled one the seven wonders of the world at the time, the Colossus of Rhodes. It is also noted that damage to the city and harbor were evident. The Greek historian Strabo discussed the collapse of the colossus in the 1st century BC. +A more studied example is The Great Chilean Earthquake of 1960, which was the most powerful earthquake in recorded history, at 9.6 on the moment magnitude scale. +The first recorded earthquake was the Mount Tai earthquake in China in 1831 BC. + + +== See also == +Paleoseismology +Historical earthquakes + + +== References == + + +== External links == +"Archaeoseismology". Academia.edu. Retrieved 16 March 2016. +"Quantitative Methods in Archaeoseismology" (PDF). 1 st INQUA - IGCP - 567 International Workshop on Earthquake Archaeology and Palaeoseismology. Archived from the original (PDF) on 21 March 2016. Retrieved 16 March 2016. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Archeo_(magazine)-0.md b/data/en.wikipedia.org/wiki/Archeo_(magazine)-0.md new file mode 100644 index 000000000..21e7d9251 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Archeo_(magazine)-0.md @@ -0,0 +1,22 @@ +--- +title: "Archeo (magazine)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Archeo_(magazine)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:07.842400+00:00" +instance: "kb-cron" +--- + +Archeo is a monthly archeology magazine based in Rome, Italy. The magazine was first published in March 1985. It features articles on archaeological news. As of 2011, Andreas Steiner was the editor of the magazine. + + +== See also == +List of magazines in Italy + + +== References == + + +== External links == +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Arqueología_Mexicana-0.md b/data/en.wikipedia.org/wiki/Arqueología_Mexicana-0.md new file mode 100644 index 000000000..2914fba0a --- /dev/null +++ b/data/en.wikipedia.org/wiki/Arqueología_Mexicana-0.md @@ -0,0 +1,23 @@ +--- +title: "Arqueología Mexicana" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Arqueología_Mexicana" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:09.048326+00:00" +instance: "kb-cron" +--- + +Arqueología Mexicana (Mexican Archaeology) is a bimonthly journal published by Editorial Raíces and the Mexican Instituto Nacional de Antropología e Historia (National Institute of Anthropology and History). The first issue, devoted to Teotihuacán, was published in April–May in 1993. + + +== Content == +Arqueología Mexicana contains articles by scholars, a wide selection of photographs on the diverse Mesoamerican cultures, as well as maps and timelines that provide a modern understanding of the Mesoamerican legacy. + + +== References == + + +== External links == +Official website (in Spanish) +WorldCat record \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Arrow_of_time-0.md b/data/en.wikipedia.org/wiki/Arrow_of_time-0.md index 0d4798be2..85ae98d32 100644 --- a/data/en.wikipedia.org/wiki/Arrow_of_time-0.md +++ b/data/en.wikipedia.org/wiki/Arrow_of_time-0.md @@ -4,7 +4,7 @@ chunk: 1/4 source: "https://en.wikipedia.org/wiki/Arrow_of_time" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:13:44.126821+00:00" +date_saved: "2026-05-05T11:15:00.259019+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Arrow_of_time-1.md b/data/en.wikipedia.org/wiki/Arrow_of_time-1.md index 6560bbb02..38bc2a5bd 100644 --- a/data/en.wikipedia.org/wiki/Arrow_of_time-1.md +++ b/data/en.wikipedia.org/wiki/Arrow_of_time-1.md @@ -4,7 +4,7 @@ chunk: 2/4 source: "https://en.wikipedia.org/wiki/Arrow_of_time" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:13:44.126821+00:00" +date_saved: "2026-05-05T11:15:00.259019+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Arrow_of_time-2.md b/data/en.wikipedia.org/wiki/Arrow_of_time-2.md index ea8237d11..c7ccdfc0d 100644 --- a/data/en.wikipedia.org/wiki/Arrow_of_time-2.md +++ b/data/en.wikipedia.org/wiki/Arrow_of_time-2.md @@ -4,7 +4,7 @@ chunk: 3/4 source: "https://en.wikipedia.org/wiki/Arrow_of_time" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:13:44.126821+00:00" +date_saved: "2026-05-05T11:15:00.259019+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Arrow_of_time-3.md b/data/en.wikipedia.org/wiki/Arrow_of_time-3.md index add91f075..bfb322489 100644 --- a/data/en.wikipedia.org/wiki/Arrow_of_time-3.md +++ b/data/en.wikipedia.org/wiki/Arrow_of_time-3.md @@ -4,7 +4,7 @@ chunk: 4/4 source: "https://en.wikipedia.org/wiki/Arrow_of_time" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:13:44.126821+00:00" +date_saved: "2026-05-05T11:15:00.259019+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/At-Tschapar-0.md b/data/en.wikipedia.org/wiki/At-Tschapar-0.md new file mode 100644 index 000000000..bdf2d9201 --- /dev/null +++ b/data/en.wikipedia.org/wiki/At-Tschapar-0.md @@ -0,0 +1,22 @@ +--- +title: "At-Tschapar" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/At-Tschapar" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:10.204691+00:00" +instance: "kb-cron" +--- + +At-Tschapar is an archaeological site in the north of Afghanistan. + + +== Description == +The At-Tschapar tower was built in the middle of the first millennium BCE. It has a diameter of about 100 metres (330 ft). The interior of the structure is completely undeveloped. One of the outer walls of the tower has an inside corridor and on the outside of it there are a series of semicircular towers that are accessible from the corridor through the doors. Along the exterior facades there are loopholes. From the corridor there are passages that go into a large, undeveloped inside courtyard. During the excavation pottery was found from the Achaemenid period. The function of the tower is unclear. It may have been a fortress or a sanctuary, or the construction may never have been completed. + + +== Literature == +Viktor Sarianidi: The Art of Old Afghanistan, Leipzig 1986, pp. 75–78 ISBN 3-527-17561-X + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Attic_Vase_Inscriptions-0.md b/data/en.wikipedia.org/wiki/Attic_Vase_Inscriptions-0.md new file mode 100644 index 000000000..dae48e97b --- /dev/null +++ b/data/en.wikipedia.org/wiki/Attic_Vase_Inscriptions-0.md @@ -0,0 +1,18 @@ +--- +title: "Attic Vase Inscriptions" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Attic_Vase_Inscriptions" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:11.393141+00:00" +instance: "kb-cron" +--- + +Attic Vase Inscriptions (AVI) is a web-based epigraphic database of ancient Attic vase inscriptions maintained by the AVI project at the University of Basel. It is an extension of Henry R. Immerwahr's CAVI (Corpus of Attic Vase Inscriptions). + + +== References == + + +== External links == +CAVI pdf \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Baaz_Rockshelter-0.md b/data/en.wikipedia.org/wiki/Baaz_Rockshelter-0.md new file mode 100644 index 000000000..6af54816e --- /dev/null +++ b/data/en.wikipedia.org/wiki/Baaz_Rockshelter-0.md @@ -0,0 +1,22 @@ +--- +title: "Baaz Rockshelter" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Baaz_Rockshelter" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:12.586275+00:00" +instance: "kb-cron" +--- + +Baaz Rockshelter is a prehistoric archaeological site in Syria. Located in the foothills of the Anti-Lebanon Mountains about 50 kilometres (31 mi) northeast of Damascus, the site consists of a small (6 by 10 metres or 20 by 33 feet) rock shelter overlooking the nearby plains and springs. +Excavations have revealed that it was intermittently occupied during the Upper Palaeolithic (c.  34,000 to 32,000 years ago and 23,000 to 21,000 years ago), Late Epipalaeolithic (c.  11,200 to 10,200 years ago), and Pre-Pottery and Pottery Neolithic. +The site was discovered in 1999 and excavated by a team from the University of Tübingen between 1999 and 2004. + + +== Further reading == +"The 1999 Excavation at Baaz Rockshelter," Tubingen-Damascus Excavation and Survey Project, Conrad, Kandel, Dyab, 2006 +"The 2000 Excavation at Baaz Rockshelter," Tubingen-Damascus Excavation and Survey Project, Conrad, Kandel, Dyab, 2006 +"The 2004 Excavation at Baaz Rockshelter," Tubingen-Damascus Excavation and Survey Project, Conrad, Kandel, Dyab, 2006 + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Beersheba_fragment_with_menorah_depiction-0.md b/data/en.wikipedia.org/wiki/Beersheba_fragment_with_menorah_depiction-0.md new file mode 100644 index 000000000..7fee83690 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Beersheba_fragment_with_menorah_depiction-0.md @@ -0,0 +1,32 @@ +--- +title: "Beersheba fragment with menorah depiction" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Beersheba_fragment_with_menorah_depiction" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:13.741702+00:00" +instance: "kb-cron" +--- + +The 'Oil Lamp Fragment' is an old remnant of a Jewish oil lamp. + + +== Discovery == +The fragment of an ancient jewish oil lamp was found unearthed the Beersheba Settlement in the Negev Desert. It was discovered during excavations beneath destroyed buildings that date back to the time of the Judaea Province. The settlement and the oil lamp itself were destroyed during the Jewish-Roman wars. + + +== The fragment == +The oil lamp fragment decorated with a nine-branched menorah. + +According to the Israel Antiquities Authority This is probably one of the earliest artistic depictions of a nine-branched menorah yet discovered. Of the few oil lamps discovered which depict menorahs, none of them have the traditional seven branches. This is because of a ruling in the Babylonian Talmud which stated that only the temple menorah itself could have seven branches. Because of this, lamps used in domestic settings commonly had between eight to eleven branches. + + +== See also == +Bar Kokhba Revolt +Bar Kokhba Revolt coinage +Simon bar Kokhba +Judaea Province +Archaeology of Israel + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Beinwil_am_See–Ägelmoos-0.md b/data/en.wikipedia.org/wiki/Beinwil_am_See–Ägelmoos-0.md new file mode 100644 index 000000000..3db10e66b --- /dev/null +++ b/data/en.wikipedia.org/wiki/Beinwil_am_See–Ägelmoos-0.md @@ -0,0 +1,18 @@ +--- +title: "Beinwil am See–Ägelmoos" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Beinwil_am_See–Ägelmoos" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:14.890611+00:00" +instance: "kb-cron" +--- + +Beinwil am See–Ägelmoos is an archaeological site in Beinwil am See in the Swiss canton of Aargau. It is a lakeside settlement (also known as a pile dwelling village or palafitte) that was probably inhabited during the Neolithic, Early Bronze Age and Late Bronze Age, i.e. between 4500 BC and 850 BC. Today (2019), the remains of the settlement lie completely submerged in Lake Hallwil. As a protective measure, they were covered with a layer of geotextile and gravel in 2017. Since 2011, the site has been part of the UNESCO World Heritage Site Prehistoric Pile Dwellings around the Alps. + + +== References == + + +== External links == + Media related to Beinwil am See–Ägelmoos at Wikimedia Commons \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Benaiah_inscription-0.md b/data/en.wikipedia.org/wiki/Benaiah_inscription-0.md new file mode 100644 index 000000000..51c502bd2 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Benaiah_inscription-0.md @@ -0,0 +1,22 @@ +--- +title: "Benaiah inscription" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Benaiah_inscription" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:16.055743+00:00" +instance: "kb-cron" +--- + +The Benaiah inscription is an ancient pottery sherd found in Israel that dates back to the 7th century BCE. The artifact is currently in the care of the Israel Antiquities Authority. + + +== The inscription == +The sherd bears a Hebrew inscription dating back to the 7th century BCE. It reads "ryhu bn bnh", which resembles the name "Zechariah son of Benaiah", a figure named in 2 Chronicles 10:24. The bowl likely originated between the reigns of Hezekiah and Zedekiah. + + +== References == + + +== See also == +List of inscriptions in biblical archaeology \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Boncuklu_Höyük-0.md b/data/en.wikipedia.org/wiki/Boncuklu_Höyük-0.md new file mode 100644 index 000000000..df26e4859 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Boncuklu_Höyük-0.md @@ -0,0 +1,26 @@ +--- +title: "Boncuklu Höyük" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Boncuklu_Höyük" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:17.319633+00:00" +instance: "kb-cron" +--- + +Boncuklu Höyük is a Neolithic archaeological site in Central Anatolia, Turkey, situated around 9 km from the more famous Çatalhöyük site. The tell is made up of the remains of one of the world's oldest villages, occupied between around 8300 to 7800 BCE. The buildings are small and oval shaped with walls constructed of mudbricks. The remains of burials of human bodies were found below the floors of the buildings. The earliest known ceramics of Anatolia have been discovered there. +The site was first recorded by Douglas Baird of the University of Liverpool in 2001. He has directed excavations there since 2006. +The site of Boncuklu is characterized by some of the first appearance of agriculture in the Anatolian plateau, through the introduction of small-scale agricultural projects. It is considered as a precussor of the large-scale agricultural developments of Çatalhöyük from 7100 BCE. + + +== See also == +Çatalhöyük +Aşıklı Höyük +Gobekli Tepe + + +== References == + + +== External links == +Boncuklu Project website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Borden_System-0.md b/data/en.wikipedia.org/wiki/Borden_System-0.md new file mode 100644 index 000000000..33f329160 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Borden_System-0.md @@ -0,0 +1,40 @@ +--- +title: "Borden System" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Borden_System" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:18.515175+00:00" +instance: "kb-cron" +--- + +The Borden System is an archaeological numbering system used throughout Canada and by the Canadian Museum System to track archaeological sites and the artefacts that come from them. Canada is one of a few countries that use a national system to identify archaeological sites. +It was created by Charles Edward Borden in 1952 at the University of British Columbia. + + +== How it Works == +The system divides Canada into a grid of blocks based on latitude and longitude. There are two divisions: major and minor blocks. +AaBb-11:1234 +A is the Major South-North Locator - Each block represents 2 degrees of Latitude from south to north (A - U) +a is the Minor South-North Locator - Each block represents 10 minutes of Latitude from south to north (a - l) +B is the Major East-West Locator - Each block represents 4 degrees of Longitude from east to west (A - W) +(north of 62 degrees each major block represents 8 degrees of longitude) +b is the Minor East-West Locator - Each block represents 10 minutes of Longitude from east to west (a - x) +(north of 62 degrees each minor block represents 20 minutes of longitude) +Therefore, a full designation: AaBb-16 represents a roughly 16 km x 16 km area and the 16th site found within that area. +Since the number that follows is the number of the site within an area, assigned when the site is discovered, the whole number really only narrows the area to approximately a 16 km square. But it allows archaeologists to designate a site and to label every artefact from the site. +The number after the colon is the artefact number: e.g., AaBb-16:0123 +Because the distance between lines of longitude get smaller with increasing latitude, the Borden System changes at 64 degrees north latitude, from a width of 4 degrees of longitude to a width of 8 degrees in order to keep the area within each designate roughly the same. + + +== Use == +In Alberta, there are 3,438 minor and 17 major blocks. Of the minor blocks, 44 percent do not have any sites recorded. +Block EgPN covers the west site of Calgary and has 766 sites-the most sites in a block in the country (This is old data - check with local authorities for up to date numbers). +Borden numbers have only been applied to archaeological sites that have been encountered and recorded, and are subject to survey and testing bias, as well as the rates of development in some areas. The actual number of cultural sites is much higher. + + +== References == + + +== External links == +"Archaeology Survey of Canada: The Borden System of Site Identification". Oracles. Archived from the original on 30 September 2007. Retrieved 2007-08-17. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Bosing_(archaeology)-0.md b/data/en.wikipedia.org/wiki/Bosing_(archaeology)-0.md new file mode 100644 index 000000000..fe8122ca4 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Bosing_(archaeology)-0.md @@ -0,0 +1,17 @@ +--- +title: "Bosing (archaeology)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Bosing_(archaeology)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:19.703729+00:00" +instance: "kb-cron" +--- + +Bosing is an unsophisticated method for the discovery of buried archaeological features such as pits and ditches dug into a thin substratum of rock, such as limestone or chalk. The technique involves hitting a block of wood laid over the ground surface with a weighty hammer and assessing the sound given out. For example, if the wood gave out a heavy thudding sound, then this would indicate that the underlying bedrock had been disturbed while undisturbed bedrock would emit a thinner and sharper tone. Methodically repeating the process across an area and noting the sound pattern will reveal the extent of the underground features. + + +== References == + + +== Sources == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Burnt_layer-0.md b/data/en.wikipedia.org/wiki/Burnt_layer-0.md new file mode 100644 index 000000000..2c5fa7220 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Burnt_layer-0.md @@ -0,0 +1,15 @@ +--- +title: "Burnt layer" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Burnt_layer" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:17:20.884330+00:00" +instance: "kb-cron" +--- + +A burnt layer or burned layer in archaeology is a stratum of earth that was formed primarily by the burning of objects or buildings. The extent of the layer is irrelevant. It can be the remains of a campfire as well as the remains of a burned down settlement. +Burnt layers are recorded in event stratigraphy, a sub-area of stratigraphy. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Chronology_protection_conjecture-0.md b/data/en.wikipedia.org/wiki/Chronology_protection_conjecture-0.md new file mode 100644 index 000000000..1b5e24bb7 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Chronology_protection_conjecture-0.md @@ -0,0 +1,17 @@ +--- +title: "Chronology protection conjecture" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Chronology_protection_conjecture" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:01.429196+00:00" +instance: "kb-cron" +--- + +The chronology protection conjecture is a hypothesis first proposed by Stephen Hawking that laws of physics beyond those of standard general relativity prevent time travel⁠‍— even when the latter theory states that it should be possible (such as in scenarios where faster than light travel is allowed). The permissibility of time travel is represented mathematically by the existence of closed timelike curves in some solutions to the field equations of general relativity. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation (also known as chronology violation). + +== Etymology == +In a 1992 paper, Hawking uses the metaphorical device of a "Chronology Protection Agency" as a personification of the aspects of physics that make time travel impossible at macroscopic scales, thus apparently preventing temporal paradoxes. He says: + +It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians. +The idea of the Chronology Protection Agency appears to be drawn playfully from the Time Patrol or Time Police concept, which has been used in many works of science fiction such as Poul Anderson's series of Time Patrol stories or Isaac Asimov's novel The End of Eternity, or in the television series Doctor Who. "The Chronology Protection Case" by Paul Levinson, published after Hawking's paper, posits a universe that goes so far as to murder any scientists who are close to inventing any means of time travel. Larry Niven, in his short story ‘Rotating Cylinders and the possibility of Global Causality Violation’ expands this concept so that the universe causes environmental catastrophe, or global civil war, or the local sun going nova, to any civilisation which shows any sign of successful construction. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Chronology_protection_conjecture-1.md b/data/en.wikipedia.org/wiki/Chronology_protection_conjecture-1.md new file mode 100644 index 000000000..187facd95 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Chronology_protection_conjecture-1.md @@ -0,0 +1,35 @@ +--- +title: "Chronology protection conjecture" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Chronology_protection_conjecture" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:01.429196+00:00" +instance: "kb-cron" +--- + +== General relativity and quantum corrections == +Many attempts to generate scenarios for closed timelike curves have been suggested, and the theory of general relativity does allow them in certain circumstances. Some theoretical solutions in general relativity that contain closed timelike curves would require an infinite universe with certain features that our universe does not appear to have, such as the universal rotation of the Gödel metric or the rotating cylinder of infinite length known as a Tipler cylinder. However, some solutions allow for the creation of closed timelike curves in a bounded region of spacetime, with the Cauchy horizon being the boundary between the region of spacetime where closed timelike curves can exist and the rest of spacetime where they cannot. One of the first such bounded time travel solutions found was constructed from a traversable wormhole, based on the idea of taking one of the two "mouths" of the wormhole on a round-trip journey at relativistic speed to create a time difference between it and the other mouth (see the discussion at Wormhole#Time travel). +General relativity does not include quantum effects on its own, and a full integration of general relativity and quantum mechanics would require a theory of quantum gravity, but there is an approximate method for modeling quantum fields in the curved spacetime of general relativity, known as semiclassical gravity. Initial attempts to apply semiclassical gravity to the traversable wormhole time machine indicated that at exactly the moment that wormhole would first allow for closed timelike curves, quantum vacuum fluctuations build up and drive the energy density to infinity in the region of the wormholes. This occurs when the two wormhole mouths, call them A and B, have been moved in such a way that it becomes possible for a particle or wave moving at the speed of light to enter mouth B at some time T2 and exit through mouth A at an earlier time T1, then travel back towards mouth B through ordinary space, and arrive at mouth B at the same time T2 that it entered B on the previous loop; in this way the same particle or wave can make a potentially infinite number of loops through the same regions of spacetime, piling up on itself. Calculations showed that this effect would not occur for an ordinary beam of radiation, because it would be "defocused" by the wormhole so that most of a beam emerging from mouth A would spread out and miss mouth B. But when the calculation was done for vacuum fluctuations, it was found that they would spontaneously refocus on the trip between the mouths, indicating that the pileup effect might become large enough to destroy the wormhole in this case. +Uncertainty about this conclusion remained, because the semiclassical calculations indicated that the pileup would only drive the energy density to infinity for an infinitesimal moment of time, after which the energy density would die down. But semiclassical gravity is considered unreliable for large energy densities or short time periods that reach the Planck scale; at these scales, a complete theory of quantum gravity is needed for accurate predictions. So, it remains uncertain whether quantum-gravitational effects might prevent the energy density from growing large enough to destroy the wormhole. Stephen Hawking conjectured that not only would the pileup of vacuum fluctuations still succeed in destroying the wormhole in quantum gravity, but also that the laws of physics would ultimately prevent any type of time machine from forming; this is the chronology protection conjecture. +Subsequent works in semiclassical gravity provided examples of spacetimes with closed timelike curves where the energy density due to vacuum fluctuations does not approach infinity in the region of spacetime outside the Cauchy horizon. However, in 1997 a general proof was found demonstrating that according to semiclassical gravity, the energy of the quantum field (more precisely, the expectation value of the quantum stress-energy tensor) must always be either infinite or undefined on the horizon itself. Both cases indicate that semiclassical methods become unreliable at the horizon and quantum gravity effects would be important there, consistent with the possibility that such effects would always intervene to prevent time machines from forming. +A definite theoretical decision on the status of the chronology protection conjecture would require a full theory of quantum gravity as opposed to semiclassical methods. There are also some arguments from string theory that seem to support chronology protection, but string theory is not yet a complete theory of quantum gravity. Experimental observation of closed timelike curves would of course demonstrate this conjecture to be false, but short of that, if physicists had a theory of quantum gravity whose predictions had been well-confirmed in other areas, this would give them a significant degree of confidence in the theory's predictions about the possibility or impossibility of time travel. +Other proposals that allow for backwards time travel but prevent time paradoxes, such as the Novikov self-consistency principle, which would ensure the timeline stays consistent, or the idea that a time traveler is taken to a parallel universe while their original timeline remains intact, do not qualify as "chronology protection". + +== See also == +Causality +Cosmic censorship hypothesis +Novikov self-consistency principle +Time travel +Wormhole + +== Notes == + +== References == +Hawking, S. W. (July 1992). "Chronology protection conjecture". Physical Review D. 46 (2): 603–611. Bibcode:1992PhRvD..46..603H. doi:10.1103/PhysRevD.46.603. ISSN 0556-2821. PMID 10014972. +Visser, Matt (2002). "The quantum physics of chronology protection". arXiv:gr-qc/0204022. +Li, Li-Xin (1996). "Must Time Machine Be Unstable against Vacuum Fluctuations?". Classical and Quantum Gravity. 13 (9): 2563–2568. arXiv:gr-qc/9703024. Bibcode:1996CQGra..13.2563L. doi:10.1088/0264-9381/13/9/019. S2CID 250909592. + +== External links == +https://web.archive.org/web/20101125122824/http://hawking.org.uk/index.php/lectures/63 +https://plus.maths.org/content/time-travel-allowed — Kip Thorne discusses time travel in general relativity, and the basis in quantum physics for the chronology protection conjecture \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Curved_spacetime-0.md b/data/en.wikipedia.org/wiki/Curved_spacetime-0.md new file mode 100644 index 000000000..d8cb4e464 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Curved_spacetime-0.md @@ -0,0 +1,27 @@ +--- +title: "Curved spacetime" +chunk: 1/5 +source: "https://en.wikipedia.org/wiki/Curved_spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:02.570747+00:00" +instance: "kb-cron" +--- + +In physics, curved spacetime is the mathematical model in which, with Einstein's theory of general relativity, gravity naturally arises, as opposed to being described as a fundamental force in Newton's static Euclidean reference frame. Objects move along geodesics—curved paths determined by the local geometry of spacetime—rather than being influenced directly by distant bodies. This framework led to two fundamental principles: coordinate independence, which asserts that the laws of physics are the same regardless of the coordinate system used, and the equivalence principle, which states that the effects of gravity are indistinguishable from those of acceleration in sufficiently small regions of space. These principles laid the groundwork for a deeper understanding of gravity through the geometry of spacetime, as formalized in Einstein's field equations. + +== Introduction == +Newton's theories assumed that motion takes place against the backdrop of a rigid Euclidean reference frame that extends throughout all space and all time. Gravity is mediated by a mysterious force, acting instantaneously across a distance, whose actions are independent of the intervening space. In contrast, Einstein denied that there is any background Euclidean reference frame that extends throughout space. Nor is there any such thing as a force of gravitation, only the structure of spacetime itself. + +In spacetime terms, the path of a satellite orbiting the Earth is not dictated by the distant influences of the Earth, Moon and Sun. Instead, the satellite moves through space only in response to local conditions. Since spacetime is everywhere locally flat when considered on a sufficiently small scale, the satellite is always following a straight line in its local inertial frame. We say that the satellite always follows along the path of a geodesic. No evidence of gravitation can be discovered following alongside the motions of a single particle. +In any analysis of spacetime, evidence of gravitation requires that one observe the relative accelerations of two bodies or two separated particles. In Fig. 5-1, two separated particles, free-falling in the gravitational field of the Earth, exhibit tidal accelerations due to local inhomogeneities in the gravitational field such that each particle follows a different path through spacetime. The tidal accelerations that these particles exhibit with respect to each other do not require forces for their explanation. Rather, Einstein described them in terms of the geometry of spacetime, i.e. the curvature of spacetime. These tidal accelerations are strictly local. It is the cumulative total effect of many local manifestations of curvature that result in the appearance of a gravitational force acting at a long range from Earth. + +Different observers viewing the scenarios presented in this figure interpret the scenarios differently depending on their knowledge of the situation. (i) A first observer, at the center of mass of particles 2 and 3 but unaware of the large mass 1, concludes that a force of repulsion exists between the particles in scenario A while a force of attraction exists between the particles in scenario B. (ii) A second observer, aware of the large mass 1, smiles at the first reporter's naiveté. This second observer knows that in reality, the apparent forces between particles 2 and 3 really represent tidal effects resulting from their differential attraction by mass 1. (iii) A third observer, trained in general relativity, knows that there are, in fact, no forces at all acting between the three objects. Rather, all three objects move along geodesics in spacetime. +Two central propositions underlie general relativity. + +The first crucial concept is coordinate independence: The laws of physics cannot depend on what coordinate system one uses. This is a major extension of the principle of relativity from the version used in special relativity, which states that the laws of physics must be the same for every observer moving in non-accelerated (inertial) reference frames. In general relativity, to use Einstein's own (translated) words, "the laws of physics must be of such a nature that they apply to systems of reference in any kind of motion." This leads to an immediate issue: In accelerated frames, one feels forces that seemingly would enable one to assess one's state of acceleration in an absolute sense. Einstein resolved this problem through the principle of equivalence. + +The equivalence principle states that in any sufficiently small region of space, the effects of gravitation are the same as those from acceleration. In Fig. 5-2, person A is in a spaceship, far from any massive objects, that undergoes a uniform acceleration of g. Person B is in a box resting on Earth. Provided that the spaceship is sufficiently small so that tidal effects are non-measurable (given the sensitivity of current gravity measurement instrumentation, A and B presumably should be Lilliputians), there are no experiments that A and B can perform which will enable them to tell which setting they are in. An alternative expression of the equivalence principle is to note that in Newton's universal law of gravitation, F = GMmg/r2 = mgg and in Newton's second law, F = mia, there is no a priori reason why the gravitational mass mg should be equal to the inertial mass mi. The equivalence principle states that these two masses are identical. +To go from the elementary description above of curved spacetime to a complete description of gravitation requires tensor calculus and differential geometry, topics both requiring considerable study. Without these mathematical tools, it is possible to write about general relativity, but it is not possible to demonstrate any non-trivial derivations. + +== Gravitational time dilation == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Curved_spacetime-1.md b/data/en.wikipedia.org/wiki/Curved_spacetime-1.md new file mode 100644 index 000000000..e8b8fa2c3 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Curved_spacetime-1.md @@ -0,0 +1,234 @@ +--- +title: "Curved spacetime" +chunk: 2/5 +source: "https://en.wikipedia.org/wiki/Curved_spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:02.570747+00:00" +instance: "kb-cron" +--- + +In the discussion of special relativity, forces played no more than a background role. Special relativity assumes the ability to define inertial frames that fill all of spacetime, all of whose clocks run at the same rate as the clock at the origin. Is this really possible? In a nonuniform gravitational field, experiment dictates that the answer is no. Gravitational fields make it impossible to construct a global inertial frame. In small enough regions of spacetime, local inertial frames are still possible. General relativity involves the systematic stitching together of these local frames into a more general picture of spacetime. +Years before publication of the general theory in 1916, Einstein used the equivalence principle to predict the existence of gravitational redshift in the following thought experiment: (i) Assume that a tower of height h (Fig. 5-3) has been constructed. (ii) Drop a particle of rest mass m from the top of the tower. It falls freely with acceleration g, reaching the ground with velocity v = (2gh)1/2, so that its total energy E, as measured by an observer on the ground, is ⁠ + + + + m + + + + + + + 1 + 2 + + + + m + + v + + 2 + + + + + / + + + + c + + 2 + + + + = + m + + + + m + g + h + + + / + + + + c + + 2 + + + + + + {\displaystyle m+{{\tfrac {1}{2}}mv^{2}}/{c^{2}}=m+{mgh}/{c^{2}}} + +⁠ (iii) A mass-energy converter transforms the total energy of the particle into a single high energy photon, which it directs upward. (iv) At the top of the tower, an energy-mass converter transforms the energy of the photon E' back into a particle of rest mass m'. +It must be that m = m', since otherwise one would be able to construct a perpetual motion device. We therefore predict that E' = m, so that + + + + + + + + E + ′ + + E + + + = + + + + h + ν + + + ′ + + + + h + ν + + + + = + + + m + + m + + + + + + m + g + h + + + c + + 2 + + + + + + + + = + 1 + − + + + + g + h + + + c + + 2 + + + + + + + {\displaystyle {\frac {E'}{E}}={\frac {h\nu \,'}{h\nu }}={\frac {m}{m+{\frac {mgh}{c^{2}}}}}=1-{\frac {gh}{c^{2}}}} + + +A photon climbing in Earth's gravitational field loses energy and is redshifted. Early attempts to measure this redshift through astronomical observations were somewhat inconclusive, but definitive laboratory observations were performed by Pound & Rebka (1959) and later by Pound & Snider (1964). +Light has an associated frequency, and this frequency may be used to drive the workings of a clock. The gravitational redshift leads to an important conclusion about time itself: Gravity makes time run slower. Suppose we build two identical clocks whose rates are controlled by some stable atomic transition. Place one clock on top of the tower, while the other clock remains on the ground. An experimenter on top of the tower observes that signals from the ground clock are lower in frequency than those of the clock next to her on the tower. Light going up the tower is just a wave, and it is impossible for wave crests to disappear on the way up. Exactly as many oscillations of light arrive at the top of the tower as were emitted at the bottom. The experimenter concludes that the ground clock is running slow, and can confirm this by bringing the tower clock down to compare side by side with the ground clock. For a 1 km tower, the discrepancy would amount to about 9.4 nanoseconds per day, easily measurable with modern instrumentation. +Clocks in a gravitational field do not all run at the same rate. Experiments such as the Pound–Rebka experiment have firmly established the distortion of time component of spacetime. The Pound–Rebka experiment says nothing about curvature of the space component of spacetime. But the theoretical arguments predicting gravitational time dilation do not depend on the details of general relativity at all. Any theory of gravity will predict gravitational time dilation if it respects the principle of equivalence. This includes Newtonian gravitation. A standard demonstration in general relativity is to show how, in the "Newtonian limit" (i.e. the particles are moving slowly, the gravitational field is weak, and the field is static), time component of the Christoffel symbols describing the geometry of spacetime alone is sufficient to derive Newton's law of gravity. +Newtonian gravitation is a theory of distorted time. General relativity is a theory of distorted spacetime. Given G as the gravitational constant, M as the mass of a Newtonian star, and orbiting bodies of insignificant mass at distance r from the star, the spacetime interval for Newtonian gravitation is one for which only the time coefficient is variable: + + + + + Δ + + s + + 2 + + + = + + ( + + 1 + − + + + + 2 + G + M + + + + c + + 2 + + + r + + + + + ) + + ( + c + Δ + t + + ) + + 2 + + + − + + ( + Δ + x + + ) + + 2 + + + − + ( + Δ + y + + ) + + 2 + + + − + ( + Δ + z + + ) + + 2 + + + + + {\displaystyle \Delta s^{2}=\left(1-{\frac {2GM}{c^{2}r}}\right)(c\Delta t)^{2}-\,(\Delta x)^{2}-(\Delta y)^{2}-(\Delta z)^{2}} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Curved_spacetime-2.md b/data/en.wikipedia.org/wiki/Curved_spacetime-2.md new file mode 100644 index 000000000..ce83c7447 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Curved_spacetime-2.md @@ -0,0 +1,419 @@ +--- +title: "Curved spacetime" +chunk: 3/5 +source: "https://en.wikipedia.org/wiki/Curved_spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:02.570747+00:00" +instance: "kb-cron" +--- + +== Distortion of space == +The + + + + ( + 1 + − + 2 + G + M + + / + + ( + + c + + 2 + + + r + ) + ) + + + {\displaystyle (1-2GM/(c^{2}r))} + + coefficient in front of + + + + ( + c + Δ + t + + ) + + 2 + + + + + {\displaystyle (c\Delta t)^{2}} + + describes the distortion of time in Newtonian gravitation, and this distortion completely accounts for all Newtonian gravitational effects. As expected, this correction factor is directly proportional to + + + + G + + + {\displaystyle G} + + and + + + + M + + + {\displaystyle M} + +, and because of the + + + + r + + + {\displaystyle r} + + in the denominator, the correction factor increases as one approaches the gravitating body, meaning that time is distorted. +But general relativity is a theory of distorted space and distorted time, so if there are terms modifying the spatial components of the spacetime interval presented above, should not their effects be seen on, say, planetary and satellite orbits due to distortion correction factors applied to the spatial terms? +The answer is that they are seen, but the effects are tiny. The reason is that planetary velocities are extremely small compared to the speed of light, so that for planets and satellites of the Solar System, the + + + + ( + c + Δ + t + + ) + + 2 + + + + + {\displaystyle (c\Delta t)^{2}} + + term dwarfs the spatial terms. +Despite the minuteness of the spatial terms, the first indications that something was wrong with Newtonian gravitation were discovered over a century-and-a-half ago. In 1859, Urbain Le Verrier, in an analysis of available timed observations of transits of Mercury over the Sun's disk from 1697 to 1848, reported that known physics could not explain the orbit of Mercury, unless there possibly existed a planet or asteroid belt within the orbit of Mercury. The perihelion of Mercury's orbit exhibited an excess rate of precession over that which could be explained by the tugs of the other planets. The ability to detect and accurately measure the minute value of this anomalous precession (only 43 arc seconds per tropical century) is testimony to the sophistication of 19th century astrometry. + +As the astronomer who had earlier discovered the existence of Neptune "at the tip of his pen" by analyzing irregularities in the orbit of Uranus, Le Verrier's announcement triggered a two-decades long period of "Vulcan-mania", as professional and amateur astronomers alike hunted for the hypothetical new planet. This search included several false sightings of Vulcan. It was ultimately established that no such planet or asteroid belt existed. +In 1916, Einstein was to show that this anomalous precession of Mercury is explained by the spatial terms in the distortion of spacetime. distortion in the temporal term, being simply an expression of Newtonian gravitation, has no part in explaining this anomalous precession. The success of his calculation was a powerful indication to Einstein's peers that the general theory of relativity could be correct. +The most spectacular of Einstein's predictions was his calculation that the distortion terms in the spatial components of the spacetime interval could be measured in the bending of light around a massive body. Light has a slope of ±1 on a spacetime diagram. Its movement in space is equal to its movement in time. For the weak field expression of the invariant interval, Einstein calculated an exactly equal but opposite sign distortion in its spatial components. + + + + + Δ + + s + + 2 + + + = + + ( + + 1 + − + + + + 2 + G + M + + + + c + + 2 + + + r + + + + + ) + + ( + c + Δ + t + + ) + + 2 + + + + + {\displaystyle \Delta s^{2}=\left(1-{\frac {2GM}{c^{2}r}}\right)(c\Delta t)^{2}} + + + + + + − + + + ( + + 1 + + + + + + 2 + G + M + + + + c + + 2 + + + r + + + + + ) + + + [ + + ( + Δ + x + + ) + + 2 + + + + + ( + Δ + y + + ) + + 2 + + + + + ( + Δ + z + + ) + + 2 + + + + ] + + + + {\displaystyle -\,\left(1+{\frac {2GM}{c^{2}r}}\right)\left[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}\right]} + + +In Newton's gravitation, the + + + + ( + 1 + − + 2 + G + M + + / + + ( + + c + + 2 + + + r + ) + ) + + + {\displaystyle (1-2GM/(c^{2}r))} + + coefficient in front of + + + + ( + c + Δ + t + + ) + + 2 + + + + + {\displaystyle (c\Delta t)^{2}} + + predicts bending of light around a star. In general relativity, the + + + + ( + 1 + + + 2 + G + M + + / + + ( + + c + + 2 + + + r + ) + ) + + + {\displaystyle (1+2GM/(c^{2}r))} + + coefficient in front of + + + + + [ + + ( + Δ + x + + ) + + 2 + + + + + ( + Δ + y + + ) + + 2 + + + + + ( + Δ + z + + ) + + 2 + + + + ] + + + + {\displaystyle \left[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}\right]} + + predicts a doubling of the total bending. +The story of the 1919 Eddington eclipse expedition and Einstein's rise to fame is well told elsewhere. + +== Sources of spacetime curvature == + +In Newton's theory of gravitation, the only source of gravitational force is mass. +In contrast, general relativity identifies several sources of spacetime curvature in addition to mass. In the Einstein field equations, +the sources of gravity are presented on the right-hand side in + + + + + T + + μ + ν + + + , + + + {\displaystyle T_{\mu \nu },} + + the stress–energy tensor. +Fig. 5-5 classifies the various sources of gravity in the stress–energy tensor: + + + + + + T + + 00 + + + + + {\displaystyle T^{00}} + + (red): The total mass–energy density, including any contributions to the potential energy from forces between the particles, as well as kinetic energy from random thermal motions. + + + + + + T + + 0 + i + + + + + {\displaystyle T^{0i}} + + and + + + + + T + + i + 0 + + + + + {\displaystyle T^{i0}} + + (orange): These are momentum density terms. Even if there is no bulk motion, energy may be transmitted by heat conduction, and the conducted energy will carry momentum. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Curved_spacetime-3.md b/data/en.wikipedia.org/wiki/Curved_spacetime-3.md new file mode 100644 index 000000000..024c0c819 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Curved_spacetime-3.md @@ -0,0 +1,114 @@ +--- +title: "Curved spacetime" +chunk: 4/5 +source: "https://en.wikipedia.org/wiki/Curved_spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:02.570747+00:00" +instance: "kb-cron" +--- + + + + + + T + + i + j + + + + + {\displaystyle T^{ij}} + + are the rates of flow of the i-component of momentum per unit area in the j-direction. Even if there is no bulk motion, random thermal motions of the particles will give rise to momentum flow, so the i = j terms (green) represent isotropic pressure, and the i ≠ j terms (blue) represent shear stresses. +One important conclusion to be derived from the equations is that, colloquially speaking, gravity itself creates gravity. Energy has mass. Even in Newtonian gravity, the gravitational field is associated with an energy, ⁠ + + + + E + = + m + g + h + , + + + {\displaystyle E=mgh,} + +⁠ called the gravitational potential energy. In general relativity, the energy of the gravitational field feeds back into creation of the gravitational field. This makes the equations nonlinear and hard to solve in anything other than weak field cases. Numerical relativity is a branch of general relativity using numerical methods to solve and analyze problems, often employing supercomputers to study black holes, gravitational waves, neutron stars and other phenomena in the strong field regime. + +=== Energy-momentum === + +In special relativity, mass-energy is closely connected to momentum. Just as space and time are different aspects of a more comprehensive entity called spacetime, mass–energy and momentum are merely different aspects of a unified, four-dimensional quantity called four-momentum. In consequence, if mass–energy is a source of gravity, momentum must also be a source. The inclusion of momentum as a source of gravity leads to the prediction that moving or rotating masses can generate fields analogous to the magnetic fields generated by moving charges, a phenomenon known as gravitomagnetism. + +It is well known that the force of magnetism can be deduced by applying the rules of special relativity to moving charges. (An eloquent demonstration of this was presented by Feynman in volume II, chapter 13–6 of his Lectures on Physics, available online.) Analogous logic can be used to demonstrate the origin of gravitomagnetism. +In Fig. 5-7a, two parallel, infinitely long streams of massive particles have equal and opposite velocities −v and +v relative to a test particle at rest and centered between the two. Because of the symmetry of the setup, the net force on the central particle is zero. Assume ⁠ + + + + v + ≪ + c + + + {\displaystyle v\ll c} + +⁠ so that velocities are simply additive. Fig. 5-7b shows exactly the same setup, but in the frame of the upper stream. The test particle has a velocity of +v, and the bottom stream has a velocity of +2v. Since the physical situation has not changed, only the frame in which things are observed, the test particle should not be attracted towards either stream. +It is not at all clear that the forces exerted on the test particle are equal. (1) Since the bottom stream is moving faster than the top, each particle in the bottom stream has a larger mass energy than a particle in the top. (2) Because of Lorentz contraction, there are more particles per unit length in the bottom stream than in the top stream. (3) Another contribution to the active gravitational mass of the bottom stream comes from an additional pressure term which, at this point, we do not have sufficient background to discuss. All of these effects together would seemingly demand that the test particle be drawn towards the bottom stream. +The test particle is not drawn to the bottom stream because of a velocity-dependent force that serves to repel a particle that is moving in the same direction as the bottom stream. This velocity-dependent gravitational effect is gravitomagnetism. +Matter in motion through a gravitomagnetic field is hence subject to so-called frame-dragging effects analogous to electromagnetic induction. It has been proposed that such gravitomagnetic forces underlie the generation of the relativistic jets (Fig. 5-8) ejected by some rotating supermassive black holes. + +=== Pressure and stress === +Quantities that are directly related to energy and momentum should be sources of gravity as well, namely internal pressure and stress. Taken together, mass-energy, momentum, pressure and stress all serve as sources of gravity: Collectively, they are what tells spacetime how to curve. +General relativity predicts that pressure acts as a gravitational source with exactly the same strength as mass–energy density. The inclusion of pressure as a source of gravity leads to dramatic differences between the predictions of general relativity versus those of Newtonian gravitation. For example, the pressure term sets a maximum limit to the mass of a neutron star. The more massive a neutron star, the more pressure is required to support its weight against gravity. The increased pressure, however, adds to the gravity acting on the star's mass. Above a certain mass determined by the Tolman–Oppenheimer–Volkoff limit, the process becomes runaway and the neutron star collapses to a black hole. +The stress terms become highly significant when performing calculations such as hydrodynamic simulations of core-collapse supernovae. +These predictions for the roles of pressure, momentum and stress as sources of spacetime curvature are elegant and play an important role in theory. In regards to pressure, the early universe was radiation dominated, and it is highly unlikely that any of the relevant cosmological data (e.g. nucleosynthesis abundances, etc.) could be reproduced if pressure did not contribute to gravity, or if it did not have the same strength as a source of gravity as mass–energy. Likewise, the mathematical consistency of the Einstein field equations would be broken if the stress terms did not contribute as a source of gravity. + +== Experimental test of the sources of spacetime curvature == + +=== Definitions: Active, passive, and inertial mass === +Bondi distinguishes between different possible types of mass: (1) active mass ( + + + + + m + + a + + + + + {\displaystyle m_{a}} + +) is the mass which acts as the source of a gravitational field; (2)passive mass ( + + + + + m + + p + + + + + {\displaystyle m_{p}} + +) is the mass which reacts to a gravitational field; (3) inertial mass ( + + + + + m + + i + + + + + {\displaystyle m_{i}} + +) is the mass which reacts to acceleration. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Curved_spacetime-4.md b/data/en.wikipedia.org/wiki/Curved_spacetime-4.md new file mode 100644 index 000000000..224d7848b --- /dev/null +++ b/data/en.wikipedia.org/wiki/Curved_spacetime-4.md @@ -0,0 +1,205 @@ +--- +title: "Curved spacetime" +chunk: 5/5 +source: "https://en.wikipedia.org/wiki/Curved_spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:02.570747+00:00" +instance: "kb-cron" +--- + + + + + + m + + p + + + + + {\displaystyle m_{p}} + + is the same as gravitational mass ( + + + + + m + + g + + + + + {\displaystyle m_{g}} + +) in the discussion of the equivalence principle. +In Newtonian theory, + +The third law of action and reaction dictates that + + + + + m + + a + + + + + {\displaystyle m_{a}} + + and + + + + + m + + p + + + + + {\displaystyle m_{p}} + + must be the same. +On the other hand, whether + + + + + m + + p + + + + + {\displaystyle m_{p}} + + and + + + + + m + + i + + + + + {\displaystyle m_{i}} + + are equal is an empirical result. +In general relativity, + +The equality of + + + + + m + + p + + + + + {\displaystyle m_{p}} + + and + + + + + m + + i + + + + + {\displaystyle m_{i}} + + is dictated by the equivalence principle. +There is no "action and reaction" principle dictating any necessary relationship between + + + + + m + + a + + + + + {\displaystyle m_{a}} + + and + + + + + m + + p + + + + + {\displaystyle m_{p}} + +. + +=== Pressure as a gravitational source === + +The classic experiment to measure the strength of a gravitational source (i.e. its active mass) was first conducted in 1797 by Henry Cavendish (Fig. 5-9a). Two small but dense balls are suspended on a fine wire, making a torsion balance. Bringing two large test masses close to the balls introduces a detectable torque. Given the dimensions of the apparatus and the measurable spring constant of the torsion wire, the gravitational constant G can be determined. +To study pressure effects by compressing the test masses is hopeless, because attainable laboratory pressures are insignificant in comparison with the mass-energy of a metal ball. +However, the repulsive electromagnetic pressures resulting from protons being tightly squeezed inside atomic nuclei are typically on the order of 1028 atm ≈ 1033 Pa ≈ 1033 kg·s−2m−1. This amounts to about 1% of the nuclear mass density of approximately 1018kg/m3 (after factoring in c2 ≈ 9×1016m2s−2). + +If pressure does not act as a gravitational source, then the ratio + + + + + m + + a + + + + / + + + m + + p + + + + + {\displaystyle m_{a}/m_{p}} + + should be lower for nuclei with higher atomic number Z, in which the electrostatic pressures are higher. L. B. Kreuzer (1968) did a Cavendish experiment using a Teflon mass suspended in a mixture of the liquids trichloroethylene and dibromoethane having the same buoyant density as the Teflon (Fig. 5-9b). Fluorine has atomic number Z = 9, while bromine has Z = 35. Kreuzer found that repositioning the Teflon mass caused no differential deflection of the torsion bar, hence establishing active mass and passive mass to be equivalent to a precision of 5×10−5. +Although Kreuzer originally considered this experiment merely to be a test of the ratio of active mass to passive mass, Clifford Will (1976) reinterpreted the experiment as a fundamental test of the coupling of sources to gravitational fields. +In 1986, Bartlett and Van Buren noted that lunar laser ranging had detected a 2 km offset between the moon's center of figure and its center of mass. This indicates an asymmetry in the distribution of Fe (abundant in the Moon's core) and Al (abundant in its crust and mantle). If pressure did not contribute equally to spacetime curvature as does mass–energy, the moon would not be in the orbit predicted by classical mechanics. They used their measurements to tighten the limits on any discrepancies between active and passive mass to about 10−12. With decades of additional lunar laser ranging data, Singh et al. (2023) reported improvement on these limits by a factor of about 100. + +=== Gravitomagnetism === + +The existence of gravitomagnetism was proven by Gravity Probe B (GP-B), a satellite-based mission which launched on 20 April 2004. The spaceflight phase lasted until 2005. The mission aim was to measure spacetime curvature near Earth, with particular emphasis on gravitomagnetism. +Initial results confirmed the relatively large geodetic effect (which is due to simple spacetime curvature, and is also known as de Sitter precession) to an accuracy of about 1%. The much smaller frame-dragging effect (which is due to gravitomagnetism, and is also known as Lense–Thirring precession) was difficult to measure because of unexpected charge effects causing variable drift in the gyroscopes. Nevertheless, by August 2008, the frame-dragging effect had been confirmed to within 15% of the expected result, while the geodetic effect was confirmed to better than 0.5%. +Subsequent measurements of frame dragging by laser-ranging observations of the LARES, LAGEOS-1 and LAGEOS-2 satellites has improved on the GP-B measurement, with results (as of 2016) demonstrating the effect to within 5% of its theoretical value, although there has been some disagreement on the accuracy of this result. +Another effort, the Gyroscopes in General Relativity (GINGER) experiment, seeks to use three 6 m ring lasers mounted at right angles to each other 1400 m below the Earth's surface to measure this effect. The first ten years of experience with a prototype ring laser gyroscope array, GINGERINO, established that the full scale experiment should be able to measure gravitomagnetism due to the Earth's rotation to within a 0.1% level or even better. + +== See also == +Spacetime topology + +== Notes == + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Dorothy_Hill_Medal-0.md b/data/en.wikipedia.org/wiki/Dorothy_Hill_Medal-0.md new file mode 100644 index 000000000..744adc0c8 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Dorothy_Hill_Medal-0.md @@ -0,0 +1,24 @@ +--- +title: "Dorothy Hill Medal" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Dorothy_Hill_Medal" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:31.038014+00:00" +instance: "kb-cron" +--- + +The Dorothy Hill Medal is awarded annually and honours the contributions of Dorothy Hill to Australian Earth science and her work in opening up tertiary science education to women. +The award supports research in the Earth sciences by female researchers up to 10 years post doctorate for research carried out mainly in Australia. +Prior to 2018 the award was known as the Dorothy Hill Award. + + +== Recipients == +Source: Australian Academy of Science + + +== See also == +List of earth sciences awards + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Elaine_Bennett_Research_Prize-0.md b/data/en.wikipedia.org/wiki/Elaine_Bennett_Research_Prize-0.md new file mode 100644 index 000000000..623a7c15d --- /dev/null +++ b/data/en.wikipedia.org/wiki/Elaine_Bennett_Research_Prize-0.md @@ -0,0 +1,23 @@ +--- +title: "Elaine Bennett Research Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Elaine_Bennett_Research_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:32.194183+00:00" +instance: "kb-cron" +--- + +The Elaine Bennett Research Prize, awarded every year by the American Economic Association, recognizes and honors outstanding research in any field of economics by a woman not more than ten years beyond her Ph.D. Prior to 2023 the award had been given every other year for a woman not more than seven years beyond her PhD. First awarded in 1998, three of the first six winners of this prize have been the first three female winners of the John Bates Clark Medal. + + +== Past recipients == + + +== See also == +List of awards honoring women +List of economics awards +John Bates Clark Medal + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Elizabeth_Blackwell_Medal-0.md b/data/en.wikipedia.org/wiki/Elizabeth_Blackwell_Medal-0.md new file mode 100644 index 000000000..dd5153eb2 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Elizabeth_Blackwell_Medal-0.md @@ -0,0 +1,34 @@ +--- +title: "Elizabeth Blackwell Medal" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Elizabeth_Blackwell_Medal" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:27.402908+00:00" +instance: "kb-cron" +--- + +The Elizabeth Blackwell Medal is awarded annually by the American Medical Women's Association. The medal is named in honor of Elizabeth Blackwell, the first woman to receive a medical degree in the United States and a pioneer in promoting the education of women in medicine. Established by Elise S. L'Esperance in 1949, 100 years after Blackwell received her medical degree, the medal is granted to a woman physician "who has made the most outstanding contributions to the cause of women in the field of medicine." Before 1993, the medal was only awarded to members of the AMWA. + + +== Recipients == +Source: AMWA + + +== See also == +List of medicine awards +List of prizes, medals, and awards for women in science +List of prizes named after people + + +== Notes == + + +== Further reading == +"Elizabeth Blackwell medal". Journal of the American Medical Women's Association. 47 (3): 68–69. May–June 1992. PMID 1624663. +Vaschak, MR (February 1975). "The Elizabeth Blackwell Annual Award, 1974". Journal of the American Medical Women's Association. 30 (2): 84–85. PMID 163270. +Mega, LT; McKinney, PA (Sep–Oct 1990). "Looking back at progress: AMWA award winners". Journal of the American Medical Women's Association. 45 (5): 200–6. PMID 2269768. + + +== External links == +Elizabeth Blackwell Award \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Elizabeth_L._Scott_Award-0.md b/data/en.wikipedia.org/wiki/Elizabeth_L._Scott_Award-0.md new file mode 100644 index 000000000..1dc0f4ca4 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Elizabeth_L._Scott_Award-0.md @@ -0,0 +1,21 @@ +--- +title: "Elizabeth L. Scott Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Elizabeth_L._Scott_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:33.387019+00:00" +instance: "kb-cron" +--- + +The Elizabeth L. Scott Award is an biennial award given (in even years) by the Committee of Presidents of Statistical Societies and named in honor of Elizabeth Scott, an American statistician. This award recognizes an individual who exemplifies the contributions of Elizabeth L. Scott’s lifelong efforts to further the careers of women in academia. The award is given to an individual who has helped foster opportunities in statistics for women and is presented at the Joint Statistical Meetings. Starting in 2020, the recipient of the award will give a lecture at the Joint Statistical Meetings. + + +== List of Award winners == + + +== See also == +List of mathematics awards + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/FASEB_Excellence_in_Science_Award-0.md b/data/en.wikipedia.org/wiki/FASEB_Excellence_in_Science_Award-0.md new file mode 100644 index 000000000..d0bb154a3 --- /dev/null +++ b/data/en.wikipedia.org/wiki/FASEB_Excellence_in_Science_Award-0.md @@ -0,0 +1,71 @@ +--- +title: "FASEB Excellence in Science Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/FASEB_Excellence_in_Science_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:34.596906+00:00" +instance: "kb-cron" +--- + +The Excellence in Science Award was established by the Federation of American Societies for Experimental Biology (FASEB) in 1989 to recognize outstanding achievement by women in biological science. All women who are members of one or more of the societies of FASEB are eligible for nomination. Nominations recognize a woman whose career achievements have contributed significantly to further our understanding of a particular discipline by excellence in research. +The award includes a $10,000 unrestricted research grant, funded by Eli Lilly and Company. + + +== Award recipients == +Source: FASEB Archived 2016-03-04 at the Wayback Machine + +1989 Marian Koshland +1990 Elizabeth Hay +1991 Ellen Vitetta +1992 Bettie Sue Masters +1993 Susan Leeman +1994 Lucille Shapiro +1995 Philippa Marrack +1996 Zena Werb +1997 Claude Klee +1998 Eva Neer +1999 Helen Blau +2000 Peng Loh +2001 Laurie Glimcher +2002 Phyllis Wise +2003 Joan A. Steitz +2004 Janet Rossant +2005 Anita Roberts +2006 Marilyn Farquhar and Elaine Fuchs +2007 Frances Arnold +2008 Mina J. Bissell +2009 Susan L. Lindquist +2010 Susan S. Taylor +2011 Gail R. Martin +2012 Susan R. Wessler +2013 Terry Orr-Weaver +2014 Kathryn V. Anderson +2015 Diane Griffin +2016 Bonnie Bassler +2017 Diane Mathis +2018 Lynne E. Maquat +2019 Barbara B. Kahn +2020 : +Lifetime Achievement : Brigid Hogan +Mid-Career Investigator : Aviv Regev +Early-Career Investigator : Karen Schindler +2021: +Lifetime Achievement : M. Celeste Simon +Mid-Career Investigator : Valentina Greco +Early-Career Investigator : Cigall Kadoch +2022: +Lifetime Achievement : Arlene H. Sharpe +Mid-Career Investigator : Sallie R. Permar +Early-Career Investigator : Smita Krishnaswamy +2023: +Lifetime Achievement : Elaine S. Jaffe +Mid-Career Investigator : Paola Arlotta +Early-Career Investigator : Diana Libuda + + +== See also == +List of biology awards + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Florence_Nightingale_David_Award-0.md b/data/en.wikipedia.org/wiki/Florence_Nightingale_David_Award-0.md new file mode 100644 index 000000000..895022410 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Florence_Nightingale_David_Award-0.md @@ -0,0 +1,22 @@ +--- +title: "Florence Nightingale David Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Florence_Nightingale_David_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:29.777856+00:00" +instance: "kb-cron" +--- + +The Florence Nightingale David Award is an award given every two years (in odd-numbered years) jointly by the Committee of Presidents of Statistical Societies and Caucus for Women in Statistics to a distinguished female statistician. + + +== Description == +The award's purpose is to "recognize a female statistician who exemplifies the contributions of Florence Nightingale David" and who "has advanced the discipline and proven herself to be an outstanding role model". Since the founding of the award, it has become a "prestigious hallmark of achievement" among female statisticians. + + +== Winners == +The Florence Nightingale David Award was first given in 2001, with David herself being given the award retroactively, dated to 1994. The winners of the award have been: + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position-0.md b/data/en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position-0.md new file mode 100644 index 000000000..101b63834 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position-0.md @@ -0,0 +1,925 @@ +--- +title: "Fourth, fifth, and sixth derivatives of position" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:05.034067+00:00" +instance: "kb-cron" +--- + +In the physics field of kinematics, the fourth, fifth and sixth derivatives of position are generalizations of velocity and acceleration. They are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. These higher-order derivatives are less common than the first three; thus their names are not as standardized, though the concept of a minimum snap trajectory has been used in robotics. +The fourth derivative is referred to as snap, leading the fifth and sixth derivatives to be "sometimes somewhat facetiously" called crackle and pop, named after the Rice Krispies mascots of the same name. The fourth derivative is also called jounce. + +== Applications == +Minimizing snap and jerk is useful in mechanical and civil engineering because it reduces vibrations and ensures smoother motion transitions. In civil engineering, railway tracks and roads are designed to limit snap, particularly around bends with varying radii of curvature. When snap is constant, the jerk changes linearly, producing a gradual increase in radial acceleration; when snap is zero, acceleration changes linearly. These profiles are often achieved using mathematical clothoid functions. The same principle is applied by roller coaster designers, who use smooth transitions in loops and helices to enhance ride comfort. +In mechanical engineering, controlling snap and jerk is important in fields such as automotive design, to prevent camfollowers from jumping off of camshafts, and manufacturing, where rapid acceleration changes in cutting tools can cause premature tool wear and uneven surface finishes. Minimum-snap and minimum-jerk trajectories are also used in trajectory optimization in robotics. Minimum-snap trajectories for quadrotors can reduce control effort, while minimum-jerk trajectories for robotic manipulators produce predictable motions that improve control performance and facilitate human-robot interaction. + +== Fourth derivative (snap/jounce) == +Snap, or jounce, is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. Equivalently, it is the second derivative of acceleration or the third derivative of velocity, +and is defined by any of the following equivalent expressions: + + + + + + s + + = + + + + + d + + + j + + + + + d + + t + + + + = + + + + + + d + + + 2 + + + + a + + + + + d + + + t + + 2 + + + + + + = + + + + + + d + + + 3 + + + + v + + + + + d + + + t + + 3 + + + + + + = + + + + + + d + + + 4 + + + + r + + + + + d + + + t + + 4 + + + + + + . + + + {\displaystyle \mathbf {s} ={\frac {\mathrm {d} \mathbf {j} }{\mathrm {d} t}}={\frac {\mathrm {d} ^{2}\mathbf {a} }{\mathrm {d} t^{2}}}={\frac {\mathrm {d} ^{3}\mathbf {v} }{\mathrm {d} t^{3}}}={\frac {\mathrm {d} ^{4}\mathbf {r} }{\mathrm {d} t^{4}}}.} + +The following equations are used for constant snap: + + + + + + + + + + j + + + + + = + + + j + + + 0 + + + + + + s + + t + , + + + + + + a + + + + + = + + + a + + + 0 + + + + + + + j + + + 0 + + + t + + + + + + 1 + 2 + + + + + s + + + t + + 2 + + + , + + + + + + v + + + + + = + + + v + + + 0 + + + + + + + a + + + 0 + + + t + + + + + + 1 + 2 + + + + + + j + + + 0 + + + + t + + 2 + + + + + + + + 1 + 6 + + + + + s + + + t + + 3 + + + , + + + + + + r + + + + + = + + + r + + + 0 + + + + + + + v + + + 0 + + + t + + + + + + 1 + 2 + + + + + + a + + + 0 + + + + t + + 2 + + + + + + + + 1 + 6 + + + + + + j + + + 0 + + + + t + + 3 + + + + + + + + 1 + 24 + + + + + s + + + t + + 4 + + + , + + + + + + + {\displaystyle {\begin{aligned}\mathbf {j} &=\mathbf {j} _{0}+\mathbf {s} t,\\\mathbf {a} &=\mathbf {a} _{0}+\mathbf {j} _{0}t+{\tfrac {1}{2}}\mathbf {s} t^{2},\\\mathbf {v} &=\mathbf {v} _{0}+\mathbf {a} _{0}t+{\tfrac {1}{2}}\mathbf {j} _{0}t^{2}+{\tfrac {1}{6}}\mathbf {s} t^{3},\\\mathbf {r} &=\mathbf {r} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} _{0}t^{2}+{\tfrac {1}{6}}\mathbf {j} _{0}t^{3}+{\tfrac {1}{24}}\mathbf {s} t^{4},\end{aligned}}} + + +where + +The notation + + + + + s + + + + {\displaystyle \mathbf {s} } + + (used by Visser) is not to be confused with the displacement vector commonly denoted similarly. +The dimensions of snap are distance per fourth power of time [LT−4]. The corresponding SI unit is metre per second to the fourth power, m/s4, m⋅s−4. + +== Fifth derivative == +The fifth derivative of the position vector with respect to time is sometimes referred to as crackle. It is the rate of change of snap with respect to time. Crackle is defined by any of the following equivalent expressions: + + + + + + c + + = + + + + + d + + + s + + + + + d + + t + + + + = + + + + + + d + + + 2 + + + + j + + + + + d + + + t + + 2 + + + + + + = + + + + + + d + + + 3 + + + + a + + + + + d + + + t + + 3 + + + + + + = + + + + + + d + + + 4 + + + + v + + + + + d + + + t + + 4 + + + + + + = + + + + + + d + + + 5 + + + + r + + + + + d + + + t + + 5 + + + + + + + + {\displaystyle \mathbf {c} ={\frac {\mathrm {d} \mathbf {s} }{\mathrm {d} t}}={\frac {\mathrm {d} ^{2}\mathbf {j} }{\mathrm {d} t^{2}}}={\frac {\mathrm {d} ^{3}\mathbf {a} }{\mathrm {d} t^{3}}}={\frac {\mathrm {d} ^{4}\mathbf {v} }{\mathrm {d} t^{4}}}={\frac {\mathrm {d} ^{5}\mathbf {r} }{\mathrm {d} t^{5}}}} + + +The following equations are used for constant crackle: + + + + + + + + + + s + + + + + = + + + s + + + 0 + + + + + + c + + t + + + + + + j + + + + + = + + + j + + + 0 + + + + + + + s + + + 0 + + + t + + + + + + 1 + 2 + + + + + c + + + t + + 2 + + + + + + + + a + + + + + = + + + a + + + 0 + + + + + + + j + + + 0 + + + t + + + + + + 1 + 2 + + + + + + s + + + 0 + + + + t + + 2 + + + + + + + + 1 + 6 + + + + + c + + + t + + 3 + + + + + + + + v + + + + + = + + + v + + + 0 + + + + + + + a + + + 0 + + + t + + + + + + 1 + 2 + + + + + + j + + + 0 + + + + t + + 2 + + + + + + + + 1 + 6 + + + + + + s + + + 0 + + + + t + + 3 + + + + + + + + 1 + 24 + + + + + c + + + t + + 4 + + + + + + + + r + + + + + = + + + r + + + 0 + + + + + + + v + + + 0 + + + t + + + + + + 1 + 2 + + + + + + a + + + 0 + + + + t + + 2 + + + + + + + + 1 + 6 + + + + + + j + + + 0 + + + + t + + 3 + + + + + + + + 1 + 24 + + + + + + s + + + 0 + + + + t + + 4 + + + + + + + + 1 + 120 + + + + + c + + + t + + 5 + + + + + + + + + {\displaystyle {\begin{aligned}\mathbf {s} &=\mathbf {s} _{0}+\mathbf {c} t\\[1ex]\mathbf {j} &=\mathbf {j} _{0}+\mathbf {s} _{0}t+{\tfrac {1}{2}}\mathbf {c} t^{2}\\[1ex]\mathbf {a} &=\mathbf {a} _{0}+\mathbf {j} _{0}t+{\tfrac {1}{2}}\mathbf {s} _{0}t^{2}+{\tfrac {1}{6}}\mathbf {c} t^{3}\\[1ex]\mathbf {v} &=\mathbf {v} _{0}+\mathbf {a} _{0}t+{\tfrac {1}{2}}\mathbf {j} _{0}t^{2}+{\tfrac {1}{6}}\mathbf {s} _{0}t^{3}+{\tfrac {1}{24}}\mathbf {c} t^{4}\\[1ex]\mathbf {r} &=\mathbf {r} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} _{0}t^{2}+{\tfrac {1}{6}}\mathbf {j} _{0}t^{3}+{\tfrac {1}{24}}\mathbf {s} _{0}t^{4}+{\tfrac {1}{120}}\mathbf {c} t^{5}\end{aligned}}} + + +where + +The dimensions of crackle are [LT−5]. The corresponding SI unit is m/s5. + +== Sixth derivative == +The sixth derivative of the position vector with respect to time is sometimes referred to as pop. It is the rate of change of crackle with respect to time. Pop is defined by any of the following equivalent expressions: \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position-1.md b/data/en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position-1.md new file mode 100644 index 000000000..8653d7255 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position-1.md @@ -0,0 +1,696 @@ +--- +title: "Fourth, fifth, and sixth derivatives of position" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:05.034067+00:00" +instance: "kb-cron" +--- + + + + + + p + + = + + + + + d + + + c + + + + + d + + t + + + + = + + + + + + d + + + 2 + + + + s + + + + + d + + + t + + 2 + + + + + + = + + + + + + d + + + 3 + + + + j + + + + + d + + + t + + 3 + + + + + + = + + + + + + d + + + 4 + + + + a + + + + + d + + + t + + 4 + + + + + + = + + + + + + d + + + 5 + + + + v + + + + + d + + + t + + 5 + + + + + + = + + + + + + d + + + 6 + + + + r + + + + + d + + + t + + 6 + + + + + + + + {\displaystyle \mathbf {p} ={\frac {\mathrm {d} \mathbf {c} }{\mathrm {d} t}}={\frac {\mathrm {d} ^{2}\mathbf {s} }{\mathrm {d} t^{2}}}={\frac {\mathrm {d} ^{3}\mathbf {j} }{\mathrm {d} t^{3}}}={\frac {\mathrm {d} ^{4}\mathbf {a} }{\mathrm {d} t^{4}}}={\frac {\mathrm {d} ^{5}\mathbf {v} }{\mathrm {d} t^{5}}}={\frac {\mathrm {d} ^{6}\mathbf {r} }{\mathrm {d} t^{6}}}} + + +The following equations are used for constant pop: + + + + + + + + + + c + + + + + = + + + c + + + 0 + + + + + + p + + t + + + + + + s + + + + + = + + + s + + + 0 + + + + + + + c + + + 0 + + + t + + + + + + 1 + 2 + + + + + p + + + t + + 2 + + + + + + + + j + + + + + = + + + j + + + 0 + + + + + + + s + + + 0 + + + t + + + + + + 1 + 2 + + + + + + c + + + 0 + + + + t + + 2 + + + + + + + + 1 + 6 + + + + + p + + + t + + 3 + + + + + + + + a + + + + + = + + + a + + + 0 + + + + + + + j + + + 0 + + + t + + + + + + 1 + 2 + + + + + + s + + + 0 + + + + t + + 2 + + + + + + + + 1 + 6 + + + + + + c + + + 0 + + + + t + + 3 + + + + + + + + 1 + 24 + + + + + p + + + t + + 4 + + + + + + + + v + + + + + = + + + v + + + 0 + + + + + + + a + + + 0 + + + t + + + + + + 1 + 2 + + + + + + j + + + 0 + + + + t + + 2 + + + + + + + + 1 + 6 + + + + + + s + + + 0 + + + + t + + 3 + + + + + + + + 1 + 24 + + + + + + c + + + 0 + + + + t + + 4 + + + + + + + + 1 + 120 + + + + + p + + + t + + 5 + + + + + + + + r + + + + + = + + + r + + + 0 + + + + + + + v + + + 0 + + + t + + + + + + 1 + 2 + + + + + + a + + + 0 + + + + t + + 2 + + + + + + + + 1 + 6 + + + + + + j + + + 0 + + + + t + + 3 + + + + + + + + 1 + 24 + + + + + + s + + + 0 + + + + t + + 4 + + + + + + + + 1 + 120 + + + + + + c + + + 0 + + + + t + + 5 + + + + + + + + 1 + 720 + + + + + p + + + t + + 6 + + + + + + + + + {\displaystyle {\begin{aligned}\mathbf {c} &=\mathbf {c} _{0}+\mathbf {p} t\\\mathbf {s} &=\mathbf {s} _{0}+\mathbf {c} _{0}t+{\tfrac {1}{2}}\mathbf {p} t^{2}\\\mathbf {j} &=\mathbf {j} _{0}+\mathbf {s} _{0}t+{\tfrac {1}{2}}\mathbf {c} _{0}t^{2}+{\tfrac {1}{6}}\mathbf {p} t^{3}\\\mathbf {a} &=\mathbf {a} _{0}+\mathbf {j} _{0}t+{\tfrac {1}{2}}\mathbf {s} _{0}t^{2}+{\tfrac {1}{6}}\mathbf {c} _{0}t^{3}+{\tfrac {1}{24}}\mathbf {p} t^{4}\\\mathbf {v} &=\mathbf {v} _{0}+\mathbf {a} _{0}t+{\tfrac {1}{2}}\mathbf {j} _{0}t^{2}+{\tfrac {1}{6}}\mathbf {s} _{0}t^{3}+{\tfrac {1}{24}}\mathbf {c} _{0}t^{4}+{\tfrac {1}{120}}\mathbf {p} t^{5}\\\mathbf {r} &=\mathbf {r} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} _{0}t^{2}+{\tfrac {1}{6}}\mathbf {j} _{0}t^{3}+{\tfrac {1}{24}}\mathbf {s} _{0}t^{4}+{\tfrac {1}{120}}\mathbf {c} _{0}t^{5}+{\tfrac {1}{720}}\mathbf {p} t^{6}\end{aligned}}} + + +where + +The dimensions of pop are [LT−6]. The corresponding SI unit is m/s6. + +== References == + +== External links == + The dictionary definition of jounce at Wiktionary \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Galilean_transformation-0.md b/data/en.wikipedia.org/wiki/Galilean_transformation-0.md new file mode 100644 index 000000000..8c1d8b756 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Galilean_transformation-0.md @@ -0,0 +1,551 @@ +--- +title: "Galilean transformation" +chunk: 1/3 +source: "https://en.wikipedia.org/wiki/Galilean_transformation" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:06.401340+00:00" +instance: "kb-cron" +--- + +In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. These transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group (assumed throughout below). Without the translations in space and time the group is the homogeneous Galilean group. The Galilean group is the group of motions of Galilean relativity acting on the four dimensions of space and time, forming the Galilean geometry. This is the passive transformation point of view. In special relativity the homogeneous and inhomogeneous Galilean transformations are, respectively, replaced by the Lorentz transformations and Poincaré transformations; conversely, the group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean transformations. +The equations below are only physically valid in a Newtonian framework, and not applicable to coordinate systems moving relative to each other at speeds approaching the speed of light. +Galileo formulated these concepts in his description of uniform motion. +The topic was motivated by his description of the motion of a ball rolling down a ramp, by which he measured the numerical value for the acceleration of gravity near the surface of the Earth. + +== Translation == + +Although the transformations are named for Galileo, it is the absolute time and space as conceived by Isaac Newton that provides their domain of definition. In essence, the Galilean transformations embody the intuitive notion of addition and subtraction of velocities as vectors. +The notation below describes the relationship under the Galilean transformation between the coordinates (x, y, z, t) and (x′, y′, z′, t′) of a single arbitrary event, as measured in two coordinate systems S and S′, in uniform relative motion (velocity v) in their common x and x′ directions, with their spatial origins coinciding at time t = t′ = 0: + + + + + + x + ′ + + = + x + − + v + t + + + {\displaystyle x'=x-vt} + + + + + + + y + ′ + + = + y + + + {\displaystyle y'=y} + + + + + + + z + ′ + + = + z + + + {\displaystyle z'=z} + + + + + + + t + ′ + + = + t + . + + + {\displaystyle t'=t.} + + +Note that the last equation holds for all Galilean transformations up to addition of a constant, and expresses the assumption of a universal time independent of the relative motion of different observers. +In the language of linear algebra, this transformation is considered a shear mapping, and is described with a matrix acting on a vector. With motion parallel to the x-axis, the transformation acts on only two components: + + + + + + + ( + + + + + x + ′ + + + + + + + t + ′ + + + + + ) + + + = + + + ( + + + + 1 + + + − + v + + + + + 0 + + + 1 + + + + ) + + + + + ( + + + + x + + + + + t + + + + ) + + + + + {\displaystyle {\begin{pmatrix}x'\\t'\end{pmatrix}}={\begin{pmatrix}1&-v\\0&1\end{pmatrix}}{\begin{pmatrix}x\\t\end{pmatrix}}} + + +Though matrix representations are not strictly necessary for Galilean transformation, they provide the means for direct comparison to transformation methods in special relativity. + +== Galilean transformations == +The Galilean symmetries can be uniquely written as the composition of a rotation, a translation and a uniform motion of spacetime. Let x represent a point in three-dimensional space, and t a point in one-dimensional time. A general point in spacetime is given by an ordered pair (x, t). +A uniform motion, with velocity v, is given by + + + + + ( + + x + + , + t + ) + ↦ + ( + + x + + + + t + + v + + , + t + ) + , + + + {\displaystyle (\mathbf {x} ,t)\mapsto (\mathbf {x} +t\mathbf {v} ,t),} + + +where v ∈ R3. A translation is given by + + + + + ( + + x + + , + t + ) + ↦ + ( + + x + + + + + a + + , + t + + + s + ) + , + + + {\displaystyle (\mathbf {x} ,t)\mapsto (\mathbf {x} +\mathbf {a} ,t+s),} + + +where a ∈ R3 and s ∈ R. A rotation is given by + + + + + ( + + x + + , + t + ) + ↦ + ( + R + + x + + , + t + ) + , + + + {\displaystyle (\mathbf {x} ,t)\mapsto (R\mathbf {x} ,t),} + + +where R : R3 → R3 is an orthogonal transformation. +As a Lie group, the group of Galilean transformations has dimension 10. + +== Galilean group == +Two Galilean transformations G(R, v, a, s) and G(R' , v′, a′, s′) compose to form a third Galilean transformation, + +G(R′, v′, a′, s′) ⋅ G(R, v, a, s) = G(R′ R, R′ v + v′, R′ a + a′ + v′ s, s′ + s). +The set of all Galilean transformations Gal(3) forms a group with composition as the group operation. +The group is sometimes represented as a matrix group with spacetime events (x, t, 1) as vectors where t is real and x ∈ R3 is a position in space. +The action is given by + + + + + + + ( + + + + R + + + v + + + a + + + + + 0 + + + 1 + + + s + + + + + 0 + + + 0 + + + 1 + + + + ) + + + + + ( + + + + x + + + + + t + + + + + 1 + + + + ) + + + = + + + ( + + + + R + x + + + v + t + + + a + + + + + t + + + s + + + + + 1 + + + + ) + + + , + + + {\displaystyle {\begin{pmatrix}R&v&a\\0&1&s\\0&0&1\end{pmatrix}}{\begin{pmatrix}x\\t\\1\end{pmatrix}}={\begin{pmatrix}Rx+vt+a\\t+s\\1\end{pmatrix}},} + + +where s is real and v, x, a ∈ R3 and R is a rotation matrix. +The composition of transformations is then accomplished through matrix multiplication. Care must be taken in the discussion whether one restricts oneself to the connected component group of the orthogonal transformations. +Gal(3) has named subgroups. The identity component is denoted SGal(3). +Let m represent the transformation matrix with parameters v, R, s, a: + + + + + { + m + : + R + = + + I + + 3 + + + } + , + + + {\displaystyle \{m:R=I_{3}\},} + + anisotropic transformations. + + + + + { + m + : + s + = + 0 + } + , + + + {\displaystyle \{m:s=0\},} + + isochronous transformations. + + + + + { + m + : + s + = + 0 + , + v + = + 0 + } + , + + + {\displaystyle \{m:s=0,v=0\},} + + spatial Euclidean transformations. + + + + + + G + + 1 + + + = + { + m + : + s + = + 0 + , + a + = + 0 + } + , + + + {\displaystyle G_{1}=\{m:s=0,a=0\},} + + uniformly special transformations / homogeneous transformations, isomorphic to Euclidean transformations. + + + + + + G + + 2 + + + = + { + m + : + v + = + 0 + , + R + = + + I + + 3 + + + } + ≅ + + ( + + + + R + + + 4 + + + , + + + + ) + + , + + + {\displaystyle G_{2}=\{m:v=0,R=I_{3}\}\cong \left(\mathbf {R} ^{4},+\right),} + + shifts of origin / translation in Newtonian spacetime. + + + + + + G + + 3 + + + = + { + m + : + s + = + 0 + , + a + = + 0 + , + v + = + 0 + } + ≅ + + S + O + + ( + 3 + ) + , + + + {\displaystyle G_{3}=\{m:s=0,a=0,v=0\}\cong \mathrm {SO} (3),} + + rotations (of reference frame) (see SO(3)), a compact group. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Galilean_transformation-1.md b/data/en.wikipedia.org/wiki/Galilean_transformation-1.md new file mode 100644 index 000000000..4cc169bd2 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Galilean_transformation-1.md @@ -0,0 +1,1482 @@ +--- +title: "Galilean transformation" +chunk: 2/3 +source: "https://en.wikipedia.org/wiki/Galilean_transformation" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:06.401340+00:00" +instance: "kb-cron" +--- + + + + + + G + + 4 + + + = + { + m + : + s + = + 0 + , + a + = + 0 + , + R + = + + I + + 3 + + + } + ≅ + + ( + + + + R + + + 3 + + + , + + + + ) + + , + + + {\displaystyle G_{4}=\{m:s=0,a=0,R=I_{3}\}\cong \left(\mathbf {R} ^{3},+\right),} + + uniform frame motions / boosts. +The parameters s, v, R, a span ten dimensions. Since the transformations depend continuously on s, v, R, a, Gal(3) is a continuous group, also called a topological group. +The structure of Gal(3) can be understood by reconstruction from subgroups. The semidirect product combination ( + + + + A + ⋊ + B + + + {\displaystyle A\rtimes B} + +) of groups is required. + + + + + + G + + 2 + + + ◃ + + S + G + a + l + + ( + 3 + ) + + + {\displaystyle G_{2}\triangleleft \mathrm {SGal} (3)} + + (G2 is a normal subgroup) + + + + + + S + G + a + l + + ( + 3 + ) + ≅ + + G + + 2 + + + ⋊ + + G + + 1 + + + + + {\displaystyle \mathrm {SGal} (3)\cong G_{2}\rtimes G_{1}} + + + + + + + G + + 4 + + + ⊴ + + G + + 1 + + + + + {\displaystyle G_{4}\trianglelefteq G_{1}} + + + + + + + G + + 1 + + + ≅ + + G + + 4 + + + ⋊ + + G + + 3 + + + + + {\displaystyle G_{1}\cong G_{4}\rtimes G_{3}} + + + + + + + S + G + a + l + + ( + 3 + ) + ≅ + + + R + + + 4 + + + ⋊ + ( + + + R + + + 3 + + + ⋊ + + S + O + + ( + 3 + ) + ) + . + + + {\displaystyle \mathrm {SGal} (3)\cong \mathbf {R} ^{4}\rtimes (\mathbf {R} ^{3}\rtimes \mathrm {SO} (3)).} + + +== Origin in group contraction == +The Lie algebra of the Galilean group is spanned by H, Pi, Ci and Lij (an antisymmetric tensor), subject to commutation relations, where + + + + + [ + H + , + + P + + i + + + ] + = + 0 + + + {\displaystyle [H,P_{i}]=0} + + + + + + [ + + P + + i + + + , + + P + + j + + + ] + = + 0 + + + {\displaystyle [P_{i},P_{j}]=0} + + + + + + [ + + L + + i + j + + + , + H + ] + = + 0 + + + {\displaystyle [L_{ij},H]=0} + + + + + + [ + + C + + i + + + , + + C + + j + + + ] + = + 0 + + + {\displaystyle [C_{i},C_{j}]=0} + + + + + + [ + + L + + i + j + + + , + + L + + k + l + + + ] + = + i + [ + + δ + + i + k + + + + L + + j + l + + + − + + δ + + i + l + + + + L + + j + k + + + − + + δ + + j + k + + + + L + + i + l + + + + + + δ + + j + l + + + + L + + i + k + + + ] + + + {\displaystyle [L_{ij},L_{kl}]=i[\delta _{ik}L_{jl}-\delta _{il}L_{jk}-\delta _{jk}L_{il}+\delta _{jl}L_{ik}]} + + + + + + [ + + L + + i + j + + + , + + P + + k + + + ] + = + i + [ + + δ + + i + k + + + + P + + j + + + − + + δ + + j + k + + + + P + + i + + + ] + + + {\displaystyle [L_{ij},P_{k}]=i[\delta _{ik}P_{j}-\delta _{jk}P_{i}]} + + + + + + [ + + L + + i + j + + + , + + C + + k + + + ] + = + i + [ + + δ + + i + k + + + + C + + j + + + − + + δ + + j + k + + + + C + + i + + + ] + + + {\displaystyle [L_{ij},C_{k}]=i[\delta _{ik}C_{j}-\delta _{jk}C_{i}]} + + + + + + [ + + C + + i + + + , + H + ] + = + i + + P + + i + + + + + + + {\displaystyle [C_{i},H]=iP_{i}\,\!} + + + + + + [ + + C + + i + + + , + + P + + j + + + ] + = + 0 + + . + + + {\displaystyle [C_{i},P_{j}]=0~.} + + +H is the generator of time translations (Hamiltonian), Pi is the generator of translations (momentum operator), Ci is the generator of rotationless Galilean transformations (Galileian boosts), and Lij stands for a generator of rotations (angular momentum operator). +This Lie Algebra is seen to be a special classical limit of the algebra of the Poincaré group, in the limit c → ∞. Technically, the Galilean group is a celebrated group contraction of the Poincaré group (which, in turn, is a group contraction of the de Sitter group SO(1,4)). +Formally, renaming the generators of momentum and boost of the latter as in + +P0 ↦ H / c +Ki ↦ c ⋅ Ci, +where c is the speed of light (or any unbounded function thereof), the commutation relations (structure constants) in the limit c → ∞ take on the relations of the former. +Generators of time translations and rotations are identified. Also note the group invariants Lmn Lmn and Pi Pi. +In matrix form, for d = 3, one may consider the regular representation (embedded in GL(5; R), from which it could be derived by a single group contraction, bypassing the Poincaré group), + + + + + i + H + = + + ( + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 1 + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + ) + + , + + + + {\displaystyle iH=\left({\begin{array}{ccccc}0&0&0&0&0\\0&0&0&0&0\\0&0&0&0&0\\0&0&0&0&1\\0&0&0&0&0\\\end{array}}\right),\qquad } + + + + + + i + + + + a + → + + + + ⋅ + + + + P + → + + + + = + + ( + + + + + 0 + + + 0 + + + 0 + + + 0 + + + + a + + 1 + + + + + + + 0 + + + 0 + + + 0 + + + 0 + + + + a + + 2 + + + + + + + 0 + + + 0 + + + 0 + + + 0 + + + + a + + 3 + + + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + ) + + , + + + + {\displaystyle i{\vec {a}}\cdot {\vec {P}}=\left({\begin{array}{ccccc}0&0&0&0&a_{1}\\0&0&0&0&a_{2}\\0&0&0&0&a_{3}\\0&0&0&0&0\\0&0&0&0&0\\\end{array}}\right),\qquad } + + + + + + i + + + + v + → + + + + ⋅ + + + + C + → + + + + = + + ( + + + + + 0 + + + 0 + + + 0 + + + + v + + 1 + + + + + 0 + + + + + 0 + + + 0 + + + 0 + + + + v + + 2 + + + + + 0 + + + + + 0 + + + 0 + + + 0 + + + + v + + 3 + + + + + 0 + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + ) + + , + + + + {\displaystyle i{\vec {v}}\cdot {\vec {C}}=\left({\begin{array}{ccccc}0&0&0&v_{1}&0\\0&0&0&v_{2}&0\\0&0&0&v_{3}&0\\0&0&0&0&0\\0&0&0&0&0\\\end{array}}\right),\qquad } + + + + + + i + + θ + + i + + + + ϵ + + i + j + k + + + + L + + j + k + + + = + + ( + + + + + 0 + + + + θ + + 3 + + + + + − + + θ + + 2 + + + + + 0 + + + 0 + + + + + − + + θ + + 3 + + + + + 0 + + + + θ + + 1 + + + + + 0 + + + 0 + + + + + + θ + + 2 + + + + + − + + θ + + 1 + + + + + 0 + + + 0 + + + 0 + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + ) + + + . + + + {\displaystyle i\theta _{i}\epsilon ^{ijk}L_{jk}=\left({\begin{array}{ccccc}0&\theta _{3}&-\theta _{2}&0&0\\-\theta _{3}&0&\theta _{1}&0&0\\\theta _{2}&-\theta _{1}&0&0&0\\0&0&0&0&0\\0&0&0&0&0\\\end{array}}\right)~.} + + +The infinitesimal group element is then + + + + + G + ( + R + , + + + + v + → + + + + , + + + + a + → + + + + , + s + ) + = + 1 + + + + 1 + + 5 + + + + + + ( + + + + + 0 + + + + θ + + 3 + + + + + − + + θ + + 2 + + + + + + v + + 1 + + + + + + a + + 1 + + + + + + + − + + θ + + 3 + + + + + 0 + + + + θ + + 1 + + + + + + v + + 2 + + + + + + a + + 2 + + + + + + + + θ + + 2 + + + + + − + + θ + + 1 + + + + + 0 + + + + v + + 3 + + + + + + a + + 3 + + + + + + + 0 + + + 0 + + + 0 + + + 0 + + + s + + + + + 0 + + + 0 + + + 0 + + + 0 + + + 0 + + + + + ) + + + + + . + . + . + + . + + + {\displaystyle G(R,{\vec {v}},{\vec {a}},s)=1\!\!1_{5}+\left({\begin{array}{ccccc}0&\theta _{3}&-\theta _{2}&v_{1}&a_{1}\\-\theta _{3}&0&\theta _{1}&v_{2}&a_{2}\\\theta _{2}&-\theta _{1}&0&v_{3}&a_{3}\\0&0&0&0&s\\0&0&0&0&0\\\end{array}}\right)+\ ...~.} + + +== Central extension of the Galilean group == +One may consider a central extension of the Lie algebra of the Galilean group, spanned by H′, P′i, C′i, L′ij and an operator M: +The so-called Bargmann algebra is obtained by imposing + + + + [ + + C + + i + + ′ + + , + + P + + j + + ′ + + ] + = + i + M + + δ + + i + j + + + + + {\displaystyle [C'_{i},P'_{j}]=iM\delta _{ij}} + +, such that M lies in the center, i.e. commutes with all other operators. +In full, this algebra is given as + + + + + [ + + H + ′ + + , + + P + + i + + ′ + + ] + = + 0 + + + + + {\displaystyle [H',P'_{i}]=0\,\!} + + + + + + [ + + P + + i + + ′ + + , + + P + + j + + ′ + + ] + = + 0 + + + + + {\displaystyle [P'_{i},P'_{j}]=0\,\!} + + + + + + [ + + L + + i + j + + ′ + + , + + H + ′ + + ] + = + 0 + + + + + {\displaystyle [L'_{ij},H']=0\,\!} + + + + + + [ + + C + + i + + ′ + + , + + C + + j + + ′ + + ] + = + 0 + + + + + {\displaystyle [C'_{i},C'_{j}]=0\,\!} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Galilean_transformation-2.md b/data/en.wikipedia.org/wiki/Galilean_transformation-2.md new file mode 100644 index 000000000..5ebe927f4 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Galilean_transformation-2.md @@ -0,0 +1,334 @@ +--- +title: "Galilean transformation" +chunk: 3/3 +source: "https://en.wikipedia.org/wiki/Galilean_transformation" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:06.401340+00:00" +instance: "kb-cron" +--- + + + + + [ + + L + + i + j + + ′ + + , + + L + + k + l + + ′ + + ] + = + i + [ + + δ + + i + k + + + + L + + j + l + + ′ + + − + + δ + + i + l + + + + L + + j + k + + ′ + + − + + δ + + j + k + + + + L + + i + l + + ′ + + + + + δ + + j + l + + + + L + + i + k + + ′ + + ] + + + + + {\displaystyle [L'_{ij},L'_{kl}]=i[\delta _{ik}L'_{jl}-\delta _{il}L'_{jk}-\delta _{jk}L'_{il}+\delta _{jl}L'_{ik}]\,\!} + + + + + + [ + + L + + i + j + + ′ + + , + + P + + k + + ′ + + ] + = + i + [ + + δ + + i + k + + + + P + + j + + ′ + + − + + δ + + j + k + + + + P + + i + + ′ + + ] + + + + + {\displaystyle [L'_{ij},P'_{k}]=i[\delta _{ik}P'_{j}-\delta _{jk}P'_{i}]\,\!} + + + + + + [ + + L + + i + j + + ′ + + , + + C + + k + + ′ + + ] + = + i + [ + + δ + + i + k + + + + C + + j + + ′ + + − + + δ + + j + k + + + + C + + i + + ′ + + ] + + + + + {\displaystyle [L'_{ij},C'_{k}]=i[\delta _{ik}C'_{j}-\delta _{jk}C'_{i}]\,\!} + + + + + + [ + + C + + i + + ′ + + , + + H + ′ + + ] + = + i + + P + + i + + ′ + + + + + + {\displaystyle [C'_{i},H']=iP'_{i}\,\!} + + +and finally + + + + + [ + + C + + i + + ′ + + , + + P + + j + + ′ + + ] + = + i + M + + δ + + i + j + + + + . + + + {\displaystyle [C'_{i},P'_{j}]=iM\delta _{ij}~.} + + +where the new parameter + + + + M + + + {\displaystyle M} + + shows up. +This extension and projective representations that this enables is determined by its group cohomology. + +== See also == +Galilean invariance +Representation theory of the Galilean group +Galilei-covariant tensor formulation +Poincaré group +Lorentz group +Lagrangian and Eulerian coordinates + +== Notes == + +== References == +Arnold, V. I. (1989). Mathematical Methods of Classical Mechanics (2 ed.). Springer-Verlag. p. 6. ISBN 0-387-96890-3. +Bargmann, V. (1954). "On Unitary Ray Representations of Continuous Groups". Annals of Mathematics. 2. 59 (1): 1–46. doi:10.2307/1969831. JSTOR 1969831. +Copernicus, Nicolaus; Kepler, Johannes; Galilei, Galileo; Newton, Isaac; Einstein, Albert (2002). Hawking, Stephen (ed.). On the Shoulders of Giants: The Great Works of Physics and Astronomy. Philadelphia, London: Running Press. pp. 515–520. ISBN 0-7624-1348-4. +Galilei, Galileo (1638i). Discorsi e Dimostrazioni Matematiche, intorno á due nuoue scienze (in Italian). Leiden: Elsevier. pp. 191–196. +Galilei, Galileo (1638e). Discourses and Mathematical Demonstrations Relating to Two New Sciences [Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze]. Translated to English 1914 by Henry Crew and Alfonso de Salvio. +Gilmore, Robert (2006). Lie Groups, Lie Algebras, and Some of Their Applications. Dover Books on Mathematics. Dover Publications. ISBN 0486445291. +Hoffmann, Banesh (1983), Relativity and Its Roots, Scientific American Books, ISBN 0-486-40676-8, Chapter 5, p. 83 +Lerner, Lawrence S. (1996), Physics for Scientists and Engineers, vol. 2, Jones and Bertlett Publishers, Inc, ISBN 0-7637-0460-1, Chapter 38 §38.2, p. 1046,1047 +Mould, Richard A. (2002), Basic relativity, Springer-Verlag, ISBN 0-387-95210-1, Chapter 2 §2.6, p. 42 +Nadjafikhah, Mehdi; Forough, Ahmad-Reza (2009). "Galilean Geometry of Motions" (PDF). Applied Sciences. 11: 91–105. +Serway, Raymond A.; Jewett, John W. (2006), Principles of Physics: A Calculus-based Text (4th ed.), Brooks/Cole - Thomson Learning, Bibcode:2006ppcb.book.....J, ISBN 0-534-49143-X, Chapter 9 §9.1, p. 261 \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Garvan–Olin_Medal-0.md b/data/en.wikipedia.org/wiki/Garvan–Olin_Medal-0.md new file mode 100644 index 000000000..b2cb7c9ba --- /dev/null +++ b/data/en.wikipedia.org/wiki/Garvan–Olin_Medal-0.md @@ -0,0 +1,33 @@ +--- +title: "Garvan–Olin Medal" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Garvan–Olin_Medal" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:43.169639+00:00" +instance: "kb-cron" +--- + +The Francis P. Garvan–John M. Olin Medal, previously called the Francis P. Garvan Medal, is an annual award that recognizes distinguished scientific accomplishment, leadership and service to chemistry by women chemists. The Award is offered by the American Chemical Society (ACS), and consists of a cash prize (US$5,000) and a medal. The medal was designed by Margaret Christian Grigor. + + +== Background == +Any individual may nominate a single eligible chemist in one year. Nominees must be a female citizen of the United States. +The award was established by Francis Garvan and Mabel Brady Garvan in 1936 in honor of their daughter. It was initially an essay contest, that ran for seven years, as a memorial to their daughter (the American Chemical Society's Prize Essay Contest). It was solely funded by the Francis P. Garvan Medal Endowment from its establishment in 1936 until 1979. W. R. Grace & Co. assumed co-sponsorship of the award from 1979 to 1983. In 1984, Olin Corporation assumed co-sponsorship. Mabel Brady Garvan remained involved with the Award through 1967. +The Garvan–Olin Award is the ACS' third-oldest award, and the first award established to honor women chemists. + + +== Award recipients == + + +== See also == +List of chemistry awards +List of science and technology awards for women + + +== References == + + +== External links == +"Francis P. Garvan-John M. Olin Medal". American Chemical Society. +Special Collections and University Archives. "Finding Aid for MS 678 Garvan Medalists Survey Collection, 1981-2000". Iowa State University. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Grace_Hopper_Celebration_of_Women_in_Computing-0.md b/data/en.wikipedia.org/wiki/Grace_Hopper_Celebration_of_Women_in_Computing-0.md new file mode 100644 index 000000000..497b8fabd --- /dev/null +++ b/data/en.wikipedia.org/wiki/Grace_Hopper_Celebration_of_Women_in_Computing-0.md @@ -0,0 +1,82 @@ +--- +title: "Grace Hopper Celebration of Women in Computing" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Grace_Hopper_Celebration_of_Women_in_Computing" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:45.565115+00:00" +instance: "kb-cron" +--- + +The Grace Hopper Celebration of Women in Computing (GHC) is a series of conferences designed to bring the research and career interests of women in computing to the forefront. It is the world's largest gathering of women and non-binary technologists. The celebration, named after computer scientist Grace Hopper, is organized by the Anita Borg Institute for Women and Technology. GHC 2022 conference was held hybrid in Orlando and virtually at the end of September 2022. + +== History == +In 1994, Anita Borg and Telle Whitney founded the Grace Hopper Celebration of Women in Computing. With the initial idea of creating a conference by and for women computer scientists, Borg and Whitney met over dinner, with a blank sheet of paper, having no idea how to start a conference, and started to plan out their vision. The first Grace Hopper Celebration of Women in Computing was held in Washington, D.C., in June 1994, and brought together 500 technical women. More than a dozen conferences have been held from 1994 to the present; the second was held in 1997 and the conference has been held annually since 2006. The sold-out 2010 conference attracted 2,147 attendees from 29 countries. Beginning in 2011, the conference has been held in a convention center to accommodate its growing size. + +== Conference structure == +The Grace Hopper Celebration consists of a combination of technical sessions and career sessions and includes a poster session, career fair, awards ceremony, and more. The conference features 650 presenters. Potential presenters submit proposals for panels, workshops, presentations, Birds of a Feather sessions, New Investigators papers, PhD Forum, and Poster Session, including ACM Student Research Competition. + +=== Tracks/Content === +The Grace Hopper Celebration 2022 featured content in 14 tracks: + +Academic +Artificial Intelligence +Career +Computer Systems Engineering +Data Science +Diversity, Equity, Inclusion & Belonging +Extended Reality, Media and Gaming +Hardware +Human Computer Interaction +Non- Traditional Technology +Open Source & Open Source Day +Product Management +Security/Privacy +Software Engineering + +=== Keynote Speakers === +The Grace Hopper Celebration features prominent women in technology. Keynote speakers at Grace Hopper Celebration 2022 included Daphe Koller, Dr. Anita Hill, Megan Rapinoe, Anne Neuberger and Frances Haugen. +Past keynote speakers included Sheryl Sandberg, Shirley Jackson, Carol Bartz, Duy-Loan Le, Kathy Pham, Megan Smith, Ginni Rometty, Nonny de la Peña, Maria Klawe, Frances E. Allen, Mary Lou Jepsen, Barbara Liskov, Susan Landau, Jennifer Mankoff, Vivienne Ming, Susan L. Graham, Melinda Gates, and Fernanda Viegas. Speaker presentations are available to watch online after the conference. + +=== Poster Session and ACM Student Research Competition === +The Grace Hopper Celebration features one of the largest technical poster sessions of any conference, with over 175 posters. Presenters can choose to have their posters considered for the ACM Student Research Competition (SRC) at the Grace Hopper Celebration, the largest SRC of any technical conference. + +=== Awards === +The Abie Awards honor women technologists and those who support women in tech. The 2022 Abie Award Winners were: + +Daphne Koller (San Francisco, California) - Technical Leadership Award Winner +Kris Dorsey (Boston, Massachusetts) - Emerging Leader Award in Honor of Denice Denton Award Winner +Katherine Vergara (Santiago, Chile) - Student of Vision Award Winner +Paula Coto (Ciudad Autonoma de Buenos Aires, Argentina) - Change Agent Award Winner +Neha Narkhede (Menlo Park, California) - Technology Entrepreneurship Award Winner +Past Abie Award winners include Ruzena Bajcsy, BlogHer, Elaine Weyuker and Unoma Ndili Okorafor. + +=== CRA-W Career Mentoring Workshops === +The Computing Research Association’s Committee on the Status of Women in Computing Research (CRA-W) sponsors a series of sessions at the Grace Hopper Celebration aimed at undergraduates, graduates, and early career researchers. Sessions cover topics such as applying to graduate school, publishing papers, networking, work-life balance, and more. + +=== K-12 Computing Teachers Workshop === +Hosted by the Computer Science Teachers Association and the Anita Borg Institute for Women and Technology, the K-12 Computing Teachers Workshop is a two-day event for K-12 teachers, covering challenges and ways to involve more girls in computer science. The workshop began in 2009, attracting more than 650 applications its first year. + +=== Technical Executive Forum === +Begun in 2007, the Technical Executive Forum convenes high-level technology executives to discuss challenges and share solutions for recruiting, retaining, and advancing technical women. In 2010, 65 executives attended the event, from companies including Microsoft, Google, and Symantec. + +=== Senior Women’s Summit === +The Senior Women's Summit is a one-day event held at the Grace Hopper Celebration, that brings together senior-level women to discuss issues facing senior technical women and provide a learning and networking platform. + +=== Grace Hopper Open Source Day === +Grace Hopper Open Source Day was held for the first time in 2011. One-day registration is open to the public and included for all conference attendees. The event includes a codeathon, skill-building workshop, and exhibition space featuring open source projects. + +Participating organizations have included Google Crisis Response, Mozilla, Sahana Software Foundation, The Women's Peer-to-Peer Network, ODK, Microsoft Disaster Response, OpenHatch, Wikimedia Foundation, E-Democracy, Systers, WordPress and OpenStack. + +=== Career Fair === +The Grace Hopper Celebration features a career fair with over 70 high-tech companies, government labs, and universities. + +=== Scholarships === +Students make up approximately half of the attendees at the Grace Hopper Celebration. The Anita Borg Institute offers scholarships to undergraduate and graduate students to attend the conference. The scholarship includes: + +Individual registration for the three-day conference +Hotel accommodations +Meal card for use at the convention center during the conference +Airfare +Travel stipend +In 2010, 321 scholarships were awarded. In addition to the GHC Scholarship, Anita Borg Institute offers the ABI-Heinz College Partnership Program. This is designed for students who have successfully completed their bachelor's degree, have been named a GHC Scholar by AnitaB.org, and are interested in obtaining a master's degree from the Heinz College at Carnegie Mellon University. GHC Scholars who are accepted into master's programs at the Heinz college are eligible for tuition scholarships of a minimum of $6,000 per semester. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Grace_Hopper_Celebration_of_Women_in_Computing-1.md b/data/en.wikipedia.org/wiki/Grace_Hopper_Celebration_of_Women_in_Computing-1.md new file mode 100644 index 000000000..208719a6c --- /dev/null +++ b/data/en.wikipedia.org/wiki/Grace_Hopper_Celebration_of_Women_in_Computing-1.md @@ -0,0 +1,38 @@ +--- +title: "Grace Hopper Celebration of Women in Computing" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Grace_Hopper_Celebration_of_Women_in_Computing" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:45.565115+00:00" +instance: "kb-cron" +--- + +=== Childcare and nursing mothers' room === +The Grace Hopper Celebration offers free childcare to all attendees, as well as an on-site nursing mothers' room. + +== Open Source Day == +Open Source Day (OSD) is the largest celebration of women in open source. OSD is an all-day hackathon (including workshops) at Grace Hopper Celebration in which participants of all skill levels learn about Open Source while contributing to projects designed to solve real-world problems. OSD is organized in two parts: projects for contributions and hands-on workshops for upskilling. + +=== Open Source Day 2022 === +Open Source Day 2022 (OSD22) took place virtually on September 16, 2022 and was open to all GHC22 ticket holders for participation. The Opening Ceremony of OSD22 featured Anne Neuberger, Nithya Ruff and Mishi Choudhary. OSD22 hosted 27 open source projects and 10 workshops. +Participants contributed code to 27 open source projects. + +== Criticisms == +The GHC conference has been criticized for a lack of diversity, particularly racial diversity, and financial inaccessibility due to the high cost of attendance. In 2019, the cost of registration, not including hotel, transportation, or other costs, was $450 for students, $600 for academics, and $1,150 for general registration. +In 2015, GHC faced criticism, including from engineer Erica Baker, when two white men and zero black women were featured as "headline" speakers. The organization responded by targeting more diversity in speakers and collecting race and ethnicity data at the following year's event. +GHC does not pay its speakers. In past years GHC required speakers to purchase their own conference ticket, but as of 2020, speakers receive complimentary registration. (In the case of two selected poster presenters, only one will receive complimentary registration.) Speakers are not paid and travel and hotel expenses are not covered. The "pay to speak" approach has been criticized by people including author and software engineer Gayle Laakmann McDowell. +In 2023, female and non-binary attendees criticized the event for being dominated by "pushy" cisgender men, some of whom were harassing the women present. + +== List of Grace Hopper Celebrations == +Past Grace Hopper Celebrations include: + +== See also == +List of awards honoring women +Richard Tapia Celebration of Diversity in Computing + +== References == + +== External links == +Grace Hopper Celebration of Women in Computing +GHC Archives Archived 2017-09-28 at the Wayback Machine \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Hertha_Sponer_Prize-0.md b/data/en.wikipedia.org/wiki/Hertha_Sponer_Prize-0.md new file mode 100644 index 000000000..541aab46c --- /dev/null +++ b/data/en.wikipedia.org/wiki/Hertha_Sponer_Prize-0.md @@ -0,0 +1,60 @@ +--- +title: "Hertha Sponer Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Hertha_Sponer_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:46.775302+00:00" +instance: "kb-cron" +--- + +The Hertha Sponer Prize is a scientific prize of the German Physical Society (German: Deutsche Physikalische Gesellschaft, DPG). It has been awarded annually since 2002 to a female scientist for outstanding scientific work in the field of physics, and was initiated by the Equal Opportunities Working Group of the DPG. The prize is intended to encourage younger female scientists by publicly recognizing them, with the hope that this recognition attracts more women to study physics. The prize consists of a certificate and award of €3,000. Nominations are for recognition of a particular work (journal article or thesis), and self-nominations are permitted. +The prize is named after the German physicist Hertha Sponer (1895–1968), who made important contributions to molecular physics and spectroscopy. + + +== Prizewinners == +Former prizewinners include: + +2002: Karina Morgenstern (Freie Universität Berlin) for dynamic scanning tunneling microscope investigations on nanostructures. +2003: Uta Fritze-von Alvensleben (Göttingen Observatory) for the investigation of galaxy evolution on cosmological time scales, in particular with regard to their interaction. +2004: Myrjam Winning (RWTH Aachen University) for contributions to metallurgy and materials science, in particular X-ray structure investigations of grain boundaries. +2005: Elena Vedmedenko (University of Hamburg) for outstanding work on the magnetism of nanostructures with applications in spintronics. +2006: Ekaterina Shamonina (University of Osnabrück) for outstanding contributions to electromagnetic metamaterials. +2007: Christine Silberhorn (University of Erlangen-Nuremberg) for work on quantum communication with continuous variables. +2008: Sylvie Roke (Max Planck Institute for Metals Research Stuttgart) for experimental and theoretical work on nonlinear optical scattering at particle surfaces. +2009: Corinna Kollath (École polytechnique, Paris) for theoretical studies of non-equilibrium states of ultracold boson and fermion atomic gases. +2010: Liu Na (University of Stuttgart) for pioneering contributions to the characterization and fabrication of three-dimensional metal nanostructures. +2011: Martina Hentschel (Max Planck Institute for the Physics of Complex Systems Dresden) for the theoretical investigation of mesoscopic electronic and optical systems, in particular optical microcavities and the radiation characteristics of microlasers. +2012: Katharina Franke (FU Berlin) for her groundbreaking work on the interaction of magnetic molecules with superconductors on the nano- and mesoscopic scale. +2013: Kerstin Tackmann (DESY) gor her outstanding work on the way to the detection of the Higgs boson at the Large Hadron Collider (LHC) at CERN. +2014: Anne Schukraft (RWTH Aachen University) for the measurement of muon neutrinos with energies up to + + + + + 10 + + 15 + + + + + {\displaystyle 10^{15}} + + eV with the IceCube detector. +2015: Ilaria Zardo (Eindhoven University of Technology) for outstanding work on understanding the lattice dynamics and electronic band structures of semiconductor nanowires with wurtzite and zincblende crystal structures. +2016 not awarded +2017: Isabelle Staude (Friedrich Schiller University Jena) in recognition of her pioneering contribution to basic research in nanophotonics. +2018: Karin Everschor-Sitte (University of Mainz) for her pioneering research on the theoretical understanding of topologically protected magnetic structures, the skyrmions. +2019: Adriana Pálffy-Buß (Max Planck Institute for Nuclear Physics) for her pioneering theoretical calculations of the interaction of high-energy radiation with atomic nuclei based on quantum effects. +2020: Priscilla Pani (DESY) for her essential contributions to the search for dark matter at the LHC. +2021: Naëmi Leo (Asociación Centro de Investigación Cooperativa en Nanociencias (CIC nanoGUNE), San Sebastián, Spain) for her outstanding contributions to the study and characterization of artificial metamaterials and ferroic systems. +2022: Elisabeth Fischer-Friedrich (Cluster of Excellence Physics of Life (PoL) at the Technical University of Dresden) for her outstanding theoretical and experimental contributions to the characterization of the mechanical properties of cells and protein condensates. +2023: Joint award to +Adinda de Wit (University of Zurich Physics Institute, Switzerland) for her outstanding experimental contributions to the first observation of the Higgs-b-Yukawa coupling and the precise determination of the Higgs couplings +Belina von Krosigk (Karlsruhe Institute of Technology) for her fundamental contributions to the direct search and understanding of dark matter through the further development of models and methodological and analytical techniques for the detection of weak signals. +2024: Juliane Borchert (INATECH, University of Freiburg) for her outstanding contributions to the understanding of processes for highly efficient perovskite solar cells. +2025: Janna Katharina Behr (German Electron Synchrotron DESY, Hamburg) for her major contributions to the search for an extended Higgs sector through Higgs decays to top quarks. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Iota_Sigma_Pi-0.md b/data/en.wikipedia.org/wiki/Iota_Sigma_Pi-0.md new file mode 100644 index 000000000..cfb320ba2 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Iota_Sigma_Pi-0.md @@ -0,0 +1,61 @@ +--- +title: "Iota Sigma Pi" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Iota_Sigma_Pi" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:48.007677+00:00" +instance: "kb-cron" +--- + +Iota Sigma Pi (ΙΣΠ) is a national honor society in the United States. It was established in 1900 and specializes in the promotion of women in the sciences, especially chemistry. It also focuses on personal and professional growth for women in these fields. As with all honor societies, they create professional networks along with recognizing achievements of women in chemistry. + + +== History == +Iota Sigma Pi was formed during a period when women gained little recognition for their work; therefore, women began to set up their own awards to highlight their abilities on their resumes. It was created by the merger of three chemistry honor societies for women that were established in the early 20th century. +Agnes Fay Morgan, department chair of the Department of Household Science and Arts at the University of California, formed Alchemi in 1900. Alchemi spread to the University of Southern California and Stanford University. In 1911, a national chemistry honor society was established at the University of Washington. A third honor society, Iota Sigma Pi, was established at the University of Nebraska in 1912. The latter two societies merged as Iota Sigma Pi in 1913 and were joined by the three chapters of Alchmi in 1916. Its first National Convention was held in 1918 at the University of Nebraska. Five of the eight chapters at that time were present. +The goals of Iota Sigma Pi were to encourage women to pursue chemistry academically, to "stimulate personal accomplishment in chemical fields" and to promote the academic, business, and social lives of its members. It continued to spread across the country, and eventually held meetings for the American Chemical Society. +Iota Sigma Pi was a charter member of the Professional Panhellenic Association in 1925. In the 1930s, there was an offer of amalgamation from the Phi Lambda Upsilon honor society for male chemists but this was refused. +Iota Sigma Pi was briefly a member of the Association of College Honor Societies or ACHS, joining in February 1955, but resigned to operate independently in 1963. In 1963, it had 19 active chapters, 8 inactive chapters, and 6,271 initiates. +As of 2025, Iota Sigma Pi has chartered 47 chapters and initiated more than 11,000 members. Its national headquarters is based at De Paul University in Chicago, Illinois. + + +== Symbols == +Iota Sigma Pi's emblem is a hexagonal key that features a crescent a circle, and the Greek letters ΙΣΠ. The society's colors are white, gold, and cedar green. Its flower is the white narcissus. Its publication is The Iotan, first published in 1941. + + +== Chapters == + +As of 2025, Iota Sigma Pi has chartered 47 chapters. + + +== Awards == + + +=== Professional awards === +The highest award from the society is the National Honorary Member which is given to female chemists who have made an exceptional and significant achievement in the field. The certificate is awarded with a prize fund of $1,500. Some of the previous winners include: Marie Sklodowska-Curie, Gerti Cori and Dorothy Hodgkin. +The Violet Diller Professional Excellence Award, named after a previous member (treasurer and president), is awarded for "accomplishments in academic, governmental, or industrial chemistry, in education, in administration, or a combination of these areas". The award consists of a certificate and a $1,000 prize fund. This award was first awarded to Joan P. Lambros in 1984. +The Agnes Fay Morgan Research Award is given to women who have achieved in the field of chemistry or biochemistry. The Centennial Award for Excellence in Undergraduate Teaching is given to those who have excelled in teaching chemistry, biochemistry, or a similar subject. The nominee must spend at least 75 percent of their time teaching undergraduates to qualify for the certificate and $500 award. + + +=== Student awards === +The Anna Louise Hoffman Award for Outstanding Achievement in Graduate Research is given to the nominee who has demonstrated outstanding chemical research. The nominee must also be a full-time graduate student to get the certification and $500 reward. There are two awards for Undergraduate Excellence in Chemistry; one must go to a first-generation student. Again, the reward is a certificate and $500. + + +== Notable members == + +As of 2025, Iota Sigma Pi has initiated more than 11,000 members. + + +== See also == +Honor society +List of chemistry societies +Professional Fraternity Association + + +== References == + + +== External links == +Iota Sigma Pi website +Iota Sigma Pi finding aid \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Irène_Joliot-Curie_Prize-0.md b/data/en.wikipedia.org/wiki/Irène_Joliot-Curie_Prize-0.md index 3049c14a7..8f4d6cce1 100644 --- a/data/en.wikipedia.org/wiki/Irène_Joliot-Curie_Prize-0.md +++ b/data/en.wikipedia.org/wiki/Irène_Joliot-Curie_Prize-0.md @@ -4,7 +4,7 @@ chunk: 1/1 source: "https://en.wikipedia.org/wiki/Irène_Joliot-Curie_Prize" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T07:09:45.866492+00:00" +date_saved: "2026-05-05T11:15:49.207837+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Jerk_(physics)-0.md b/data/en.wikipedia.org/wiki/Jerk_(physics)-0.md new file mode 100644 index 000000000..e11fb58c3 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Jerk_(physics)-0.md @@ -0,0 +1,357 @@ +--- +title: "Jerk (physics)" +chunk: 1/4 +source: "https://en.wikipedia.org/wiki/Jerk_(physics)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:07.559806+00:00" +instance: "kb-cron" +--- + +Jerk (also known as jolt) is the rate of change of an object's acceleration over time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s3 (SI units) or standard gravities per second(g0/s). + +== Expressions == +As a vector, jerk j can be expressed as the first time derivative of acceleration, second time derivative of velocity, and third time derivative of position: + + + + + + j + + = + + + + + d + + + a + + + + + d + + t + + + + = + + + + + + d + + + 2 + + + + v + + + + + d + + + t + + 2 + + + + + + = + + + + + + d + + + 3 + + + + r + + + + + d + + + t + + 3 + + + + + + , + + + {\displaystyle \mathbf {j} ={\frac {\mathrm {d} \mathbf {a} }{\mathrm {d} t}}={\frac {\mathrm {d} ^{2}\mathbf {v} }{\mathrm {d} t^{2}}}={\frac {\mathrm {d} ^{3}\mathbf {r} }{\mathrm {d} t^{3}}},} + + +where a is acceleration, v is velocity, r is position, and t is time. +Third-order differential equations of the form + + + + + J + + ( + + + + x + + . + . + . + + + + , + + + + x + ¨ + + + + , + + + + x + ˙ + + + + , + x + + ) + + = + 0 + + + {\displaystyle J\left({\overset {\mathbf {...} }{x}},{\ddot {x}},{\dot {x}},x\right)=0} + + +are sometimes called jerk equations. When converted to an equivalent system of three ordinary first-order non-linear differential equations, jerk equations are the minimal setting for solutions showing chaotic behaviour. This condition generates mathematical interest in jerk systems. Systems involving fourth-order derivatives or higher are accordingly called hyperjerk systems. + +== Physiological effects and human perception == + +Human body position is controlled by balancing the forces of antagonistic muscles. In balancing a given force, such as holding up a weight, the postcentral gyrus establishes a control loop to achieve the desired equilibrium. If the force changes too quickly, the muscles cannot relax or tense fast enough and overshoot in either direction, causing a temporary loss of control. The reaction time for responding to changes in force depends on physiological limitations and the attention level of the brain: an expected change will be stabilized faster than a sudden decrease or increase of load. +To avoid vehicle passengers losing control over body motion and getting injured, it is necessary to limit the exposure to both the maximum force (acceleration) and maximum jerk, since time is needed to adjust muscle tension and adapt to even limited stress changes. Sudden changes in acceleration can cause injuries such as whiplash. Excessive jerk may also result in an uncomfortable ride, even at levels that do not cause injury. Engineers expend considerable design effort minimizing "jerky motion" on elevators, trams, and other conveyances. +For example, consider the effects of acceleration and jerk when riding in a car: + +Skilled and experienced drivers can accelerate smoothly, but beginners often provide a jerky ride. When changing gears in a car with a foot-operated clutch, the accelerating force is limited by engine power, but an inexperienced driver can cause severe jerk because of intermittent force closure over the clutch. +The feeling of being pressed into the seats in a high-powered sports car is due to the acceleration. As the car launches from rest, there is a large positive jerk as its acceleration rapidly increases. After the launch, there is a small, sustained negative jerk as the force of air resistance increases with the car's velocity, gradually decreasing acceleration and reducing the force pressing the passenger into the seat. When the car reaches its top speed, the acceleration has reached 0 and remains constant, after which there is no jerk until the driver decelerates or changes direction. +When braking suddenly or during collisions, passengers whip forward with an initial acceleration that is larger than during the rest of the braking process because muscle tension regains control of the body quickly after the onset of braking or impact. These effects are not modeled in vehicle testing because cadavers and crash test dummies do not have active muscle control. +To minimize the jerk, curves along roads are designed to be clothoids as are railroad curves and roller coaster loops. + +== In human kinematics == +Human motion tends to minimize the sums of squares of the jerks for the motion along a pre-defined path. As an optimization problem, this can be stated as, + + + + + + + + + + + minimize + + j + + + + + + + + + ∫ + + 0 + + + t + + + + | + + + j + + ( + s + ) + + + | + + + 2 + + + d + s + + + + + + + s + u + b + j + e + c + t + + t + o + + + + + + x + + ( + 0 + ) + = + + + x + + + + i + + + + + + + + + + + + x + + ( + t + ) + = + + + x + + + + f + + + + + + + + + + + + v + + ( + 0 + ) + = + + + v + + + + i + + + + + + + + + + + + v + + ( + t + ) + = + + + v + + + + f + + + + + + + + + + {\displaystyle {\begin{aligned}&{\underset {\mathbf {j} }{\operatorname {minimize} }}&&\int _{0}^{t}|\mathbf {j} (s)|^{2}ds\\&\operatorname {subject\;to} &&\mathbf {x} (0)=\mathbf {x} _{\mathrm {i} }\\&&&\mathbf {x} (t)=\mathbf {x} _{\mathrm {f} }\\&&&\mathbf {v} (0)=\mathbf {v} _{\mathrm {i} }\\&&&\mathbf {v} (t)=\mathbf {v} _{\mathrm {f} }\end{aligned}}} + +It has been shown that this is equivalent to the two-thirds speed-curvature power law for humans. + +== Force, acceleration, and jerk == +For a constant mass m, acceleration a is directly proportional to force F according to Newton's second law of motion: + + + + + + F + + = + m + + a + + + + {\displaystyle \mathbf {F} =m\mathbf {a} } + + +In classical mechanics of rigid bodies, there are no forces associated with the derivatives of acceleration; however, physical systems experience oscillations and deformations as a result of jerk. In designing the Hubble Space Telescope, NASA set limits on both jerk and jounce. +The Abraham–Lorentz force is the recoil force on an accelerating charged particle emitting radiation. This force is proportional to the particle's jerk and to the square of its charge. The Wheeler–Feynman absorber theory is a more advanced theory, applicable in a relativistic and quantum environment, and accounting for self-energy. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Jerk_(physics)-1.md b/data/en.wikipedia.org/wiki/Jerk_(physics)-1.md new file mode 100644 index 000000000..26bce13b8 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Jerk_(physics)-1.md @@ -0,0 +1,342 @@ +--- +title: "Jerk (physics)" +chunk: 2/4 +source: "https://en.wikipedia.org/wiki/Jerk_(physics)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:07.559806+00:00" +instance: "kb-cron" +--- + +== In an idealized setting == +Discontinuities in acceleration do not occur in real-world environments because of deformation, quantum mechanics effects, and other causes. However, a jump-discontinuity in acceleration and, accordingly, unbounded jerk are feasible in an idealized setting, such as an idealized point mass moving along a piecewise smooth, whole continuous path. The jump-discontinuity occurs at points where the path is not smooth. Extrapolating from these idealized settings, one can qualitatively describe, explain and predict the effects of jerk in real situations. +Jump-discontinuity in acceleration can be modeled using a Dirac delta function in jerk, scaled to the height of the jump. Integrating jerk over time across the Dirac delta yields the jump-discontinuity. +For example, consider a path along an arc of radius r, which tangentially connects to a straight line. The whole path is continuous, and its pieces are smooth. Now assume a point particle moves with constant speed along this path, so its tangential acceleration is zero. The centripetal acceleration given by ⁠v2/r⁠ is normal to the arc and inward. When the particle passes the connection of pieces, it experiences a jump-discontinuity in acceleration given by ⁠v2/r⁠, and it undergoes a jerk that can be modeled by a Dirac delta, scaled to the jump-discontinuity. +For a more tangible example of discontinuous acceleration, consider an ideal spring–mass system with the mass oscillating on an idealized surface with friction. The force on the mass is equal to the vector sum of the spring force and the kinetic frictional force. When the velocity changes sign (at the maximum and minimum displacements), the magnitude of the force on the mass changes by twice the magnitude of the frictional force, because the spring force is continuous and the frictional force reverses direction with velocity. The jump in acceleration equals the force on the mass divided by the mass. That is, each time the mass passes through a minimum or maximum displacement, the mass experiences a discontinuous acceleration, and the jerk contains a Dirac delta until the mass stops. The static friction force adapts to the residual spring force, establishing equilibrium with zero net force and zero velocity. +Consider the example of a braking and decelerating car. The brake pads generate kinetic frictional forces and constant braking torques on the disks (or drums) of the wheels. Rotational velocity decreases linearly to zero with constant angular deceleration. The frictional force, torque, and car deceleration suddenly reach zero, which indicates a Dirac delta in physical jerk. The Dirac delta is smoothed down by the real environment, the cumulative effects of which are analogous to damping of the physiologically perceived jerk. This example neglects the effects of tire sliding, suspension dipping, real deflection of all ideally rigid mechanisms, etc. +Another example of significant jerk, analogous to the first example, is the cutting of a rope with a particle on its end. Assume the particle is oscillating in a circular path with non-zero centripetal acceleration. When the rope is cut, the particle's path changes abruptly to a straight path, and the force in the inward direction changes suddenly to zero. Imagine a monomolecular fiber cut by a laser; the particle would experience very high rates of jerk because of the extremely short cutting time. + +== In rotation == + +Consider a rigid body rotating about a fixed axis in an inertial reference frame. If its angular position as a function of time is θ(t), the angular velocity, acceleration, and jerk can be expressed as follows: + +Angular velocity, + + + + ω + ( + t + ) + = + + + + θ + ˙ + + + + ( + t + ) + = + + + + + d + + θ + ( + t + ) + + + + d + + t + + + + + + {\displaystyle \omega (t)={\dot {\theta }}(t)={\frac {\mathrm {d} \theta (t)}{\mathrm {d} t}}} + +, is the time derivative of θ(t). +Angular acceleration, + + + + α + ( + t + ) + = + + + + ω + ˙ + + + + ( + t + ) + = + + + + + d + + ω + ( + t + ) + + + + d + + t + + + + + + {\displaystyle \alpha (t)={\dot {\omega }}(t)={\frac {\mathrm {d} \omega (t)}{\mathrm {d} t}}} + +, is the time derivative of ω(t). +Angular jerk, + + + + ζ + ( + t + ) + = + + + + α + ˙ + + + + ( + t + ) + = + + + + ω + ¨ + + + + ( + t + ) + = + + + θ + + . + . + . + + + + ( + t + ) + + + {\displaystyle \zeta (t)={\dot {\alpha }}(t)={\ddot {\omega }}(t)={\overset {...}{\theta }}(t)} + +, is the time derivative of α(t). +Angular acceleration equals the torque acting on the body, divided by the body's moment of inertia with respect to the momentary axis of rotation. A change in torque results in angular jerk. +The general case of a rotating rigid body can be modeled using kinematic screw theory, which includes one axial vector, angular velocity Ω(t), and one polar vector, linear velocity v(t). From this, the angular acceleration is defined as + + + + + + α + + ( + t + ) + = + + + + d + + + + d + + t + + + + + ω + + ( + t + ) + = + + + + ω + ˙ + + + + ( + t + ) + + + {\displaystyle {\boldsymbol {\alpha }}(t)={\frac {\mathrm {d} }{\mathrm {d} t}}{\boldsymbol {\omega }}(t)={\dot {\boldsymbol {\omega }}}(t)} + + +and the angular jerk is given by + + + + + + ζ + + ( + t + ) + = + + + + d + + + + d + + t + + + + + α + + ( + t + ) + = + + + + α + ˙ + + + + ( + t + ) + = + + + + ω + ¨ + + + + ( + t + ) + + + {\displaystyle {\boldsymbol {\zeta }}(t)={\frac {\mathrm {d} }{\mathrm {d} t}}{\boldsymbol {\alpha }}(t)={\dot {\boldsymbol {\alpha }}}(t)={\ddot {\boldsymbol {\omega }}}(t)} + + +taking the angular acceleration from Angular acceleration § Particle in three dimensions as + + + + + + α + + = + + + + d + + ω + + + + d + t + + + + = + + + + + r + + × + + a + + + + r + + 2 + + + + + − + + + 2 + r + + + + + + d + r + + + d + t + + + + + ω + + + + {\displaystyle {\boldsymbol {\alpha }}={\frac {d{\boldsymbol {\omega }}}{dt}}={\frac {\mathbf {r} \times \mathbf {a} }{r^{2}}}-{\frac {2}{r}}{\frac {dr}{dt}}{\boldsymbol {\omega }}} + +, we obtain \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Jerk_(physics)-2.md b/data/en.wikipedia.org/wiki/Jerk_(physics)-2.md new file mode 100644 index 000000000..c46fef738 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Jerk_(physics)-2.md @@ -0,0 +1,829 @@ +--- +title: "Jerk (physics)" +chunk: 3/4 +source: "https://en.wikipedia.org/wiki/Jerk_(physics)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:07.559806+00:00" +instance: "kb-cron" +--- + + + + + + + + + + ζ + + = + + + + d + + α + + + + d + t + + + + = + + + 1 + + r + + 2 + + + + + + ( + + + r + + × + + + + d + + a + + + + d + t + + + + + + + + + d + + r + + + + d + t + + + + × + + a + + + ) + + − + + + 2 + + r + + 3 + + + + + + + + d + r + + + d + t + + + + + ( + + + r + + × + + a + + + ) + + + + + + + + + + + + + 2 + + r + + 2 + + + + + + + ( + + + + d + r + + + d + t + + + + ) + + + 2 + + + + ω + + − + + + 2 + r + + + + + + + d + + 2 + + + r + + + d + + t + + 2 + + + + + + + ω + + − + + + 2 + r + + + + + + d + r + + + d + t + + + + + + + d + + ω + + + + d + t + + + + + + + + + + {\displaystyle {\begin{aligned}{\boldsymbol {\zeta }}={\frac {d{\boldsymbol {\alpha }}}{dt}}={\frac {1}{r^{2}}}\left(\mathbf {r} \times {\frac {d\mathbf {a} }{dt}}+{\frac {d\mathbf {r} }{dt}}\times \mathbf {a} \right)-{\frac {2}{r^{3}}}{\frac {dr}{dt}}\left(\mathbf {r} \times \mathbf {a} \right)\\\\+{\frac {2}{r^{2}}}\left({\frac {dr}{dt}}\right)^{2}{\boldsymbol {\omega }}-{\frac {2}{r}}{\frac {d^{2}r}{dt^{2}}}{\boldsymbol {\omega }}-{\frac {2}{r}}{\frac {dr}{dt}}{\frac {d{\boldsymbol {\omega }}}{dt}}\end{aligned}}} + + +replacing + + + + + + + d + + ω + + + + d + t + + + + + + {\displaystyle {\frac {d{\boldsymbol {\omega }}}{dt}}} + + we can have the last item as + + + + + + + + + − + + + 2 + r + + + + + + d + r + + + d + t + + + + + + + d + + ω + + + + d + t + + + + + + + = + − + + + 2 + r + + + + + + d + r + + + d + t + + + + + ( + + + + + + r + + × + + a + + + + r + + 2 + + + + + − + + + 2 + r + + + + + + d + r + + + d + t + + + + + ω + + + ) + + + + + + + + + + + = + − + + + 2 + + r + + 3 + + + + + + + + d + r + + + d + t + + + + + ( + + + r + + × + + a + + + ) + + + + + + 4 + + r + + 2 + + + + + + + ( + + + + d + r + + + d + t + + + + ) + + + 2 + + + + ω + + + + + + + + {\displaystyle {\begin{aligned}-{\frac {2}{r}}{\frac {dr}{dt}}{\frac {d{\boldsymbol {\omega }}}{dt}}&=-{\frac {2}{r}}{\frac {dr}{dt}}\left({\frac {\mathbf {r} \times \mathbf {a} }{r^{2}}}-{\frac {2}{r}}{\frac {dr}{dt}}{\boldsymbol {\omega }}\right)\\\\&=-{\frac {2}{r^{3}}}{\frac {dr}{dt}}\left(\mathbf {r} \times \mathbf {a} \right)+{\frac {4}{r^{2}}}\left({\frac {dr}{dt}}\right)^{2}{\boldsymbol {\omega }}\end{aligned}}} + +, and we finally get + + + + + + + + + + ζ + + = + + + + + r + + × + + j + + + + r + + 2 + + + + + + + + + + + v + + × + + a + + + + r + + 2 + + + + + − + + + 4 + + r + + 3 + + + + + + + + d + r + + + d + t + + + + + ( + + + r + + × + + a + + + ) + + + + + + 6 + + r + + 2 + + + + + + + ( + + + + d + r + + + d + t + + + + ) + + + 2 + + + + ω + + − + + + 2 + r + + + + + + + d + + 2 + + + r + + + d + + t + + 2 + + + + + + + ω + + + + + + + + {\displaystyle {\begin{aligned}{\boldsymbol {\zeta }}={\frac {\mathbf {r} \times \mathbf {j} }{r^{2}}}+{\frac {\mathbf {v} \times \mathbf {a} }{r^{2}}}-{\frac {4}{r^{3}}}{\frac {dr}{dt}}\left(\mathbf {r} \times \mathbf {a} \right)+{\frac {6}{r^{2}}}\left({\frac {dr}{dt}}\right)^{2}{\boldsymbol {\omega }}-{\frac {2}{r}}{\frac {d^{2}r}{dt^{2}}}{\boldsymbol {\omega }}\end{aligned}}} + + +or vice versa, replacing + + + + + ( + + + r + + × + + a + + + ) + + + + {\displaystyle \left(\mathbf {r} \times \mathbf {a} \right)} + + with + + + + + α + + + + {\displaystyle {\boldsymbol {\alpha }}} + +: + + + + + + + + + + ζ + + = + + + + + r + + × + + j + + + + r + + 2 + + + + + + + + + + + v + + × + + a + + + + r + + 2 + + + + + − + + + 4 + r + + + + + + d + r + + + d + t + + + + + α + + − + + + 2 + + r + + 2 + + + + + + + ( + + + + d + r + + + d + t + + + + ) + + + 2 + + + + ω + + − + + + 2 + r + + + + + + + d + + 2 + + + r + + + d + + t + + 2 + + + + + + + ω + + + + + + + + {\displaystyle {\begin{aligned}{\boldsymbol {\zeta }}={\frac {\mathbf {r} \times \mathbf {j} }{r^{2}}}+{\frac {\mathbf {v} \times \mathbf {a} }{r^{2}}}-{\frac {4}{r}}{\frac {dr}{dt}}{\boldsymbol {\alpha }}-{\frac {2}{r^{2}}}\left({\frac {dr}{dt}}\right)^{2}{\boldsymbol {\omega }}-{\frac {2}{r}}{\frac {d^{2}r}{dt^{2}}}{\boldsymbol {\omega }}\end{aligned}}} + + +For example, consider a Geneva drive, a device used for creating intermittent rotation of a driven wheel (the blue wheel in the animation) by continuous rotation of a driving wheel (the red wheel in the animation). During one cycle of the driving wheel, the driven wheel's angular position θ changes by 90 degrees and then remains constant. Because of the finite thickness of the driving wheel's fork (the slot for the driving pin), this device generates a discontinuity in the angular acceleration α, and an unbounded angular jerk ζ in the driven wheel. +Jerk does not preclude the Geneva drive from being used in applications such as movie projectors and cams. In movie projectors, the film advances frame-by-frame, but the projector operation has low noise and is highly reliable because of the low film load (only a small section of film weighing a few grams is driven), the moderate speed (2.4 m/s), and the low friction. + +With cam drive systems, use of a dual cam can avoid the jerk of a single cam; however, the dual cam is bulkier and more expensive. The dual-cam system has two cams on one axle that shifts a second axle by a fraction of a revolution. The graphic shows step drives of one-sixth and one-third rotation per one revolution of the driving axle. There is no radial clearance because two arms of the stepped wheel are always in contact with the double cam. Generally, combined contacts may be used to avoid the jerk (and wear and noise) associated with a single follower (such as a single follower gliding along a slot and changing its contact point from one side of the slot to the other can be avoided by using two followers sliding along the same slot, one side each). + +== In elastically deformable matter == + +An elastically deformable mass deforms under an applied force (or acceleration); the deformation is a function of its stiffness and the magnitude of the force. If the change in force is slow, the jerk is small, and the propagation of deformation is considered instantaneous as compared to the change in acceleration. The distorted body acts as if it were in a quasistatic regime, and only a changing force (nonzero jerk) can cause propagation of mechanical waves (or electromagnetic waves for a charged particle); therefore, for nonzero to high jerk, a shock wave and its propagation through the body should be considered. +The propagation of deformation is shown in the graphic "Compression wave patterns" as a compressional plane wave through an elastically deformable material. Also shown, for angular jerk, are the deformation waves propagating in a circular pattern, which causes shear stress and possibly other modes of vibration. The reflection of waves along the boundaries cause constructive interference patterns (not pictured), producing stresses that may exceed the material's limits. The deformation waves may cause vibrations, which can lead to noise, wear, and failure, especially in cases of resonance. + +The graphic captioned "Pole with massive top" shows a block connected to an elastic pole and a massive top. The pole bends when the block accelerates, and when the acceleration stops, the top will oscillate (damped) under the regime of pole stiffness. One could argue that a greater (periodic) jerk might excite a larger amplitude of oscillation because small oscillations are damped before reinforcement by a shock wave. One can also argue that a larger jerk might increase the probability of exciting a resonant mode because the larger wave components of the shock wave have higher frequencies and Fourier coefficients. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Jerk_(physics)-3.md b/data/en.wikipedia.org/wiki/Jerk_(physics)-3.md new file mode 100644 index 000000000..1eacf7bba --- /dev/null +++ b/data/en.wikipedia.org/wiki/Jerk_(physics)-3.md @@ -0,0 +1,63 @@ +--- +title: "Jerk (physics)" +chunk: 4/4 +source: "https://en.wikipedia.org/wiki/Jerk_(physics)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:07.559806+00:00" +instance: "kb-cron" +--- + +To reduce the amplitude of excited stress waves and vibrations, one can limit jerk by shaping motion and making the acceleration continuous with slopes as flat as possible. Due to limitations of abstract models, algorithms for reducing vibrations include higher derivatives, such as jounce, or suggest continuous regimes for both acceleration and jerk. One concept for limiting jerk is to shape acceleration and deceleration sinusoidally with zero acceleration in between (see graphic captioned "Sinusoidal acceleration profile"), making the speed appear sinusoidal with constant maximum speed. The jerk, however, will remain discontinuous at the points where acceleration enters and leaves the zero phases. + +== In the geometric design of roads and tracks == + +Roads and tracks are designed to limit the jerk caused by changes in their curvature. Design standards for high-speed rail vary from 0.2 m/s3 to 0.6 m/s3. Track transition curves limit the jerk when transitioning from a straight line to a curve, or vice versa. Recall that in constant-speed motion along an arc, acceleration is zero in the tangential direction and nonzero in the inward normal direction. Transition curves gradually increase the curvature and, consequently, the centripetal acceleration. +An Euler spiral, the theoretically optimum transition curve, linearly increases centripetal acceleration and results in constant jerk (see image above). In real-world applications, the plane of the track is inclined (cant) along the curved sections. The incline causes vertical acceleration, which is a design consideration for wear on the track and embankment. The Wiener Kurve (Viennese Curve) is a patented curve designed to minimize this wear. +Rollercoasters are also designed with track transitions to limit jerk. When entering a loop, acceleration values can reach around 4g (40 m/s2), and riding in this high acceleration environment is only possible with track transitions. S-shaped curves, such as figure eights, also use track transitions for smooth rides. + +== In motion control == +In motion control, the design focus is on straight, linear motion, with the need to move a system from one steady position to another (point-to-point motion). The design concern from a jerk perspective is vertical jerk; the jerk from tangential acceleration is effectively zero since linear motion is non-rotational. +Motion control applications include passenger elevators and machining tools. Limiting vertical jerk is considered essential for elevator riding convenience. ISO 8100-34 specifies measurement methods for elevator ride quality with respect to jerk, acceleration, vibration, and noise; however, the standard does not specify levels for acceptable or unacceptable ride quality. It is reported that most passengers rate a vertical jerk of 2 m/s3 as acceptable and 6 m/s3 as intolerable. For hospitals, 0.7 m/s3 is the recommended limit. +A primary design goal for motion control is to minimize the transition time without exceeding speed, acceleration, or jerk limits. Consider a third-order motion-control profile with quadratic ramping and deramping phases in velocity. + +This motion profile consists of the following seven segments: +Acceleration build up — positive jerk limit; linear increase in acceleration to the positive acceleration limit; quadratic increase in velocity +Upper acceleration limit — zero jerk; linear increase in velocity +Acceleration ramp down — negative jerk limit; linear decrease in acceleration; (negative) quadratic increase in velocity, approaching the desired velocity limit +Velocity limit — zero jerk; zero acceleration +Deceleration build up — negative jerk limit; linear decrease in acceleration to the negative acceleration limit; (negative) quadratic decrease in velocity +Lower deceleration limit — zero jerk; linear decrease in velocity +Deceleration ramp down — positive jerk limit; linear increase in acceleration to zero; quadratic decrease in velocity; approaching the desired position at zero speed and zero acceleration + +Segment four's time period (constant velocity) varies with distance between the two positions. If this distance is so small that omitting segment four would not suffice, then segments two and six (constant acceleration) could be equally reduced, and the constant velocity limit would not be reached. If this modification does not sufficiently reduce the crossed distance, then segments one, three, five, and seven could be shortened by an equal amount, and the constant acceleration limits would not be reached. +Other motion profile strategies are used, such as minimizing the square of jerk for a given transition time and, as discussed above, sinusoidal-shaped acceleration profiles. Motion profiles are tailored for specific applications including machines, people movers, chain hoists, automobiles, and robotics. + +=== In manufacturing === +Jerk is an important consideration in manufacturing processes. Rapid changes in acceleration of a cutting tool can lead to premature tool wear and result in uneven cuts; consequently, modern motion controllers include jerk limitation features. In mechanical engineering, jerk, in addition to velocity and acceleration, is considered in the development of cam profiles because of tribological implications and the ability of the actuated body to follow the cam profile without chatter. +Jerk is often considered when vibration is a concern. A device that measures jerk is called a "jerkmeter". + +== Further derivatives == + +Further time derivatives have also been named, as snap or jounce (fourth derivative), crackle (fifth derivative), and pop (sixth derivative). Time derivatives of position of higher order than four appear rarely. +The terms snap, crackle, and pop‍—‌for the fourth, fifth, and sixth derivatives of position‍—‌were inspired by the advertising mascots Snap, Crackle, and Pop. + +== See also == +Geomagnetic jerk +Shock (mechanics) +Yank + +== References == + +=== Sources === +Sprott JC (2003). Chaos and Time-Series Analysis. Oxford University Press. ISBN 0-19-850839-5. +Sprott JC (1997). "Some simple chaotic jerk functions" (PDF). Am J Phys. 65 (6): 537–43. Bibcode:1997AmJPh..65..537S. doi:10.1119/1.18585. Archived from the original (PDF) on 2010-06-13. Retrieved 2009-09-28. +Blair G (2005). "Making the Cam" (PDF). Race Engine Technology (10). Archived (PDF) from the original on 2008-05-15. Retrieved 2009-09-29. + +== External links == +What is the term used for the third derivative of position? Archived 2016-11-30 at the Wayback Machine, description of jerk in the Usenet Physics FAQ Archived 2011-06-23 at the Wayback Machine +Mathematics of Motion Control Profiles Archived 2020-10-02 at the Wayback Machine +Elevator-Ride-Quality Archived 2022-03-28 at the Wayback Machine +Elevator manufacturer brochure +Patent of Wiener Kurve +(in German) Description of Wiener Kurve \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Joan_&_Joseph_Birman_Research_Prize_in_Topology_and_Geometry-0.md b/data/en.wikipedia.org/wiki/Joan_&_Joseph_Birman_Research_Prize_in_Topology_and_Geometry-0.md new file mode 100644 index 000000000..ed6b04c40 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Joan_&_Joseph_Birman_Research_Prize_in_Topology_and_Geometry-0.md @@ -0,0 +1,32 @@ +--- +title: "Joan & Joseph Birman Research Prize in Topology and Geometry" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Joan_&_Joseph_Birman_Research_Prize_in_Topology_and_Geometry" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:26.249558+00:00" +instance: "kb-cron" +--- + +The Joan & Joseph Birman Research Prize in Topology and Geometry is a prize given every other year by the Association for Women in Mathematics to an outstanding young female researcher in topology or geometry. The prize fund for the award was endowed by a donation in 2013 from Joan Birman and her husband, Joseph Birman, and first awarded in 2015. + + +== Winners == +Elisenda Grigsby (2015), for her research in low-dimensional topology, particularly in knot theory and categorified invariants. +Emmy Murphy (2017), for her research in symplectic geometry where she developed new techniques for studying symplectic manifolds and contact geometry. +Kathryn Mann (2019), for "major breakthroughs in the theory of dynamics of group actions on manifolds". +Emily Riehl (2021), for "deep and foundational work in category theory and homotopy theory". +Kristen Hendricks (2023), for "highly influential work on equivariant aspects of Floer homology theories". +Mona Merling (2025), for "innovative and impactful research in algebraic K-theory, equivariant homotopy theory, and their applications to manifold theory". + + +== See also == +List of awards honoring women +List of mathematics awards + + +== References == + + +== External links == +AWM Birman Research Prize, Association for Women in Mathematics \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Krieger–Nelson_Prize-0.md b/data/en.wikipedia.org/wiki/Krieger–Nelson_Prize-0.md new file mode 100644 index 000000000..e23c42f6b --- /dev/null +++ b/data/en.wikipedia.org/wiki/Krieger–Nelson_Prize-0.md @@ -0,0 +1,28 @@ +--- +title: "Krieger–Nelson Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Krieger–Nelson_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:50.372357+00:00" +instance: "kb-cron" +--- + +The Krieger–Nelson Prize is presented by the Canadian Mathematical Society in recognition of an outstanding woman in mathematics. It was first +awarded in 1995. The award is named after Cecilia Krieger and Evelyn Nelson, both known for their contributions to mathematics in Canada. + + +== Recipients == +While the award has largely been awarded to a female mathematician working at a Canadian University, it has also been awarded to Canadian-born or -educated women working outside of the country. For example, Cathleen Morawetz, past president of the American Mathematical Society, and a faculty member at the Courant Institute of Mathematical Sciences (a division of New York University) was awarded the Krieger–Nelson Prize in 1997. (Morawetz was educated at the University of Toronto in Toronto, Canada). According to the call for applications, the award winner should be a "member of the Canadian mathematical community". +The recipient of the Krieger–Nelson Prize delivers a lecture to the Canadian Mathematical Society, typically during its summer meeting. + + +== See also == +List of mathematics awards + + +== References == + + +== External links == +Krieger–Nelson Prize, Canadian Mathematical Society. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Lise_Meitner_Lectures-0.md b/data/en.wikipedia.org/wiki/Lise_Meitner_Lectures-0.md new file mode 100644 index 000000000..3817fa471 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Lise_Meitner_Lectures-0.md @@ -0,0 +1,46 @@ +--- +title: "Lise Meitner Lectures" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Lise_Meitner_Lectures" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:56.346937+00:00" +instance: "kb-cron" +--- + +The Lise Meitner Lectures (LML) are a series of public lectures in honour of Lise Meitner. The lectures are organized jointly by the German Physical Society and the Austrian Physical Society, with the intention to showcase outstanding female scientists in physics or related fields. The annual lecture series was launched in 2008, when Lise Meitner's birthday celebrated its 130th anniversary. In October 2008, the Lise Meitner Lecture was held in Vienna and Berlin with an accompanying exhibition. The annual lecture series not only aims at increasing the visibility of successful female researchers, but also at encouraging girls and young women towards careers in physics. + + +== Awardees == +2025: Anne L’Huillier, „Attosecond pulses of light for studying electron dynamics“ +2024: Lisa Kaltenegger, "Alien Earths: Searching for a Second Earth - Challenges, Opportunities and Adventures" +2023: Donna Strickland, "Generating High-Intensity, Ultrashort Optical Pulses" +2022: Viola Priesemann, "Learning in living neuronal networks" (Lernen in lebenden neuronalen Netzwerken) +2021: Claudia Draxl, "Quantum-based Materials Modeling and Artificial Intelligence for Tackling Societal Challenges" +2019: Halina Rubinsztein-Dunlop, "Sculpted light in nano- and microsystems" +2017/18: Nicola Spaldin, "New materials for a new age" (DPG 2018/ÖPG 2017) +2017/18: Johanna Stachel, "Erforschung von Urknallmaterie an der Weltmaschine LHC" (DPG 2017/ÖPG 2018) +2016: Petra Schwille, "Ist Leben konstruierbar?" +2015: Cornelia Denz, "Material in neuem Licht - wie maßgeschneidertes Licht Materie strukturieren und anordnen kann" +2014: Felicitas Pauss, "Das Higgs-Teilchen: Unsichtbares sichtbar und Unmögliches möglich machen" +2013: Jocelyn Bell Burnell, "Pulsars and extreme physics" +2012: Renate Loll, "More than meets the eye: probing the Planckian structure of spacetime" +2010: Anna Frebel, "Die ältesten Sterne im Universum und die chemische Entwicklung unserer Galaxie" +2009: Cecilia Jarlskog, "Symmetries – exact and broken" +2008: Mildred Dresselhaus, "Why are we so excited about nano-carbons?" + + +== See also == +Lise Meitner Distinguished Lecture +Meitner Medal +Ludwig Boltzmann Prize + + +== References == + + +== External links == +Lise-Meitner-Lectures featured by the German Physical Society +Lise-Meitner-Lectures featured by the Austrian Physical Society +Dates of the Lise-Meitner-Lecture +Exhibition catalog Lise Meitner Lecture 2008 \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_female_Nobel_laureates-0.md b/data/en.wikipedia.org/wiki/List_of_female_Nobel_laureates-0.md new file mode 100644 index 000000000..22b53ad1d --- /dev/null +++ b/data/en.wikipedia.org/wiki/List_of_female_Nobel_laureates-0.md @@ -0,0 +1,60 @@ +--- +title: "List of female Nobel laureates" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/List_of_female_Nobel_laureates" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:51.507842+00:00" +instance: "kb-cron" +--- + +The Nobel Prizes are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to Mankind." Additionally, the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (often referred to as the Nobel Prize in Economics) was established by Sveriges Riksbank in 1968 and is awarded to a "person or persons in the field of economic sciences who have produced work of outstanding importance." +As of 2025, according to the Nobel Foundation, 68 Nobel Prizes and the Memorial Prize in Economic Sciences have been awarded to 67 women (Marie Curie has been honoured twice, first in Physics in 1903, then in Chemistry in 1911). Unique Nobel Prize laureates include 894 men, 64 women, and 27 organizations. +The approximate distribution of Nobel prizes awarded to women is as follows (regularly updated list from the Nobel Foundation can be found on their website at "Nobel-Prize awarded women" ): + +twenty women have won the Nobel Peace Prize (16.3% of 110 awarded); +eighteen have won the Nobel Prize in Literature (15% of 120 awarded); +fourteen have won the Nobel Prize in Physiology or Medicine (5.6% of 230 awarded); +eight have won the Nobel Prize in Chemistry (4.1% of 191 awarded); +five have won the Nobel Prize in Physics (1.8% of 224 awarded); +and three (Elinor Ostrom, Esther Duflo and Claudia Goldin) have won the Nobel Memorial Prize in Economic Sciences (2.17% of 92 awarded). +The first woman to win a Nobel Prize was Marie Skłodowska-Curie, who won the Nobel Prize in Physics in 1903 with Pierre Curie, and Henri Becquerel. Curie is also the first person and the only woman to have won multiple Nobel Prizes; in 1911, she won the Nobel Prize in Chemistry. Curie's daughter, Irène Joliot-Curie, won the Nobel Prize in Chemistry in 1935, making the two the only mother–daughter pair to have won Nobel Prizes and of Pierre and Irène Curie the only father-daughter pair to have won Nobel Prizes by the same occasion, whilst there are 6 father-son pairs who have won Nobel Prizes by comparison. +The most recent women to be awarded a Nobel Prize were Maria Corina Machado for Peace, Mary Brunkow for Physiology or Medicine (2025), Han Kang in Literature (2024), Claudia Goldin in Economics, Narges Mohammadi for Peace, Anne L'Huillier in Physics and Katalin Karikó in Physiology or Medicine (2023), Annie Ernaux in Literature and Carolyn R. Bertozzi for Chemistry (2022), Maria Ressa for Peace (2021), Louise Glück in Literature, Andrea M. Ghez in Physics, Emmanuelle Charpentier and Jennifer Doudna in Chemistry (2020). The most Nobel Prizes awarded to women in a single year was in 2009, when five women became laureates in four categories. + + +== Female laureates == + + +=== Physiology or Medicine === + + +=== Physics === + + +=== Chemistry === + + +=== Literature === + + +=== Peace === + + +=== Economic Sciences === + + +== Notes == + + +== References == +Specific + +General + +"Nobel Prize awarded women". Nobel Foundation. Retrieved 2022-10-06. +"Women - Nobel Prize laureates". nobelists.org. Retrieved 24 June 2024. + + +== Further reading == +Sanchez, Chelsey (2 November 2021). "These Are the Four Women Who Won Nobel Prizes in 2020". Harper's Bazaar. Retrieved 22 May 2022. +Alan Asaid (26 September 2009). "Så ratade Akademien kvinnorna" [How the Academy Rejected the Women]. SvD (in Swedish). \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_female_nominators_for_the_Nobel_Prize-0.md b/data/en.wikipedia.org/wiki/List_of_female_nominators_for_the_Nobel_Prize-0.md new file mode 100644 index 000000000..125469037 --- /dev/null +++ b/data/en.wikipedia.org/wiki/List_of_female_nominators_for_the_Nobel_Prize-0.md @@ -0,0 +1,35 @@ +--- +title: "List of female nominators for the Nobel Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/List_of_female_nominators_for_the_Nobel_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:35.878491+00:00" +instance: "kb-cron" +--- + +The Nobel Prize (Swedish: Nobelpriset) is a set of five different prizes that, according to its benefactor Alfred Nobel in his 1895 will, must be awarded "to those who, during the preceding year, have conferred the greatest benefit to humankind". The five prizes are awarded in the fields of Physics, Chemistry, Physiology or Medicine, Literature, and Peace. +Since 1901, numerous nominators have forwarded their nominations of distinguished individuals or organizations for the prize, and most of these nominators were women. The following is a list of the female nominators for the prestigious Nobel Prize: + + +== Physics == +The Nobel Committee for Physics sends confidential forms to persons who are competent and qualified to nominate. According to the nomination process, the individuals are considered the qualified nominators for the physics prize: + + +== Chemistry == +For the chemistry prize, the following individuals are considered as qualified nominators: + + +== Physiology or Medicine == +For the physiology or medicine prize, the following individuals are entitled to nominate: + + +== Literature == +The Nobel Committee of the Swedish Academy sends invitation letters to persons who are qualified to nominate for the Nobel Prize in Literature. The following individuals are eligible forwarding nominations: + + +== Peace == +According to the statutes of the Nobel Foundation, a nomination is considered valid if it is submitted by a person or a group of people who falls within one of the following categories: + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Memorial_Prize_in_Economic_Sciences-0.md b/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Memorial_Prize_in_Economic_Sciences-0.md new file mode 100644 index 000000000..273d031e7 --- /dev/null +++ b/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Memorial_Prize_in_Economic_Sciences-0.md @@ -0,0 +1,33 @@ +--- +title: "List of female nominees for the Nobel Memorial Prize in Economic Sciences" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Memorial_Prize_in_Economic_Sciences" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:37.126969+00:00" +instance: "kb-cron" +--- + +The Nobel Memorial Prize in Economic Sciences is an annual award established in 1969 by Sweden's central bank, Sveriges Riksbank. Though not one of the original Nobel Prizes, it was founded to celebrate the bank's 300th anniversary and in memory of Alfred Nobel. The laureates are chosen in a manner similar to the Nobel Prizes and receives the recognition during the Nobel ceremonies. +As of 2025, 68 Nobel Prizes and the Memorial Prize in Economic Sciences have been awarded to 67 women and since 1901, the year wherein the awarding of the prizes began, hundreds of women have already been nominated and shortlisted carefully in each field. From 1969 to 1972, four women have been nominated for the Nobel Memorial Prize until 2009 when the first female economist was subsequently awarded. +In 1969, British economist Joan Robinson became the first ever woman to be nominated for a Nobel Memorial Prize in Economic Sciences. She was nominated multiple times and shortlisted in 1975 and 1976 but remained unrewarded with The New York Times explaining that "[Ms. Robinson] did not win the prize because [the committee] feared that she would either refuse it or, worse, use the Nobel limelight to attack mainstream economics." Of the currently revealed female nominees, the notable economists Karin Kock-Lindberg, Elizabeth Ellis Hoyt, Barbara Ward and Sadie Alexander were not included. Currently, the Nobel archives has revealed nominations from 1969 to 1972, the other enlisted women were verified nominations based on public and private news agencies. + + +== Nominees by their first nomination == + + +== Notes == + + +== See also == +List of Nobel laureates +List of female Nobel laureates +List of economists +Matilda effect + + +== References == + + +== External links == +Alan Asaid (26 September 2009). "Så ratade Akademien kvinnorna" [How the Academy Rejected the Women]. SvD (in Swedish). \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Chemistry-0.md b/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Chemistry-0.md new file mode 100644 index 000000000..8f29e2384 --- /dev/null +++ b/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Chemistry-0.md @@ -0,0 +1,33 @@ +--- +title: "List of female nominees for the Nobel Prize in Chemistry" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Chemistry" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:38.377804+00:00" +instance: "kb-cron" +--- + +The Nobel Prize (Swedish: Nobelpriset) is a set of five different prizes that, according to its benefactor Alfred Nobel, in his 1895 will, must be awarded "to those who, during the preceding year, have conferred the greatest benefit to humankind". The five prizes are awarded in the fields of Physiology or Medicine, Physics, Chemistry, Literature, and Peace. +As of 2025, 68 Nobel Prizes and the Memorial Prize in Economic Sciences have been awarded to 67 women and since 1901, the year wherein the awarding of the prizes began, hundreds of women have already been nominated and shortlisted carefully in each field. From 1901 to 1975, 15 women have been nominated for the Nobel Prize in Chemistry and 3 of these nominees were subsequently awarded. +In 1911, Polish-French scientist Marie Curie became the first ever women to win a solo Nobel Prize in Chemistry. She became and the only woman to have won two Nobel Prizes: in 1903, she was awarded the Nobel Prize in Physics alongside her husband, Pierre Curie, and Henri Becquerel. Curie's daughter, Irène Joliot-Curie, eventually became the second recipient of the Nobel Prize in Chemistry in 1935, making the two the only mother-daughter pair to have won Nobel Prizes. Of the currently revealed female nominees, the notable scientists Marie Pasteur, Nadezhda Ziber-Shumova, Laura Alberta Linton, Alice Ball, Julia Lermontova, Muriel Onslow, Margarete von Wrangell, Mary Engle Pennington, Pauline Ramart, Gertrud Kornfeld, Maud Menten, Clara Benson, Maria Lipp, Astrid Cleve, Ellen Gleditsch, Marianne Angermann, Helen Parsons, Katharine Burr Blodgett, Elizabeth Rona, Sibyl and Icie Hoobler were not included. Currently, the Nobel archives has revealed nominations from 1901 to 1975, the other enlisted women were verified nominations based on public and private news agencies. + + +== Nominees by their first nomination == + + +== Notes == + + +== See also == +List of Nobel laureates +List of female Nobel laureates +List of female scientists in the 20th century +Matilda effect + + +== References == + + +== External links == +Alan Asaid (26 September 2009). "Så ratade Akademien kvinnorna" [How the Academy Rejected the Women]. SvD (in Swedish). \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Physics-0.md b/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Physics-0.md new file mode 100644 index 000000000..6c98d4067 --- /dev/null +++ b/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Physics-0.md @@ -0,0 +1,33 @@ +--- +title: "List of female nominees for the Nobel Prize in Physics" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Physics" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:39.542386+00:00" +instance: "kb-cron" +--- + +The Nobel Prize (Swedish: Nobelpriset) is a set of five different prizes that, according to its benefactor Alfred Nobel, in his 1895 will, must be awarded "to those who, during the preceding year, have conferred the greatest benefit to humankind". The five prizes are awarded in the fields of Physiology or Medicine, Physics, Chemistry, Literature, and Peace. +As of 2025, 68 Nobel Prizes and the Memorial Prize in Economic Sciences have been awarded to 67 women and since 1901, the year wherein the awarding of the prizes began, hundreds of women have already been nominated and shortlisted carefully in each field. From 1902 to 1975, 13 women have been nominated for the Nobel Prize in Physics and three of the nominees were subsequently awarded. +The first woman to win a Nobel Prize was Marie Curie, who won the Nobel Prize in Physics in 1903 with her husband, Pierre Curie, and Henri Becquerel. Curie is also the only woman to have won multiple Nobel Prizes; in 1911, she won the Nobel Prize in Chemistry. Curie's daughter, Irène Joliot-Curie, won the Nobel Prize in Chemistry in 1935, making the two the only mother-daughter pair to have won Nobel Prizes. Of the currently revealed female nominees, the notable scientists Alice Ball, Henrietta Swan Leavitt, Hertha Ayrton, Harriet Brooks, Agnes Pockels, Annie Jump Cannon, Margaret Eliza Maltby, Mileva Marić, Elizabeth Alexander, Maud Menten, Elda Emma Anderson, Hertha Sponer, Kathleen Lonsdale, Geertruida de Haas-Lorentz, Hendrika Johanna van Leeuwen, Luise Lange, Katherine Burr Blodgett, Jeanne Ferrier, Cecilia Payne-Gaposchkin, Marie-Antoinette Tonnelat, Toshiko Yuasa, Ruby Payne-Scott, Katharina Boll-Dornberger, Grete Hermann and Leona Woods were not included. Currently, the Nobel archives has revealed nominations from 1901 to 1975, the other enlisted women were verified nominations based on public and private news agencies. + + +== Nominees by their first nomination == + + +== Notes == + + +== See also == +List of Nobel laureates +List of female Nobel laureates +List of female scientists in the 20th century +Matilda effect + + +== References == + + +== External links == +Alan Asaid (26 September 2009). "Så ratade Akademien kvinnorna" [How the Academy Rejected the Women]. SvD (in Swedish). \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Physiology_or_Medicine-0.md b/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Physiology_or_Medicine-0.md new file mode 100644 index 000000000..6bf432b19 --- /dev/null +++ b/data/en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Physiology_or_Medicine-0.md @@ -0,0 +1,33 @@ +--- +title: "List of female nominees for the Nobel Prize in Physiology or Medicine" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/List_of_female_nominees_for_the_Nobel_Prize_in_Physiology_or_Medicine" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:40.767824+00:00" +instance: "kb-cron" +--- + +The Nobel Prize (Swedish: Nobelpriset) is a set of five different prizes that, according to its benefactor Alfred Nobel, in his 1895 will, must be awarded "to those who, during the preceding year, have conferred the greatest benefit to humankind". The five prizes are awarded in the fields of Physiology or Medicine, Physics, Chemistry, Literature, and Peace. +As of 2025, 68 Nobel Prizes and the Memorial Prize in Economic Sciences have been awarded to 67 women and since 1901, the year wherein the awarding of the prizes began, hundreds of women have already been nominated and shortlisted carefully in each field. From 1912 to 1956, 19 women have been nominated for the Nobel Prize in Physiology or Medicine wherein one was declared invalid, one was purportedly recommended and one was subsequently awarded. +In 1912, Mary Edwards Walker became the first ever woman nominated for prize in physiology or medicine but her nomination was later declared invalid by the Nobel Committee because her nominator was not invited to nominate that year. Hence, Cécile Vogt-Mugnier, nominated first in 1922, became the official first female nominee but never won despite numerous recommendations. She was followed by Maud Slye who was nominated in the year 1923, but again never won. Only in 1947, that the Nobel Prize in Physiology or Medicine was finally awarded to a woman, Gerty Cori, sharing with her husband Carl Ferdinand Cori. Of the currently revealed female nominees, the physiologists Nettie Stevens, Alice Ball, Ida Henrietta Hyde, María Orosa, Florence R. Sabin, Rosalind Franklin, Louise Pearce, Esther Killick, Hattie Alexander, Dorothy Hansine Andersen, Mary Barber, Frieda Robscheit-Robbins, Virginia Apgar, Olga Bridgman and Alice Catherine Evans were not included. Currently, the Nobel archives has revealed nominations from 1901 to 1956, the other enlisted women were verified nominations based on public and private news agencies. + + +== Nominees by their first nomination == + + +== Notes == + + +== See also == +List of Nobel laureates +List of female Nobel laureates +List of female scientists in the 20th century +Matilda effect + + +== References == + + +== External links == +Alan Asaid (26 September 2009). "Så ratade Akademien kvinnorna" [How the Academy Rejected the Women]. SvD (in Swedish). \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_science_and_technology_awards_for_women-0.md b/data/en.wikipedia.org/wiki/List_of_science_and_technology_awards_for_women-0.md index 14760c0fd..f8b4bcfba 100644 --- a/data/en.wikipedia.org/wiki/List_of_science_and_technology_awards_for_women-0.md +++ b/data/en.wikipedia.org/wiki/List_of_science_and_technology_awards_for_women-0.md @@ -4,7 +4,7 @@ chunk: 1/1 source: "https://en.wikipedia.org/wiki/List_of_science_and_technology_awards_for_women" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T07:54:39.212429+00:00" +date_saved: "2026-05-05T11:15:19.164035+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Margaret_Oakley_Dayhoff_Award-0.md b/data/en.wikipedia.org/wiki/Margaret_Oakley_Dayhoff_Award-0.md new file mode 100644 index 000000000..42370fa80 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Margaret_Oakley_Dayhoff_Award-0.md @@ -0,0 +1,69 @@ +--- +title: "Margaret Oakley Dayhoff Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Margaret_Oakley_Dayhoff_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:52.712131+00:00" +instance: "kb-cron" +--- + +The Margaret Oakley Dayhoff Award from the Biophysical Society in Rockville, Maryland, is given to a woman who "holds very high promise or has achieved prominence while developing the early stages of a career in biophysical research". It is "one of the top national honors" in biophysics. The award was established in 1984 in honor of Margaret Dayhoff, a biophysicist associated with the Biophysical Society and the National Biomedical Research Foundation. + + +== Award recipients == +Source: Biophysical Society + +1984/85: Dagmar Ringe and Bonnie Ann Wallace +1985/86: Barbara A. Lewis +1986/87: Barbara E. Ehrlich +1987/88: Rachel E. Klevit +1988/89: Nancy L. Thompson +1989/90: Anne Walter +1990/91: Jeanne Rudzki Small +1991/92: Hazel M. Holden and Francine R. Smith +1992/93: Carol Vandenberg +1993/94: Jean S. Baum +1994/95: Hillary C. M. Nelson +1995/96: Lynne Regan +1996/97: Susan Marqusee +1997/98: Bonnie Anne Berger +1998/99: Judith R. Mourant +1999: Lydia Gregoret +2000/2001: Millie M. Georgiadis and Ka Yee Christina Lee +2002: Gina MacDonald +2003: Hao Wu +2004: Dorothee Kern +2005: Sarah Keller +2006: Anne Hinderliter +2007: Kalina Hristova +2008: Judith Klein-Seetharaman +2009: Teresa Giraldez, Adrienne L. Fairhall, and Jin Zhang +2010: Crina Nimigean and Maria Spies +2011: Diane Lidke +2012: Lucy R. Forrest +2013: Jennifer L. Ross and Katherine Henzler-Wildman +2014: Sarah Veatch +2015: Antonina Roll-Mecak +2016: Sophie Dumont and Polina Lishko +2017: Julie S. Biteen +2018: Carrie L. Partch +2019: Meytal Landau +2020: Valeria Vásquez +2021: Randy Stockbridge +2022: Gabriela Schlau-Cohen +2023: Elizabeth H. Kellogg + + +== See also == +List of biology awards +List of prizes, medals, and awards for women in science +Prizes named after people + + +== Notes == + + +== External links == +Margaret Oakley Dayhoff Award page +Dayhoff Award, NLM \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Margaret_W._Rossiter_History_of_Women_in_Science_Prize-0.md b/data/en.wikipedia.org/wiki/Margaret_W._Rossiter_History_of_Women_in_Science_Prize-0.md index 30f492b7f..56ab8db29 100644 --- a/data/en.wikipedia.org/wiki/Margaret_W._Rossiter_History_of_Women_in_Science_Prize-0.md +++ b/data/en.wikipedia.org/wiki/Margaret_W._Rossiter_History_of_Women_in_Science_Prize-0.md @@ -4,7 +4,7 @@ chunk: 1/1 source: "https://en.wikipedia.org/wiki/Margaret_W._Rossiter_History_of_Women_in_Science_Prize" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T09:28:14.378453+00:00" +date_saved: "2026-05-05T11:15:53.943095+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Maria_Goeppert-Mayer_Award-0.md b/data/en.wikipedia.org/wiki/Maria_Goeppert-Mayer_Award-0.md new file mode 100644 index 000000000..4e814b970 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Maria_Goeppert-Mayer_Award-0.md @@ -0,0 +1,23 @@ +--- +title: "Maria Goeppert-Mayer Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Maria_Goeppert-Mayer_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:44.372924+00:00" +instance: "kb-cron" +--- + +The Maria Goeppert-Mayer Award is an annual prize presented by the American Physical Society in recognition of an outstanding contribution to physics research by a woman. It recognizes and enhances outstanding achievements by women physicists in the early years of their careers. +The prize has been awarded since 1986 and is named after Maria Goeppert-Mayer, Nobel laureate in 1963 with J. Hans D. Jensen and Eugene Paul Wigner. Goeppert-Mayer and Jensen were awarded their prize "for their discovery of the nuclear shell structure". Goeppert-Mayer was the second woman to receive a Nobel Prize in Physics after Marie Curie. + + +== Recipients == +Source: + + +== See also == +List of physics awards + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Metric_tensor_(general_relativity)-0.md b/data/en.wikipedia.org/wiki/Metric_tensor_(general_relativity)-0.md new file mode 100644 index 000000000..39b4917fb --- /dev/null +++ b/data/en.wikipedia.org/wiki/Metric_tensor_(general_relativity)-0.md @@ -0,0 +1,687 @@ +--- +title: "Metric tensor (general relativity)" +chunk: 1/3 +source: "https://en.wikipedia.org/wiki/Metric_tensor_(general_relativity)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:08.849054+00:00" +instance: "kb-cron" +--- + +In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past. +In general relativity, the metric tensor plays the role of the gravitational potential in the classical theory of gravitation, although the physical content of the associated equations is entirely different. Gutfreund and Renn say "that in general relativity the gravitational potential is represented by the metric tensor." + +== Notation and conventions == +This article works with a metric signature that is mostly positive (− + + +); see sign convention. The gravitation constant + + + + G + + + {\displaystyle G} + + will be kept explicit. This article employs the Einstein summation convention, where repeated indices are automatically summed over. + +== Definition == +Mathematically, spacetime is represented by a four-dimensional differentiable manifold + + + + M + + + {\displaystyle M} + + and the metric tensor is given as a covariant, second-degree, symmetric tensor on + + + + M + + + {\displaystyle M} + +, conventionally denoted by + + + + g + + + {\displaystyle g} + +. Moreover, the metric is required to be nondegenerate with signature (− + + +). A manifold + + + + M + + + {\displaystyle M} + + equipped with such a metric is a type of Lorentzian manifold. +Explicitly, the metric tensor is a symmetric bilinear form on each tangent space of + + + + M + + + {\displaystyle M} + + that varies in a smooth (or differentiable) manner from point to point. Given two tangent vectors + + + + u + + + {\displaystyle u} + + and + + + + v + + + {\displaystyle v} + + at a point + + + + x + + + {\displaystyle x} + + in + + + + M + + + {\displaystyle M} + +, the metric can be evaluated on + + + + u + + + {\displaystyle u} + + and + + + + v + + + {\displaystyle v} + + to give a real number: + + + + + + g + + x + + + ( + u + , + v + ) + = + + g + + x + + + ( + v + , + u + ) + ∈ + + R + + . + + + {\displaystyle g_{x}(u,v)=g_{x}(v,u)\in \mathbb {R} .} + + +This is a generalization of the dot product of ordinary Euclidean space. Unlike Euclidean space – where the dot product is positive definite – the metric is indefinite and gives each tangent space the structure of Minkowski space. + +== Local coordinates and matrix representations == +Physicists usually work in local coordinates (i.e. coordinates defined on some local patch of + + + + M + + + {\displaystyle M} + +). In local coordinates + + + + + x + + μ + + + + + {\displaystyle x^{\mu }} + + (where + + + + μ + + + {\displaystyle \mu } + + is an index that runs from 0 to 3) the metric can be written in the form + + + + + g + = + + g + + μ + ν + + + d + + x + + μ + + + ⊗ + d + + x + + ν + + + . + + + {\displaystyle g=g_{\mu \nu }dx^{\mu }\otimes dx^{\nu }.} + + +The factors + + + + d + + x + + μ + + + + + {\displaystyle dx^{\mu }} + + are one-form gradients of the scalar coordinate fields + + + + + x + + μ + + + + + {\displaystyle x^{\mu }} + +. The metric is thus a linear combination of tensor products of one-form gradients of coordinates. The coefficients + + + + + g + + μ + ν + + + + + {\displaystyle g_{\mu \nu }} + + are a set of 16 real-valued functions (since the tensor + + + + g + + + {\displaystyle g} + + is a tensor field, which is defined at all points of a spacetime manifold). In order for the metric to be symmetric + + + + + g + + μ + ν + + + = + + g + + ν + μ + + + , + + + {\displaystyle g_{\mu \nu }=g_{\nu \mu },} + + +giving 10 independent coefficients. +If the local coordinates are specified, or understood from context, the metric can be written as a 4 × 4 symmetric matrix with entries + + + + + g + + μ + ν + + + + + {\displaystyle g_{\mu \nu }} + +. The nondegeneracy of + + + + + g + + μ + ν + + + + + {\displaystyle g_{\mu \nu }} + + means that this matrix is non-singular (i.e. has non-vanishing determinant), while the Lorentzian signature of + + + + g + + + {\displaystyle g} + + implies that the matrix has one negative and three positive eigenvalues. Physicists often refer to this matrix or the coordinates + + + + + g + + μ + ν + + + + + {\displaystyle g_{\mu \nu }} + + themselves as the metric (see, however, abstract index notation). +With the quantities + + + + d + + x + + μ + + + + + {\displaystyle dx^{\mu }} + + being regarded as the components of an infinitesimal coordinate displacement four-vector (not to be confused with the one-forms of the same notation above), the metric determines the invariant square of an infinitesimal line element, often referred to as an interval. The interval is often denoted + + + + + d + + s + + 2 + + + = + + g + + μ + ν + + + d + + x + + μ + + + d + + x + + ν + + + . + + + {\displaystyle ds^{2}=g_{\mu \nu }dx^{\mu }dx^{\nu }.} + + +The interval + + + + d + + s + + 2 + + + + + {\displaystyle ds^{2}} + + imparts information about the causal structure of spacetime. When + + + + d + + s + + 2 + + + < + 0 + + + {\displaystyle ds^{2}<0} + +, the interval is timelike and the square root of the absolute value of + + + + d + + s + + 2 + + + + + {\displaystyle ds^{2}} + + is an incremental proper time. Only timelike intervals can be physically traversed by a massive object. When + + + + d + + s + + 2 + + + = + 0 + + + {\displaystyle ds^{2}=0} + +, the interval is lightlike, and can only be traversed by (massless) things that move at the speed of light. When + + + + d + + s + + 2 + + + > + 0 + + + {\displaystyle ds^{2}>0} + +, the interval is spacelike and the square root of + + + + d + + s + + 2 + + + + + {\displaystyle ds^{2}} + + acts as an incremental proper length. Spacelike intervals cannot be traversed, since they connect events that are outside each other's light cones. Events can be causally related only if they are within each other's light cones. +The components of the metric depend on the choice of local coordinate system. Under a change of coordinates + + + + + x + + μ + + + → + + x + + + + μ + ¯ + + + + + + + {\displaystyle x^{\mu }\to x^{\bar {\mu }}} + +, the metric components transform as + + + + + + g + + + + + μ + ¯ + + + + + + + ν + ¯ + + + + + + = + + + + ∂ + + x + + ρ + + + + + ∂ + + x + + + + μ + ¯ + + + + + + + + + + + ∂ + + x + + σ + + + + + ∂ + + x + + + + ν + ¯ + + + + + + + + + g + + ρ + σ + + + = + + Λ + + ρ + + + + + + + + + + μ + ¯ + + + + + + + Λ + + σ + + + + + + + + + + ν + ¯ + + + + + + + g + + ρ + σ + + + . + + + {\displaystyle g_{{\bar {\mu }}{\bar {\nu }}}={\frac {\partial x^{\rho }}{\partial x^{\bar {\mu }}}}{\frac {\partial x^{\sigma }}{\partial x^{\bar {\nu }}}}g_{\rho \sigma }=\Lambda ^{\rho }{}_{\bar {\mu }}\,\Lambda ^{\sigma }{}_{\bar {\nu }}\,g_{\rho \sigma }.} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Metric_tensor_(general_relativity)-1.md b/data/en.wikipedia.org/wiki/Metric_tensor_(general_relativity)-1.md new file mode 100644 index 000000000..827c6c7e6 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Metric_tensor_(general_relativity)-1.md @@ -0,0 +1,1044 @@ +--- +title: "Metric tensor (general relativity)" +chunk: 2/3 +source: "https://en.wikipedia.org/wiki/Metric_tensor_(general_relativity)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:08.849054+00:00" +instance: "kb-cron" +--- + +== Properties == +The metric tensor plays a key role in index manipulation. In index notation, the coefficients + + + + + g + + μ + ν + + + + + {\displaystyle g_{\mu \nu }} + + of the metric tensor + + + + + g + + + + {\displaystyle \mathbf {g} } + + provide a link between covariant and contravariant components of other tensors. Contracting the contravariant index of a tensor with one of a covariant metric tensor coefficient has the effect of lowering the index + + + + + + g + + μ + ν + + + + A + + ν + + + = + + A + + μ + + + + + {\displaystyle g_{\mu \nu }A^{\nu }=A_{\mu }} + + +and similarly a contravariant metric coefficient raises the index + + + + + + g + + μ + ν + + + + A + + ν + + + = + + A + + μ + + + . + + + {\displaystyle g^{\mu \nu }A_{\nu }=A^{\mu }.} + + +Applying this property of raising and lowering indices to the metric tensor components themselves leads to the property + + + + + + g + + μ + ν + + + + g + + ν + λ + + + = + + δ + + μ + + + λ + + + + + {\displaystyle g_{\mu \nu }g^{\nu \lambda }=\delta _{\mu }^{\lambda }} + + +For a diagonal metric (one for which coefficients + + + + + g + + μ + ν + + + = + 0 + , + + ∀ + μ + ≠ + ν + + + {\displaystyle g_{\mu \nu }=0,\,\forall \mu \neq \nu } + +; i.e. the basis vectors are orthogonal to each other), this implies that a given covariant coefficient of the metric tensor is the inverse of the corresponding contravariant coefficient + + + + + g + + 00 + + + = + ( + + g + + 00 + + + + ) + + − + 1 + + + , + + g + + 11 + + + = + ( + + g + + 11 + + + + ) + + − + 1 + + + + + {\displaystyle g_{00}=(g^{00})^{-1},g_{11}=(g^{11})^{-1}} + +, etc. + +== Examples == + +=== Flat spacetime === +The simplest example of a Lorentzian manifold is flat spacetime, which can be given as R4 with coordinates + + + + ( + t + , + x + , + y + , + z + ) + + + {\displaystyle (t,x,y,z)} + + and the metric + + + + + d + + s + + 2 + + + = + − + + c + + 2 + + + d + + t + + 2 + + + + + d + + x + + 2 + + + + + d + + y + + 2 + + + + + d + + z + + 2 + + + = + + η + + μ + ν + + + d + + x + + μ + + + d + + x + + ν + + + . + + + {\displaystyle ds^{2}=-c^{2}dt^{2}+dx^{2}+dy^{2}+dz^{2}=\eta _{\mu \nu }dx^{\mu }dx^{\nu }.} + + +These coordinates actually cover all of R4. The flat space metric (or Minkowski metric) is often denoted by the symbol η and is the metric used in special relativity. In the above coordinates, the matrix representation of η is + + + + + η + = + + + ( + + + + − + + c + + 2 + + + + + 0 + + + 0 + + + 0 + + + + + 0 + + + 1 + + + 0 + + + 0 + + + + + 0 + + + 0 + + + 1 + + + 0 + + + + + 0 + + + 0 + + + 0 + + + 1 + + + + ) + + + + + {\displaystyle \eta ={\begin{pmatrix}-c^{2}&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}} + + +(An alternative convention replaces coordinate + + + + t + + + {\displaystyle t} + + by + + + + c + t + + + {\displaystyle ct} + +, and defines + + + + η + + + {\displaystyle \eta } + + as in Minkowski space § Standard basis.) +In spherical coordinates + + + + ( + t + , + r + , + θ + , + ϕ + ) + + + {\displaystyle (t,r,\theta ,\phi )} + +, the flat space metric takes the form + + + + + d + + s + + 2 + + + = + − + + c + + 2 + + + d + + t + + 2 + + + + + d + + r + + 2 + + + + + + r + + 2 + + + d + + Ω + + 2 + + + + + {\displaystyle ds^{2}=-c^{2}dt^{2}+dr^{2}+r^{2}d\Omega ^{2}} + + +where + + + + + d + + Ω + + 2 + + + = + d + + θ + + 2 + + + + + + sin + + 2 + + + ⁡ + θ + + d + + ϕ + + 2 + + + + + {\displaystyle d\Omega ^{2}=d\theta ^{2}+\sin ^{2}\theta \,d\phi ^{2}} + + +is the standard metric on the 2-sphere. + +=== Black hole metrics === +The Schwarzschild metric describes an uncharged, non-rotating black hole. There are also metrics that describe rotating and charged black holes. + +==== Schwarzschild metric ==== +Besides the flat space metric the most important metric in general relativity is the Schwarzschild metric which can be given in one set of local coordinates by + + + + + d + + s + + 2 + + + = + − + + ( + + 1 + − + + + + 2 + G + M + + + r + + c + + 2 + + + + + + + ) + + + c + + 2 + + + d + + t + + 2 + + + + + + + ( + + 1 + − + + + + 2 + G + M + + + r + + c + + 2 + + + + + + + ) + + + − + 1 + + + d + + r + + 2 + + + + + + r + + 2 + + + d + + Ω + + 2 + + + + + {\displaystyle ds^{2}=-\left(1-{\frac {2GM}{rc^{2}}}\right)c^{2}dt^{2}+\left(1-{\frac {2GM}{rc^{2}}}\right)^{-1}dr^{2}+r^{2}d\Omega ^{2}} + + +where, again, + + + + d + + Ω + + 2 + + + + + {\displaystyle d\Omega ^{2}} + + is the standard metric on the 2-sphere. Here, + + + + G + + + {\displaystyle G} + + is the gravitation constant and + + + + M + + + {\displaystyle M} + + is a constant with the dimensions of mass. Its derivation can be found here. The Schwarzschild metric approaches the Minkowski metric as + + + + M + + + {\displaystyle M} + + approaches zero (except at the origin where it is undefined). Similarly, when + + + + r + + + {\displaystyle r} + + goes to infinity, the Schwarzschild metric approaches the Minkowski metric. +With coordinates + + + + + + ( + + + x + + 0 + + + , + + x + + 1 + + + , + + x + + 2 + + + , + + x + + 3 + + + + ) + + = + ( + c + t + , + r + , + θ + , + φ + ) + + , + + + {\displaystyle \left(x^{0},x^{1},x^{2},x^{3}\right)=(ct,r,\theta ,\varphi )\,,} + + the metric can be written as + + + + + + g + + μ + ν + + + = + + + [ + + + + − + + ( + + 1 + − + + + + 2 + G + M + + + r + + c + + 2 + + + + + + + ) + + + + 0 + + + 0 + + + 0 + + + + + 0 + + + + + ( + + 1 + − + + + + 2 + G + M + + + r + + c + + 2 + + + + + + + ) + + + − + 1 + + + + + 0 + + + 0 + + + + + 0 + + + 0 + + + + r + + 2 + + + + + 0 + + + + + 0 + + + 0 + + + 0 + + + + r + + 2 + + + + sin + + 2 + + + ⁡ + θ + + + + ] + + + + . + + + {\displaystyle g_{\mu \nu }={\begin{bmatrix}-\left(1-{\frac {2GM}{rc^{2}}}\right)&0&0&0\\0&\left(1-{\frac {2GM}{rc^{2}}}\right)^{-1}&0&0\\0&0&r^{2}&0\\0&0&0&r^{2}\sin ^{2}\theta \end{bmatrix}}\,.} + + +Several other systems of coordinates have been devised for the Schwarzschild metric: Eddington–Finkelstein coordinates, Gullstrand–Painlevé coordinates, Kruskal–Szekeres coordinates, and Lemaître coordinates. + +==== Rotating and charged black holes ==== +The Schwarzschild solution supposes an object that is not rotating in space and is not charged. To account for charge, the metric must satisfy the Einstein field equations like before, as well as Maxwell's equations in a curved spacetime. A charged, non-rotating mass is described by the Reissner–Nordström metric. +Rotating black holes are described by the Kerr metric (uncharged) and the Kerr–Newman metric (charged). + +=== Other metrics === + +Other notable metrics are: + +Alcubierre metric, +de Sitter/anti-de Sitter metrics, +Friedmann–Lemaître–Robertson–Walker metric, +Isotropic coordinates, +Lemaître–Tolman metric, +Peres metric, +Rindler coordinates, +Weyl–Lewis–Papapetrou coordinates, +Gödel metric. +Some of them are without the event horizon or can be without the gravitational singularity. + +== Volume == +The metric g induces a natural volume form (up to a sign), which can be used to integrate over a region of a manifold. Given local coordinates + + + + + x + + μ + + + + + {\displaystyle x^{\mu }} + + for the manifold, the volume form can be written + + + + + + + v + o + l + + + g + + + = + ± + + + + | + + det + ( + + g + + μ + ν + + + ) + + | + + + + + d + + x + + 0 + + + ∧ + d + + x + + 1 + + + ∧ + d + + x + + 2 + + + ∧ + d + + x + + 3 + + + + + {\displaystyle \mathrm {vol} _{g}=\pm {\sqrt {\left|\det(g_{\mu \nu })\right|}}\,dx^{0}\wedge dx^{1}\wedge dx^{2}\wedge dx^{3}} + + +where + + + + det + ( + + g + + μ + ν + + + ) + + + {\displaystyle \det(g_{\mu \nu })} + + is the determinant of the matrix of components of the metric tensor for the given coordinate system. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Metric_tensor_(general_relativity)-2.md b/data/en.wikipedia.org/wiki/Metric_tensor_(general_relativity)-2.md new file mode 100644 index 000000000..2fa644a3e --- /dev/null +++ b/data/en.wikipedia.org/wiki/Metric_tensor_(general_relativity)-2.md @@ -0,0 +1,519 @@ +--- +title: "Metric tensor (general relativity)" +chunk: 3/3 +source: "https://en.wikipedia.org/wiki/Metric_tensor_(general_relativity)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:08.849054+00:00" +instance: "kb-cron" +--- + +== Curvature == +The metric + + + + g + + + {\displaystyle g} + + completely determines the curvature of spacetime. According to the fundamental theorem of Riemannian geometry, there is a unique connection ∇ on any semi-Riemannian manifold that is compatible with the metric and torsion-free. This connection is called the Levi-Civita connection. The Christoffel symbols of this connection are given in terms of partial derivatives of the metric in local coordinates + + + + + x + + μ + + + + + {\displaystyle x^{\mu }} + + by the formula + + + + + + Γ + + λ + + + + + + + + μ + ν + + + = + + + 1 + 2 + + + + g + + λ + ρ + + + + ( + + + + + ∂ + + g + + ρ + μ + + + + + ∂ + + x + + ν + + + + + + + + + + + ∂ + + g + + ρ + ν + + + + + ∂ + + x + + μ + + + + + + − + + + + ∂ + + g + + μ + ν + + + + + ∂ + + x + + ρ + + + + + + + ) + + = + + + 1 + 2 + + + + g + + λ + ρ + + + + ( + + + g + + ρ + μ + , + ν + + + + + + g + + ρ + ν + , + μ + + + − + + g + + μ + ν + , + ρ + + + + ) + + + + {\displaystyle \Gamma ^{\lambda }{}_{\mu \nu }={\frac {1}{2}}g^{\lambda \rho }\left({\frac {\partial g_{\rho \mu }}{\partial x^{\nu }}}+{\frac {\partial g_{\rho \nu }}{\partial x^{\mu }}}-{\frac {\partial g_{\mu \nu }}{\partial x^{\rho }}}\right)={\frac {1}{2}}g^{\lambda \rho }\left(g_{\rho \mu ,\nu }+g_{\rho \nu ,\mu }-g_{\mu \nu ,\rho }\right)} + + +(where commas indicate partial derivatives). +The curvature of spacetime is then given by the Riemann curvature tensor which is defined in terms of the Levi-Civita connection ∇. In local coordinates this tensor is given by: + + + + + + + + R + + ρ + + + + + σ + μ + ν + + + = + + ∂ + + μ + + + + Γ + + ρ + + + + + + + + ν + σ + + + − + + ∂ + + ν + + + + Γ + + ρ + + + + + + + + μ + σ + + + + + + Γ + + ρ + + + + + + + + μ + λ + + + + Γ + + λ + + + + + + + + ν + σ + + + − + + Γ + + ρ + + + + + + + + ν + λ + + + + Γ + + λ + + + + + + + + μ + σ + + + . + + + {\displaystyle {R^{\rho }}_{\sigma \mu \nu }=\partial _{\mu }\Gamma ^{\rho }{}_{\nu \sigma }-\partial _{\nu }\Gamma ^{\rho }{}_{\mu \sigma }+\Gamma ^{\rho }{}_{\mu \lambda }\Gamma ^{\lambda }{}_{\nu \sigma }-\Gamma ^{\rho }{}_{\nu \lambda }\Gamma ^{\lambda }{}_{\mu \sigma }.} + + +The curvature is then expressible purely in terms of the metric + + + + g + + + {\displaystyle g} + + and its derivatives. + +== Einstein's equations == +One of the core ideas of general relativity is that the metric (and the associated geometry of spacetime) is determined by the matter and energy content of spacetime. Einstein's field equations: + + + + + + R + + μ + ν + + + − + + + 1 + 2 + + + R + + g + + μ + ν + + + = + + + + 8 + π + G + + + c + + 4 + + + + + + + T + + μ + ν + + + + + {\displaystyle R_{\mu \nu }-{\frac {1}{2}}Rg_{\mu \nu }={\frac {8\pi G}{c^{4}}}\,T_{\mu \nu }} + + +where the Ricci curvature tensor + + + + + + R + + ν + ρ + + + + + + + + = + + + + d + e + f + + + + + + + + + + R + + μ + + + + + ν + μ + ρ + + + + + {\displaystyle R_{\nu \rho }\ {\stackrel {\mathrm {def} }{=}}\ {R^{\mu }}_{\nu \mu \rho }} + + +and the scalar curvature + + + + + R + + + + + + = + + + + d + e + f + + + + + + + + g + + μ + ν + + + + R + + μ + ν + + + + + {\displaystyle R\ {\stackrel {\mathrm {def} }{=}}\ g^{\mu \nu }R_{\mu \nu }} + + +relate the metric (and the associated curvature tensors) to the stress–energy tensor + + + + + T + + μ + ν + + + + + {\displaystyle T_{\mu \nu }} + +. This tensor equation is a complicated set of nonlinear partial differential equations for the metric components. Exact solutions of Einstein's field equations are very difficult to find. + +== See also == +Alternatives to general relativity +Introduction to the mathematics of general relativity +Mathematics of general relativity +Ricci calculus + +== References == + +See general relativity resources for a list of references. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Nancy_Millis_Medal_for_Women_in_Science-0.md b/data/en.wikipedia.org/wiki/Nancy_Millis_Medal_for_Women_in_Science-0.md new file mode 100644 index 000000000..87c886b30 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Nancy_Millis_Medal_for_Women_in_Science-0.md @@ -0,0 +1,35 @@ +--- +title: "Nancy Millis Medal for Women in Science" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Nancy_Millis_Medal_for_Women_in_Science" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:59.803463+00:00" +instance: "kb-cron" +--- + +The Nancy Millis Medal for Women in Science, also known as the Nancy Millis Medal, is an annual award conferred by the Australian Academy of Science. It is named in honour of the microbiologist Nancy Millis (1922–2012) and recognises women scientists, with eight to 15 years' experience after completing their PhD, for their outstanding contribution to research and leadership. + + +== Winners == +The medal was first awarded in 2014 and annually since: + +2014: Emma Johnston +2015: Tamara Davis +2016: Elena Belousova +2017: Kerrie Ann Wilson +2018: Marie-Liesse Asselin-Labat +2019: Jacqueline Batley +2020: Kate Schroder and Nicole Bell +2021: Angela Moles and Cathryn Trott +2022: Vanessa Peterson +2023: Renae Ryan +2024: Anita Ho-Baillie +2025: Natasha Hurley-Walker + + +== References == + + +== External links == +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Noether_Lecture-0.md b/data/en.wikipedia.org/wiki/Noether_Lecture-0.md new file mode 100644 index 000000000..df5004461 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Noether_Lecture-0.md @@ -0,0 +1,33 @@ +--- +title: "Noether Lecture" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Noether_Lecture" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:00.975014+00:00" +instance: "kb-cron" +--- + +The Noether Lecture is a distinguished lecture series that honors women "who have made fundamental and sustained contributions to the mathematical sciences". The Association for Women in Mathematics (AWM) established the annual lectures in 1980 as the Emmy Noether Lectures, in honor of one of the leading mathematicians of her time. In 2013 it was renamed the AWM-AMS Noether Lecture and since 2015 is sponsored jointly with the American Mathematical Society (AMS). The recipient delivers the lecture at the yearly American Joint Mathematics Meetings held in January. +The ICM Emmy Noether Lecture is an additional lecture series, sponsored by the International Mathematical Union. Beginning in 1994 this lecture was delivered at the International Congress of Mathematicians, held every four years. In 2010 the lecture series was made permanent. +The 2021 Noether Lecture was supposed to have been given by Andrea Bertozzi of UCLA, but it was cancelled. The cancellation was made during the George Floyd protests: "This decision comes as many of this nation rise up in protest over racial discrimination and brutality by police". Although she intended to speak on other topics, Bertozzi is known for research on the mathematics of policing, and in a letter to the AMS, Sol Garfunkel concluded that "the reason for her exclusion was one of her areas of research". In an official blog of the AMS, a group calling themselves The Just Mathematics Collective called for a boycott of mathematical collaborations with police, dismissing Garfunkel's letter as "intended to further dismiss the boycott" and celebrating the cancellation of Bertozzi's lecture. + + +== Noether Lecturer == + + +== ICM Emmy Noether Lecturers == + + +== See also == +Falconer Lecture +Kovalevsky Lecture +List of mathematics awards +List of things named after Emmy Noether + + +== References == + + +== External links == +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/OWSD-Elsevier_Foundation_Award-0.md b/data/en.wikipedia.org/wiki/OWSD-Elsevier_Foundation_Award-0.md index 985491004..c66d914ed 100644 --- a/data/en.wikipedia.org/wiki/OWSD-Elsevier_Foundation_Award-0.md +++ b/data/en.wikipedia.org/wiki/OWSD-Elsevier_Foundation_Award-0.md @@ -4,7 +4,7 @@ chunk: 1/1 source: "https://en.wikipedia.org/wiki/OWSD-Elsevier_Foundation_Award" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T06:48:59.638426+00:00" +date_saved: "2026-05-05T11:16:02.233826+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Pearl_Meister_Greengard_Prize-0.md b/data/en.wikipedia.org/wiki/Pearl_Meister_Greengard_Prize-0.md new file mode 100644 index 000000000..91fbda074 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Pearl_Meister_Greengard_Prize-0.md @@ -0,0 +1,58 @@ +--- +title: "Pearl Meister Greengard Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Pearl_Meister_Greengard_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:55.141343+00:00" +instance: "kb-cron" +--- + +The Pearl Meister Greengard Prize is an award for women scientists in biology given annually by the Rockefeller University. +The Prize was founded by Nobel laureate Paul Greengard and his wife Ursula von Rydingsvard in honor of Greengard's mother, Pearl Meister Greengard, who died giving birth to him. Greengard began funding the award in 1998. Greengard donated the full share of his 2000 Nobel Prize to the fund, and was able to use his new publicity to attract additional funding for the award, which was launched in 2004. The award is meant to shine a spotlight on exceptional female scientists, since, as Greengard observed, "[women] are not yet receiving awards and honors at a level commensurate with their achievements." +The award includes a $100,000 honorarium (previously $50,000). +Three recipients of the Prize, Carol Greider, Elizabeth Blackburn and Katalin Karikó, have gone on to receive the Nobel Prize in Physiology or Medicine. One recipient, Jennifer Doudna, received the Nobel Prize in Chemistry. + + +== Winners == +Source: Rockefeller University Archived August 12, 2017, at the Wayback Machine + +Nicole Marthe Le Douarin (2004) +Philippa Marrack (2005) +Mary Frances Lyon (2006) +Gail R. Martin, Beatrice Mintz, Elizabeth Robertson (2007) +Elizabeth Blackburn, Carol Greider, Vicki Lundblad (2008) +Suzanne Cory (2009) +Janet Rowley and Mary-Claire King (2010) +Brenda Milner (2011) +Joan Steitz (2012) +Huda Y. Zoghbi (2013) +Lucy Shapiro (2014) +Helen Hobbs (2015) +Bonnie Bassler (2016) +JoAnne Stubbe (2017) +Jennifer Doudna (2018) +Xiaowei Zhuang (2019) +Joanne Chory (2020) +Pamela Björkman (2021) +Katalin Karikó (2022) +Lily Jan, Eve Marder (2023) +Svetlana Mojsov (2024) +Maria Jasin (2025) + + +== See also == +List of prizes, medals, and awards for women in science +List of biology awards + + +== References == + + +== External links == +Pearl Meister Greengard Prize Website, The Rockefeller University +The Man Who Loves Women Who Love Science, The Huffington Post, November 3, 2011 +Three Share Nobel Prize in Medicine for Studies of the Brain, The New York Times, October 10, 2000 +Spending the Nobel Prize Archived March 16, 2012, at the Wayback Machine, The Scientist, September 29, 2006 +How Nobel Winners Spend Their Prize Money, Time Magazine, October 10, 2008 +How One Nobel Laureate Gave Another A Hand, CBS Evening News, December 6, 2009 \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Present-0.md b/data/en.wikipedia.org/wiki/Present-0.md new file mode 100644 index 000000000..ed76637d0 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Present-0.md @@ -0,0 +1,80 @@ +--- +title: "Present" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Present" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:40.578384+00:00" +instance: "kb-cron" +--- + +The present is the period of time that is occurring right now. The present is in contrast to the past, the period of time that has already occurred; and the future, the period of time that has yet to occur. +It is sometimes represented as a hyperplane in space-time, typically called "now", although modern physics demonstrates that such a hyperplane cannot be defined uniquely for observers in relative motion. The present may also be viewed as a duration. + + +== Historiography == +Contemporary history describes the historical timeframe immediately relevant to the present time and is a certain perspective of modern history. + + +== Philosophy and religion == + + +=== Philosophy of time === + +"The present" raises the question: "How is it that all sentient beings experience now at the same time?" There is no logical reason why this should be the case and no easy answer to the question. + + +=== In Buddhism === +Buddhism and many of its associated paradigms emphasize the importance of living in the present moment—being fully aware of what is happening, and not dwelling on the past or worrying about the future. This does not mean that they encourage hedonism, but merely that constant focus on one's current position in space and time (rather than future considerations, or past reminiscence) will aid one in relieving suffering. They teach that those who live in the present moment are the happiest. A number of meditative techniques aim to help the practiser live in the present moment. + + +=== Christianity and eternity === +Christianity views God as being outside of time and, from the divine perspective past, present and future are actualized in the now of eternity. This trans-temporal conception of God has been proposed as a solution to the problem of divine foreknowledge (i.e. how can God know what we will do in the future without us being determined to do it) since at least Boethius. Thomas Aquinas offers the metaphor of a watchman, representing God, standing on a height looking down on a valley to a road where past, present and future, represented by the individuals and their actions strung out along its length, are all visible simultaneously to God. Therefore, God's knowledge is not tied to any particular date. + + +== Physical science == + + +=== Special relativity === + The original intent of the accompanying light cones diagram was to portray a 3-dimensional object having access to the past, present, and future in the present moment (4th dimension). +It follows from Albert Einstein's Special Theory of Relativity that there is no such thing as absolute simultaneity. When care is taken to operationalise "the present", it follows that the events that can be labeled as "simultaneous" with a given event, can not be in direct cause-effect relationship. Such collections of events are perceived differently by different observers. Instead, when focusing on "now" as the events perceived directly, not as a recollection or a speculation, for a given observer "now" takes the form of the observer's past light cone. The light cone of a given event is objectively defined as the collection of events in causal relationship to that event, but each event has a different associated light cone. One has to conclude that in relativistic models of physics there is no place for "the present" as an absolute element of reality, and only refers to things that are close to us. Einstein phrased this as: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion". + + +=== Cosmology === + +In physical cosmology, the present time in the chronology of the universe is estimated at 13.8 billion years after the singularity determining the arrow of time. +In terms of the cosmic expansion history, it is in the dark-energy-dominated era, after the universe's matter content has become diluted enough for dark energy to dominate the total energy density. It is also in the universe's Stelliferous Era, after enough time for superclusters to have formed (at about 5 billion years), but before the accelerating expansion of the universe has removed the local supercluster beyond the cosmological horizon (at about 150 billion years). + + +=== Archaeology, geology, etc. === +In radiocarbon dating, the "present" is defined as AD 1950. + + +== Grammar == +In English grammar, actions are classified according to one of the following twelve verb tenses: past (past, past continuous, past perfect, or past perfect continuous), present (present, present continuous, present perfect, or present perfect continuous), or future (future, future continuous, future perfect, or future perfect continuous). The present tense refers to things that are currently happening or are always the case. For example, in the sentence, "she walks home every day," the verb "walks" is in the present tense because it refers to an action that is regularly occurring in the present circumstances. +Verbs in the present continuous tense indicate actions that are currently happening and will continue for a period of time. In the sentence, "she is walking home," the verb phrase "is walking" is in the present continuous tense because it refers to a current action that will continue until a certain endpoint (when "she" reaches home). Verbs in the present perfect tense indicate actions that started in the past and is completed at the time of speaking. For example, in the sentence, "She has walked home," the verb phrase "has walked" is in the present perfect tense because it describes an action that began in the past and is finished as of the current reference to the action. Finally, verbs in the present perfect continuous tense refer to actions that have been continuing up until the current time, thus combining the characteristics of both the continuous and perfect tenses. An example of a present perfect continuous verb phrase can be found in the sentence, "she has been walking this route for a week now," where "has been walking" indicates an action that was happening continuously in the past and continues to happen continuously in the present. + + +== See also == +Arrow of time +Contemporary history +Deixis +Near real-time computing +Observation +Philosophical presentism +Self +Specious present +Time perception + + +== References == + + +=== Bibliography === +Greene, Brian, (2004). The Fabric of the Cosmos: Space, Time, and the Texture of Reality Knopf. ISBN 0-375-41288-3 +Stepath, Katrin, (2006). Gegenwartskonzepte, Würzburg. ISBN 3-8260-3292-6 + + +== External links == + Quotations related to present at Wikiquote +The Experience and Perception of Time \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Problem_of_time-0.md b/data/en.wikipedia.org/wiki/Problem_of_time-0.md index 41dee0ed5..7f291cd6a 100644 --- a/data/en.wikipedia.org/wiki/Problem_of_time-0.md +++ b/data/en.wikipedia.org/wiki/Problem_of_time-0.md @@ -4,7 +4,7 @@ chunk: 1/2 source: "https://en.wikipedia.org/wiki/Problem_of_time" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:06:10.503318+00:00" +date_saved: "2026-05-05T11:14:41.783356+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Problem_of_time-1.md b/data/en.wikipedia.org/wiki/Problem_of_time-1.md index 9b92f0b73..1fbf9c655 100644 --- a/data/en.wikipedia.org/wiki/Problem_of_time-1.md +++ b/data/en.wikipedia.org/wiki/Problem_of_time-1.md @@ -4,7 +4,7 @@ chunk: 2/2 source: "https://en.wikipedia.org/wiki/Problem_of_time" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:06:10.503318+00:00" +date_saved: "2026-05-05T11:14:41.783356+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Proper_time-0.md b/data/en.wikipedia.org/wiki/Proper_time-0.md new file mode 100644 index 000000000..11e0e84db --- /dev/null +++ b/data/en.wikipedia.org/wiki/Proper_time-0.md @@ -0,0 +1,514 @@ +--- +title: "Proper time" +chunk: 1/4 +source: "https://en.wikipedia.org/wiki/Proper_time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:10.123733+00:00" +instance: "kb-cron" +--- + +In relativity, proper time along a timelike world line is defined as the time as measured by a clock following that line. The proper time interval between two events on a world line is the change in proper time, which is independent of coordinates, and is a Lorentz scalar. The interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line. +The proper time interval between two events depends not only on the events, but also the world line connecting them, and hence on the motion of the clock between the events. It is expressed as an integral over the world line (analogous to arc length in Euclidean space). An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated (inertial) clock between the same two events. The twin paradox is an example of this effect. + +By convention, proper time is usually represented by the Greek letter τ (tau) to distinguish it from coordinate time represented by t. Coordinate time is the time between two events as measured by an observer using that observer's own method of assigning a time to an event. In the special case of an inertial observer in special relativity, the time is measured using the observer's clock and the observer's definition of simultaneity. +The concept of proper time was introduced by Hermann Minkowski in 1908, and is an important feature of Minkowski diagrams. + +== Mathematical formalism == +The formal definition of proper time involves describing the path through spacetime that represents a clock, observer, or test particle, and the metric structure of that spacetime. Proper time is the pseudo-Riemannian arc length of world lines in four-dimensional spacetime. From the mathematical point of view, coordinate time is assumed to be predefined and an expression for proper time as a function of coordinate time is required. On the other hand, proper time is measured experimentally and coordinate time is calculated from the proper time of inertial clocks. +Proper time can only be defined for timelike paths through spacetime which allow for the construction of an accompanying set of physical rulers and clocks. The same formalism for spacelike paths leads to a measurement of proper distance rather than proper time. For lightlike paths, there exists no concept of proper time and it is undefined as the spacetime interval is zero. Instead, an arbitrary and physically irrelevant affine parameter unrelated to time must be introduced. + +=== In special relativity === +With the timelike convention for the metric signature, the Minkowski metric is defined by + + + + + + η + + μ + ν + + + = + + + ( + + + + 1 + + + 0 + + + 0 + + + 0 + + + + + 0 + + + − + 1 + + + 0 + + + 0 + + + + + 0 + + + 0 + + + − + 1 + + + 0 + + + + + 0 + + + 0 + + + 0 + + + − + 1 + + + + ) + + + , + + + {\displaystyle \eta _{\mu \nu }={\begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}},} + + +and the coordinates by + + + + + ( + + x + + 0 + + + , + + x + + 1 + + + , + + x + + 2 + + + , + + x + + 3 + + + ) + = + ( + c + t + , + x + , + y + , + z + ) + + + {\displaystyle (x^{0},x^{1},x^{2},x^{3})=(ct,x,y,z)} + + +for arbitrary Lorentz frames. +In any such frame an infinitesimal interval, here assumed timelike, between two events is expressed as + +and separates points on a trajectory of a particle (think clock{?}). The same interval can be expressed in coordinates such that at each moment, the particle is at rest. Such a frame is called an instantaneous rest frame, denoted here by the coordinates + + + + ( + c + τ + , + + x + + τ + + + , + + y + + τ + + + , + + z + + τ + + + ) + + + {\displaystyle (c\tau ,x_{\tau },y_{\tau },z_{\tau })} + + for each instant. Due to the invariance of the interval (instantaneous rest frames taken at different times are related by Lorentz transformations) one may write + + + + + d + + s + + 2 + + + = + + c + + 2 + + + d + + τ + + 2 + + + − + d + + x + + τ + + + 2 + + + − + d + + y + + τ + + + 2 + + + − + d + + z + + τ + + + 2 + + + = + + c + + 2 + + + d + + τ + + 2 + + + , + + + {\displaystyle ds^{2}=c^{2}d\tau ^{2}-dx_{\tau }^{2}-dy_{\tau }^{2}-dz_{\tau }^{2}=c^{2}d\tau ^{2},} + + +since in the instantaneous rest frame, the particle or the frame itself is at rest, i.e., + + + + d + + x + + τ + + + = + d + + y + + τ + + + = + d + + z + + τ + + + = + 0 + + + {\displaystyle dx_{\tau }=dy_{\tau }=dz_{\tau }=0} + +. Since the interval is assumed timelike (ie. + + + + d + + s + + 2 + + + > + 0 + + + {\displaystyle ds^{2}>0} + +), taking the square root of the above yields + + + + + d + s + = + c + d + τ + , + + + {\displaystyle ds=cd\tau ,} + + +or + + + + + d + τ + = + + + + d + s + + c + + + . + + + {\displaystyle d\tau ={\frac {ds}{c}}.} + + +Given this differential expression for τ, the proper time interval is defined as + +Here P is the worldline from some initial event to some final event with the ordering of the events fixed by the requirement that the final event occurs later according to the clock than the initial event. +Using (1) and again the invariance of the interval, one may write + +where + + + + + ( + + x + + 0 + + + , + + x + + 1 + + + , + + x + + 2 + + + , + + x + + 3 + + + ) + : + [ + a + , + b + ] + → + P + + + {\displaystyle (x^{0},x^{1},x^{2},x^{3}):[a,b]\rightarrow P} + + +is an arbitrary bijective parametrization of the worldline P +such that + + + + + ( + + x + + 0 + + + ( + a + ) + , + + x + + 1 + + + ( + a + ) + , + + x + + 2 + + + ( + a + ) + , + + x + + 3 + + + ( + a + ) + ) + + + and + + + ( + + x + + 0 + + + ( + b + ) + , + + x + + 1 + + + ( + b + ) + , + + x + + 2 + + + ( + b + ) + , + + x + + 3 + + + ( + b + ) + ) + + + {\displaystyle (x^{0}(a),x^{1}(a),x^{2}(a),x^{3}(a))\quad {\text{and}}\quad (x^{0}(b),x^{1}(b),x^{2}(b),x^{3}(b))} + + +give the endpoints of P and a < b; v(t) is the coordinate speed at coordinate time t; and x(t), y(t), and z(t) are space coordinates. The first expression is manifestly Lorentz invariant. They are all Lorentz invariant, since proper time and proper time intervals are coordinate-independent by definition. +If t, x, y, z, are parameterised by a parameter λ, this can be written as \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Proper_time-1.md b/data/en.wikipedia.org/wiki/Proper_time-1.md new file mode 100644 index 000000000..fb6d47611 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Proper_time-1.md @@ -0,0 +1,846 @@ +--- +title: "Proper time" +chunk: 2/4 +source: "https://en.wikipedia.org/wiki/Proper_time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:10.123733+00:00" +instance: "kb-cron" +--- + + + + + Δ + τ + = + ∫ + + + + + ( + + + + d + t + + + d + λ + + + + ) + + + 2 + + + − + + + 1 + + c + + 2 + + + + + + [ + + + + ( + + + + d + x + + + d + λ + + + + ) + + + 2 + + + + + + + ( + + + + d + y + + + d + λ + + + + ) + + + 2 + + + + + + + ( + + + + d + z + + + d + λ + + + + ) + + + 2 + + + + ] + + + + + d + λ + . + + + {\displaystyle \Delta \tau =\int {\sqrt {\left({\frac {dt}{d\lambda }}\right)^{2}-{\frac {1}{c^{2}}}\left[\left({\frac {dx}{d\lambda }}\right)^{2}+\left({\frac {dy}{d\lambda }}\right)^{2}+\left({\frac {dz}{d\lambda }}\right)^{2}\right]}}\,d\lambda .} + + +If the motion of the particle is constant, the expression simplifies to + + + + + Δ + τ + = + + + + + ( + + Δ + t + + ) + + + 2 + + + − + + + + + ( + + Δ + x + + ) + + + 2 + + + + c + + 2 + + + + + − + + + + + ( + + Δ + y + + ) + + + 2 + + + + c + + 2 + + + + + − + + + + + ( + + Δ + z + + ) + + + 2 + + + + c + + 2 + + + + + + + , + + + {\displaystyle \Delta \tau ={\sqrt {\left(\Delta t\right)^{2}-{\frac {\left(\Delta x\right)^{2}}{c^{2}}}-{\frac {\left(\Delta y\right)^{2}}{c^{2}}}-{\frac {\left(\Delta z\right)^{2}}{c^{2}}}}},} + + +where Δ means the change in coordinates between the initial and final events. The definition in special relativity generalizes straightforwardly to general relativity as follows below. + +=== In general relativity === +Proper time is defined in general relativity as follows: Given a pseudo-Riemannian manifold with a local coordinates xμ and equipped with a metric tensor gμν, the proper time interval Δτ between two events along a timelike path P is given by the line integral + +This expression is, as it should be, invariant under coordinate changes. It reduces (in appropriate coordinates) to the expression of special relativity in flat spacetime. +In the same way that coordinates can be chosen such that x1, x2, x3 = const in special relativity, this can be done in general relativity too. Then, in these coordinates, + + + + + Δ + τ + = + + ∫ + + P + + + d + τ + = + + ∫ + + P + + + + + 1 + c + + + + + + g + + 00 + + + + + d + + x + + 0 + + + . + + + {\displaystyle \Delta \tau =\int _{P}d\tau =\int _{P}{\frac {1}{c}}{\sqrt {g_{00}}}dx^{0}.} + + +This expression generalizes definition (2) and can be taken as the definition. Then using invariance of the interval, equation (4) follows from it in the same way (3) follows from (2), except that here arbitrary coordinate changes are allowed. + +== Examples in special relativity == + +=== Example 1: The twin paradox === +For a twin paradox scenario, let there be an observer A who moves between the A-coordinates (0,0,0,0) and (10 years, 0, 0, 0) inertially. This means that A stays at + + + + x + = + y + = + z + = + 0 + + + {\displaystyle x=y=z=0} + + for 10 years of A-coordinate time. The proper time interval for A between the two events is then + + + + + Δ + + τ + + A + + + = + + + ( + 10 + + years + + + ) + + 2 + + + + + = + 10 + + years + + . + + + {\displaystyle \Delta \tau _{A}={\sqrt {(10{\text{ years}})^{2}}}=10{\text{ years}}.} + + +So being "at rest" in a special relativity coordinate system means that proper time and coordinate time are the same. +Let there now be another observer B who travels in the x direction from (0,0,0,0) for 5 years of A-coordinate time at 0.866c to (5 years, 4.33 light-years, 0, 0). Once there, B accelerates, and travels in the other spatial direction for another 5 years of A-coordinate time to (10 years, 0, 0, 0). For each leg of the trip, the proper time interval can be calculated using A-coordinates, and is given by + + + + + Δ + + τ + + l + e + g + + + = + + + ( + + 5 years + + + ) + + 2 + + + − + ( + + 4.33 years + + + ) + + 2 + + + + + = + + + 6.25 + + + + y + e + a + r + s + + + 2 + + + + + = + + 2.5 years + + . + + + {\displaystyle \Delta \tau _{leg}={\sqrt {({\text{5 years}})^{2}-({\text{4.33 years}})^{2}}}={\sqrt {6.25\;\mathrm {years} ^{2}}}={\text{2.5 years}}.} + + +So the total proper time for observer B to go from (0,0,0,0) to (5 years, 4.33 light-years, 0, 0) and then to (10 years, 0, 0, 0) is + + + + + Δ + + τ + + B + + + = + 2 + Δ + + τ + + l + e + g + + + = + + 5 years + + . + + + {\displaystyle \Delta \tau _{B}=2\Delta \tau _{leg}={\text{5 years}}.} + + +Thus it is shown that the proper time equation incorporates the time dilation effect. In fact, for an object in a SR (special relativity) spacetime traveling with velocity + + + + v + + + {\displaystyle v} + + for a time + + + + Δ + T + + + {\displaystyle \Delta T} + +, the proper time interval experienced is + + + + + Δ + τ + = + + + Δ + + T + + 2 + + + − + + + ( + + + + + v + + x + + + Δ + T + + c + + + ) + + + 2 + + + − + + + ( + + + + + v + + y + + + Δ + T + + c + + + ) + + + 2 + + + − + + + ( + + + + + v + + z + + + Δ + T + + c + + + ) + + + 2 + + + + + = + Δ + T + + + 1 + − + + + + v + + 2 + + + + c + + 2 + + + + + + + , + + + {\displaystyle \Delta \tau ={\sqrt {\Delta T^{2}-\left({\frac {v_{x}\Delta T}{c}}\right)^{2}-\left({\frac {v_{y}\Delta T}{c}}\right)^{2}-\left({\frac {v_{z}\Delta T}{c}}\right)^{2}}}=\Delta T{\sqrt {1-{\frac {v^{2}}{c^{2}}}}},} + + +which is the SR time dilation formula. + +=== Example 2: The rotating disk === +An observer rotating around another inertial observer is in an accelerated frame of reference. For such an observer, the incremental ( + + + + d + τ + + + {\displaystyle d\tau } + +) form of the proper time equation is needed, along with a parameterized description of the path being taken, as shown below. +Let there be an observer C on a disk rotating in the xy plane at a coordinate angular rate of + + + + ω + + + {\displaystyle \omega } + + and who is at a distance of r from the center of the disk with the center of the disk at x = y = z = 0. The path of observer C is given by + + + + ( + T + , + + r + cos + ⁡ + ( + ω + T + ) + , + + r + sin + ⁡ + ( + ω + T + ) + , + + 0 + ) + + + {\displaystyle (T,\,r\cos(\omega T),\,r\sin(\omega T),\,0)} + +, where + + + + T + + + {\displaystyle T} + + is the current coordinate time. When r and + + + + ω + + + {\displaystyle \omega } + + are constant, + + + + d + x + = + − + r + ω + sin + ⁡ + ( + ω + T + ) + + d + T + + + {\displaystyle dx=-r\omega \sin(\omega T)\,dT} + + and + + + + d + y + = + r + ω + cos + ⁡ + ( + ω + T + ) + + d + T + + + {\displaystyle dy=r\omega \cos(\omega T)\,dT} + +. The incremental proper time formula then becomes + + + + + d + τ + = + + + d + + T + + 2 + + + − + + + ( + + + + r + ω + + c + + + ) + + + 2 + + + + sin + + 2 + + + ⁡ + ( + ω + T + ) + + d + + T + + 2 + + + − + + + ( + + + + r + ω + + c + + + ) + + + 2 + + + + cos + + 2 + + + ⁡ + ( + ω + T + ) + + d + + T + + 2 + + + + + = + d + T + + + 1 + − + + + ( + + + + r + ω + + c + + + ) + + + 2 + + + + + . + + + {\displaystyle d\tau ={\sqrt {dT^{2}-\left({\frac {r\omega }{c}}\right)^{2}\sin ^{2}(\omega T)\;dT^{2}-\left({\frac {r\omega }{c}}\right)^{2}\cos ^{2}(\omega T)\;dT^{2}}}=dT{\sqrt {1-\left({\frac {r\omega }{c}}\right)^{2}}}.} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Proper_time-2.md b/data/en.wikipedia.org/wiki/Proper_time-2.md new file mode 100644 index 000000000..04cc4957a --- /dev/null +++ b/data/en.wikipedia.org/wiki/Proper_time-2.md @@ -0,0 +1,899 @@ +--- +title: "Proper time" +chunk: 3/4 +source: "https://en.wikipedia.org/wiki/Proper_time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:10.123733+00:00" +instance: "kb-cron" +--- + +So for an observer rotating at a constant distance of r from a given point in spacetime at a constant angular rate of ω between coordinate times + + + + + T + + 1 + + + + + {\displaystyle T_{1}} + + and + + + + + T + + 2 + + + + + {\displaystyle T_{2}} + +, the proper time experienced will be + + + + + + ∫ + + + T + + 1 + + + + + + T + + 2 + + + + + d + τ + = + ( + + T + + 2 + + + − + + T + + 1 + + + ) + + + 1 + − + + + ( + + + + r + ω + + c + + + ) + + + 2 + + + + + = + Δ + T + + + 1 + − + + v + + 2 + + + + / + + + c + + 2 + + + + + , + + + {\displaystyle \int _{T_{1}}^{T_{2}}d\tau =(T_{2}-T_{1}){\sqrt {1-\left({\frac {r\omega }{c}}\right)^{2}}}=\Delta T{\sqrt {1-v^{2}/c^{2}}},} + + +as + + + + v + = + r + ω + + + {\displaystyle v=r\omega } + + for a rotating observer. This result is the same as for the linear motion example, and shows the general application of the integral form of the proper time formula. + +== Examples in general relativity == +The difference between SR and general relativity (GR) is that in GR one can use any metric which is a solution of the Einstein field equations, not just the Minkowski metric. Because inertial motion in curved spacetimes lacks the simple expression it has in SR, the line integral form of the proper time equation must always be used. + +=== Example 3: The rotating disk (again) === +An appropriate coordinate conversion done against the Minkowski metric creates coordinates where an object on a rotating disk stays in the same spatial coordinate position. The new coordinates are + + + + + r + = + + + + x + + 2 + + + + + + y + + 2 + + + + + + + {\displaystyle r={\sqrt {x^{2}+y^{2}}}} + + +and + + + + + θ + = + arctan + ⁡ + + ( + + + y + x + + + ) + + − + ω + t + . + + + {\displaystyle \theta =\arctan \left({\frac {y}{x}}\right)-\omega t.} + + +The t and z coordinates remain unchanged. In this new coordinate system, the incremental proper time equation is + + + + + d + τ + = + + + + [ + + 1 + − + + + ( + + + + r + ω + + c + + + ) + + + 2 + + + + ] + + d + + t + + 2 + + + − + + + + d + + r + + 2 + + + + + c + + 2 + + + + + − + + + + + r + + 2 + + + + d + + θ + + 2 + + + + + c + + 2 + + + + + − + + + + d + + z + + 2 + + + + + c + + 2 + + + + + − + 2 + + + + + r + + 2 + + + ω + + d + t + + d + θ + + + c + + 2 + + + + + + + . + + + {\displaystyle d\tau ={\sqrt {\left[1-\left({\frac {r\omega }{c}}\right)^{2}\right]dt^{2}-{\frac {dr^{2}}{c^{2}}}-{\frac {r^{2}\,d\theta ^{2}}{c^{2}}}-{\frac {dz^{2}}{c^{2}}}-2{\frac {r^{2}\omega \,dt\,d\theta }{c^{2}}}}}.} + + +With r, θ, and z being constant over time, this simplifies to + + + + + d + τ + = + d + t + + + 1 + − + + + ( + + + + r + ω + + c + + + ) + + + 2 + + + + + , + + + {\displaystyle d\tau =dt{\sqrt {1-\left({\frac {r\omega }{c}}\right)^{2}}},} + + +which is the same as in Example 2. +Now let there be an object off of the rotating disk and at inertial rest with respect to the center of the disk and at a distance of R from it. This object has a coordinate motion described by dθ = −ω dt, which describes the inertially at-rest object of counter-rotating in the view of the rotating observer. Now the proper time equation becomes + + + + + d + τ + = + + + + [ + + 1 + − + + + ( + + + + R + ω + + c + + + ) + + + 2 + + + + ] + + d + + t + + 2 + + + − + + + ( + + + + R + ω + + c + + + ) + + + 2 + + + + d + + t + + 2 + + + + + 2 + + + ( + + + + R + ω + + c + + + ) + + + 2 + + + + d + + t + + 2 + + + + + = + d + t + . + + + {\displaystyle d\tau ={\sqrt {\left[1-\left({\frac {R\omega }{c}}\right)^{2}\right]dt^{2}-\left({\frac {R\omega }{c}}\right)^{2}\,dt^{2}+2\left({\frac {R\omega }{c}}\right)^{2}\,dt^{2}}}=dt.} + + +So for the inertial at-rest observer, coordinate time and proper time are once again found to pass at the same rate, as expected and required for the internal self-consistency of relativity theory. + +=== Example 4: The Schwarzschild solution – time on the Earth === +The Schwarzschild solution has an incremental proper time equation of + + + + + d + τ + = + + + + ( + + 1 + − + + + + 2 + m + + r + + + + ) + + d + + t + + 2 + + + − + + + 1 + + c + + 2 + + + + + + + ( + + 1 + − + + + + 2 + m + + r + + + + ) + + + − + 1 + + + d + + r + + 2 + + + − + + + + r + + 2 + + + + c + + 2 + + + + + d + + ϕ + + 2 + + + − + + + + r + + 2 + + + + c + + 2 + + + + + + sin + + 2 + + + ⁡ + ( + ϕ + ) + + d + + θ + + 2 + + + + + , + + + {\displaystyle d\tau ={\sqrt {\left(1-{\frac {2m}{r}}\right)dt^{2}-{\frac {1}{c^{2}}}\left(1-{\frac {2m}{r}}\right)^{-1}dr^{2}-{\frac {r^{2}}{c^{2}}}d\phi ^{2}-{\frac {r^{2}}{c^{2}}}\sin ^{2}(\phi )\,d\theta ^{2}}},} + + +where + +t is time as calibrated with a clock distant from and at inertial rest with respect to the Earth, +r is a radial coordinate (which is effectively the distance from the Earth's center), +ɸ is a co-latitudinal coordinate, the angular separation from the North Pole in radians. +θ is a longitudinal coordinate, analogous to the longitude on the Earth's surface but independent of the Earth's rotation. This is also given in radians. +m is the geometrized mass of the Earth, m = GM/c2, +M is the mass of the Earth, +G is the gravitational constant. +To demonstrate the use of the proper time relationship, several sub-examples involving the Earth will be used here. +For the Earth, M = 5.9742×1024 kg, meaning that m = 4.4354×10−3 m. When standing on the North Pole, we can assume + + + + d + r + = + d + θ + = + d + ϕ + = + 0 + + + {\displaystyle dr=d\theta =d\phi =0} + + (meaning that we are neither moving up or down or along the surface of the Earth). In this case, the Schwarzschild solution proper time equation becomes + + + + d + τ + = + d + t + + + + 1 + − + 2 + m + + / + + r + + + + + {\textstyle d\tau =dt\,{\sqrt {1-2m/r}}} + +. Then using the polar radius of the Earth as the radial coordinate (or + + + + r + = + + 6,356,752 metres + + + + {\displaystyle r={\text{6,356,752 metres}}} + +), we find that + + + + + d + τ + = + + + + ( + + 1 + − + 1.3908 + × + + 10 + + − + 9 + + + + ) + + + d + + t + + 2 + + + + + = + + ( + + 1 + − + 6.9540 + × + + 10 + + − + 10 + + + + ) + + + d + t + . + + + {\displaystyle d\tau ={\sqrt {\left(1-1.3908\times 10^{-9}\right)\;dt^{2}}}=\left(1-6.9540\times 10^{-10}\right)\,dt.} + + +At the equator, the radius of the Earth is r = 6378137 m. In addition, the rotation of the Earth needs to be taken into account. This imparts on an observer an angular velocity of + + + + d + θ + + / + + d + t + + + {\displaystyle d\theta /dt} + + of 2π divided by the sidereal period of the Earth's rotation, 86162.4 seconds. So + + + + d + θ + = + 7.2923 + × + + 10 + + − + 5 + + + + d + t + + + {\displaystyle d\theta =7.2923\times 10^{-5}\,dt} + +. The proper time equation then produces + + + + + d + τ + = + + + + ( + + 1 + − + 1.3908 + × + + 10 + + − + 9 + + + + ) + + d + + t + + 2 + + + − + 2.4069 + × + + 10 + + − + 12 + + + + d + + t + + 2 + + + + + = + + ( + + 1 + − + 6.9660 + × + + 10 + + − + 10 + + + + ) + + + d + t + . + + + {\displaystyle d\tau ={\sqrt {\left(1-1.3908\times 10^{-9}\right)dt^{2}-2.4069\times 10^{-12}\,dt^{2}}}=\left(1-6.9660\times 10^{-10}\right)\,dt.} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Proper_time-3.md b/data/en.wikipedia.org/wiki/Proper_time-3.md new file mode 100644 index 000000000..2425947ba --- /dev/null +++ b/data/en.wikipedia.org/wiki/Proper_time-3.md @@ -0,0 +1,36 @@ +--- +title: "Proper time" +chunk: 4/4 +source: "https://en.wikipedia.org/wiki/Proper_time" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:10.123733+00:00" +instance: "kb-cron" +--- + +From a non-relativistic point of view this should have been the same as the previous result. This example demonstrates how the proper time equation is used, even though the Earth rotates and hence is not spherically symmetric as assumed by the Schwarzschild solution. To describe the effects of rotation more accurately the Kerr metric may be used. + +== See also == +Lorentz transformation +Minkowski space +Proper length +Proper acceleration +Proper mass +Proper velocity +Clock hypothesis +Peres metric + +== Footnotes == + +== References == +Cook, R. J. (2004). "Physical time and physical space in general relativity". Am. J. Phys. 72 (2): 214–219. Bibcode:2004AmJPh..72..214C. doi:10.1119/1.1607338. ISSN 0002-9505. +Foster, J.; Nightingale, J.D. (1978). A short course in general relativity. Essex: Longman Scientific and Technical. ISBN 0-582-44194-3. +Kleppner, D.; Kolenkow, R.J. (1978). An introduction to mechanics. McGraw–Hill. ISBN 0-07-035048-5. +Kopeikin, Sergei; Efroimsky, Michael; Kaplan, George (2011). Relativistic Celestial Mechanics of the Solar System. John Wiley & Sons. ISBN 978-3-527-40856-6. +Landau, L. D.; Lifshitz, E. M. (1975). The classical theory of fields. Course of theoretical physics. Vol. 2 (4th ed.). Oxford: Butterworth–Heinemann. ISBN 0-7506-2768-9. +Lawden, Derek F. (2012). An Introduction to Tensor Calculus: Relativity and Cosmology. Courier Corporation. ISBN 978-0-486-13214-3. +Lovelock, David; Rund, Hanno (1989), Tensors, Differential Forms, and Variational Principles, New York: Dover Publications, ISBN 0-486-65840-6 +Minkowski, Hermann (1908), "Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern", Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-August-Universität zu Göttingen, Göttingen{{citation}}: CS1 maint: deprecated archival service (link) +Poisson, Eric (2004), A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics, Cambridge University Press, ISBN 978-0521537803 +Weinberg, Steven (1972), Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, New York: John Wiley & Sons, ISBN 978-0-471-92567-5 +Zwiebach, Barton (2004). A First Course in String Theory (first ed.). Cambridge University Press. ISBN 0-521-83143-1. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Quantum_logic_clock-0.md b/data/en.wikipedia.org/wiki/Quantum_logic_clock-0.md new file mode 100644 index 000000000..7c9954cfd --- /dev/null +++ b/data/en.wikipedia.org/wiki/Quantum_logic_clock-0.md @@ -0,0 +1,41 @@ +--- +title: "Quantum logic clock" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Quantum_logic_clock" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:43.041649+00:00" +instance: "kb-cron" +--- + +A quantum clock is a type of atomic clock with laser cooled single ions confined together in an electromagnetic ion trap. Developed in 2010 by physicists at the U.S. National Institute of Standards and Technology, the clock was 37 times more precise than the then-existing international standard. The quantum logic clock is based on an aluminium spectroscopy ion with a logic atom. +Both the aluminum-based quantum clock and the mercury-based optical atomic clock track time by the ion vibration at an optical frequency using a UV laser, that is 100,000 times higher than the microwave frequencies used in NIST-F1 and other similar time standards around the world. Quantum clocks like this are able to be far more precise than microwave standards. + + +== Accuracy == + +The NIST team are not able to measure clock ticks per second because the definition of a second is based on the standard NIST-F1, which cannot measure a machine more precise than itself. However, the aluminum ion clock's measured frequency to the current standard is 1121015393207857.4(7) Hz. NIST have attributed the clock's accuracy to the fact that it is insensitive to background magnetic and electric fields, and unaffected by temperature. +In March 2008, physicists at NIST described an experimental quantum logic clock based on individual ions of beryllium and aluminum. This clock was compared to NIST's mercury ion clock. These were the most accurate clocks that had been constructed, with neither clock gaining nor losing time at a rate that would exceed a second in over a billion years. +In February 2010, NIST physicists described a second, enhanced version of the quantum logic clock based on individual ions of magnesium and aluminium. Considered the world's most precise clock in 2010 with a fractional frequency inaccuracy of 8.6 × 10−18, it offers more than twice the precision of the original. + +In terms of standard deviation, the quantum logic clock deviates one second every 3.68 billion years, while the then current international standard NIST-F1 Caesium fountain atomic clock uncertainty was about 3.1 × 10−16 expected to neither gain nor lose a second in more than 100 million years. + In July 2019, NIST scientists demonstrated such a clock with total uncertainty of 9.4 × 10−19 (deviates one second every 33.7 billion years), which is the first demonstration of a clock with uncertainty below 10−18. + + +== Quantum time dilation == + +In a 2020 paper scientists illustrated that and how quantum clocks could experience a possibly experimentally testable superposition of proper times via time dilation of the theory of relativity by which time passes slower for one object in relation to another object when the former moves at a higher velocity. In "quantum time dilation" one of the two clocks moves in a superposition of two localized momentum wave packets, resulting in a change to the classical time dilation. + + +== Other accurate experimental clocks == +The accuracy of quantum-logic clocks was briefly superseded by optical lattice clocks based on strontium-87 and ytterbium-171 until 2019. An experimental optical lattice clock was described in a 2014 Nature paper. +In 2015 JILA evaluated the absolute frequency uncertainty of their latest strontium-87 429 THz (429228004229873.0 Hz) +optical lattice clock at 2.1 × 10−18, which corresponds to a measurable gravitational time dilation for an elevation change of 2 cm (0.79 in) on planet Earth that according to JILA/NIST Fellow Jun Ye is "getting really close to being useful for relativistic geodesy". +At this frequency uncertainty, this JILA optical lattice optical clock is expected to neither gain nor lose a second in more than 15 billion years. + + +== See also == +Atomic clock + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Rachel_Carson_Prize_(environmentalist_award)-0.md b/data/en.wikipedia.org/wiki/Rachel_Carson_Prize_(environmentalist_award)-0.md new file mode 100644 index 000000000..ff871aa7a --- /dev/null +++ b/data/en.wikipedia.org/wiki/Rachel_Carson_Prize_(environmentalist_award)-0.md @@ -0,0 +1,46 @@ +--- +title: "Rachel Carson Prize (environmentalist award)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Rachel_Carson_Prize_(environmentalist_award)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:03.522202+00:00" +instance: "kb-cron" +--- + +The Rachel Carson Prize (Rachel Carson-prisen) is an international environmental award, established in Stavanger, Norway in 1991 to commemorate the achievements of environmentalist Rachel Carson and to award efforts in her spirit. The prize is awarded to a woman who has distinguished herself in outstanding work for the environment in Norway or internationally. +The prize was established spontaneously during a 1989 meeting in Stavanger, on the initiative of speaker Berit Ås. The prize consists of money and the sculpture The Cormorant by artist Irma Bruun Hodne. + + +== Awardees == +1991: Sidsel Mørck, Norwegian author and activist +1993: Bergljot Børresen, Norwegian veterinarian +1995: Anne Grieg, Norwegian psychiatrist +1997: Berit Ås, Norwegian feminist and professor in social psychology +1999: Theo Colborn, American zoologist +2001: Renate Künast, German Federal Minister of Consumer Protection, Food and Agriculture +2003: Åshild Dale, Norwegian farmer +2005: Malin Falkenmark, Swedish professor in hydrology +2007: Sheila Watt-Cloutier, Canadian Inuit climate activist +2009: Marie-Monique Robin, French journalist +2011: Marilyn Mehlmann, Swedish environmentalist and writer +2013: Sam Fanshawe, British marine conservationist +2015: Mozhgan Savabieasfahani, Iranian environmental toxicologist +2016: Gabrielle Hecht +2017: Sylvia Earle +2019: Greta Thunberg, Swedish climate activist +2021: Maja Lunde, Norwegian author + + +== See also == + +Women in science +List of prizes, medals, and awards for women in science +List of environmental awards + + +== References == + + +== External links == +Official website (English) \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Relaxation_(physics)-0.md b/data/en.wikipedia.org/wiki/Relaxation_(physics)-0.md index f9b3a9ec3..62bf405b1 100644 --- a/data/en.wikipedia.org/wiki/Relaxation_(physics)-0.md +++ b/data/en.wikipedia.org/wiki/Relaxation_(physics)-0.md @@ -4,7 +4,7 @@ chunk: 1/2 source: "https://en.wikipedia.org/wiki/Relaxation_(physics)" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:13:24.533010+00:00" +date_saved: "2026-05-05T11:15:11.342227+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Relaxation_(physics)-1.md b/data/en.wikipedia.org/wiki/Relaxation_(physics)-1.md index 8d6173431..79c8c4dd6 100644 --- a/data/en.wikipedia.org/wiki/Relaxation_(physics)-1.md +++ b/data/en.wikipedia.org/wiki/Relaxation_(physics)-1.md @@ -4,7 +4,7 @@ chunk: 2/2 source: "https://en.wikipedia.org/wiki/Relaxation_(physics)" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T11:13:24.533010+00:00" +date_saved: "2026-05-05T11:15:11.342227+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Repetition_(Kierkegaard_book)-0.md b/data/en.wikipedia.org/wiki/Repetition_(Kierkegaard_book)-0.md new file mode 100644 index 000000000..a56056d84 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Repetition_(Kierkegaard_book)-0.md @@ -0,0 +1,37 @@ +--- +title: "Repetition (Kierkegaard book)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Repetition_(Kierkegaard_book)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:44.246777+00:00" +instance: "kb-cron" +--- + +Repetition: A Venture in Experimental Psychology (Danish: Gjentagelsen: Et Forsøg i den eksperimenterende Psychologi) is an 1843 book of philosophical fiction by Søren Kierkegaard that is semi-autobiographical. The book was written under the pseudonym Constantin Constantius to reflect its theme of repetition. The book's narrator explores the question of whether true repetition can exist and includes his experiments with this idea and his interactions with an unnamed melancholic character referred to only as the "Young Man". +Kierkegaard published Fear and Trembling, Three Upbuilding Discourses, and Repetition all on the same date, 16 October 1843. While Abraham was the main character in Fear and Trembling, and the Three Upbuilding Discourses were about love, Repetition presents a noticeable contrast between the other two books. + + +== Content == +Kierkegaard used the pseudonym Constantin Constantius in this book, reflecting the theme of Repetition. Constantin is currently conducting experiments into whether repetition is possible. The book includes his experiments and his relation to a nameless patient known only as the Young Man. Every patient must have a problem. +The Young Man has fallen in love with a girl, proposed marriage, the proposal has been accepted, but now he has changed his mind. Constantin becomes the young man's confidant. Coincidentally, the problem that the Young Man had is the same problem Kierkegaard had with Regine Olsen. He had proposed to her, she had accepted but he had changed his mind. Kierkegaard was accused of "experimenting with the affections of his fiancée". + + +== Analysis == +Charles K. Bellinger says Either/Or, Fear and Trembling and Repetition are works of fiction, "novelistic" in character; they focus on the boundaries between different spheres of existence, such as the aesthetic and the ethical, and the ethical and the religious; they often focus on the subject of marriage; they can be traced back to Kierkegaard's relationship with Regine." There is much in this work that is autobiographical in nature. How much is left up to the reader. Kierkegaard explores the conscious choices this Young Man makes. +Kierkegaard said "Seneca has said that when a person has reached his thirtieth year he ought to know his constitution so well that he can be his own physician; I likewise believe that when a person has reached a certain age he ought to be able to be his own pastor. Not as if I would in any way minimize participation in public worship and the guidance given there, but I do think one ought to have one’s view settled with regard to the most important relationships, which, furthermore, one seldom hears preached about in the stricter sense. To devotional books and printed sermons, I have an idiosyncratic aversion, that is why I resort to Scripture when I cannot go to church." In Repetition he followed his own advice and became his own psychologist. + + +== Structure == +Part One: Report by Constantin Constantius +Part Two: Repetition +Letters from the Young Man, August 15 - January 13 +Incidental Observations by Constantin Constantius +Letter From The Young Man, May 31 +Concluding Letter By Constantin Constanius, Copenhagen, August 1843 + + +== Notes == + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Rosalind_Franklin_Award-0.md b/data/en.wikipedia.org/wiki/Rosalind_Franklin_Award-0.md new file mode 100644 index 000000000..891cdc4f8 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Rosalind_Franklin_Award-0.md @@ -0,0 +1,51 @@ +--- +title: "Rosalind Franklin Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Rosalind_Franklin_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:41.962016+00:00" +instance: "kb-cron" +--- + +The Royal Society Rosalind Franklin Award was established in 2003 and is awarded annually by the Royal Society to an individual for outstanding work in any field of Science, technology, engineering, and mathematics (STEM) and to support the promotion of women in STEM. It is named in honour of Rosalind Franklin and initially funded by the Department of Trade and Industry (DTI) and subsequently the Department for Innovation, Universities and Skills (DIUS) as part of its efforts to promote women in STEM. Women are a significantly underrepresented group in STEM making up less than 9% of the United Kingdom's full-time and part-time professors in science. The award consists of a medal and a grant of £30,000. The recipient delivers a lecture as part of the Society's public lecture series, some of which are available on YouTube. + + +== Laureates == +2003: Susan Gibson on Make me a molecule. Awarded presented by Patricia Hewitt, serving Minister for Women and Equalities. +2004: Carol V. Robinson on Finding the right balance. +2005: Christine Davies on The quandary of the quark. +2006: Andrea Brand on Constructing a nervous system: stem cells to synapses +2007: Ottoline Leyser on Thinking like a vegetable: how plants decide what to do +2008: Eleanor Maguire on Mapping memory: the brains behind remembering +2009: Sunetra Gupta on Surviving pandemics: a pathogen's perspective +2010: Katherine Blundell on Black holes and spin offs +2011: Francesca Happé on When will we understand Autism Spectrum Disorders? +2012: Polly Arnold on Extracting value from waste through a little chemistry with U +2013: Sarah-Jayne Blakemore for her scientific achievements +2014: Rachel McKendry for her scientific achievement. +2015: Lucy Carpenter for her scientific achievement and her suitability as a role model +2016: Jo Dunkley for her research in the cosmic microwave background and her innovative project to support and encourage girls studying physics. +2017: Essi Viding for her achievements in the field of experimental psychology +2018: Tamsin Mather for her work in the field of volcanology +2019: Nguyen TK Thanh for her work in nanotechnology +2020: Julia Gog for her achievements in the field of mathematics and her impactful project proposal with its potential for a long-term legacy. +2021: Suzanne Imber for her achievements in the field of planetary science and her well-considered project proposal with a potential for a high impact +2022: Diane Saunders for "her innovative mentoring and training project to support and empower undergraduates and early-career female researchers in plant sciences at postgraduate and postdoctoral levels". +2023: Karen Johnson for her achievements in environmental engineering and her impactful project explaining the importance and of soil health and how and why it should be conserved +2024: Jess Wade for "her achievements in functional materials and outstanding project which will support early career women scientists to pursue academic careers in materials sciences". +2025: Clare Burrage "for her achievements in theoretical cosmology and her proposed project which aims to inspire and engage girls of all ages with physics" + + +== Rosalind Franklin Award Committee == +As of 2018 the Rosalind Franklin award committee (which takes the decision on the prize each year) includes: + +Frances Ashcroft +Edward Hinds +Lucy Carpenter +Thomas James Simpson +Frances Kirwan +Eric Priest + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Rosalind_Franklin_Fellowship-0.md b/data/en.wikipedia.org/wiki/Rosalind_Franklin_Fellowship-0.md new file mode 100644 index 000000000..d26fb3565 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Rosalind_Franklin_Fellowship-0.md @@ -0,0 +1,135 @@ +--- +title: "Rosalind Franklin Fellowship" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Rosalind_Franklin_Fellowship" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:04.728636+00:00" +instance: "kb-cron" +--- + +The Rosalind Franklin Fellowship (RFF) is an initiation of University of Groningen, the Netherlands. It is named in honor of Rosalind Franklin. The purpose of the RFF program is to promote the advancement of talented international researchers at the highest levels of the institution. + + +== History == +The program is co-funded by the European Union and primarily directed at female academics, who have a PhD and substantial post-graduation work experience, and who aim for a career towards full professorship at a European top research university. The 5-year fellowship is given to female academics with outstanding track record, including high-quality publications, external funding, and leadership, and provides the fellow with salary and research funds to start a research group and conduct independent research. +In 2009, Queen Máxima of the Netherlands joined the Fellowship Ceremony. The RFF program, since its initiation in 2003 and as of 2019, has successfully supported more than 80 female academics, who now constitute more than 10% of the female professors of the university. + + +== Fellows == +2019–2020 +Sandy Schmidt, Science and Engineering +Hannah Dugdale, Science and Engineering +Julia Kamenz, Science and Engineering +Inge Holtman, Medical Sciences +Hilde Bras, Arts +Sumaya Albalooshi, Economics and Business +Mònica Colominas Aparicio, Theology and Religious Studies +Valentina Gallo, Campus Fryslân +Zoé Christoff, Science and Engineering +Helle Hansen, Science and Engineering +Renata Raidou, Science and Engineering +Kasia Tych, Science and Engineering +Jagoda Slawinska, Science and Engineering +Jingxiu Xie, Science and Engineering +Elisabeth Wilhelm, Science and Engineering +Lisa Herzog, Philosophy +Ema Dimastrogiovanni, Science and Engineering +Cecília Salgado Guimarães da Silva, Science and Engineering +Annette Bergemann, Economics and Business +Tessa Quax, Science and Engineering +2017–2018 + +Sofia Fernandes Da Silva Ranchordás, Law +Lingyu Wang, Science and Engineering +Manuela Vecchi, KVI- Cart +Milena Nikolova, Economics and Business +Antje Schmitt, Behavioural and Social Sciences +Jessica de Bloom, Economics and Business +Başak Bilecen, Behavioural and Social Sciences +Rieneke Slager, Economics and Business +2015–2016 +Su Lam, UMCG (Experimental Cardiology) +Judith Daniels, Social Sciences (Psychology) +Janette Burgess, UMCG (Cell Biology) +Iris Jonkers, UMCG (Genetics) +Marit Westerterp, UMCG +Miriam Kunz, UMCG (Geriatrics) +Judith Paridaen, UMCG (Ageing Biology) +Lucy Avraamidou, Science and Engineering +Kerstin Bunte, Science and Engineering +Julia Even, Science and Engineering +Pratika Dayal, Science and Engineering (Astronomy) +Amalia Dolga, Science and Engineering (Molecular Pharmacology) +Anastasia Borschevsky, Science and Engineering +Marthe Walvoort, Science and Engineering (Chemical Biology) +Jing Wan, Economics and Business (Marketing) +2013–2014 +Dorina Buda (FRW, Tourism) +Susanne Tauber (FEB, HRM&OB) +Raquel Ortega Argilés (FEB, GR&M) +Martine Maan (FSE, CBN) +Ykelien Boersma (FSE, GRIP) +Anna Salvati (FSE, GRIP) +Mónica López López (GMW, Orthopedagogy) +Stefania Travagnin (GGW, Religious Studies) +Brigit Toebes (Law, Constitutional Law and International Law) +Merel Keijzer (Let, Applied Linguistics) +Romana Schirhagl (UMCG, Biomedical Engineering) +Sophia Bruggeman (UMCG, Paediatrics) +Maaike Oosterveer (UMCG, Paediatrics) +Sonja Pyott (UMCG, ENT) +2011–2012 +Karina Isabel Caputi (FSE, Sterrenkunde) +Angela Casini (FSE, Medicinale Anorganische Chemie) +Jennifer Jordan (FEB, HRM & OB) +Jia Liu (FEB, Marketing) +Alexandra Zhernakova (UMCG, Genetics) +Pascale Francis Dijkers (UMCG, Cell Biology) +Kathrin Thedieck (UMCG) +Maria Colomé Tatché (UMCG) +Olha Cherednychenko (Law, Private Law) +Caroline Fournet (Law, Criminal Law) +Catarina Dutilh Novaes (FWB, Theoretical Philosophy) +Tamara Witschge (Let, Journalism) +Lidewijde de Jong (Let, Archeology) +Joanne van der Woude (Let, English) +Aleksandra Biegun (KVI, Proton Therapy) +2009–2010 +Bregje Wertheim (FSE, Biology) +Anke Terwisscha van Scheltinga (FSE) +Tamalika Banerjee (FSE, Physics) +Sabrina Corbellini (LET, Dutch Literature) +Monika Baár (LET, History) +Carolina Armenteros (LET, History) +Dineke Verbeek (UMCG, Neurology) +Ingrid Nijholt (UMCG, Neuroscience) +Barbara Bakker (UMCG, Biochemistry) +Nicoletta Kahya (UMCG, Cellbiology) +Deniz Başkent (UMCG, Biophysics) +Barbara Van Leeuwen (UMCG, Chirurgische Oncologie) +Joke Spikman (UMCG/GMW, Neuropsychologie) +Jeanne Mifsud Bonnici (Law) +Hinke Haisma (FRW) +Mirjam Dür (FSE, Mathematics) +Sonja Smets (FSE, Artificial Intelligence and FWB, Theoretical Philosophy) +2007 +Maria Antonietta Loi (FSE, Physics) +Martina Schmidt (FSE, Pharmacy) +Irene Tieleman (FSE, Biology) +Laura Spierdijk (FEB) +Monika Schmid (LET), Engels +Marie-Christine Opdenakker (GMW, Educational Science) +Floor Rink (FEB, Organizational Psychology) +Ute Bültmann (UMCG, Psychische Gezondheid en arbeidsparticipatie) +Marianne Rots (UMCG, Pathologie en Laboratoriumgeneeskunde) +Jetta Bijlsma (UMCG, Medical Microbiology) +Ellen Nollen (UMCG, Genetics) +Eriko Takano (FSE, Microbial Physiology) +2003 +Beatriz Noheda (FSE, Physics) +Elisabetta Pallante (FSE, Physics) +Charlotte Hemelrijk (FSE, Biology) + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Ruby_Payne-Scott_Medal_and_Lecture-0.md b/data/en.wikipedia.org/wiki/Ruby_Payne-Scott_Medal_and_Lecture-0.md new file mode 100644 index 000000000..5afb6a72f --- /dev/null +++ b/data/en.wikipedia.org/wiki/Ruby_Payne-Scott_Medal_and_Lecture-0.md @@ -0,0 +1,18 @@ +--- +title: "Ruby Payne-Scott Medal and Lecture" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Ruby_Payne-Scott_Medal_and_Lecture" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:05.880128+00:00" +instance: "kb-cron" +--- + +The Ruby Payne-Scott Medal and Lecture for women in science is a distinguished career award that acknowledges outstanding Australian women researchers in the biological sciences or physical science. It is conferred by the Australian Academy of Science and is awarded to researchers who are usually resident in, and conduct their research predominantly in Australia. +This award, established in 2021, honours the contributions of Ruby Payne-Scott, particularly in the fields of radiophysics and radio astronomy. + + +== Recipients == + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Ruth_I._Michler_Memorial_Prize-0.md b/data/en.wikipedia.org/wiki/Ruth_I._Michler_Memorial_Prize-0.md new file mode 100644 index 000000000..ff305573f --- /dev/null +++ b/data/en.wikipedia.org/wiki/Ruth_I._Michler_Memorial_Prize-0.md @@ -0,0 +1,40 @@ +--- +title: "Ruth I. Michler Memorial Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Ruth_I._Michler_Memorial_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:57.464640+00:00" +instance: "kb-cron" +--- + +The Ruth I. Michler Memorial Prize is an annual prize in mathematics, awarded by the Association for Women in Mathematics to honor outstanding research by a female mathematician who has recently earned tenure. The prize funds the winner to spend a semester as a visiting faculty member at Cornell University, working with the faculty there and presenting a distinguished lecture on their research. It is named after Ruth I. Michler (1967–2000), a German-American mathematician born at Cornell, who died in a road accident at the age of 33. +The award was first offered in 2007. Its winners and their lectures have included: + +Rebecca Goldin (2007), "The Geometry of Polygons" +Irina Mitrea (2008), "Boundary-Value Problems for Higher-Order Elliptic Operators" +Maria Gordina (2009), "Lie's Third Theorem in Infinite Dimensions" +Patricia Hersh (2010), "Regular CS Complexes, Total Positivity and Bruhat Order" +Anna Mazzucato (2011), "The Analysis of Incompressible Fluids at High Reynolds Numbers" +Ling Long (2012), "Atkin and Swinnerton-Dyer Congruences" +Megumi Harada (2013), "Newton-Okounkov bodies and integrable systems" +Sema Salur (2014), "Manifolds with G2 structure and beyond" +Malabika Pramanik (2015), "Needles, Bushes, Hairbrushes, and Polynomials" +Pallavi Dani (2016), "Large-scale geometry of right-angled Coxeter groups" +Julia Gordon (2017), "Wilkie's theorem and (ineffective) uniform bounds" +Julie Bergner (2018), "2-Segal structures and the Waldhausen S-construction" +Anna Skripka (2019), "Untangling noncommutativity with operator integrals" +Shabnam Akhtari (2021), "Representation of integers by binary forms" +Emily E. Witt (2022), "Local cohomology: An algebraic tool capturing geometric data" +Lauren M. Childs (2023), "Modeling infectious disease dynamics: A case study of malaria immunity" +Alexandra Seceleanu (2024), "Symmetric Ideals" +Ling Xiao (2025), "The boundary value problem with prescribed singularity" +Martha E. Precup (2026) + + +== See also == +List of awards honoring women +List of mathematics awards + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Ruth_Lyttle_Satter_Prize_in_Mathematics-0.md b/data/en.wikipedia.org/wiki/Ruth_Lyttle_Satter_Prize_in_Mathematics-0.md new file mode 100644 index 000000000..374a18470 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Ruth_Lyttle_Satter_Prize_in_Mathematics-0.md @@ -0,0 +1,27 @@ +--- +title: "Ruth Lyttle Satter Prize in Mathematics" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Ruth_Lyttle_Satter_Prize_in_Mathematics" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:09.458770+00:00" +instance: "kb-cron" +--- + +The Ruth Lyttle Satter Prize in Mathematics, also called the Satter Prize, is one of twenty-one prizes given out by the American Mathematical Society (AMS). It is presented biennially in recognition of an outstanding contribution to mathematics research by a woman in the previous six years. The award was funded in 1990 using a donation from Joan Birman, in memory of her sister, Ruth Lyttle Satter, who worked primarily in biological sciences, and was a proponent for equal opportunities for women in science. First awarded in 1991, the award is intended to "honor [Satter's] commitment to research and to encourage women in science". The winner is selected by the council of the AMS, based on the recommendation of a selection committee. The prize is awarded at the Joint Mathematics Meetings during odd numbered years, and has always carried a modest cash reward. Since 2003, the prize has been $5,000, while from 1997 to 2001, the prize came with $1,200, and $4,000 prior to that. If a joint award is given, the prize money is split between the recipients. +Dusa McDuff was the first recipient of the award, for her work on symplectic geometry. A joint award was given for the first time in 2001, when Karen E. Smith and Sijue Wu shared the award. The 2013 prize winner was Maryam Mirzakhani, who, the following year, became the first woman to be awarded the Fields Medal, which is considered to be the highest honor a mathematician can receive. She won both awards for her work on "the geometry of Riemann surfaces and their moduli spaces". The most recent winner is Ana Caraiani, who was awarded the prize in 2025 "for contributions to arithmetic geometry and number theory: in particular, the Langlands program.". + + +== Recipients == + + +== See also == +List of mathematics awards + + +== References == + + +=== Sources === +Case, Bettye; Leggett, Anne, eds. (2005). Complexities: Women in Mathematics. Princeton University Press. ISBN 0-691-11462-5. +Morrow, Charlene; Perl, Teri, eds. (1998). Notable Women in Mathematics: A Biographical Dictionary. Westport, Connecticut: Greenwood Press. p. 140. ISBN 0-313-29131-4. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Sadosky_Prize-0.md b/data/en.wikipedia.org/wiki/Sadosky_Prize-0.md new file mode 100644 index 000000000..0dad02c23 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Sadosky_Prize-0.md @@ -0,0 +1,32 @@ +--- +title: "Sadosky Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Sadosky_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:07.056560+00:00" +instance: "kb-cron" +--- + +The AWM–Sadosky Prize in Analysis is a prize given every other year by the Association for Women in Mathematics to an outstanding young female researcher in mathematical analysis. It was established in 2012, and is named after Cora Sadosky, a mathematician specializing in analysis who became president of the AWM. +The winners have included: + +Svitlana Mayboroda (2014), for her research on "boundary value problems for second and higher order elliptic equations in non-smooth media". +Daniela De Silva (2016), for "fundamental contributions to the regularity theory of nonlinear elliptic partial differential equations and non-local integro-differential equations". +Lillian Pierce (2018), for research that "spans and connects a broad spectrum of problems ranging from character sums in number theory to singular integral operators in Euclidean spaces". +Mihaela Ignatova (2020), "in recognition of her contributions to the analysis of partial differential equations, in particular in fluid mechanics". +Yaiza Canzani (2022), "in recognition of outstanding contributions in spectral geometry and microlocal analysis". +Robin Neumayer (2024), for "outstanding contributions to calculus of variations, partial differential equations, and geometric analysis". +Hong Wang (2026), for "solving central problems in harmonic analysis through the introduction of ground-breaking ideas. In particular, for substantial contributions to the Fourier restriction problem, the Kakeya conjecture, and geometric measure theory". + + +== See also == +List of awards honoring women +List of mathematics awards + + +== References == + + +== External links == +AWM–Sadosky Prize in Analysis, Association for Women in Mathematics \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Saruhashi_Prize-0.md b/data/en.wikipedia.org/wiki/Saruhashi_Prize-0.md new file mode 100644 index 000000000..25b410688 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Saruhashi_Prize-0.md @@ -0,0 +1,23 @@ +--- +title: "Saruhashi Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Saruhashi_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:08.225591+00:00" +instance: "kb-cron" +--- + +The Saruhashi Prize (猿橋賞) is an annual prize awarded to a Japanese woman researcher in the natural sciences. The prize recognises accomplishments in research as well as the mentoring of other women scientists. +Japanese geochemist Katsuko Saruhashi retired from her position as the director of the Geochemical Research Laboratory in 1980. Her co-workers gifted her ¥5 million and she used the money to establish the Association for the Bright Future of Women Scientists in 1980. The association distributes an annual ¥300,000 prize. It is only available to scientists who are under the age of 50. +The book My Life: Twenty Japanese Women Scientists, edited by Yoshihide Kozai, includes essays by twenty of the Saruhashi Prize winners. + + +== Recipients == + + +== See also == +List of general science and technology awards + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Sharon_Keillor_Award_for_Women_in_Engineering_Education-0.md b/data/en.wikipedia.org/wiki/Sharon_Keillor_Award_for_Women_in_Engineering_Education-0.md new file mode 100644 index 000000000..7170fd98c --- /dev/null +++ b/data/en.wikipedia.org/wiki/Sharon_Keillor_Award_for_Women_in_Engineering_Education-0.md @@ -0,0 +1,22 @@ +--- +title: "Sharon Keillor Award for Women in Engineering Education" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Sharon_Keillor_Award_for_Women_in_Engineering_Education" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:10.654193+00:00" +instance: "kb-cron" +--- + +The Sharon Keillor Award for Women in Engineering Education "recognizes and honors outstanding women engineering educators." Recipients hold an earned doctoral degree in an engineering discipline or related field, have at least five years of teaching experience in an engineering school, and have "an outstanding record in teaching engineering students." +The award has been given annually since 2001. + + +== Recipients == + + +== See also == +List of engineering awards + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-0.md b/data/en.wikipedia.org/wiki/Spacetime-0.md new file mode 100644 index 000000000..c47d9447a --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-0.md @@ -0,0 +1,40 @@ +--- +title: "Spacetime" +chunk: 1/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur. +Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. +In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space. This interpretation proved vital to the general theory of relativity, wherein spacetime is curved by mass and energy. + +== Fundamentals == + +=== Definitions === +Non-relativistic classical mechanics treats time as a universal quantity of measurement that is uniform throughout, is separate from space, and is agreed on by all observers. Classical mechanics assumes that time has a constant rate of passage, independent of the observer's state of motion, or anything external. It assumes that space is Euclidean: it assumes that space follows the geometry of common sense. +In the context of special relativity, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer. General relativity provides an explanation of how gravitational fields can slow the passage of time for an object as seen by an observer outside the field. +In ordinary space, a position is specified by three numbers, known as dimensions. In the Cartesian coordinate system, these are often called x, y and z. A point in spacetime is called an event, and requires four numbers to be specified: the three-dimensional location in space, plus the position in time (Fig. 1). An event is represented by a set of coordinates x, y, z and t. Spacetime is thus four-dimensional. +Unlike the analogies used in popular writings to explain events, such as firecrackers or sparks, mathematical events have zero duration and represent a single point in spacetime. Although it is possible to be in motion relative to the popping of a firecracker or a spark, it is not possible for an observer to be in motion relative to an event. +The path of a particle through spacetime can be considered to be a sequence of events. The series of events can be linked together to form a curve that represents the particle's progress through spacetime. That path is called the particle's world line. +Mathematically, spacetime is a manifold, which is to say, it appears locally "flat" near each point in the same way that, at small enough scales, the surface of a globe appears to be flat. A scale factor, + + + + c + + + {\displaystyle c} + + (conventionally called the speed-of-light) relates distances measured in space to distances measured in time. The magnitude of this scale factor (nearly 300,000 kilometres or 190,000 miles in space being equivalent to one second in time), along with the fact that spacetime is a manifold, implies that at ordinary, non-relativistic speeds and at ordinary, human-scale distances, there is little that humans might observe that is noticeably different from what they might observe if the world were Euclidean. It was only with the advent of sensitive scientific measurements in the mid-1800s, such as the Fizeau experiment and the Michelson–Morley experiment, that puzzling discrepancies began to be noted between observation versus predictions based on the implicit assumption of Euclidean space. + +In special relativity, an observer will, in most cases, mean a frame of reference from which a set of objects or events is being measured. This usage differs significantly from the ordinary English meaning of the term. Reference frames are inherently nonlocal constructs, and according to this usage of the term, it does not make sense to speak of an observer as having a location. +In Fig. 1-1, imagine that the frame under consideration is equipped with a dense lattice of clocks, synchronized within this reference frame, that extends indefinitely throughout the three dimensions of space. Any specific location within the lattice is not important. The latticework of clocks is used to determine the time and position of events taking place within the whole frame. The term observer refers to the whole ensemble of clocks associated with one inertial frame of reference. +In this idealized case, every point in space has a clock associated with it, and thus the clocks register each event instantly, with no time delay between an event and its recording. A real observer will see a delay between the emission of a signal and its detection due to the speed of light. To synchronize the clocks, in the data reduction following an experiment, the time when a signal is received will be corrected to reflect its actual time were it to have been recorded by an idealized lattice of clocks. +In many books on special relativity, especially older ones, the word "observer" is used in the more ordinary sense of the word. It is usually clear from context which meaning has been adopted. +Physicists distinguish between what one measures or observes, after one has factored out signal propagation delays, versus what one visually sees without such corrections. Failing to understand the difference between what one measures and what one sees is the source of much confusion among students of relativity. + +== History == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-1.md b/data/en.wikipedia.org/wiki/Spacetime-1.md new file mode 100644 index 000000000..6cff0ce27 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-1.md @@ -0,0 +1,23 @@ +--- +title: "Spacetime" +chunk: 2/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +By the mid-1800s, various experiments such as the observation of the Arago spot and differential measurements of the speed of light in air versus water were considered to have proven the wave nature of light as opposed to a corpuscular theory. Propagation of waves was then assumed to require the existence of a waving medium; in the case of light waves, this was considered to be a hypothetical luminiferous aether. The various attempts to establish the properties of this hypothetical medium yielded contradictory results. For example, the Fizeau experiment of 1851, conducted by French physicist Hippolyte Fizeau, demonstrated that the speed of light in flowing water was less than the sum of the speed of light in air plus the speed of the water by an amount dependent on the water's index of refraction. +Among other issues, the dependence of the partial aether-dragging implied by this experiment on the index of refraction (which is dependent on wavelength) led to the unpalatable conclusion that aether simultaneously flows at different speeds for different colors of light. The Michelson–Morley experiment of 1887 (Fig. 1-2) showed no differential influence of Earth's motions through the hypothetical aether on the speed of light, and the most likely explanation, complete aether dragging, was in conflict with the observation of stellar aberration. +George Francis FitzGerald in 1889, and Hendrik Lorentz in 1892, independently proposed that material bodies traveling through the fixed aether were physically affected by their passage, contracting in the direction of motion by an amount that was exactly what was necessary to explain the negative results of the Michelson–Morley experiment. No length changes occur in directions transverse to the direction of motion. +By 1904, Lorentz had expanded his theory such that he had arrived at equations formally identical with those that Einstein was to derive later, i.e. the Lorentz transformation. As a theory of dynamics (the study of forces and torques and their effect on motion), his theory assumed actual physical deformations of the physical constituents of matter. Lorentz's equations predicted a quantity that he called local time, with which he could explain the aberration of light, the Fizeau experiment and other phenomena. + +Henri Poincaré was the first to combine space and time into spacetime. He argued in 1898 that the simultaneity of two events is a matter of convention. In 1900, he recognized that Lorentz's "local time" is actually what is indicated by moving clocks by applying an explicitly operational definition of clock synchronization assuming constant light speed. In 1900 and 1904, he suggested the inherent undetectability of the aether by emphasizing the validity of what he called the principle of relativity. In 1905/1906 he mathematically perfected Lorentz's theory of electrons in order to bring it into accordance with the postulate of relativity. +While discussing various hypotheses on Lorentz invariant gravitation, he introduced the innovative concept of a 4-dimensional spacetime by defining various four-vectors, namely four-position, four-velocity, and four-force. He did not pursue the 4-dimensional formalism in subsequent papers, however, stating that this line of research seemed to "entail great pain for limited profit", ultimately concluding "that three-dimensional language seems the best suited to the description of our world". Even as late as 1909, Poincaré continued to describe the dynamical interpretation of the Lorentz transform. +In 1905, Albert Einstein analyzed special relativity in terms of kinematics (the study of moving bodies without reference to forces) rather than dynamics. His results were mathematically equivalent to those of Lorentz and Poincaré. He obtained them by recognizing that the entire theory can be built upon two postulates: the principle of relativity and the principle of the constancy of light speed. His work was filled with vivid imagery involving the exchange of light signals between clocks in motion, careful measurements of the lengths of moving rods, and other such examples. +Einstein in 1905 superseded previous attempts of an electromagnetic mass–energy relation by introducing the general equivalence of mass and energy, which was instrumental for his subsequent formulation of the equivalence principle in 1907, which declares the equivalence of inertial and gravitational mass. By using the mass–energy equivalence, Einstein showed that the gravitational mass of a body is proportional to its energy content, which was one of the early results in developing general relativity. While it would appear that he did not at first think geometrically about spacetime, in the further development of general relativity, Einstein fully incorporated the spacetime formalism. +When Einstein published in 1905, another of his competitors, his former mathematics professor Hermann Minkowski, had also arrived at most of the basic elements of special relativity. Max Born recounted a meeting he had made with Minkowski, seeking to be Minkowski's student/collaborator: + +I went to Cologne, met Minkowski and heard his celebrated lecture 'Space and Time' delivered on 2 September 1908. [...] He told me later that it came to him as a great shock when Einstein published his paper in which the equivalence of the different local times of observers moving relative to each other was pronounced; for he had reached the same conclusions independently but did not publish them because he wished first to work out the mathematical structure in all its splendor. He never made a priority claim and always gave Einstein his full share in the great discovery. +Minkowski had been concerned with the state of electrodynamics after Michelson's disruptive experiments at least since the summer of 1905, when Minkowski and David Hilbert led an advanced seminar attended by notable physicists of the time to study the papers of Lorentz, Poincaré et al. Minkowski saw Einstein's work as an extension of Lorentz's, and was most directly influenced by Poincaré. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-10.md b/data/en.wikipedia.org/wiki/Spacetime-10.md new file mode 100644 index 000000000..d37d7cb92 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-10.md @@ -0,0 +1,434 @@ +--- +title: "Spacetime" +chunk: 11/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +The Galilean transformations and their consequent commonsense law of addition of velocities work well in our ordinary low-speed world of planes, cars and balls. Beginning in the mid-1800s, however, sensitive scientific instrumentation began finding anomalies that did not fit well with the ordinary addition of velocities. +Lorentz transformations are used to transform the coordinates of an event from one frame to another in special relativity. +The Lorentz factor appears in the Lorentz transformations: + + + + + + + + + + t + ′ + + + + + = + γ + + ( + + t + − + + + + v + x + + + c + + 2 + + + + + + ) + + + + + + + x + ′ + + + + + = + γ + + ( + + x + − + v + t + + ) + + + + + + + y + ′ + + + + + = + y + + + + + + z + ′ + + + + + = + z + + + + + + + {\displaystyle {\begin{aligned}t'&=\gamma \left(t-{\frac {vx}{c^{2}}}\right)\\x'&=\gamma \left(x-vt\right)\\y'&=y\\z'&=z\end{aligned}}} + + +The inverse Lorentz transformations are: + + + + + + + + + t + + + + = + γ + + ( + + + t + ′ + + + + + + + v + + x + ′ + + + + c + + 2 + + + + + + ) + + + + + + x + + + + = + γ + + ( + + + x + ′ + + + + v + + t + ′ + + + ) + + + + + + y + + + + = + + y + ′ + + + + + + z + + + + = + + z + ′ + + + + + + + + {\displaystyle {\begin{aligned}t&=\gamma \left(t'+{\frac {vx'}{c^{2}}}\right)\\x&=\gamma \left(x'+vt'\right)\\y&=y'\\z&=z'\end{aligned}}} + + +When v ≪ c and x is small enough, the v2/c2 and vx/c2 terms approach zero, and the Lorentz transformations approximate to the Galilean transformations. + + + + + + t + ′ + + = + γ + ( + t + − + v + x + + / + + + c + + 2 + + + ) + , + + + {\displaystyle t'=\gamma (t-vx/c^{2}),} + + + + + + + x + ′ + + = + γ + ( + x + − + v + t + ) + + + {\displaystyle x'=\gamma (x-vt)} + + etc., most often really mean + + + + Δ + + t + ′ + + = + γ + ( + Δ + t + − + v + Δ + x + + / + + + c + + 2 + + + ) + , + + + {\displaystyle \Delta t'=\gamma (\Delta t-v\Delta x/c^{2}),} + + + + + + Δ + + x + ′ + + = + γ + ( + Δ + x + − + v + Δ + t + ) + + + {\displaystyle \Delta x'=\gamma (\Delta x-v\Delta t)} + + etc. Although for brevity the Lorentz transformation equations are written without deltas, x means Δx, etc. We are, in general, always concerned with the space and time differences between events. +Calling one set of transformations the normal Lorentz transformations and the other the inverse transformations is misleading, since there is no intrinsic difference between the frames. Different authors call one or the other set of transformations the "inverse" set. The forwards and inverse transformations are trivially related to each other, since the S frame can only be moving forwards or reverse with respect to S′. So inverting the equations simply entails switching the primed and unprimed variables and replacing v with −v. +Example: Terence and Stella are at an Earth-to-Mars space race. Terence is an official at the starting line, while Stella is a participant. At time t = t′ = 0, Stella's spaceship accelerates instantaneously to a speed of 0.5 c. The distance from Earth to Mars is 300 light-seconds (about 90.0×106 km). Terence observes Stella crossing the finish-line clock at t = 600.00 s. But Stella observes the time on her ship chronometer to be ⁠ + + + + + t + + ′ + + + = + γ + + ( + + t + − + v + x + + / + + + c + + 2 + + + + ) + + = + 519.62 + + + s + + + + {\displaystyle t^{\prime }=\gamma \left(t-vx/c^{2}\right)=519.62\ {\text{s}}} + +⁠ as she passes the finish line, and she calculates the distance between the starting and finish lines, as measured in her frame, to be 259.81 light-seconds (about 77.9×106 km). +1). + +==== Deriving the Lorentz transformations ==== + +There have been many dozens of derivations of the Lorentz transformations since Einstein's original work in 1905, each with its particular focus. Although Einstein's derivation was based on the invariance of the speed of light, there are other physical principles that may serve as starting points. Ultimately, these alternative starting points can be considered different expressions of the underlying principle of locality, which states that the influence that one particle exerts on another can not be transmitted instantaneously. +The derivation given here and illustrated in Fig. 3-5 is based on one presented by Bais and makes use of previous results from the Relativistic Composition of Velocities, Time Dilation, and Length Contraction sections. Event P has coordinates (w, x) in the black "rest system" and coordinates (w′, x′) in the red frame that is moving with velocity parameter β = v/c. To determine w′ and x′ in terms of w and x (or the other way around) it is easier at first to derive the inverse Lorentz transformation. + +There can be no such thing as length expansion/contraction in the transverse directions. y' must equal y and z′ must equal z, otherwise whether a fast moving 1 m ball could fit through a 1 m circular hole would depend on the observer. The first postulate of relativity states that all inertial frames are equivalent, and transverse expansion/contraction would violate this law. +From the drawing, w = a + b and x = r + s +From previous results using similar triangles, we know that s/a = b/r = v/c = β. +Because of time dilation, a = γw′ +Substituting equation (4) into s/a = β yields s = γw′β. +Length contraction and similar triangles give us r = γx′ and b = βr = βγx′ +Substituting the expressions for s, a, r and b into the equations in Step 2 immediately yield + + + + + + + + w + + + + = + γ + + w + ′ + + + + β + γ + + x + ′ + + + + + + x + + + + = + γ + + x + ′ + + + + β + γ + + w + ′ + + + + + + + + {\displaystyle {\begin{aligned}w&=\gamma w'+\beta \gamma x'\\x&=\gamma x'+\beta \gamma w'\end{aligned}}} + + +The above equations are alternate expressions for the t and x equations of the inverse Lorentz transformation, as can be seen by substituting ct for w, ct′ for w′, and v/c for β. From the inverse transformation, the equations of the forwards transformation can be derived by solving for t′ and x′. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-11.md b/data/en.wikipedia.org/wiki/Spacetime-11.md new file mode 100644 index 000000000..f560530c6 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-11.md @@ -0,0 +1,276 @@ +--- +title: "Spacetime" +chunk: 12/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +==== Linearity of the Lorentz transformations ==== +The Lorentz transformations have a mathematical property called linearity, since x′ and t′ are obtained as linear combinations of x and t, with no higher powers involved. The linearity of the transformation reflects a fundamental property of spacetime that was tacitly assumed in the derivation, namely, that the properties of inertial frames of reference are independent of location and time. In the absence of gravity, spacetime looks the same everywhere. All inertial observers will agree on what constitutes accelerating and non-accelerating motion. Any one observer can use her own measurements of space and time, but there is nothing absolute about them. Another observer's conventions will do just as well. +A result of linearity is that if two Lorentz transformations are applied sequentially, the result is also a Lorentz transformation. +Example: Terence observes Stella speeding away from him at 0.500 c, and he can use the Lorentz transformations with β = 0.500 to relate Stella's measurements to his own. Stella, in her frame, observes Ursula traveling away from her at 0.250 c, and she can use the Lorentz transformations with β = 0.250 to relate Ursula's measurements with her own. Because of the linearity of the transformations and the relativistic composition of velocities, Terence can use the Lorentz transformations with β = 0.666 to relate Ursula's measurements with his own. + +=== Doppler effect === + +The Doppler effect is the change in frequency or wavelength of a wave for a receiver and source in relative motion. For simplicity, we consider here two basic scenarios: (1) The motions of the source and/or receiver are exactly along the line connecting them (longitudinal Doppler effect), and (2) the motions are at right angles to the said line (transverse Doppler effect). We are ignoring scenarios where they move along intermediate angles. + +==== Longitudinal Doppler effect ==== +The classical Doppler analysis deals with waves that are propagating in a medium, such as sound waves or water ripples, and which are transmitted between sources and receivers that are moving towards or away from each other. The analysis of such waves depends on whether the source, the receiver, or both are moving relative to the medium. Given the scenario where the receiver is stationary with respect to the medium, and the source is moving directly away from the receiver at a speed of vs for a velocity parameter of βs, the wavelength is increased, and the observed frequency f is given by + + + + + f + = + + + 1 + + 1 + + + + β + + s + + + + + + + f + + 0 + + + + + {\displaystyle f={\frac {1}{1+\beta _{s}}}f_{0}} + + +On the other hand, given the scenario where source is stationary, and the receiver is moving directly away from the source at a speed of vr for a velocity parameter of βr, the wavelength is not changed, but the transmission velocity of the waves relative to the receiver is decreased, and the observed frequency f is given by + + + + + f + = + ( + 1 + − + + β + + r + + + ) + + f + + 0 + + + + + {\displaystyle f=(1-\beta _{r})f_{0}} + + +Light, unlike sound or water ripples, does not propagate through a medium, and there is no distinction between a source moving away from the receiver or a receiver moving away from the source. Fig. 3-6 illustrates a relativistic spacetime diagram showing a source separating from the receiver with a velocity parameter + + + + β + , + + + {\displaystyle \beta ,} + + so that the separation between source and receiver at time + + + + w + + + {\displaystyle w} + + is + + + + β + w + + + {\displaystyle \beta w} + +. Because of time dilation, + + + + w + = + γ + + w + ′ + + . + + + {\displaystyle w=\gamma w'.} + + Since the slope of the green light ray is −1, + + + + T + = + w + + + β + w + = + γ + + w + ′ + + ( + 1 + + + β + ) + . + + + {\displaystyle T=w+\beta w=\gamma w'(1+\beta ).} + + Hence, the relativistic Doppler effect is given by + + + + + f + = + + + + + 1 + − + β + + + 1 + + + β + + + + + + + f + + 0 + + + . + + + {\displaystyle f={\sqrt {\frac {1-\beta }{1+\beta }}}\,f_{0}.} + + +==== Transverse Doppler effect ==== + +Suppose that a source and a receiver, both approaching each other in uniform inertial motion along non-intersecting lines, are at their closest approach to each other. It would appear that the classical analysis predicts that the receiver detects no Doppler shift. Due to subtleties in the analysis, that expectation is not necessarily true. Nevertheless, when appropriately defined, transverse Doppler shift is a relativistic effect that has no classical analog. The subtleties are these: + +In scenario (a), the point of closest approach is frame-independent and represents the moment where there is no change in distance versus time (i.e. dr/dt = 0 where r is the distance between receiver and source) and hence no longitudinal Doppler shift. The source observes the receiver as being illuminated by light of frequency f′, but also observes the receiver as having a time-dilated clock. In frame S, the receiver is therefore illuminated by blueshifted light of frequency + + + + + f + = + + f + ′ + + γ + = + + f + ′ + + + / + + + + 1 + − + + β + + 2 + + + + + + + {\displaystyle f=f'\gamma =f'/{\sqrt {1-\beta ^{2}}}} + + +In scenario (b) the illustration shows the receiver being illuminated by light from when the source was closest to the receiver, even though the source has moved on. Because the source's clocks are time dilated as measured in frame S, and since dr/dt was equal to zero at this point, the light from the source, emitted from this closest point, is redshifted with frequency + + + + + f + = + + f + ′ + + + / + + γ + = + + f + ′ + + + + 1 + − + + β + + 2 + + + + + + + {\displaystyle f=f'/\gamma =f'{\sqrt {1-\beta ^{2}}}} + + +Scenarios (c) and (d) can be analyzed by simple time dilation arguments. In (c), the receiver observes light from the source as being blueshifted by a factor of + + + + γ + + + {\displaystyle \gamma } + +, and in (d), the light is redshifted. The only seeming complication is that the orbiting objects are in accelerated motion. However, if an inertial observer looks at an accelerating clock, only the clock's instantaneous speed is important when computing time dilation. (The converse, however, is not true.) Most reports of transverse Doppler shift refer to the effect as a redshift and analyze the effect in terms of scenarios (b) or (d). \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-12.md b/data/en.wikipedia.org/wiki/Spacetime-12.md new file mode 100644 index 000000000..cb1bf606e --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-12.md @@ -0,0 +1,363 @@ +--- +title: "Spacetime" +chunk: 13/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +=== Energy and momentum === + +==== Extending momentum to four dimensions ==== + +In classical mechanics, the state of motion of a particle is characterized by its mass and its velocity. Linear momentum, the product of a particle's mass and velocity, is a vector quantity, possessing the same direction as the velocity: p = mv. It is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. +In relativistic mechanics, the momentum vector is extended to four dimensions. Added to the momentum vector is a time component that allows the spacetime momentum vector to transform like the spacetime position vector ⁠ + + + + ( + x + , + t + ) + + + {\displaystyle (x,t)} + +⁠. In exploring the properties of the spacetime momentum, we start, in Fig. 3-8a, by examining what a particle looks like at rest. In the rest frame, the spatial component of the momentum is zero, i.e. p = 0, but the time component equals mc. +We can obtain the transformed components of this vector in the moving frame by using the Lorentz transformations, or we can read it directly from the figure because we know that ⁠ + + + + ( + m + c + + ) + + ′ + + + = + γ + m + c + + + {\displaystyle (mc)^{\prime }=\gamma mc} + +⁠ and ⁠ + + + + + p + + ′ + + + = + − + β + γ + m + c + + + {\displaystyle p^{\prime }=-\beta \gamma mc} + +⁠, since the red axes are rescaled by gamma. Fig. 3-8b illustrates the situation as it appears in the moving frame. It is apparent that the space and time components of the four-momentum go to infinity as the velocity of the moving frame approaches c. +We will use this information shortly to obtain an expression for the four-momentum. + +==== Momentum of light ==== + +Light particles, or photons, travel at the speed of c, the constant that is conventionally known as the speed of light. This statement is not a tautology, since many modern formulations of relativity do not start with constant speed of light as a postulate. Photons therefore propagate along a lightlike world line and, in appropriate units, have equal space and time components for every observer. +A consequence of Maxwell's theory of electromagnetism is that light carries energy and momentum, and that their ratio is a constant: ⁠ + + + + E + + / + + p + = + c + + + {\displaystyle E/p=c} + +⁠. Rearranging, ⁠ + + + + E + + / + + c + = + p + + + {\displaystyle E/c=p} + +⁠, and since for photons, the space and time components are equal, E/c must therefore be equated with the time component of the spacetime momentum vector. +Photons travel at the speed of light, yet have finite momentum and energy. For this to be so, the mass term in γmc must be zero, meaning that photons are massless particles. Infinity times zero is an ill-defined quantity, but E/c is well-defined. +By this analysis, if the energy of a photon equals E in the rest frame, it equals ⁠ + + + + + E + + ′ + + + = + ( + 1 + − + β + ) + γ + E + + + {\displaystyle E^{\prime }=(1-\beta )\gamma E} + +⁠ in a moving frame. This result can be derived by inspection of Fig. 3-9 or by application of the Lorentz transformations, and is consistent with the analysis of Doppler effect given previously. + +==== Mass–energy relationship ==== +Consideration of the interrelationships between the various components of the relativistic momentum vector led Einstein to several important conclusions. + +In the low speed limit as β = v/c approaches zero, γ approaches 1, so the spatial component of the relativistic momentum ⁠ + + + + β + γ + m + c + = + γ + m + v + + + {\displaystyle \beta \gamma mc=\gamma mv} + +⁠ approaches mv, the classical term for momentum. Following this perspective, γm can be interpreted as a relativistic generalization of m. Einstein proposed that the relativistic mass of an object increases with velocity according to the formula ⁠ + + + + + m + + rel + + + = + γ + m + + + {\displaystyle m_{\text{rel}}=\gamma m} + +⁠. +Likewise, comparing the time component of the relativistic momentum with that of the photon, ⁠ + + + + γ + m + c + = + + m + + rel + + + c + = + E + + / + + c + + + {\displaystyle \gamma mc=m_{\text{rel}}c=E/c} + +⁠, so that Einstein arrived at the relationship ⁠ + + + + E + = + + m + + rel + + + + c + + 2 + + + + + {\displaystyle E=m_{\text{rel}}c^{2}} + +⁠. Simplified to the case of zero velocity, this is Einstein's equation relating energy and mass. +Another way of looking at the relationship between mass and energy is to consider a series expansion of γmc2 at low velocity: + + + + + + + + + E + + + + = + γ + m + + c + + 2 + + + = + + + + m + + c + + 2 + + + + + 1 + − + + β + + 2 + + + + + + + + + + + + = + m + + c + + 2 + + + + + + + 1 + 2 + + + m + + v + + 2 + + + + + ⋯ + + + + + + + {\displaystyle {\begin{aligned}E&=\gamma mc^{2}={\frac {mc^{2}}{\sqrt {1-\beta ^{2}}}}\\&=mc^{2}+{\frac {1}{2}}mv^{2}+\cdots \end{aligned}}} + + +The second term is just an expression for the kinetic energy of the particle. Mass indeed appears to be another form of energy. +The concept of relativistic mass that Einstein introduced in 1905, mrel, although amply validated every day in particle accelerators around the globe (or indeed in any instrumentation whose use depends on high velocity particles, such as electron microscopes, old-fashioned color television sets, etc.), has nevertheless not proven to be a fruitful concept in physics in the sense that it is not a concept that has served as a basis for other theoretical development. Relativistic mass, for instance, plays no role in general relativity. +For this reason, as well as for pedagogical concerns, most physicists currently prefer a different terminology when referring to the relationship between mass and energy. "Relativistic mass" is a deprecated term. The term "mass" by itself refers to the rest mass or invariant mass, and is equal to the invariant length of the relativistic momentum vector. Expressed as a formula, + + + + + + E + + 2 + + + − + + p + + 2 + + + + c + + 2 + + + = + + m + + rest + + + 2 + + + + c + + 4 + + + + + {\displaystyle E^{2}-p^{2}c^{2}=m_{\text{rest}}^{2}c^{4}} + + +This formula applies to all particles, massless as well as massive. For photons where mrest equals zero, it yields, ⁠ + + + + E + = + ± + p + c + + + {\displaystyle E=\pm pc} + +⁠. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-13.md b/data/en.wikipedia.org/wiki/Spacetime-13.md new file mode 100644 index 000000000..1faee4031 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-13.md @@ -0,0 +1,423 @@ +--- +title: "Spacetime" +chunk: 14/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +==== Four-momentum ==== +Because of the close relationship between mass and energy, the four-momentum (also called 4-momentum) is also called the energy–momentum 4-vector. Using an uppercase P to represent the four-momentum and a lowercase p to denote the spatial momentum, the four-momentum may be written as + + + + + P + ≡ + ( + E + + / + + c + , + + + + p + → + + + + ) + = + ( + E + + / + + c + , + + p + + x + + + , + + p + + y + + + , + + p + + z + + + ) + + + {\displaystyle P\equiv (E/c,{\vec {p}})=(E/c,p_{x},p_{y},p_{z})} + + or alternatively, + + + + + P + ≡ + ( + E + , + + + + p + → + + + + ) + = + ( + E + , + + p + + x + + + , + + p + + y + + + , + + p + + z + + + ) + + + {\displaystyle P\equiv (E,{\vec {p}})=(E,p_{x},p_{y},p_{z})} + + using the convention that + + + + c + = + 1. + + + {\displaystyle c=1.} + + +=== Conservation laws === + +In physics, conservation laws state that certain particular measurable properties of an isolated physical system do not change as the system evolves over time. In 1915, Emmy Noether discovered that underlying each conservation law is a fundamental symmetry of nature. The fact that physical processes do not care where in space they take place (space translation symmetry) yields conservation of momentum, the fact that such processes do not care when they take place (time translation symmetry) yields conservation of energy, and so on. In this section, we examine the Newtonian views of conservation of mass, momentum and energy from a relativistic perspective. + +==== Total momentum ==== + +To understand how the Newtonian view of conservation of momentum needs to be modified in a relativistic context, we examine the problem of two colliding bodies limited to a single dimension. +In Newtonian mechanics, two extreme cases of this problem may be distinguished yielding mathematics of minimum complexity: + +The two bodies rebound from each other in a completely elastic collision. +The two bodies stick together and continue moving as a single particle. This second case is the case of completely inelastic collision. +For both cases (1) and (2), momentum, mass, and total energy are conserved. However, kinetic energy is not conserved in cases of inelastic collision. A certain fraction of the initial kinetic energy is converted to heat. +In case (2), two masses with momentums ⁠ + + + + + + p + + + 1 + + + = + + m + + 1 + + + + + v + + + 1 + + + + + {\displaystyle {\boldsymbol {p}}_{\boldsymbol {1}}=m_{1}{\boldsymbol {v}}_{\boldsymbol {1}}} + +⁠ +and ⁠ + + + + + + p + + + 2 + + + = + + m + + 2 + + + + + v + + + 2 + + + + + {\displaystyle {\boldsymbol {p}}_{\boldsymbol {2}}=m_{2}{\boldsymbol {v}}_{\boldsymbol {2}}} + +⁠ collide to produce a single particle of conserved mass ⁠ + + + + m + = + + m + + 1 + + + + + + m + + 2 + + + + + {\displaystyle m=m_{1}+m_{2}} + +⁠ traveling at the center of mass velocity of the original system, + + + + + + v + + c + m + + + + = + + ( + + + m + + 1 + + + + + v + + 1 + + + + + + + m + + 2 + + + + + v + + 2 + + + + + ) + + + / + + + ( + + + m + + 1 + + + + + + m + + 2 + + + + ) + + + + {\displaystyle {\boldsymbol {v_{cm}}}=\left(m_{1}{\boldsymbol {v_{1}}}+m_{2}{\boldsymbol {v_{2}}}\right)/\left(m_{1}+m_{2}\right)} + +. The total momentum ⁠ + + + + + p + = + + p + + 1 + + + + + + p + + 2 + + + + + + {\displaystyle {\boldsymbol {p=p_{1}+p_{2}}}} + +⁠ is conserved. +Fig. 3-10 illustrates the inelastic collision of two particles from a relativistic perspective. The time components ⁠ + + + + + E + + 1 + + + + / + + c + + + {\displaystyle E_{1}/c} + +⁠ and ⁠ + + + + + E + + 2 + + + + / + + c + + + {\displaystyle E_{2}/c} + +⁠ add up to total E/c of the resultant vector, meaning that energy is conserved. Likewise, the space components ⁠ + + + + + + p + + 1 + + + + + + {\displaystyle {\boldsymbol {p_{1}}}} + +⁠ and ⁠ + + + + + + p + + 2 + + + + + + {\displaystyle {\boldsymbol {p_{2}}}} + +⁠ add up to form p of the resultant vector. The four-momentum is, as expected, a conserved quantity. However, the invariant mass of the fused particle, given by the point where the invariant hyperbola of the total momentum intersects the energy axis, is not equal to the sum of the invariant masses of the individual particles that collided. Indeed, it is larger than the sum of the individual masses: ⁠ + + + + m + > + + m + + 1 + + + + + + m + + 2 + + + + + {\displaystyle m>m_{1}+m_{2}} + +⁠. +Looking at the events of this scenario in reverse sequence, we see that non-conservation of mass is a common occurrence: when an unstable elementary particle spontaneously decays into two lighter particles, total energy is conserved, but the mass is not. Part of the mass is converted into kinetic energy. + +==== Choice of reference frames ==== + +The freedom to choose any frame in which to perform an analysis allows us to pick one which may be particularly convenient. For analysis of momentum and energy problems, the most convenient frame is usually the "center-of-momentum frame" (also called the zero-momentum frame, or COM frame). This is the frame in which the space component of the system's total momentum is zero. Fig. 3-11 illustrates the breakup of a high speed particle into two daughter particles. In the lab frame, the daughter particles are preferentially emitted in a direction oriented along the original particle's trajectory. In the COM frame, however, the two daughter particles are emitted in opposite directions, although their masses and the magnitude of their velocities are generally not the same. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-14.md b/data/en.wikipedia.org/wiki/Spacetime-14.md new file mode 100644 index 000000000..2c8bb5e83 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-14.md @@ -0,0 +1,158 @@ +--- +title: "Spacetime" +chunk: 15/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +==== Energy and momentum conservation ==== +In a Newtonian analysis of interacting particles, transformation between frames is simple because all that is necessary is to apply the Galilean transformation to all velocities. Since ⁠ + + + + + v + ′ + + = + v + − + u + + + {\displaystyle v'=v-u} + +⁠, the momentum ⁠ + + + + + p + ′ + + = + p + − + m + u + + + {\displaystyle p'=p-mu} + +⁠. If the total momentum of an interacting system of particles is observed to be conserved in one frame, it will likewise be observed to be conserved in any other frame. +Conservation of momentum in the COM frame amounts to the requirement that p = 0 both before and after collision. In the Newtonian analysis, conservation of mass dictates that ⁠ + + + + m + = + + m + + 1 + + + + + + m + + 2 + + + + + {\displaystyle m=m_{1}+m_{2}} + +⁠. In the simplified, one-dimensional scenarios that we have been considering, only one additional constraint is necessary before the outgoing momenta of the particles can be determined—an energy condition. In the one-dimensional case of a completely elastic collision with no loss of kinetic energy, the outgoing velocities of the rebounding particles in the COM frame will be precisely equal and opposite to their incoming velocities. In the case of a completely inelastic collision with total loss of kinetic energy, the outgoing velocities of the rebounding particles will be zero. +Newtonian momenta, calculated as ⁠ + + + + p + = + m + v + + + {\displaystyle p=mv} + +⁠, fail to behave properly under Lorentzian transformation. The linear transformation of velocities ⁠ + + + + + v + ′ + + = + v + − + u + + + {\displaystyle v'=v-u} + +⁠ is replaced by the highly nonlinear +⁠ + + + + + v + + ′ + + + = + ( + v + − + u + ) + + / + + ( + 1 + − + + v + u + + + / + + + + c + + 2 + + + + ) + + + {\displaystyle v^{\prime }=(v-u)/(1-{vu}/{c^{2}})} + +⁠ so that a calculation demonstrating conservation of momentum in one frame will be invalid in other frames. Einstein was faced with either having to give up conservation of momentum, or to change the definition of momentum. This second option was what he chose. + +The relativistic conservation law for energy and momentum replaces the three classical conservation laws for energy, momentum and mass. Mass is no longer conserved independently, because it has been subsumed into the total relativistic energy. This makes the relativistic conservation of energy a simpler concept than in nonrelativistic mechanics, because the total energy is conserved without any qualifications. Kinetic energy converted into heat or internal potential energy shows up as an increase in mass. + +== Introduction to curved spacetime == + +== Technical topics == + +=== Is spacetime really curved? === +In Poincaré's conventionalist views, the essential criteria according to which one should select a Euclidean versus non-Euclidean geometry would be economy and simplicity. A realist would say that Einstein discovered spacetime to be non-Euclidean. A conventionalist would say that Einstein merely found it more convenient to use non-Euclidean geometry. The conventionalist would maintain that Einstein's analysis said nothing about what the geometry of spacetime really is. +Such being said, + +Is it possible to represent general relativity in terms of flat spacetime? +Are there any situations where a flat spacetime interpretation of general relativity may be more convenient than the usual curved spacetime interpretation? +In response to the first question, a number of authors including Deser, Grishchuk, Rosen, Weinberg, etc. have provided various formulations of gravitation as a field in a flat manifold. Those theories are variously called "bimetric gravity", the "field-theoretical approach to general relativity", and so forth. Kip Thorne has provided a popular review of these theories. +The flat spacetime paradigm posits that matter creates a gravitational field that causes rulers to shrink when they are turned from circumferential orientation to radial, and that causes the ticking rates of clocks to dilate. The flat spacetime paradigm is fully equivalent to the curved spacetime paradigm in that they both represent the same physical phenomena. However, their mathematical formulations are entirely different. Working physicists routinely switch between using curved and flat spacetime techniques depending on the requirements of the problem. The flat spacetime paradigm is convenient when performing approximate calculations in weak fields. Hence, flat spacetime techniques tend be used when solving gravitational wave problems, while curved spacetime techniques tend be used in the analysis of black holes. + +=== Asymptotic symmetries === \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-15.md b/data/en.wikipedia.org/wiki/Spacetime-15.md new file mode 100644 index 000000000..4f9c385f5 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-15.md @@ -0,0 +1,179 @@ +--- +title: "Spacetime" +chunk: 16/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +The spacetime symmetry group for Special Relativity is the Poincaré group, which is a ten-dimensional group of three Lorentz boosts, three rotations, and four spacetime translations. It is logical to ask what symmetries if any might apply in General Relativity. A tractable case might be to consider the symmetries of spacetime as seen by observers located far away from all sources of the gravitational field. The naive expectation for asymptotically flat spacetime symmetries might be simply to extend and reproduce the symmetries of flat spacetime of special relativity, viz., the Poincaré group. +In 1962 Hermann Bondi, M. G. van der Burg, A. W. Metzner and Rainer K. Sachs addressed this asymptotic symmetry problem in order to investigate the flow of energy at infinity due to propagating gravitational waves. Their first step was to decide on some physically sensible boundary conditions to place on the gravitational field at lightlike infinity to characterize what it means to say a metric is asymptotically flat, making no a priori assumptions about the nature of the asymptotic symmetry group—not even the assumption that such a group exists. Then after designing what they considered to be the most sensible boundary conditions, they investigated the nature of the resulting asymptotic symmetry transformations that leave invariant the form of the boundary conditions appropriate for asymptotically flat gravitational fields. +What they found was that the asymptotic symmetry transformations actually do form a group and the structure of this group does not depend on the particular gravitational field that happens to be present. This means that, as expected, one can separate the kinematics of spacetime from the dynamics of the gravitational field at least at spatial infinity. The puzzling surprise in 1962 was their discovery of a rich infinite-dimensional group (the so-called BMS group) as the asymptotic symmetry group, instead of the finite-dimensional Poincaré group, which is a subgroup of the BMS group. Not only are the Lorentz transformations asymptotic symmetry transformations, there are also additional transformations that are not Lorentz transformations but are asymptotic symmetry transformations. In fact, they found an additional infinity of transformation generators known as supertranslations. This implies the conclusion that General Relativity (GR) does not reduce to special relativity in the case of weak fields at long distances. + +=== Riemannian geometry === + +=== Curved manifolds === + +For physical reasons, a spacetime continuum is mathematically defined as a four-dimensional, smooth, connected Lorentzian manifold + + + + ( + M + , + g + ) + + + {\displaystyle (M,g)} + +. This means the smooth Lorentz metric + + + + g + + + {\displaystyle g} + + has signature + + + + ( + 3 + , + 1 + ) + + + {\displaystyle (3,1)} + +. The metric determines the geometry of spacetime, as well as determining the geodesics of particles and light beams. About each point (event) on this manifold, coordinate charts are used to represent observers in reference frames. Usually, Cartesian coordinates + + + + ( + x + , + y + , + z + , + t + ) + + + {\displaystyle (x,y,z,t)} + + are used. Moreover, for simplicity's sake, units of measurement are usually chosen such that the speed of light + + + + c + + + {\displaystyle c} + + is equal to 1. +A reference frame (observer) can be identified with one of these coordinate charts; any such observer can describe any event + + + + p + + + {\displaystyle p} + +. Another reference frame may be identified by a second coordinate chart about + + + + p + + + {\displaystyle p} + +. Two observers (one in each reference frame) may describe the same event + + + + p + + + {\displaystyle p} + + but obtain different descriptions. +Usually, many overlapping coordinate charts are needed to cover a manifold. Given two coordinate charts, one containing + + + + p + + + {\displaystyle p} + + (representing an observer) and another containing + + + + q + + + {\displaystyle q} + + (representing another observer), the intersection of the charts represents the region of spacetime in which both observers can measure physical quantities and hence compare results. The relation between the two sets of measurements is given by a non-singular coordinate transformation on this intersection. The idea of coordinate charts as local observers who can perform measurements in their vicinity also makes good physical sense, as this is how one actually collects physical data—locally. +For example, two observers, one of whom is on Earth, but the other one who is on a fast rocket to Jupiter, may observe a comet crashing into Jupiter (this is the event + + + + p + + + {\displaystyle p} + +). In general, they will disagree about the exact location and timing of this impact, i.e., they will have different 4-tuples + + + + ( + x + , + y + , + z + , + t + ) + + + {\displaystyle (x,y,z,t)} + + (as they are using different coordinate systems). Although their kinematic descriptions will differ, dynamical (physical) laws, such as momentum conservation and the first law of thermodynamics, will still hold. In fact, relativity theory requires more than this in the sense that it stipulates these (and all other physical) laws must take the same form in all coordinate systems. This introduces tensors into relativity, by which all physical quantities are represented. +Geodesics are said to be timelike, null, or spacelike if the tangent vector to one point of the geodesic is of this nature. Paths of particles and light beams in spacetime are represented by timelike and null (lightlike) geodesics, respectively. + +=== Privileged character of 3+1 spacetime === + +== See also == + +== Notes == + +== References == + +== Further reading == +Barrow, John D.; Tipler, Frank J. (1986). The Anthropic Cosmological Principle (1st ed.). Oxford University Press. ISBN 978-0-19-282147-8. LCCN 87028148. +George F. Ellis and Ruth M. Williams (1992) Flat and curved space–times. Oxford University Press. ISBN 0-19-851164-7 +Lorentz, H. A., Einstein, Albert, Minkowski, Hermann, and Weyl, Hermann (1952) The Principle of Relativity: A Collection of Original Memoirs. Dover. +Lucas, John Randolph (1973) A Treatise on Time and Space. London: Methuen. +Penrose, Roger (2004). The Road to Reality. Oxford: Oxford University Press. ISBN 0-679-45443-8. Chapters 17–18. +Taylor, E. F.; Wheeler, John A. (1992). Spacetime Physics, Second Edition. Internet Archive: W. H. Freeman. ISBN 0-7167-2327-1. +Arkani-Hamed, Nima (1 December 2017). The Doom of Spacetime: Why It Must Dissolve Into More Fundamental Structures (Speech). The 2,384th Meeting Of The Society. Washington, D.C. Retrieved 16 July 2022. + +== External links == + + Media related to Spacetime at Wikimedia Commons +Albert Einstein on space–time 13th edition Encyclopædia Britannica Historical: Albert Einstein's 1926 article +Encyclopedia of Space–time and gravitation Scholarpedia Expert articles +Stanford Encyclopedia of Philosophy: "Space and Time: Inertial Frames" by Robert DiSalle. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-2.md b/data/en.wikipedia.org/wiki/Spacetime-2.md new file mode 100644 index 000000000..8ff7d3618 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-2.md @@ -0,0 +1,382 @@ +--- +title: "Spacetime" +chunk: 3/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +On 5 November 1907 (a little more than a year before his death), Minkowski introduced his geometric interpretation of spacetime in a lecture to the Göttingen Mathematical society with the title, The Relativity Principle (Das Relativitätsprinzip). On 21 September 1908, Minkowski presented his talk, Space and Time (Raum und Zeit), to the German Society of Scientists and Physicians. The opening words of Space and Time include Minkowski's statement that "Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence." Space and Time included the first public presentation of spacetime diagrams (Fig. 1-4), and included a remarkable demonstration that the concept of the invariant interval (discussed below), along with the empirical observation that the speed of light is finite, allows derivation of the entirety of special relativity. +The spacetime concept and the Lorentz group are closely connected to certain types of sphere, hyperbolic, or conformal geometries and their transformation groups already developed in the 19th century, in which invariant intervals analogous to the spacetime interval are used. +Einstein, for his part, was initially dismissive of Minkowski's geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital. In 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity. Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime. + +== Spacetime in special relativity == + +=== Spacetime interval === + +In three dimensions, the distance + + + + Δ + + d + + + + {\displaystyle \Delta {d}} + + between two points can be defined using the Pythagorean theorem: + + + + + ( + Δ + + d + + + ) + + 2 + + + = + ( + Δ + + x + + + ) + + 2 + + + + + ( + Δ + + y + + + ) + + 2 + + + + + ( + Δ + + z + + + ) + + 2 + + + + + {\displaystyle (\Delta {d})^{2}=(\Delta {x})^{2}+(\Delta {y})^{2}+(\Delta {z})^{2}} + + +Although two viewers may measure the x, y, and z position of the two points using different coordinate systems, the distance between the points will be the same for both, assuming that they are measuring using the same units. The distance is "invariant". +In special relativity, however, the distance between two points is no longer the same if measured by two different observers, when one of the observers is moving, because of Lorentz contraction. The situation is even more complicated if the two points are separated in time as well as in space. For example, if one observer sees two events occur at the same place, but at different times, a person moving with respect to the first observer will see the two events occurring at different places, because the moving point of view sees itself as stationary, and the position of the event as receding or approaching. Thus, a different measure must be used to measure the effective "distance" between two events. +In four-dimensional spacetime, the analog to distance is the interval. Although time comes in as a fourth dimension, it is treated differently than the spatial dimensions. Minkowski space hence differs in important respects from four-dimensional Euclidean space. The fundamental reason for merging space and time into spacetime is that space and time are separately not invariant, which is to say that, under the proper conditions, different observers will disagree on the length of time between two events (because of time dilation) or the distance between the two events (because of length contraction). Special relativity provides a new invariant, called the spacetime interval, which combines distances in space and in time. All observers who measure the time and distance between any two events will end up computing the same spacetime interval. Suppose an observer measures two events as being separated in time by + + + + Δ + t + + + {\displaystyle \Delta t} + + and a spatial distance + + + + Δ + x + . + + + {\displaystyle \Delta x.} + + Then the squared spacetime interval + + + + ( + Δ + + s + + + ) + + 2 + + + + + {\displaystyle (\Delta {s})^{2}} + + between the two events that are separated by a distance + + + + Δ + + x + + + + {\displaystyle \Delta {x}} + + in space and by + + + + Δ + + c + t + + = + c + Δ + t + + + {\displaystyle \Delta {ct}=c\Delta t} + + in the + + + + c + t + + + {\displaystyle ct} + +-coordinate is: + + + + + ( + Δ + s + + ) + + 2 + + + = + ( + Δ + c + t + + ) + + 2 + + + − + ( + Δ + x + + ) + + 2 + + + , + + + {\displaystyle (\Delta s)^{2}=(\Delta ct)^{2}-(\Delta x)^{2},} + + +or for three space dimensions, + + + + + ( + Δ + s + + ) + + 2 + + + = + ( + Δ + c + t + + ) + + 2 + + + − + ( + Δ + x + + ) + + 2 + + + − + ( + Δ + y + + ) + + 2 + + + − + ( + Δ + z + + ) + + 2 + + + . + + + {\displaystyle (\Delta s)^{2}=(\Delta ct)^{2}-(\Delta x)^{2}-(\Delta y)^{2}-(\Delta z)^{2}.} + + +The constant + + + + c + , + + + {\displaystyle c,} + + the speed of light, converts time + + + + t + + + {\displaystyle t} + + units (like seconds) into space units (like meters). The squared interval + + + + Δ + + s + + 2 + + + + + {\displaystyle \Delta s^{2}} + + is a measure of separation between events A and B that are time separated and in addition space separated either because there are two separate objects undergoing events, or because a single object in space is moving inertially between its events. The separation interval is the difference between the square of the spatial distance separating event B from event A and the square of the spatial distance traveled by a light signal in that same time interval + + + + Δ + t + + + {\displaystyle \Delta t} + +. If the event separation is due to a light signal, then this difference vanishes and + + + + Δ + s + = + 0 + + + {\displaystyle \Delta s=0} + +. +When the event considered is infinitesimally close to each other, then we may write + + + + + d + + s + + 2 + + + = + + c + + 2 + + + d + + t + + 2 + + + − + d + + x + + 2 + + + − + d + + y + + 2 + + + − + d + + z + + 2 + + + . + + + {\displaystyle ds^{2}=c^{2}dt^{2}-dx^{2}-dy^{2}-dz^{2}.} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-3.md b/data/en.wikipedia.org/wiki/Spacetime-3.md new file mode 100644 index 000000000..f409b1d45 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-3.md @@ -0,0 +1,411 @@ +--- +title: "Spacetime" +chunk: 4/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +In a different inertial frame, say with coordinates + + + + ( + + t + ′ + + , + + x + ′ + + , + + y + ′ + + , + + z + ′ + + ) + + + {\displaystyle (t',x',y',z')} + +, the spacetime interval + + + + d + + s + ′ + + + + {\displaystyle ds'} + + can be written in a same form as above. Because of the constancy of speed of light, the light events in all inertial frames belong to zero interval, + + + + d + s + = + d + + s + ′ + + = + 0 + + + {\displaystyle ds=ds'=0} + +. For any other infinitesimal event where + + + + d + s + ≠ + 0 + + + {\displaystyle ds\neq 0} + +, one can prove that + + + + d + + s + + 2 + + + = + d + + s + + ′ + + 2 + + + + + + {\displaystyle ds^{2}=ds'^{2}} + + +which in turn upon integration leads to + + + + s + = + + s + ′ + + + + {\displaystyle s=s'} + +. The invariance of the spacetime interval between the same events for all inertial frames of reference is one of the fundamental results of special theory of relativity. +Although for brevity, one frequently sees interval expressions expressed without deltas, including in most of the following discussion, it should be understood that in general, + + + + x + + + {\displaystyle x} + + means + + + + Δ + + x + + + + {\displaystyle \Delta {x}} + +, etc. We are always concerned with differences of spatial or temporal coordinate values belonging to two events, and since there is no preferred origin, single coordinate values have no essential meaning. + +The equation above is similar to the Pythagorean theorem, except with a minus sign between the + + + + ( + c + t + + ) + + 2 + + + + + {\displaystyle (ct)^{2}} + + and the + + + + + x + + 2 + + + + + {\displaystyle x^{2}} + + terms. The spacetime interval is the quantity + + + + + s + + 2 + + + , + + + {\displaystyle s^{2},} + + not + + + + s + + + {\displaystyle s} + + itself. The reason is that unlike distances in Euclidean geometry, intervals in Minkowski spacetime can be negative. Rather than deal with square roots of negative numbers, physicists customarily regard + + + + + s + + 2 + + + + + {\displaystyle s^{2}} + + as a distinct symbol in itself, rather than the square of something. + +Note: There are two sign conventions in use in the relativity literature: + + + + + + s + + 2 + + + = + ( + c + t + + ) + + 2 + + + − + + x + + 2 + + + − + + y + + 2 + + + − + + z + + 2 + + + + + {\displaystyle s^{2}=(ct)^{2}-x^{2}-y^{2}-z^{2}} + + +and + + + + + + s + + 2 + + + = + − + ( + c + t + + ) + + 2 + + + + + + x + + 2 + + + + + + y + + 2 + + + + + + z + + 2 + + + + + {\displaystyle s^{2}=-(ct)^{2}+x^{2}+y^{2}+z^{2}} + + +These sign conventions are associated with the metric signatures (+−−−) and (−+++). A minor variation is to place the time coordinate last rather than first. Both conventions are widely used within the field of study. +In the following discussion, we use the first convention. +In general + + + + + s + + 2 + + + + + {\displaystyle s^{2}} + + can assume any real number value. If + + + + + s + + 2 + + + + + {\displaystyle s^{2}} + + is positive, the spacetime interval is referred to as timelike. Since spatial distance traversed by any massive object is always less than distance traveled by the light for the same time interval, positive intervals are always timelike. If + + + + + s + + 2 + + + + + {\displaystyle s^{2}} + + is negative, the spacetime interval is said to be spacelike. Spacetime intervals are equal to zero when + + + + x + = + ± + c + t + . + + + {\displaystyle x=\pm ct.} + + In other words, the spacetime interval between two events on the world line of something moving at the speed of light is zero. Such an interval is termed lightlike or null. A photon arriving in our eye from a distant star will not have aged, despite having (from our perspective) spent years in its passage. +A spacetime diagram is typically drawn with only a single space and a single time coordinate. Fig. 2-1 presents a spacetime diagram illustrating the world lines (i.e. paths in spacetime) of two photons, A and B, originating from the same event and going in opposite directions. In addition, C illustrates the world line of a slower-than-light-speed object. The vertical time coordinate is scaled by + + + + c + + + {\displaystyle c} + + so that it has the same units (meters) as the horizontal space coordinate. Since photons travel at the speed of light, their world lines have a slope of ±1. In other words, every meter that a photon travels to the left or right requires approximately 3.3 nanoseconds of time. + +=== Reference frames === + +To gain insight in how spacetime coordinates measured by observers in different reference frames compare with each other, it is useful to work with a simplified setup with frames in a standard configuration. With care, this allows simplification of the math with no loss of generality in the conclusions that are reached. In Fig. 2-2, two Galilean reference frames (i.e. conventional 3-space frames) are displayed in relative motion. Frame S belongs to a first observer O, and frame S′ (pronounced "S prime") belongs to a second observer O′. + +The x, y, z axes of frame S are oriented parallel to the respective primed axes of frame S′. +Frame S′ moves in the x-direction of frame S with a constant velocity v as measured in frame S. +The origins of frames S and S′ are coincident when time t = 0 for frame S and t′ = 0 for frame S′. +Fig. 2-3a redraws Fig. 2-2 in a different orientation. Fig. 2-3b illustrates a relativistic spacetime diagram from the viewpoint of observer O. Since S and S′ are in standard configuration, their origins coincide at times t = 0 in frame S and t′ = 0 in frame S′. The ct′ axis passes through the events in frame S′ which have x′ = 0. But the points with x′ = 0 are moving in the x-direction of frame S with velocity v, so that they are not coincident with the ct axis at any time other than zero. Therefore, the ct′ axis is tilted with respect to the ct axis by an angle θ given by + + + + + tan + ⁡ + ( + θ + ) + = + v + + / + + c + . + + + {\displaystyle \tan(\theta )=v/c.} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-4.md b/data/en.wikipedia.org/wiki/Spacetime-4.md new file mode 100644 index 000000000..7e939cb1b --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-4.md @@ -0,0 +1,23 @@ +--- +title: "Spacetime" +chunk: 5/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +The x′ axis is also tilted with respect to the x axis. To determine the angle of this tilt, we recall that the slope of the world line of a light pulse is always ±1. Fig. 2-3c presents a spacetime diagram from the viewpoint of observer O′. Event P represents the emission of a light pulse at x′ = 0, ct′ = −a. The pulse is reflected from a mirror situated at distance a from the light source (event Q), and returns to the light source at x′ = 0, ct′ = a (event R). +The same events P, Q, R are plotted in Fig. 2-3b in the frame of observer O. The light paths have slopes = 1 and −1, so that △PQR forms a right triangle with PQ and QR both at 45 degrees to the x and ct axes. Since OP = OQ = OR, the angle between x′ and x must also be θ. +While the rest frame has space and time axes that meet at right angles, the moving frame is drawn with axes that meet at an acute angle. The frames are actually equivalent. The asymmetry is due to unavoidable distortions in how spacetime coordinates can map onto a Cartesian plane, and should be considered no stranger than the manner in which, on a Mercator projection of the Earth, the relative sizes of land masses near the poles (Greenland and Antarctica) are highly exaggerated relative to land masses near the Equator. + +=== Light cone === + +In Fig. 2–4, event O is at the origin of a spacetime diagram, and the two diagonal lines represent all events that have zero spacetime interval with respect to the origin event. These two lines form what is called the light cone of the event O, since adding a second spatial dimension (Fig. 2-5) makes the appearance that of two right circular cones meeting with their apices at O. One cone extends into the future (t>0), the other into the past (t<0). + +A light (double) cone divides spacetime into separate regions with respect to its apex. The interior of the future light cone consists of all events that are separated from the apex by more time (temporal distance) than necessary to cross their spatial distance at lightspeed; these events comprise the timelike future of the event O. Likewise, the timelike past comprises the interior events of the past light cone. So in timelike intervals Δct is greater than Δx, making timelike intervals positive. +The region exterior to the light cone consists of events that are separated from the event O by more space than can be crossed at lightspeed in the given time. These events comprise the so-called spacelike region of the event O, denoted "Elsewhere" in Fig. 2-4. Events on the light cone itself are said to be lightlike (or null separated) from O. Because of the invariance of the spacetime interval, all observers will assign the same light cone to any given event, and thus will agree on this division of spacetime. +The light cone has an essential role within the concept of causality. It is possible for a not-faster-than-light-speed signal to travel from the position and time of O to the position and time of D (Fig. 2-4). It is hence possible for event O to have a causal influence on event D. The future light cone contains all the events that could be causally influenced by O. Likewise, it is possible for a not-faster-than-light-speed signal to travel from the position and time of A, to the position and time of O. The past light cone contains all the events that could have a causal influence on O. In contrast, assuming that signals cannot travel faster than the speed of light, any event, like e.g. B or C, in the spacelike region (Elsewhere), cannot either affect event O, nor can they be affected by event O employing such signalling. Under this assumption any causal relationship between event O and any events in the spacelike region of a light cone is excluded. + +=== Relativity of simultaneity === \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-5.md b/data/en.wikipedia.org/wiki/Spacetime-5.md new file mode 100644 index 000000000..40ad97335 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-5.md @@ -0,0 +1,132 @@ +--- +title: "Spacetime" +chunk: 6/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +All observers will agree that for any given event, an event within the given event's future light cone occurs after the given event. Likewise, for any given event, an event within the given event's past light cone occurs before the given event. The before–after relationship observed for timelike-separated events remains unchanged no matter what the reference frame of the observer, i.e. no matter how the observer may be moving. The situation is quite different for spacelike-separated events. Fig. 2-4 was drawn from the reference frame of an observer moving at v = 0. From this reference frame, event C is observed to occur after event O, and event B is observed to occur before event O. +From a different reference frame, the orderings of these non-causally-related events can be reversed. In particular, one notes that if two events are simultaneous in a particular reference frame, they are necessarily separated by a spacelike interval and thus are noncausally related. The observation that simultaneity is not absolute, but depends on the observer's reference frame, is termed the relativity of simultaneity. +Fig. 2-6 illustrates the use of spacetime diagrams in the analysis of the relativity of simultaneity. The events in spacetime are invariant, but the coordinate frames transform as discussed above for Fig. 2-3. The three events (A, B, C) are simultaneous from the reference frame of an observer moving at v = 0. From the reference frame of an observer moving at v = 0.3c, the events appear to occur in the order C, B, A. From the reference frame of an observer moving at v = −0.5c, the events appear to occur in the order A, B, C. The white line represents a plane of simultaneity being moved from the past of the observer to the future of the observer, highlighting events residing on it. The gray area is the light cone of the observer, which remains invariant. +A spacelike spacetime interval gives the same distance that an observer would measure if the events being measured were simultaneous to the observer. A spacelike spacetime interval hence provides a measure of proper distance, i.e. the true distance = + + + + + + − + + s + + 2 + + + + + . + + + {\displaystyle {\sqrt {-s^{2}}}.} + + Likewise, a timelike spacetime interval gives the same measure of time as would be presented by the cumulative ticking of a clock that moves along a given world line. A timelike spacetime interval hence provides a measure of the proper time = + + + + + + + s + + 2 + + + + + . + + + {\displaystyle {\sqrt {s^{2}}}.} + + +=== Invariant hyperbola === + +In Euclidean space (having spatial dimensions only), the set of points equidistant (using the Euclidean metric) from some point form a circle (in two dimensions) or a sphere (in three dimensions). In (1+1)-dimensional Minkowski spacetime (having one temporal and one spatial dimension), the points at some constant spacetime interval away from the origin (using the Minkowski metric) form curves given by the two equations + + + + + ( + c + t + + ) + + 2 + + + − + + x + + 2 + + + = + ± + + s + + 2 + + + , + + + {\displaystyle (ct)^{2}-x^{2}=\pm s^{2},} + + +with + + + + + s + + 2 + + + + + {\displaystyle s^{2}} + +some positive real constant. These equations describe two families of hyperbolae in an x–ct spacetime diagram, which are termed invariant hyperbolae. +In Fig. 2-7a, each magenta hyperbola connects all events having some fixed spacelike separation from the origin, while the green hyperbolae connect events of equal timelike separation. +The magenta hyperbolae, which cross the x axis, are timelike curves, which is to say that these hyperbolae represent actual paths that can be traversed by (constantly accelerating) particles in spacetime: Between any two events on one hyperbola a causality relation is possible, because the inverse of the slope—representing the necessary speed—for all secants is less than + + + + c + + + {\displaystyle c} + +. On the other hand, the green hyperbolae, which cross the ct axis, are spacelike curves because all intervals along these hyperbolae are spacelike intervals: No causality is possible between any two points on one of these hyperbolae, because all secants represent speeds larger than + + + + c + + + {\displaystyle c} + +. +Fig. 2-7b reflects the situation in (1+2)-dimensional Minkowski spacetime (one temporal and two spatial dimensions) with the corresponding hyperboloids. The invariant hyperbolae displaced by spacelike intervals from the origin generate hyperboloids of one sheet, while the invariant hyperbolae displaced by timelike intervals from the origin generate hyperboloids of two sheets. +The (1+2)-dimensional boundary between space- and time-like hyperboloids, established by the events forming a zero spacetime interval to the origin, is made up by degenerating the hyperboloids to the light cone. In (1+1)-dimensions the hyperbolae degenerate to the two grey 45°-lines depicted in Fig. 2-7a. + +=== Time dilation and length contraction === + +Fig. 2-8 illustrates the invariant hyperbola for all events that can be reached from the origin in a proper time of 5 meters (approximately 1.67×10−8 s). Different world lines represent clocks moving at different speeds. A clock that is stationary with respect to the observer has a world line that is vertical, and the elapsed time measured by the observer is the same as the proper time. For a clock traveling at 0.3 c, the elapsed time measured by the observer is 5.24 meters (1.75×10−8 s), while for a clock traveling at 0.7 c, the elapsed time measured by the observer is 7.00 meters (2.34×10−8 s). +This illustrates the phenomenon known as time dilation. Clocks that travel faster take longer (in the observer frame) to tick out the same amount of proper time, and they travel further along the x–axis within that proper time than they would have without time dilation. The measurement of time dilation by two observers in different inertial reference frames is mutual. If observer O measures the clocks of observer O′ as running slower in his frame, observer O′ in turn will measure the clocks of observer O as running slower. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-6.md b/data/en.wikipedia.org/wiki/Spacetime-6.md new file mode 100644 index 000000000..80e83aeb0 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-6.md @@ -0,0 +1,26 @@ +--- +title: "Spacetime" +chunk: 7/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +Length contraction, like time dilation, is a manifestation of the relativity of simultaneity. Measurement of length requires measurement of the spacetime interval between two events that are simultaneous in one's frame of reference. But events that are simultaneous in one frame of reference are, in general, not simultaneous in other frames of reference. +Fig. 2-9 illustrates the motions of a 1 m rod that is traveling at 0.5 c along the x axis. The edges of the blue band represent the world lines of the rod's two endpoints. The invariant hyperbola illustrates events separated from the origin by a spacelike interval of 1 m. The endpoints O and B measured when t′ = 0 are simultaneous events in the S′ frame. But to an observer in frame S, events O and B are not simultaneous. To measure length, the observer in frame S measures the endpoints of the rod as projected onto the x-axis along their world lines. The projection of the rod's world sheet onto the x axis yields the foreshortened length OC. +(not illustrated) Drawing a vertical line through A so that it intersects the x′ axis demonstrates that, even as OB is foreshortened from the point of view of observer O, OA is likewise foreshortened from the point of view of observer O′. In the same way that each observer measures the other's clocks as running slow, each observer measures the other's rulers as being contracted. +In regards to mutual length contraction, Fig. 2-9 illustrates that the primed and unprimed frames are mutually rotated by a hyperbolic angle (analogous to ordinary angles in Euclidean geometry). Because of this rotation, the projection of a primed meter-stick onto the unprimed x-axis is foreshortened, while the projection of an unprimed meter-stick onto the primed x′-axis is likewise foreshortened. + +=== Mutual time dilation and the twin paradox === + +==== Mutual time dilation ==== +Mutual time dilation and length contraction tend to strike beginners as inherently self-contradictory concepts. If an observer in frame S measures a clock, at rest in frame S', as running slower than his', while S' is moving at speed v in S, then the principle of relativity requires that an observer in frame S' likewise measures a clock in frame S, moving at speed −v in S', as running slower than hers. How two clocks can run both slower than the other, is an important question that "goes to the heart of understanding special relativity." +This apparent contradiction stems from not correctly taking into account the different settings of the necessary, related measurements. These settings allow for a consistent explanation of the only apparent contradiction. It is not about the abstract ticking of two identical clocks, but about how to measure in one frame the temporal distance of two ticks of a moving clock. It turns out that in mutually observing the duration between ticks of clocks, each moving in the respective frame, different sets of clocks must be involved. In order to measure in frame S the tick duration of a moving clock W′ (at rest in S′), one uses two additional, synchronized clocks W1 and W2 at rest in two arbitrarily fixed points in S with the spatial distance d. + +Two events can be defined by the condition "two clocks are simultaneously at one place", i.e., when W′ passes each W1 and W2. For both events the two readings of the collocated clocks are recorded. The difference of the two readings of W1 and W2 is the temporal distance of the two events in S, and their spatial distance is d. The difference of the two readings of W′ is the temporal distance of the two events in S′. In S′ these events are only separated in time, they happen at the same place in S′. Because of the invariance of the spacetime interval spanned by these two events, and the nonzero spatial separation d in S, the temporal distance in S′ must be smaller than the one in S: the smaller temporal distance between the two events, resulting from the readings of the moving clock W′, belongs to the slower running clock W′. +Conversely, for judging in frame S′ the temporal distance of two events on a moving clock W (at rest in S), one needs two clocks at rest in S′. + +In this comparison the clock W is moving by with velocity −v. Recording again the four readings for the events, defined by "two clocks simultaneously at one place", results in the analogous temporal distances of the two events, now temporally and spatially separated in S′, and only temporally separated but collocated in S. To keep the spacetime interval invariant, the temporal distance in S must be smaller than in S′, because of the spatial separation of the events in S′: now clock W is observed to run slower. +The necessary recordings for the two judgements, with "one moving clock" and "two clocks at rest" in respectively S or S′, involves two different sets, each with three clocks. Since there are different sets of clocks involved in the measurements, there is no inherent necessity that the measurements be reciprocally "consistent" such that, if one observer measures the moving clock to be slow, the other observer measures the other clock to be fast. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-7.md b/data/en.wikipedia.org/wiki/Spacetime-7.md new file mode 100644 index 000000000..bddfdbfb5 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-7.md @@ -0,0 +1,24 @@ +--- +title: "Spacetime" +chunk: 8/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +Fig. 2-10 illustrates the previous discussion of mutual time dilation with Minkowski diagrams. The upper picture reflects the measurements as seen from frame S "at rest" with unprimed, rectangular axes, and frame S′ "moving with v > 0", coordinatized by primed, oblique axes, slanted to the right; the lower picture shows frame S′ "at rest" with primed, rectangular coordinates, and frame S "moving with −v < 0", with unprimed, oblique axes, slanted to the left. +Each line drawn parallel to a spatial axis (x, x′) represents a line of simultaneity. All events on such a line have the same time value (ct, ct′). Likewise, each line drawn parallel to a temporal axis (ct, ct′) represents a line of equal spatial coordinate values (x, x′). + +One may designate in both pictures the origin O (= O′) as the event, where the respective "moving clock" is collocated with the "first clock at rest" in both comparisons. Obviously, for this event the readings on both clocks in both comparisons are zero. As a consequence, the worldlines of the moving clocks are the slanted to the right ct′-axis (upper pictures, clock W′) and the slanted to the left ct-axes (lower pictures, clock W). The worldlines of W1 and W′1 are the corresponding vertical time axes (ct in the upper pictures, and ct′ in the lower pictures). +In the upper picture the place for W2 is taken to be Ax > 0, and thus the worldline (not shown in the pictures) of this clock intersects the worldline of the moving clock (the ct′-axis) in the event labelled A, where "two clocks are simultaneously at one place". In the lower picture the place for W′2 is taken to be Cx′ < 0, and so in this measurement the moving clock W passes W′2 in the event C. +In the upper picture the ct-coordinate At of the event A (the reading of W2) is labeled B, thus giving the elapsed time between the two events, measured with W1 and W2, as OB. For a comparison, the length of the time interval OA, measured with W′, must be transformed to the scale of the ct-axis. This is done by the invariant hyperbola (see also Fig. 2-8) through A, connecting all events with the same spacetime interval from the origin as A. This yields the event C on the ct-axis, and obviously: OC < OB, the "moving" clock W′ runs slower. +To show the mutual time dilation immediately in the upper picture, the event D may be constructed as the event at x′ = 0 (the location of clock W′ in S′), that is simultaneous to C (OC has equal spacetime interval as OA) in S′. This shows that the time interval OD is longer than OA, showing that the "moving" clock runs slower. +In the lower picture the frame S is moving with velocity −v in the frame S′ at rest. The worldline of clock W is the ct-axis (slanted to the left), the worldline of W′1 is the vertical ct′-axis, and the worldline of W′2 is the vertical through event C, with ct′-coordinate D. The invariant hyperbola through event C scales the time interval OC to OA, which is shorter than OD; also, B is constructed (similar to D in the upper pictures) as simultaneous to A in S, at x = 0. The result OB > OC corresponds again to above. +The word "measure" is important. In classical physics an observer cannot affect an observed object, but the object's state of motion can affect the observer's observations of the object. + +==== Twin paradox ==== +Many introductions to special relativity illustrate the differences between Galilean relativity and special relativity by posing a series of "paradoxes". These paradoxes are, in fact, ill-posed problems, resulting from our unfamiliarity with velocities comparable to the speed of light. The remedy is to solve many problems in special relativity and to become familiar with its so-called counter-intuitive predictions. The geometrical approach to studying spacetime is considered one of the best methods for developing a modern intuition. +The twin paradox is a thought experiment involving identical twins, one of whom makes a journey into space in a high-speed rocket, returning home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin observes the other twin as moving, and so at first glance, it would appear that each should find the other to have aged less. The twin paradox sidesteps the justification for mutual time dilation presented above by avoiding the requirement for a third clock. Nevertheless, the twin paradox is not a true paradox because it is easily understood within the context of special relativity. +The impression that a paradox exists stems from a misunderstanding of what special relativity states. Special relativity does not declare all frames of reference to be equivalent, only inertial frames. The traveling twin's frame is not inertial during periods when she is accelerating. Furthermore, the difference between the twins is observationally detectable: the traveling twin needs to fire her rockets to be able to return home, while the stay-at-home twin does not. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-8.md b/data/en.wikipedia.org/wiki/Spacetime-8.md new file mode 100644 index 000000000..9fbe4cdf7 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-8.md @@ -0,0 +1,86 @@ +--- +title: "Spacetime" +chunk: 9/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +These distinctions should result in a difference in the twins' ages. The spacetime diagram of Fig. 2-11 presents the simple case of a twin going straight out along the x axis and immediately turning back. From the standpoint of the stay-at-home twin, there is nothing puzzling about the twin paradox at all. The proper time measured along the traveling twin's world line from O to C, plus the proper time measured from C to B, is less than the stay-at-home twin's proper time measured from O to A to B. More complex trajectories require integrating the proper time between the respective events along the curve (i.e. the path integral) to calculate the total amount of proper time experienced by the traveling twin. +Complications arise if the twin paradox is analyzed from the traveling twin's point of view. +Weiss's nomenclature, designating the stay-at-home twin as Terence and the traveling twin as Stella, is hereafter used. +Stella is not in an inertial frame. Given this fact, it is sometimes incorrectly stated that full resolution of the twin paradox requires general relativity: + +A pure SR analysis would be as follows: Analyzed in Stella's rest frame, she is motionless for the entire trip. When she fires her rockets for the turnaround, she experiences a pseudo force which resembles a gravitational force. Figs. 2-6 and 2-11 illustrate the concept of lines (planes) of simultaneity: Lines parallel to the observer's x-axis (xy-plane) represent sets of events that are simultaneous in the observer frame. In Fig. 2-11, the blue lines connect events on Terence's world line which, from Stella's point of view, are simultaneous with events on her world line. (Terence, in turn, would observe a set of horizontal lines of simultaneity.) Throughout both the outbound and the inbound legs of Stella's journey, she measures Terence's clocks as running slower than her own. But during the turnaround (i.e. between the bold blue lines in the figure), a shift takes place in the angle of her lines of simultaneity, corresponding to a rapid skip-over of the events in Terence's world line that Stella considers to be simultaneous with her own. Therefore, at the end of her trip, Stella finds that Terence has aged more than she has. +Although general relativity is not required to analyze the twin paradox, application of the Equivalence Principle of general relativity does provide some additional insight into the subject. Stella is not stationary in an inertial frame. Analyzed in Stella's rest frame, she is motionless for the entire trip. When she is coasting her rest frame is inertial, and Terence's clock will appear to run slow. But when she fires her rockets for the turnaround, her rest frame is an accelerated frame and she experiences a force which is pushing her as if she were in a gravitational field. Terence will appear to be high up in that field and because of gravitational time dilation, his clock will appear to run fast, so much so that the net result will be that Terence has aged more than Stella when they are back together. The theoretical arguments predicting gravitational time dilation are not exclusive to general relativity. Any theory of gravity will predict gravitational time dilation if it respects the principle of equivalence, including Newton's theory. + +=== Gravitation === +This introductory section has focused on the spacetime of special relativity, since it is the easiest to describe. Minkowski spacetime is flat, takes no account of gravity, is uniform throughout, and serves as nothing more than a static background for the events that take place in it. The presence of gravity greatly complicates the description of spacetime. In general relativity, spacetime is no longer a static background, but actively interacts with the physical systems that it contains. Spacetime curves in the presence of matter, can propagate waves, bends light, and exhibits a host of other phenomena. A few of these phenomena are described in the later sections of this article. + +== Basic mathematics of spacetime == + +=== Galilean transformations === + +A basic goal is to be able to compare measurements made by observers in relative motion. If there is an observer O in frame S who has measured the time and space coordinates of an event, assigning this event three Cartesian coordinates and the time as measured on his lattice of synchronized clocks (x, y, z, t) (see Fig. 1-1). A second observer O′ in a different frame S′ measures the same event in her coordinate system and her lattice of synchronized clocks (x′, y′, z′, t′). With inertial frames, neither observer is under acceleration, and a simple set of equations allows us to relate coordinates (x, y, z, t) to (x′, y′, z′, t′). Given that the two coordinate systems are in standard configuration, meaning that they are aligned with parallel (x, y, z) coordinates and that t = 0 when t′ = 0, the coordinate transformation is as follows: + + + + + + x + ′ + + = + x + − + v + t + + + {\displaystyle x'=x-vt} + + + + + + + y + ′ + + = + y + + + {\displaystyle y'=y} + + + + + + + z + ′ + + = + z + + + {\displaystyle z'=z} + + + + + + + t + ′ + + = + t + . + + + {\displaystyle t'=t.} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Spacetime-9.md b/data/en.wikipedia.org/wiki/Spacetime-9.md new file mode 100644 index 000000000..1847c9622 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Spacetime-9.md @@ -0,0 +1,313 @@ +--- +title: "Spacetime" +chunk: 10/16 +source: "https://en.wikipedia.org/wiki/Spacetime" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:12.625899+00:00" +instance: "kb-cron" +--- + +Fig. 3-1 illustrates that in Newton's theory, time is universal, not the velocity of light. Consider the following thought experiment: The red arrow illustrates a train that is moving at 0.4 c with respect to the platform. Within the train, a passenger shoots a bullet with a speed of 0.4 c in the frame of the train. The blue arrow illustrates that a person standing on the train tracks measures the bullet as traveling at 0.8 c. This is in accordance with our naive expectations. +More generally, assuming that frame S′ is moving at velocity v with respect to frame S, then within frame S′, observer O′ measures an object moving with velocity u′. Velocity u with respect to frame S, since x = ut, x′ = x − vt, and t = t′, can be written as x′ = ut − vt = (u − v)t = (u − v)t′. This leads to u′ = x′/t′ and ultimately + + + + + + u + ′ + + = + u + − + v + + + {\displaystyle u'=u-v} + + or + + + + u + = + + u + ′ + + + + v + , + + + {\displaystyle u=u'+v,} + + +which is the common-sense Galilean law for the addition of velocities. + +=== Relativistic composition of velocities === + +The composition of velocities is quite different in relativistic spacetime. To reduce the complexity of the equations slightly, we introduce a common shorthand for the ratio of the speed of an object relative to light, + + + + + β + = + v + + / + + c + + + {\displaystyle \beta =v/c} + + +Fig. 3-2a illustrates a red train that is moving forward at a speed given by v/c = β = s/a. From the primed frame of the train, a passenger shoots a bullet with a speed given by u′/c = β′ = n/m, where the distance is measured along a line parallel to the red x′ axis rather than parallel to the black x axis. What is the composite velocity u of the bullet relative to the platform, as represented by the blue arrow? Referring to Fig. 3-2b: + +From the platform, the composite speed of the bullet is given by u = c(s + r)/(a + b). +The two yellow triangles are similar because they are right triangles that share a common angle α. In the large yellow triangle, the ratio s/a = v/c = β. +The ratios of corresponding sides of the two yellow triangles are constant, so that r/a = b/s = n/m = β′. So b = u′s/c and r = u′a/c. +Substitute the expressions for b and r into the expression for u in step 1 to yield Einstein's formula for the addition of velocities: + + + + + u + = + + + + v + + + + u + ′ + + + + 1 + + + ( + v + + u + ′ + + + / + + + c + + 2 + + + ) + + + + . + + + {\displaystyle u={v+u' \over 1+(vu'/c^{2})}.} + + +The relativistic formula for addition of velocities presented above exhibits several important features: + +If u′ and v are both very small compared with the speed of light, then the product vu′/c2 becomes vanishingly small, and the overall result becomes indistinguishable from the Galilean formula (Newton's formula) for the addition of velocities: u = u′ + v. The Galilean formula is a special case of the relativistic formula applicable to low velocities. +If u′ is set equal to c, then the formula yields u = c regardless of the starting value of v. The velocity of light is the same for all observers regardless their motions relative to the emitting source. + +=== Time dilation and length contraction revisited === + +It is straightforward to obtain quantitative expressions for time dilation and length contraction. Fig. 3-3 is a composite image containing individual frames taken from two previous animations, simplified and relabeled for the purposes of this section. +To reduce the complexity of the equations slightly, there are a variety of different shorthand notations for ct: + + + + + + T + + = + c + t + + + {\displaystyle \mathrm {T} =ct} + + and + + + + w + = + c + t + + + {\displaystyle w=ct} + + are common. +One also sees very frequently the use of the convention + + + + c + = + 1. + + + {\displaystyle c=1.} + + +In Fig. 3-3a, segments OA and OK represent equal spacetime intervals. Time dilation is represented by the ratio OB/OK. The invariant hyperbola has the equation w = √x2 + k2 where k = OK, and the red line representing the world line of a particle in motion has the equation w = x/β = xc/v. A bit of algebraic manipulation yields + + + + O + B + = + O + K + + / + + + + 1 + − + + v + + 2 + + + + / + + + c + + 2 + + + + + . + + + {\textstyle OB=OK/{\sqrt {1-v^{2}/c^{2}}}.} + + +The expression involving the square root symbol appears very frequently in relativity, and one over the expression is called the Lorentz factor, denoted by the Greek letter gamma + + + + γ + + + {\displaystyle \gamma } + +: + + + + + γ + = + + + 1 + + 1 + − + + v + + 2 + + + + / + + + c + + 2 + + + + + + = + + + 1 + + 1 + − + + β + + 2 + + + + + + + + {\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}={\frac {1}{\sqrt {1-\beta ^{2}}}}} + + +If v is greater than or equal to c, the expression for + + + + γ + + + {\displaystyle \gamma } + + becomes physically meaningless, implying that c is the maximum possible speed in nature. For any v greater than zero, the Lorentz factor will be greater than one, although the shape of the curve is such that for low speeds, the Lorentz factor is extremely close to one. +In Fig. 3-3b, segments OA and OK represent equal spacetime intervals. Length contraction is represented by the ratio OB/OK. The invariant hyperbola has the equation x = √w2 + k2, where k = OK, and the edges of the blue band representing the world lines of the endpoints of a rod in motion have slope 1/β = c/v. Event A has coordinates +(x, w) = (γk, γβk). Since the tangent line through A and B has the equation w = (x − OB)/β, we have γβk = (γk − OB)/β and + + + + + O + B + + / + + O + K + = + γ + ( + 1 + − + + β + + 2 + + + ) + = + + + 1 + γ + + + + + {\displaystyle OB/OK=\gamma (1-\beta ^{2})={\frac {1}{\gamma }}} + + +=== Lorentz transformations === \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Suffrage_Science_award-0.md b/data/en.wikipedia.org/wiki/Suffrage_Science_award-0.md new file mode 100644 index 000000000..1e22bbe99 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Suffrage_Science_award-0.md @@ -0,0 +1,304 @@ +--- +title: "Suffrage Science award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Suffrage_Science_award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:11.854355+00:00" +instance: "kb-cron" +--- + +The Suffrage Science award is a prize for women in science, engineering and computing founded in 2011, on the 100th anniversary of International Women's Day by the MRC London Institute of Medical Sciences (LMS). There are three categories of award: +life sciences +engineering and physical sciences +mathematics and computing. +The life sciences award was founded in 2011. Every year there are 10 laureates from research backgrounds and one laureate for communication. The engineering and physical sciences award was founded in 2013. Every year there are 12 laureates from areas spanning physics, chemistry and more. The math and computing award was launched on Ada Lovelace Day, 2016. Every year there are five laureates from mathematics, five laureates from computing and one laureate for science communication and the public awareness of science. + + +== Laureates == +Laureates have included: + + +=== 2026 === +Life Sciences + +Chrystalina Antoniades, University of Oxford +Sarah Cooley, Earth Science Data Professionals Organization +Cara Croft, Queen Mary University of London +Camille Dion, Medical Sciences, London +Dima A. Hammoud, NIH Clinical Centre +Karoline Kuchenbaecker, University College, London +Madeline Lancaster, LMB, Cambridge +Liset Menéndez de la Prida, Instituto Cajal CSIC, Spain +Arwen Pearson, University of Hamburg +Kate Watkins, University of Oxford +Dana Pe'er, HHMI, US + + +=== 2026 === +Maths and Computing + +Abigail Sellen, Microsoft Research, Cambridge +Vanessa Didelez, University of Bremen, Germany +Susanne Bødker, Aarhus University, Denmark +Anne Gégout-Petit, University of Lorraine, France +Sara Bernardini, University of Oxford +Judy Robertson, University of Edinburgh +Els Goetghebeur, Ghent University, Belgium +Azalea Rand, Imperial College, London +Anja Schlömerkemper, Universitat Würzburg, Germany + + +=== 2025 === +Engineering and Physical Sciences + +Alice Bunn, OBE, Institution of Mechanical Engineers +Danielle Julie Carrier, University of Tennessee +Francisca de Haan, Central European University +Iryna Herzon, University of Helsinki +Peace Korshiwor Amoatey, University of Ghana +Catherine Le Visage, Nantes Université +Priyamvada Natarajan, Yale University +Thuc-Quyen Nguyen, University of California, Santa Barbara +Rachel Oliver, University of Cambridge +Suzanne Ramsay, European Southern Observatory +Jayne Wallace, Oxford Nanopore Technologies +Gerlind Wallon, European Molecular Biology Organization + + +=== 2024 === +Life Sciences winners are: + +Areej Abuhammad, University of Jordan, Jordan +Prisca Liberali, FMI, Basel +Frederique Magdinier, Marseille Medical Genetics, France +Azahara Oliva, Cornell University +Lynn Rochester, University of Newcastle +Marta Shahbazi, MRC LMB, Cambridge +Monica Shokeen, Washington University School of Medicine +Faraneh Vargha-Khadem, UCL Institute of Child Health, London +elina Wray, UCL Queen Square Institute of Neurology, London + + +=== 2021 === +Engineering and Physical Sciences winners are: + +Gaitee Hussain, European Space Agency, The Netherlands +Syma Khalid, University of Southampton, UK +Natalie Stingelin, Georgia Institute of Technology, USA +Ina van Berckelaer-Onnes, Leiden University, The Netherlands +Hayaatun Sillem, CBE, Royal Academy of Engineering, UK +Ruth Cameron, University of Cambridge, UK +Elin Röös, Swedish University of Agricultural Sciences, Sweden +Maria Dolores Martín Bermudo, Centro Andaluz de Biología del Desarrollo, Spain +Samaya Nissanke, University of Amsterdam and Nikhef, The Netherlands +Gerjo van Osch, Erasmus University Medical Center, The Netherlands +Valérie Orsat, McGill University, Canada +Mary Anti Chama, University of Ghana, Ghana + + +=== 2020 === + +Life Sciences award winners are: + +Kelly Nguyen (scientist), MRC Laboratory of Molecular Biology +Naomi Matsuura, University of Toronto, Canada +Elspeth Garman, University of Oxford, UK +Veronique Miron, University of Edinburgh, UK +Cécile Martinat, I-STEM, France +Zena Werb, University of California, San Francisco, USA +Samantha Joye, University of Georgia, USA +Gisou van der Goot, EPFL Lausanne, Switzerland +Karalyn Patterson, University of Cambridge, UK +Laura Colgin, University of Texas Austin, USA +Claudia Mazzà, University of Sheffield, UK + +Maths and Computing award winners are: + +Rhian Daniel, Cardiff University +Juhyun Park, Lancaster University, UK, and ENSIIE, France +Apala Majumdar, University of Strathclyde +Bianca de Stavola, University College London +Sara Lombardo, Loughborough University +Wendy Mackay, Inria, Paris-Saclay, France +Yvonne Rogers, University College London +Alexandra Silva, University College London +Nobuko Yoshida, Imperial College London +Sue Sentance, King’s College London Raspberry Pi Foundation +Anne-Marie Imafidon, STEMettes + + +=== 2019 === + +Engineering and Physical Sciences + +Moira Jardine +Sarah Harris +Róisín Owens +Tiny de Keuster Universiteit Gent +Karen Holford +Serena Best +Tara Garnett +Isabel Palacios +Amina Helmi +Sue Kimber +Marzieh Moosavi-Nasab +Melinda Duer + + +=== 2018 === + +Life sciences: + +Cathy Price +Rebecca Voorhees +Claire Rougeulle +Denise Head +Jenny Martin +Anna Wu +Mikala Egeblad +Irene Miguel-Aliaga +Anat Mirelman +Elizabeth Bradbury +Susan M. Gaines +Maths and Computing + +Ruth Keogh +Tereza Neocleous +Nina Snaith +Daniela De Angelis +Eugenie Hunsicker +Sally Fincher +Julie McCann +Jane Hillston +Ursula Martin +Hannah Dee +Vicky Neale + + +=== 2017 === + +Engineering + +Lyndsay Fletcher +Sarah Staniland +Rylie Green +Kerstin Meints +Sheila Rowan +Cathy Holt +Sabine Gabrysch +Marta Vicente-Crespo +Marileen Dogterom +Sheila MacNeil +Zohreh Azimifar +Sharon Ashbrook + + +=== 2016 === + +Life sciences: + +Kia Nobre +Lori Passmore +Déborah Bourc'his +Uraina Clark +Michelle James +Marja Jäätelä +Corinne Houart +Sally John +Catherina Becker +Pippa Goldschmidt +Maths and computing: + +Christl Donnelly +Jane Hutton +Frances Kirwan +Sylvia Richardson +Gwyneth Stallard +Ann Blandford +Muffy Calder +Leslie Ann Goldberg +Wendy Hall +Carron Shankland +Celia Hoyles +Shafi Goldwasser +Marta Kwiatkowska +Emma McCoy + + +=== 2015 === + +Lucie Green +Lorna Dougan +Anne Vanhoestenberghe +Susan Condor, Loughborough +Anne Neville +Ruth Wilcox, Leeds +Anna Goodman (scientist) London School of Hygiene & Tropical Medicine (LSHTM) +Silvia Muñoz-Descalzo University of Bath +Patricia Bassereau, Curie institute +Alicia El Haj +Tamsin Edwards +Polly Arnold + + +=== 2014 === + +Irene Tracey +Shannon Au +Anne Ferguson-Smith +Xiaomeng Xu +Jane Endicott +Sarah Bohndiek +Anja Groth +Kate Storey +Eleftheria Zeggini +Lynda Erskine +Jennifer Rohn + + +=== 2013 === + +Julia Higgins +Molly Stevens +Lesley Yellowlees +Eileen Ingham +Jennifer Nichols +Sally Macintyre +Susan Gathercole +Clare Elwell +Petra Schwille +Maggie Aderin-Pocock +Kathy Sykes + + +=== 2012 === + +Emily Holmes +Tracey Barett +Nicole Soranzo +Bianca Acevedo +Francoise Barre-Sinoussi +Elizabeth Murchison +Edith Heard +Marysia Placzek +Sarah Teichmann +Christiana Ruhrberg +Georgina Ferry + + +=== 2011 === + +Sarah-Jayne Blakemore +Mary Collins +Sally Davies +Helen Fisher +Vivienne Parry +Sohaila Rastan +Elizabeth Robertson +Janet Thornton +Fiona Watt +Brenda Maddox + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/T-symmetry-0.md b/data/en.wikipedia.org/wiki/T-symmetry-0.md new file mode 100644 index 000000000..83f8a5149 --- /dev/null +++ b/data/en.wikipedia.org/wiki/T-symmetry-0.md @@ -0,0 +1,67 @@ +--- +title: "T-symmetry" +chunk: 1/4 +source: "https://en.wikipedia.org/wiki/T-symmetry" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:13.998744+00:00" +instance: "kb-cron" +--- + +T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal, + + + + + T + : + t + ↦ + − + t + . + + + {\displaystyle T:t\mapsto -t.} + + +Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal. In other words, time is said to be non-symmetric, or asymmetric, except for special equilibrium states when the second law of thermodynamics predicts the time symmetry to hold. However, quantum noninvasive measurements are predicted to violate time symmetry even in equilibrium, contrary to their classical counterparts, although this has not yet been experimentally confirmed. +Time asymmetries (see Arrow of time) generally are caused by one of three categories: + +intrinsic to the dynamic physical law (e.g., for the weak force) +due to the initial conditions of the universe (e.g., for the second law of thermodynamics) +due to measurements (e.g., for the noninvasive measurements) + +== Macroscopic phenomena == + +=== The second law of thermodynamics === + +Daily experience shows that T-symmetry does not hold for the behavior of bulk materials. Of these macroscopic laws, most notable is the second law of thermodynamics. Many other phenomena, such as the relative motion of bodies with friction, or viscous motion of fluids, reduce to this, because the underlying mechanism is the dissipation of usable energy (for example, kinetic energy) into heat. +The question of whether this time-asymmetric dissipation is really inevitable has been considered by many physicists, often in the context of Maxwell's demon. The name comes from a thought experiment described by James Clerk Maxwell in which a microscopic demon guards a gate between two halves of a room. It only lets slow molecules into one half, only fast ones into the other. By eventually making one side of the room cooler than before and the other hotter, it seems to reduce the entropy of the room, and reverse the arrow of time. Many analyses have been made of this; all show that when the entropy of room and demon are taken together, this total entropy does increase. Modern analyses of this problem have taken into account Claude E. Shannon's relation between entropy and information. Many interesting results in modern computing are closely related to this problem—reversible computing, quantum computing and physical limits to computing, are examples. These seemingly metaphysical questions are today, in these ways, slowly being converted into hypotheses of the physical sciences. +The current consensus hinges upon the Boltzmann–Shannon identification of the logarithm of phase space volume with the negative of Shannon information, and hence to entropy. In this notion, a fixed initial state of a macroscopic system corresponds to relatively low entropy because the coordinates of the molecules of the body are constrained. As the system evolves in the presence of dissipation, the molecular coordinates can move into larger volumes of phase space, becoming more uncertain, and thus leading to increase in entropy. + +=== Big Bang === + +One resolution to irreversibility is to say that the constant increase of entropy we observe happens only because of the initial state of our universe. Other possible states of the universe (for example, a universe at heat death equilibrium) would actually result in no increase of entropy. In this view, the apparent T-asymmetry of our universe is a problem in cosmology: why did the universe start with a low entropy? This view, supported by cosmological observations (such as the isotropy of the cosmic microwave background) connects this problem to the question of initial conditions of the universe. + +=== Black holes === + +The laws of gravity seem to be time reversal invariant in classical mechanics; however, specific solutions need not be. +An object can cross through the event horizon of a black hole from the outside, and then fall rapidly to the central region where our understanding of physics breaks down. Since within a black hole the forward light-cone is directed towards the center and the backward light-cone is directed outward, it is not even possible to define time-reversal in the usual manner. The only way anything can escape from a black hole is as Hawking radiation. +The time reversal of a black hole would be a hypothetical object known as a white hole. From the outside they appear similar. While a black hole has a beginning and is inescapable, a white hole has an ending and cannot be entered. The forward light-cones of a white hole are directed outward; and its backward light-cones are directed towards the center. +The event horizon of a black hole may be thought of as a surface moving outward at the local speed of light and is just on the edge between escaping and falling back. The event horizon of a white hole is a surface moving inward at the local speed of light and is just on the edge between being swept outward and succeeding in reaching the center. They are two different kinds of horizons—the horizon of a white hole is like the horizon of a black hole turned inside-out. +The modern view of black hole irreversibility is to relate it to the second law of thermodynamics, since black holes are viewed as thermodynamic objects. For example, according to the gauge–gravity duality conjecture, all microscopic processes in a black hole are reversible, and only the collective behavior is irreversible, as in any other macroscopic, thermal system. + +=== Kinetic consequences: detailed balance and Onsager reciprocal relations === + +In physical and chemical kinetics, T-symmetry of the mechanical microscopic equations implies two important laws: the principle of detailed balance and the Onsager reciprocal relations. T-symmetry of the microscopic description together with its kinetic consequences are called microscopic reversibility. + +=== Effect of time reversal on some variables of classical physics === + +==== Even ==== + +Classical variables that do not change upon time reversal include: + +==== Odd ==== + +Classical variables that time reversal negates include: \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/T-symmetry-1.md b/data/en.wikipedia.org/wiki/T-symmetry-1.md new file mode 100644 index 000000000..48df0a071 --- /dev/null +++ b/data/en.wikipedia.org/wiki/T-symmetry-1.md @@ -0,0 +1,360 @@ +--- +title: "T-symmetry" +chunk: 2/4 +source: "https://en.wikipedia.org/wiki/T-symmetry" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:13.998744+00:00" +instance: "kb-cron" +--- + +==== Example: Magnetic Field and Onsager reciprocal relations ==== +Let us consider the example of a system of charged particles subject to a constant external magnetic field: in this case the canonical time reversal operation that reverses the velocities and the time + + + + t + + + {\displaystyle t} + + and keeps the coordinates untouched is no more a symmetry for the system. Under this consideration, it seems that only Onsager–Casimir reciprocal relations could hold; these equalities relate two different systems, one subject to + + + + + + + B + → + + + + + + {\displaystyle {\vec {B}}} + + and another to + + + + − + + + + B + → + + + + + + {\displaystyle -{\vec {B}}} + +, and so their utility is limited. However, it was proved that it is possible to find other time reversal operations which preserve the dynamics and so Onsager reciprocal relations; in conclusion, one cannot state that the presence of a magnetic field always breaks T-symmetry. + +== Microscopic phenomena: time reversal invariance == +Most systems are asymmetric under time reversal, but there may be phenomena with symmetry. In classical mechanics, a velocity v reverses under the operation of T, but an acceleration does not. Therefore, one models dissipative phenomena through terms that are odd in v. However, delicate experiments in which known sources of dissipation are removed reveal that the laws of mechanics are time reversal invariant. Dissipation itself is originated in the second law of thermodynamics. +The motion of a charged body in a magnetic field, B involves the velocity through the Lorentz force term v×B, and might seem at first to be asymmetric under T. A closer look assures us that B also changes sign under time reversal. This happens because a magnetic field is produced by an electric current, J, which reverses sign under T. Thus, the motion of classical charged particles in electromagnetic fields is also time reversal invariant. (Despite this, it is still useful to consider the time-reversal non-invariance in a local sense when the external field is held fixed, as when the magneto-optic effect is analyzed. This allows one to analyze the conditions under which optical phenomena that locally break time-reversal, such as Faraday isolators and directional dichroism, can occur.) +Physics separates the laws of motion, called kinematics, from the laws of force, called dynamics. Following the classical kinematics of Newton's laws of motion, the kinematics of quantum mechanics is built in such a way that it presupposes nothing about the time reversal symmetry of the dynamics. In other words, if the dynamics are invariant, then the kinematics will allow it to remain invariant; if the dynamics is not, then the kinematics will also show this. The structure of the quantum laws of motion are richer, and we examine these next. + +=== Time reversal in quantum mechanics === + +This section contains a discussion of the three most important properties of time reversal in quantum mechanics; chiefly, + +that it must be represented as an anti-unitary operator, +that it protects non-degenerate quantum states from having an electric dipole moment, +that it has two-dimensional representations with the property T2 = −1 (for fermions). +The strangeness of this result is clear if one compares it with parity. If parity transforms a pair of quantum states into each other, then the sum and difference of these two basis states are states of good parity. Time reversal does not behave like this. It seems to violate the theorem that all abelian groups be represented by one-dimensional irreducible representations. The reason it does this is that it is represented by an anti-unitary operator. It thus opens the way to spinors in quantum mechanics. +On the other hand, the notion of quantum-mechanical time reversal turns out to be a useful tool for the development of physically motivated quantum computing and simulation settings, providing, at the same time, relatively simple tools to assess their complexity. For instance, quantum-mechanical time reversal was used to develop novel boson sampling schemes and to prove the duality between two fundamental optical operations, beam splitter and squeezing transformations. + +=== Formal notation === + +In formal mathematical presentations of T-symmetry, three different kinds of notation for T need to be carefully distinguished: the T that is an involution, capturing the actual reversal of the time coordinate, the T that is an ordinary finite dimensional matrix, acting on spinors and vectors, and the T that is an operator on an infinite-dimensional Hilbert space. +For a real (not complex) classical (unquantized) scalar field + + + + ϕ + + + {\displaystyle \phi } + +, the time reversal involution can simply be written as + + + + + + + T + + + ϕ + ( + t + , + + + + x + → + + + + ) + = + + ϕ + + ′ + + + ( + − + t + , + + + + x + → + + + + ) + = + s + ϕ + ( + t + , + + + + x + → + + + + ) + + + {\displaystyle {\mathsf {T}}\phi (t,{\vec {x}})=\phi ^{\prime }(-t,{\vec {x}})=s\phi (t,{\vec {x}})} + + +as time reversal leaves the scalar value at a fixed spacetime point unchanged, up to an overall sign + + + + s + = + ± + 1 + + + {\displaystyle s=\pm 1} + +. A slightly more formal way to write this is + + + + + + + T + + + : + ϕ + ( + t + , + + + + x + → + + + + ) + ↦ + + ϕ + + ′ + + + ( + − + t + , + + + + x + → + + + + ) + = + s + ϕ + ( + t + , + + + + x + → + + + + ) + + + {\displaystyle {\mathsf {T}}:\phi (t,{\vec {x}})\mapsto \phi ^{\prime }(-t,{\vec {x}})=s\phi (t,{\vec {x}})} + + +which has the advantage of emphasizing that + + + + + + T + + + + + {\displaystyle {\mathsf {T}}} + + is a map, and thus the "mapsto" notation + + + + ↦ + + , + + + {\displaystyle \mapsto ~,} + + whereas + + + + + ϕ + + ′ + + + ( + − + t + , + + + + x + → + + + + ) + = + s + ϕ + ( + t + , + + + + x + → + + + + ) + + + {\displaystyle \phi ^{\prime }(-t,{\vec {x}})=s\phi (t,{\vec {x}})} + + is a factual statement relating the old and new fields to one-another. +Unlike scalar fields, spinor and vector fields + + + + ψ + + + {\displaystyle \psi } + + might have a non-trivial behavior under time reversal. In this case, one has to write + + + + + + + T + + + : + ψ + ( + t + , + + + + x + → + + + + ) + ↦ + + ψ + + ′ + + + ( + − + t + , + + + + x + → + + + + ) + = + T + ψ + ( + t + , + + + + x + → + + + + ) + + + {\displaystyle {\mathsf {T}}:\psi (t,{\vec {x}})\mapsto \psi ^{\prime }(-t,{\vec {x}})=T\psi (t,{\vec {x}})} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/T-symmetry-2.md b/data/en.wikipedia.org/wiki/T-symmetry-2.md new file mode 100644 index 000000000..6772ef7d4 --- /dev/null +++ b/data/en.wikipedia.org/wiki/T-symmetry-2.md @@ -0,0 +1,521 @@ +--- +title: "T-symmetry" +chunk: 3/4 +source: "https://en.wikipedia.org/wiki/T-symmetry" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:13.998744+00:00" +instance: "kb-cron" +--- + +where + + + + T + + + {\displaystyle T} + + is just an ordinary matrix. For complex fields, complex conjugation may be required, for which the mapping + + + + K + : + ( + x + + + i + y + ) + ↦ + ( + x + − + i + y + ) + + + {\displaystyle K:(x+iy)\mapsto (x-iy)} + + can be thought of as a 2×2 matrix. For a Dirac spinor, + + + + T + + + {\displaystyle T} + + cannot be written as a 4×4 matrix, because, in fact, complex conjugation is indeed required; however, it can be written as an 8×8 matrix, acting on the 8 real components of a Dirac spinor. +In the general setting, there is no ab initio value to be given for + + + + T + + + {\displaystyle T} + +; its actual form depends on the specific equation or equations which are being examined. In general, one simply states that the equations must be time-reversal invariant, and then solves for the explicit value of + + + + T + + + {\displaystyle T} + + that achieves this goal. In some cases, generic arguments can be made. Thus, for example, for spinors in three-dimensional Euclidean space, or four-dimensional Minkowski space, an explicit transformation can be given. It is conventionally given as + + + + + T + = + + e + + i + π + + J + + y + + + + + K + + + {\displaystyle T=e^{i\pi J_{y}}K} + + +where + + + + + J + + y + + + + + {\displaystyle J_{y}} + + is the y-component of the angular momentum operator and + + + + K + + + {\displaystyle K} + + is complex conjugation, as before. This form follows whenever the spinor can be described with a linear differential equation that is first-order in the time derivative, which is generally the case in order for something to be validly called "a spinor". +The formal notation now makes it clear how to extend time-reversal to an arbitrary tensor field + + + + + ψ + + a + b + c + ⋯ + + + + + {\displaystyle \psi _{abc\cdots }} + + In this case, + + + + + + + T + + + : + + ψ + + a + b + c + ⋯ + + + ( + t + , + + + + x + → + + + + ) + ↦ + + ψ + + a + b + c + ⋯ + + + ′ + + + ( + − + t + , + + + + x + → + + + + ) + = + + + + T + + a + + + + + d + + + + + + + T + + b + + + + + e + + + + + + + T + + c + + + + + f + + + ⋯ + + ψ + + d + e + f + ⋯ + + + ( + t + , + + + + x + → + + + + ) + + + {\displaystyle {\mathsf {T}}:\psi _{abc\cdots }(t,{\vec {x}})\mapsto \psi _{abc\cdots }^{\prime }(-t,{\vec {x}})={T_{a}}^{d}\,{T_{b}}^{e}\,{T_{c}}^{f}\cdots \psi _{def\cdots }(t,{\vec {x}})} + + +Covariant tensor indexes will transform as + + + + + + + T + + a + + + + + b + + + = + + + ( + + T + + − + 1 + + + + ) + + b + + + + + a + + + + + {\displaystyle {T_{a}}^{b}={(T^{-1})_{b}}^{a}} + + and so on. For quantum fields, there is also a third T, written as + + + + + + T + + + , + + + {\displaystyle {\mathcal {T}},} + + which is actually an infinite dimensional operator acting on a Hilbert space. It acts on quantized fields + + + + Ψ + + + {\displaystyle \Psi } + + as + + + + + + + T + + + : + Ψ + ( + t + , + + + + x + → + + + + ) + ↦ + + Ψ + + ′ + + + ( + − + t + , + + + + x + → + + + + ) + = + + + T + + + Ψ + ( + t + , + + + + x + → + + + + ) + + + + T + + + + − + 1 + + + + + {\displaystyle {\mathsf {T}}:\Psi (t,{\vec {x}})\mapsto \Psi ^{\prime }(-t,{\vec {x}})={\mathcal {T}}\Psi (t,{\vec {x}}){\mathcal {T}}^{-1}} + + +This can be thought of as a special case of a tensor with one covariant, and one contravariant index, and thus two + + + + + + T + + + + + {\displaystyle {\mathcal {T}}} + +'s are required. +All three of these symbols capture the idea of time-reversal; they differ with respect to the specific space that is being acted on: functions, vectors/spinors, or infinite-dimensional operators. The remainder of this article is not cautious to distinguish these three; the T that appears below is meant to be either + + + + + + T + + + + + {\displaystyle {\mathsf {T}}} + + or + + + + T + + + {\displaystyle T} + + or + + + + + + T + + + , + + + {\displaystyle {\mathcal {T}},} + + depending on context, left for the reader to infer. + +=== Anti-unitary representation of time reversal === + +Eugene Wigner showed that a symmetry operation S of a Hamiltonian is represented, in quantum mechanics either by a unitary operator, S = U, or an antiunitary one , S = UK where U is unitary, and K denotes a basis-dependent complex conjugation operator. These are the only operations that act on Hilbert space so as to preserve the length of the projection of any one state-vector onto another state-vector. + +For a particle with spin J, one can use the representation + + + + + T + = + η + + e + + − + i + π + + J + + y + + + + / + + ℏ + + + K + , + + + {\displaystyle T=\eta e^{-i\pi J_{y}/\hbar }K,} + + +where Jy is the y-component of the spin, and use of TJT−1 = −J has been made, and + + + + η + + + {\displaystyle \eta } + + is an arbitrary phase. + +=== Electric dipole moments === + +This has an interesting consequence on the electric dipole moment (EDM) of any particle. The EDM is defined through the shift in the energy of a state when it is put in an external electric field: Δe = d·E + E·δ·E, where d is called the EDM and δ, the induced dipole moment. One important property of an EDM is that the energy shift due to it changes sign under a parity transformation. However, since d is a vector, its expectation value in a state |ψ⟩ must be proportional to ⟨ψ| J |ψ⟩, that is the expected spin. Thus, under time reversal, an invariant state must have vanishing EDM. In other words, a non-vanishing EDM signals both P and T symmetry-breaking. +Some molecules, such as water, must have EDM irrespective of whether T is a symmetry. This is correct; if a quantum system has degenerate ground states that transform into each other under parity, then time reversal need not be broken to give EDM. +Experimentally observed bounds on the electric dipole moment of the nucleon currently set stringent limits on the violation of time reversal symmetry in the strong interactions, and their modern theory: quantum chromodynamics. Then, using the CPT invariance of a relativistic quantum field theory, this puts strong bounds on strong CP violation. +Experimental bounds on the electron electric dipole moment also place limits on theories of particle physics and their parameters. + +=== Kramers' theorem === + +For T, which is an anti-unitary Z2 symmetry generator + +where Φ is a diagonal matrix of phases. As a result, U = ΦUT and UT = UΦ, showing that \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/T-symmetry-3.md b/data/en.wikipedia.org/wiki/T-symmetry-3.md new file mode 100644 index 000000000..7f93aeb96 --- /dev/null +++ b/data/en.wikipedia.org/wiki/T-symmetry-3.md @@ -0,0 +1,65 @@ +--- +title: "T-symmetry" +chunk: 4/4 +source: "https://en.wikipedia.org/wiki/T-symmetry" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:13.998744+00:00" +instance: "kb-cron" +--- + +This means that the entries in Φ are ±1, as a result of which one may have either T2 = ±1. This is specific to the anti-unitarity of T. For a unitary operator, such as the parity, any phase is allowed. +Next, take a Hamiltonian invariant under T. Let |a⟩ and T|a⟩ be two quantum states of the same energy. Now, if T2 = −1, then one finds that the states are orthogonal: a result called Kramers' theorem. This implies that if T2 = −1, then there is a twofold degeneracy in the state. This result in non-relativistic quantum mechanics presages the spin statistics theorem of quantum field theory. +Quantum states that give unitary representations of time reversal, i.e., have T2 = 1, are characterized by a multiplicative quantum number, sometimes called the T-parity. + +=== Time reversal of the known dynamical laws === + +Particle physics codified the basic laws of dynamics into the Standard Model. This is formulated as a quantum field theory that has CPT symmetry, i.e., the laws are invariant under simultaneous operation of time reversal, parity and charge conjugation. However, time reversal itself is seen not to be a symmetry (this is usually called CP violation). There are two possible origins of this asymmetry, one through the mixing of different flavours of quarks in their weak decays, the second through a direct CP violation in strong interactions. The first is seen in experiments; the second is strongly constrained by the non-observation of the EDM of a neutron. +Time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe. + +=== Time reversal of noninvasive measurements === +Strong measurements (both classical and quantum) are certainly disturbing, causing asymmetry due to the second law of thermodynamics. However, +noninvasive measurements should not disturb the evolution, so they are expected to be time-symmetric. Surprisingly, it is true only in classical physics but not in quantum physics, even in a thermodynamically invariant equilibrium state. This type of asymmetry is independent of CPT symmetry but has not yet been confirmed experimentally due to extreme conditions of the checking proposal. + +=== Negative group delay in quantum systems === + +In 2024, experiments by the University of Toronto showed that under certain quantum conditions, photons can exhibit "negative time" behavior. When interacting with atomic clouds, photons appeared to exit the medium before entering it, indicating a negative group delay, especially near atomic resonance. Using the cross-Kerr effect, the team measured atomic excitation by observing phase shifts in a weak probe beam. The results showed that atomic excitation times varied from negative to positive, depending on the pulse width. For narrow pulses, the excitation time was approximately −0.82 times the non-post-selected excitation time (τ0), while for broader pulses, it was around 0.54 times τ0. These findings align with theoretical predictions and highlight the non-classical nature of quantum mechanics, opening new possibilities for quantum computing and photonics. + +== See also == +Arrow of time +Causality (physics) +Computing applications +Limits of computation +Quantum computing +Reversible computing +Standard Model +CKM matrix +CP violation +CPT invariance +Neutrino mass +Strong CP problem +Wheeler–Feynman absorber theory +Loschmidt's paradox +Maxwell's demon +Microscopic reversibility +Second law of thermodynamics +Time translation symmetry +Time reversal (disambiguation) + +== References == + +=== Inline citations === + +=== General references === +Maxwell's demon: entropy, information, computing, edited by H.S.Leff and A.F. Rex (IOP publishing, 1990) ISBN 0-7503-0057-4 +Maxwell's demon, 2: entropy, classical and quantum information, edited by H.S.Leff and A.F. Rex (IOP publishing, 2003) ISBN 0-7503-0759-5 +The emperor's new mind: concerning computers, minds, and the laws of physics, by Roger Penrose (Oxford university press, 2002) ISBN 0-19-286198-0 +Sozzi, M.S. (2008). Discrete symmetries and CP violation. Oxford University Press. ISBN 978-0-19-929666-8. +Birss, R. R. (1964). Symmetry and Magnetism. John Wiley & Sons, Inc., New York. +Multiferroic materials with time-reversal breaking optical properties +CP violation, by I.I. Bigi and A.I. Sanda (Cambridge University Press, 2000) ISBN 0-521-44349-0 +Particle Data Group on CP violation +the Babar experiment in SLAC +the BELLE experiment in KEK +the KTeV experiment in Fermilab +the CPLEAR experiment in CERN \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Tadahiro_Aizawa-0.md b/data/en.wikipedia.org/wiki/Tadahiro_Aizawa-0.md new file mode 100644 index 000000000..29af8f08c --- /dev/null +++ b/data/en.wikipedia.org/wiki/Tadahiro_Aizawa-0.md @@ -0,0 +1,15 @@ +--- +title: "Tadahiro Aizawa" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Tadahiro_Aizawa" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:39.061290+00:00" +instance: "kb-cron" +--- + +Tadahiro Aizawa (相沢 忠洋, Aizawa Tadahiro; June 21, 1926 – May 22, 1989) was a Japanese archaeologist. Aizawa, an amateur stone tool collector who had been peddling nattō, discovered a microlith in Iwajuku, Gunma in 1946, which was recognized in 1949 as a Paleolithic site that had previously been thought not to exist in Japan. + + +== References == +Keiji Imamura. Prehistoric Japan: new perspectives on insular East Asia p. 19. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Tagea_Brandt_Rejselegat-0.md b/data/en.wikipedia.org/wiki/Tagea_Brandt_Rejselegat-0.md new file mode 100644 index 000000000..64eb979ea --- /dev/null +++ b/data/en.wikipedia.org/wiki/Tagea_Brandt_Rejselegat-0.md @@ -0,0 +1,31 @@ +--- +title: "Tagea Brandt Rejselegat" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Tagea_Brandt_Rejselegat" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:13.042805+00:00" +instance: "kb-cron" +--- + +The Tagea Brandts Rejselegat (Travel Scholarship) is a Danish award to women who have made a significant contribution in science, literature or art. The grant, which is given without application, was created and endowed by Danish industrialist Vilhelm Brandt (1854–1921) in 1905 in honor of his wife, Tagea Brandt. +It is awarded annually on 17 March, her birthday. +The charter of 1922 provides that it shall be given to outstanding women in science, art, music, literature and theater arts (particularly in this case to actresses at the Royal Danish Theatre). The intent is for the awardee to both broaden her horizons while promoting Danish society abroad, and to benefit from vacation and rest time. +The first scholarships were given in 1924; the first time the amount was DKK 10.000, in 1958 it was increased to DKK 15.000, in 1967 to 25.000, later to 50,000, and currently it is DKK 75.000, which usually is given to 2-3 women annually. + + +== Recipients of the Tagea Brandt Award == + + +== See also == +Tagea Brandt +Women in Denmark +List of awards honoring women +List of European art awards + + +== References == + + +== External links == +"Tagea Brandts Rejselegat" [Tagea Brandt's Travel Scholarship]. Litterære priser, medaljer, legater mv [Literary prizes, medals, scholarships, etc] (in Danish). Retrieved 6 September 2010. List of recipients. Self-published, but with references .{{cite web}}: CS1 maint: postscript (link) \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Taiwan_Outstanding_Women_in_Science_Awards-0.md b/data/en.wikipedia.org/wiki/Taiwan_Outstanding_Women_in_Science_Awards-0.md new file mode 100644 index 000000000..13d55bbdf --- /dev/null +++ b/data/en.wikipedia.org/wiki/Taiwan_Outstanding_Women_in_Science_Awards-0.md @@ -0,0 +1,28 @@ +--- +title: "Taiwan Outstanding Women in Science Awards" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Taiwan_Outstanding_Women_in_Science_Awards" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:14.207961+00:00" +instance: "kb-cron" +--- + +The Taiwan Outstanding Women in Science Award (TOWIS, Chinese: 台灣傑出女科學家獎; Tongyong Pinyin: Táiwān jiéchū nyǔ kēsyuéjiā jiǎng; Tâi-lô: Tâi-uân kia̍t-tshut lú kho-ha̍k-ka tsióng was jointly established in 2007 by L'Oréal Taiwan and the Chien-Shiung Wu Foundation. It aims to encourage young female students to pursue scientific research as their career by recognizing outstanding female scientists. This award is also known colloquially as the "Taiwan Women's Nobel Prize". The awards include the "Outstanding Award", the "Young Talent Award" and the "Mong Tsui-Chu Scholarship" added in 2012. The scientists participating in the selection are mainly from the three fields of material science, mathematics and information science. The winners are announced annually in March. + + +== Laureates == + + +== See also == +List of science and technology awards for women +Women in STEM fields +Women in engineering +Women in science + + +== References == + + +== External links == +Taiwan Outstanding Women in Science Awards \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Tempora_mutantur-0.md b/data/en.wikipedia.org/wiki/Tempora_mutantur-0.md new file mode 100644 index 000000000..840a2bf43 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Tempora_mutantur-0.md @@ -0,0 +1,76 @@ +--- +title: "Tempora mutantur" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Tempora_mutantur" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:46.612633+00:00" +instance: "kb-cron" +--- + +Tempora mutantur is a Latin adage that refers to the changes brought about by the passage of time. It also appears in various longer hexametric forms, most commonly Tempora mutantur, nos et mutamur in illis, meaning "Times are changed; we also are changed with them". This hexameter is not found in Classical Latin, but is a variant of phrases of Ovid, to whom it is sometimes mis-attributed. In fact, it dates to 16th-century Germany, the time of the Protestant Reformation, and it subsequently was popularised in various forms. + +== Wording == +Tempora mutantur, nos et mutamur in illis +can be strictly translated as: +"Times are changed; we, too, are changed within them." +Like many adages and proverbial maxims drawn from the Latin cultural tradition, this line is in the hexameter verse used in Greek and Latin epic poetry. All other Latin verses cited in this page are hexameters as well. +The fact that et follows nos and is accented in the hexameter's rhythm gives an emphasis to it. In this position et, normally meaning "and," can take an emphatic meaning and signify "also, too," or "even". + +== Grammar == +"Tempora," a neuter plural and the subject of the first clause, means "times". "Mutantur" is a third person plural present passive, meaning "are changed." "Nos" is the personal pronoun and subject of the second clause, meaning "we," with emphatic force. "Mutamur" is the first person plural present passive, meaning "are changed" as well. "In illis" is an ablative plural referring back to "tempora" and so means "within them". The sentence is also a hexameter verse. + +== History == +Change is an ancient theme in Western philosophy, in which the contribution of the pre-Socratic Heraclitus has been influential. It is summarized in Ancient Greek as panta rhei (πάντα ῥεῖ, "everything flows"). The Latin formulation tempora mutantur is not classical, and does not have a generally accepted attribution – it is often identified as "traditional" – though it is frequently misattributed, particularly to Ovid. It is typically considered a variant of omnia mutantur "everything is changed", specifically from Ovid's Metamorphoses, in the phrase omnia mutantur, nihil interit "everything is changed, nothing perishes". However, the earliest attestation is from the German theologian Caspar Huberinus (1500–1553), who instead uses tempora mutantur as a variant of tempora labuntur "time slips away", from Ovid's Fasti. But the phrase tempora mutantur is in the passive, where as labuntur is form of a deponent verb; its passive form conveys an active meaning. +Various longer Latin forms and vernacular translations appear in 16th and early 17th century; these are discussed below. + +=== German === +The earliest attestations are in German Latin literature of the 16th century: +Prior to 1554, the Protestant Reformer Caspar Huberinus completes Ovid's verse in Fasti with tempora mutantur. Ovid's Fasti, VI, 771–772 reads: + +Tempora labuntur, tacitisque senescimus annis, +et fugiunt freno non remorante dies. +The times slip away, and we grow old with the silent years, +and the days flee unchecked by a rein. +Fasti was popular in the 16th century, and this passage, near the end of the last extant book of the Fasti, is interpreted as expressing the poet's own old age. +Huberinus rewrites the second line as: + +Tempora labuntur, tacitisque senescimus annis; +Tempora mutantur, nosque mutamur in illis. +"Times are slipping away, and we get older by (through, during, with, because of) the silent years" +(nosque = the same as nos et, with different hexameter rhythm) +The German translation is added in 1565 by Johannes Nas: + +Tempora mutantur et nos mutamur in ipsis; +Die zeit wirdt verendert / und wir in der zeit. +(ipsis = "themselves") +Finally a couplet dedicated by Matthew Borbonius in 1595 to emperor Lothair I. Also selected for the anthology Delitiae Poetarum Germanorum, 1612, vol. 1, p. 685 (GIF). + +=== English === +In English vernacular literature it is quoted as "proverbial" in William Harrison's Description of England, 1577, p. 170, part of Holinshed's Chronicles, in the form: + +Tempora mutantur, et nos mutamur in illis +with the translation: +"The times change, and we change with them." +It appears in John Lyly's Euphues I 276, 1578, as cited in Dictionary of Proverbs, by George Latimer Apperson, Martin Manser, p. 582 as + +"The tymes are chaunged as Ouid sayeth, and wee are chaunged in the times." +in modern spelling: +"The times are changed, as Ovid says, and we are changed in the times." +It gained popularity as a couplet by John Owen, in his popular Epigrammata, 1613 Lib. I. ad Edoardum Noel, epigram 58 O Tempora!: + +Tempora mutantur, nos et mutamur in illis; +Quo modo? fit semper tempore pejor homo. +in direct translation (of second line): +"How's that? The man (mankind) always gets worse with time" +Translated by Harvey, 1677, as: + +"The Times are Chang'd, and in them Chang'd are we: +How? Man as Times grow worse, grows worse we see." + +=== Incorrect attributions === +It is incorrectly attributed to Cicero, presumably a confusion with his O tempora o mores! It is sometimes attributed to Borbonius (1595), though he was predated by over 50 years by others. +Georg Büchmann, Geflügelte Worte: Der Citatenschatz des deutschen Volkes, ed. K. Weidling, 1898 edition, p. 506, confuses historical and poetical reality naming emperor Lothair I as the source and the couplet by Matthias Borbonius printed in 1612 as the quote. +Brewer's Dictionary 1898 edition confuses Borbonius' first name (Matthew) with another poet (Nicholas), the entry reading: + +"Omnia mutantur, nos et mutamur in illis," is by Nicholas Borbonius, a Latin poet of the sixteenth century. Dr. Sandys says that the Emperor Lothair, of the Holy Roman Empire, had already said, "Tempora mutantur, nos et mutamur in illis." \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Tempora_mutantur-1.md b/data/en.wikipedia.org/wiki/Tempora_mutantur-1.md new file mode 100644 index 000000000..97e7282a9 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Tempora_mutantur-1.md @@ -0,0 +1,26 @@ +--- +title: "Tempora mutantur" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Tempora_mutantur" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:46.612633+00:00" +instance: "kb-cron" +--- + +== Cultural references == +Joseph Haydn gave his Symphony No. 64 the title Tempora mutantur. +In James Joyce's novel A Portrait of the Artist as a Young Man, the cronies of the protagonist's (Stephen Dedalus's) father ask him to prove his ability in Latin by asking him "whether it was correct to say: tempora mutantur nos et mutamur or tempora mutantur et nos mutamur in illis." The phrase is meant to be an ironic reference to the decline in fortunes of the Dedalus family at this point in the novel. +In Pierson v. Post, dissenting judge and future US Supreme Court Justice Henry Brockholst Livingston argued "If any thing, therefore, in the digests or pandects shall appear to militate against the defendant in error, who, on this occasion, was foxhunter, we have only to say tempora mutantur, and if men themselves change with the times, why should not laws also undergo an alteration?" +The English print-maker William Washington (1885-1956) added the adage as an inscription to his 1929 engraving, St Olave's, Southwark, which depicts the demolition of St Olave's Church, Southwark, London, in 1928 to make way for modern development. +The adage is inscribed on the Convention Center at Caesars Palace in Las Vegas. +In July 2017 "Tempora mutantur, et nos mutamur in illis" was the first tweet of UK Conservative politician Jacob Rees-Mogg. +In the Yes, Prime Minister episode ‘The National Education Service’, Cabinet Secretary Sir Humphrey Appleby recites the phrase after Prime Minister Jim Hacker claims that "hardly anybody knows [Latin] nowadays". + +== See also == +Impermanence + +== References == + +== External links == + Quotations related to Change at Wikiquote \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Temporal_logic-0.md b/data/en.wikipedia.org/wiki/Temporal_logic-0.md new file mode 100644 index 000000000..8143f9bfa --- /dev/null +++ b/data/en.wikipedia.org/wiki/Temporal_logic-0.md @@ -0,0 +1,21 @@ +--- +title: "Temporal logic" +chunk: 1/4 +source: "https://en.wikipedia.org/wiki/Temporal_logic" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:47.815934+00:00" +instance: "kb-cron" +--- + +In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am always hungry", "I will eventually be hungry", or "I will be hungry until I eat something"). It is sometimes also used to refer to tense logic, a modal logic-based system of temporal logic introduced by Arthur Prior in the late 1950s, with important contributions by Hans Kamp. It has been further developed by computer scientists, notably Amir Pnueli, and logicians. +Temporal logic has found an important application in formal verification, where it is used to state requirements of hardware or software systems. For instance, one may wish to say that whenever a request is made, access to a resource is eventually granted, but it is never granted to two requestors simultaneously. Such a statement can conveniently be expressed in a temporal logic. + +== Motivation == +Consider the statement "I am hungry". Though its meaning is constant in time, the statement's truth value can vary in time. Sometimes it is true, and sometimes false, but never simultaneously true and false. In a temporal logic, a statement can have a truth value that varies in time—in contrast with an atemporal logic, which applies only to statements whose truth values are constant in time. This treatment of truth-value over time differentiates temporal logic from computational verb logic. +Temporal logic always has the ability to reason about a timeline. So-called "linear-time" logics are restricted to this type of reasoning. Branching-time logics, however, can reason about multiple timelines. This permits in particular treatment of environments that may act unpredictably. +To continue the example, in a branching-time logic we may state that "there is a possibility that I will stay hungry forever", and that "there is a possibility that eventually I am no longer hungry". If we do not know whether or not I will ever be fed, these statements can both be true. + +== History == +Although Aristotle's logic is almost entirely concerned with the theory of the categorical syllogism, there are passages in his work that are now seen as anticipations of temporal logic, and may imply an early, partially developed form of first-order temporal modal bivalent logic. Aristotle was particularly concerned with the problem of future contingents, where he could not accept that the principle of bivalence applies to statements about future events, i.e. that we can presently decide if a statement about a future event is true or false, such as "there will be a sea battle tomorrow". +Prior to Arthur Prior's work, there had been little development for millennia, Charles Sanders Peirce noted in the 19th century: \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Temporal_logic-1.md b/data/en.wikipedia.org/wiki/Temporal_logic-1.md new file mode 100644 index 000000000..ecb7da304 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Temporal_logic-1.md @@ -0,0 +1,69 @@ +--- +title: "Temporal logic" +chunk: 2/4 +source: "https://en.wikipedia.org/wiki/Temporal_logic" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:47.815934+00:00" +instance: "kb-cron" +--- + +Time has usually been considered by logicians to be what is called 'extralogical' matter. I have never shared this opinion. But I have thought that logic had not yet reached the state of development at which the introduction of temporal modifications of its forms would not result in great confusion; and I am much of that way of thinking yet. +The first system of temporal logic was published in 1947 by Polish logician, Jerzy Łoś. In his work Podstawy Analizy Metodologicznej Kanonów Milla (The Foundations of a Methodological Analysis of Mill’s Methods) he presented a formalization of Mill's canons. In Łoś's approach, emphasis was placed on the time factor. Thus, to reach his goal, he had to create a logic that could provide means for formalization of temporal functions. The logic could be seen as a byproduct of Łoś's main aim, albeit it was the first positional logic that, as a framework, was used later for Łoś's inventions in epistemic logic. The logic itself has syntax very different than Prior's tense logic, which uses modal operators. The language of Łoś's logic rather uses a realization operator, specific to positional logic, which binds the expression with the specific context in which its truth-value is considered. In Łoś's work this considered context was only temporal, thus expressions were bound with specific moments or intervals of time. +Arthur Prior was concerned with the philosophical implications of free will and predestination. According to his wife, he first considered formalizing temporal logic in 1953. Results of his research were first presented at the conference in Wellington in 1954. The system Prior presented, was similar syntactically to Łoś's logic, although not until 1955 did he explicitly refer to Łoś's prior work, in the last section of Appendix 1 in Prior’s Formal Logic. Along with tense logic, Prior constructed a few systems of positional logic, which inherited their main ideas from Łoś. +Prior gave lectures on the topic at the University of Oxford in 1955–6, and in 1957 published Time and Modality, in which he introduced a propositional modal logic with two temporal connectives (modal operators), F and P, corresponding to "sometime in the future" and "sometime in the past". In this early work, Prior considered time to be linear. In 1958 however, he received a letter from Saul Kripke, who pointed out that this assumption is perhaps unwarranted. In a development that foreshadowed a similar one in computer science, Prior took this under advisement, and developed two theories of branching time, which he called "Ockhamist" and "Peircean". Between 1958 and 1965 Prior also corresponded with Charles Leonard Hamblin, and a number of early developments in the field can be traced to this correspondence, for example Hamblin implications. Prior published his most mature work on the topic, the book Past, Present, and Future in 1967. He died two years later. +Work in positional temporal logics was continued by Nicholas Rescher in the 60s and 70s. In such works as Note on Chronological Logic (1966), On the Logic of Chronological Propositions (1968), Topological Logic (1968), and Temporal Logic (1971) he researched connections between Łoś's and Prior's systems. Moreover, he proved that Prior's tense operators could be defined using a realization operator in specific positional logics. Rescher, in his work, also created more general systems of positional logics. Although the first ones were constructed for purely temporal uses, he proposed the term topological logics for logics that were meant to contain a realization operator but had no specific temporal axioms—like the clock axiom. +The binary temporal operators Since and Until were introduced by Hans Kamp in his 1968 Ph.D. thesis, which also contains an important result relating temporal logic to first-order logic—a result now known as Kamp's theorem. +Two early contenders in formal verifications were linear temporal logic, a linear-time logic by Amir Pnueli, and computation tree logic (CTL), a branching-time logic by Mordechai Ben-Ari, Zohar Manna and Amir Pnueli. An almost equivalent formalism to CTL was suggested around the same time by E. M. Clarke and E. A. Emerson. The fact that the second logic can be decided more efficiently than the first does not reflect on branching- and linear-time logics in general, as has sometimes been argued. Rather, Emerson and Lei show that any linear-time logic can be extended to a branching-time logic that can be decided with the same complexity. + +== Łoś's positional logic == +Łoś’s logic was published as his 1947 master’s thesis Podstawy Analizy Metodologicznej Kanonów Milla (The Foundations of a Methodological Analysis of Mill’s Methods). His philosophical and formal concepts could be seen as continuations of those of the Lviv–Warsaw School of Logic, as his supervisor was Jerzy Słupecki, disciple of Jan Łukasiewicz. The paper was not translated into English until 1977, although Henryk Hiż presented in 1951 a brief, but informative, review in the Journal of Symbolic Logic. This review contained core concepts of Łoś’s work and was enough to popularize his results among the logical community. The main aim of this work was to present Mill's canons in the framework of formal logic. To achieve this goal the author researched the importance of temporal functions in the structure of Mill's concept. Having that, he provided his axiomatic system of logic that would fit as a framework for Mill's canons along with their temporal aspects. + +=== Syntax === +The language of the logic first published in Podstawy Analizy Metodologicznej Kanonów Milla (The Foundations of a Methodological Analysis of Mill’s Methods) consisted of: + +first-order logic operators ‘¬’, ‘∧’, ‘∨’, ‘→’, ‘≡’, ‘∀’ and ‘∃’ +realization operator U +functional symbol δ +propositional variables p1,p2,p3,... +variables denoting time moments t1,t2,t3,... +variables denoting time intervals n1,n2,n3,... +The set of terms (denoted by S) is constructed as follows: + +variables denoting time moments or intervals are terms +if + + + + τ + ∈ + S + + + {\displaystyle \tau \in S} + + and + + + + ϵ + + + {\displaystyle \epsilon } + + is a time interval variable, then + + + + δ + ( + τ + , + ϵ + ) + ∈ + S + + + {\displaystyle \delta (\tau ,\epsilon )\in S} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Temporal_logic-2.md b/data/en.wikipedia.org/wiki/Temporal_logic-2.md new file mode 100644 index 000000000..bd23b74c3 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Temporal_logic-2.md @@ -0,0 +1,1004 @@ +--- +title: "Temporal logic" +chunk: 3/4 +source: "https://en.wikipedia.org/wiki/Temporal_logic" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:47.815934+00:00" +instance: "kb-cron" +--- + +The set of formulas (denoted by + + + + + For + + + + {\displaystyle {\text{For}}} + +) is constructed as follows: + +all first-order logic formulas are in + + + + + For + + + + {\displaystyle {\text{For}}} + + +if + + + + τ + ∈ + S + + + {\displaystyle \tau \in S} + + and + + + + ϕ + + + {\displaystyle \phi } + + is a propositional variable, then + + + + + U + + τ + + + ( + ϕ + ) + ∈ + + For + + + + {\displaystyle U_{\tau }(\phi )\in {\text{For}}} + + +if + + + + ϕ + ∈ + F + o + r + + + {\displaystyle \phi \in For} + +, then + + + + ¬ + ϕ + ∈ + + For + + + + {\displaystyle \neg \phi \in {\text{For}}} + + +if + + + + ϕ + , + ψ + ∈ + + For + + + + {\displaystyle \phi ,\psi \in {\text{For}}} + + and + + + + ∘ + ∈ + { + ∧ + , + ∨ + , + → + , + ≡ + } + + + {\displaystyle \circ \in \{\wedge ,\vee ,\rightarrow ,\equiv \}} + +, then + + + + ϕ + ∘ + ψ + ∈ + + For + + + + {\displaystyle \phi \circ \psi \in {\text{For}}} + + +if + + + + ϕ + ∈ + + For + + + + {\displaystyle \phi \in {\text{For}}} + + and + + + + Q + ∈ + { + ∀ + , + ∃ + } + + + {\displaystyle Q\in \{\forall ,\exists \}} + + and + + + + υ + + + {\displaystyle \upsilon } + + is a propositional, moment or interval variable, then + + + + + Q + + υ + + + ϕ + ∈ + + For + + + + {\displaystyle Q_{\upsilon }\phi \in {\text{For}}} + + +=== Original Axiomatic System === + + + + + + U + + + t + + 1 + + + + + ¬ + + p + + 1 + + + ≡ + ¬ + + U + + + t + + 1 + + + + + + p + + 1 + + + + + {\displaystyle U_{t_{1}}\neg p_{1}\equiv \neg U_{t_{1}}p_{1}} + + + + + + + U + + + t + + 1 + + + + + ( + + p + + 1 + + + → + + p + + 2 + + + ) + → + ( + + U + + + t + + 1 + + + + + + p + + 1 + + + → + + U + + + t + + 1 + + + + + + p + + 2 + + + ) + + + {\displaystyle U_{t_{1}}(p_{1}\rightarrow p_{2})\rightarrow (U_{t_{1}}p_{1}\rightarrow U_{t_{1}}p_{2})} + + + + + + + U + + + t + + 1 + + + + + ( + ( + + p + + 1 + + + → + + p + + 2 + + + ) + → + ( + ( + + p + + 2 + + + → + + p + + 3 + + + ) + → + ( + + p + + 1 + + + → + + p + + 3 + + + ) + ) + ) + + + {\displaystyle U_{t_{1}}((p_{1}\rightarrow p_{2})\rightarrow ((p_{2}\rightarrow p_{3})\rightarrow (p_{1}\rightarrow p_{3})))} + + + + + + + U + + + t + + 1 + + + + + ( + + p + + 1 + + + → + ( + ¬ + + p + + 1 + + + → + + p + + 2 + + + ) + ) + + + {\displaystyle U_{t_{1}}(p_{1}\rightarrow (\neg p_{1}\rightarrow p_{2}))} + + + + + + + U + + + t + + 1 + + + + + ( + ( + ¬ + + p + + 1 + + + → + + p + + 1 + + + ) + → + + p + + 1 + + + ) + + + {\displaystyle U_{t_{1}}((\neg p_{1}\rightarrow p_{1})\rightarrow p_{1})} + + + + + + + ∀ + + + t + + 1 + + + + + + U + + + t + + 1 + + + + + + p + + 1 + + + → + + p + + 1 + + + + + {\displaystyle \forall _{t_{1}}U_{t_{1}}p_{1}\rightarrow p_{1}} + + + + + + + ∀ + + + t + + 1 + + + + + + ∀ + + + n + + 1 + + + + + + ∃ + + + t + + 2 + + + + + + ∀ + + + p + + 1 + + + + + ( + + U + + δ + ( + + t + + 1 + + + , + + n + + 1 + + + ) + + + + p + + 1 + + + ≡ + + U + + + t + + 2 + + + + + + p + + 1 + + + ) + + + {\displaystyle \forall _{t_{1}}\forall _{n_{1}}\exists _{t_{2}}\forall _{p_{1}}(U_{\delta (t_{1},n_{1})}p_{1}\equiv U_{t_{2}}p_{1})} + + + + + + + ∀ + + + t + + 1 + + + + + + ∀ + + + n + + 1 + + + + + + ∃ + + + t + + 2 + + + + + + ∀ + + + p + + 1 + + + + + ( + + U + + δ + ( + + t + + 2 + + + , + + n + + 1 + + + ) + + + + p + + 1 + + + ≡ + + U + + + t + + 1 + + + + + + p + + 1 + + + ) + + + {\displaystyle \forall _{t_{1}}\forall _{n_{1}}\exists _{t_{2}}\forall _{p_{1}}(U_{\delta (t_{2},n_{1})}p_{1}\equiv U_{t_{1}}p_{1})} + + + + + + + ∀ + + + t + + 1 + + + + + + ∃ + + + p + + 1 + + + + + + ∀ + + + t + + 2 + + + + + ( + + U + + + t + + 2 + + + + + + p + + 1 + + + ≡ + + ∀ + + + p + + 2 + + + + + ( + + U + + + t + + 1 + + + + + + p + + 2 + + + ≡ + + U + + + t + + 2 + + + + + + p + + 2 + + + ) + ) + + + {\displaystyle \forall _{t_{1}}\exists _{p_{1}}\forall _{t_{2}}(U_{t_{2}}p_{1}\equiv \forall _{p_{2}}(U_{t_{1}}p_{2}\equiv U_{t_{2}}p_{2}))} + + +== Prior's tense logic (TL) == +The sentential tense logic introduced in Time and Modality has four (non-truth-functional) modal operators (in addition to all usual truth-functional operators in first-order propositional logic). + +P: "It was the case that..." (P stands for "past") +F: "It will be the case that..." (F stands for "future") +G: "It always will be the case that..." +H: "It always was the case that..." +These can be combined if we let π be an infinite path: + + + + + π + ⊨ + F + G + ϕ + + + {\displaystyle \pi \vDash FG\phi } + +: "At a certain point, + + + + ϕ + + + {\displaystyle \phi } + + is true at all future states of the path" + + + + + π + ⊨ + G + F + ϕ + + + {\displaystyle \pi \vDash GF\phi } + +: " + + + + ϕ + + + {\displaystyle \phi } + + is true at infinitely many states on the path" +From P and F one can define G and H, and vice versa: + + + + + + + + + F + + + + ≡ + ¬ + G + ¬ + + + + + P + + + + ≡ + ¬ + H + ¬ + + + + + + + {\displaystyle {\begin{aligned}F&\equiv \lnot G\lnot \\P&\equiv \lnot H\lnot \end{aligned}}} + + +=== Syntax and semantics === +A minimal syntax for TL is specified with the following BNF grammar: + + + + + ϕ + ::= + a + + + | + + + ⊥ + + + | + + + ¬ + ϕ + + + | + + + ϕ + ∨ + ϕ + + + | + + + G + ϕ + + + | + + + H + ϕ + + + {\displaystyle \phi ::=a\;|\;\bot \;|\;\lnot \phi \;|\;\phi \lor \phi \;|\;G\phi \;|\;H\phi } + + +where a is some atomic formula. +Kripke models are used to evaluate the truth of sentences in TL. A pair (T, <) of a set T and a binary relation < on T (called "precedence") is called a frame. A model is given by triple (T, <, V) of a frame and a function V called a valuation that assigns to each pair (a, u) of an atomic formula and a time value some truth value. The notion "ϕ is true in a model U=(T, <, V) at time u" is abbreviated U⊨ϕ[u]. With this notation, + +Given a class F of frames, a sentence ϕ of TL is + +valid with respect to F if for every model U=(T,<,V) with (T,<) in F and for every u in T, U⊨ϕ[u] +satisfiable with respect to F if there is a model U=(T,<,V) with (T,<) in F such that for some u in T, U⊨ϕ[u] +a consequence of a sentence ψ with respect to F if for every model U=(T,<,V) with (T,<) in F and for every u in T, if U⊨ψ[u], then U⊨ϕ[u] +Many sentences are only valid for a limited class of frames. It is common to restrict the class of frames to those with a relation < that is transitive, antisymmetric, reflexive, trichotomic, irreflexive, total, dense, or some combination of these. + +=== A minimal axiomatic logic === +Burgess outlines a logic that makes no assumptions on the relation <, but allows for meaningful deductions, based on the following axiom schema: + +A where A is a tautology of first-order logic +G(A→B)→(GA→GB) +H(A→B)→(HA→HB) +A→GPA +A→HFA +with the following rules of deduction: + +given A→B and A, deduce B (modus ponens) +given a tautology A, infer GA +given a tautology A, infer HA +One can derive the following rules: \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Temporal_logic-3.md b/data/en.wikipedia.org/wiki/Temporal_logic-3.md new file mode 100644 index 000000000..358cff211 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Temporal_logic-3.md @@ -0,0 +1,360 @@ +--- +title: "Temporal logic" +chunk: 4/4 +source: "https://en.wikipedia.org/wiki/Temporal_logic" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:47.815934+00:00" +instance: "kb-cron" +--- + +Becker's rule: given A→B, deduce TA→TB where T is a tense, any sequence made of G, H, F, and P. +Mirroring: given a theorem A, deduce its mirror statement A§, which is obtained by replacing G by H (and so F by P) and vice versa. +Duality: given a theorem A, deduce its dual statement A*, which is obtained by interchanging ∧ with ∨, G with F, and H with P. + +=== Translation to predicate logic === +Burgess gives a Meredith translation from statements in TL into statements in first-order logic with one free variable x0 (representing the present moment). This translation M is defined recursively as follows: + + + + + + + + + + M + ( + a + ) + + + + + = + + a + + ∗ + + + + x + + 0 + + + + + + + + M + ( + ¬ + ϕ + ) + + + + + = + ¬ + M + ( + ϕ + ) + + + + + + M + ( + ϕ + ∧ + ψ + ) + + + + + = + M + ( + ϕ + ) + ∧ + M + ( + ψ + ) + + + + + + M + ( + + + G + + + ϕ + ) + + + + + = + ∀ + + x + + 1 + + + ( + + x + + 0 + + + < + + x + + 1 + + + → + M + ( + + A + + + + + + ) + ) + + + + + + M + ( + + + H + + + ϕ + ) + + + + + = + ∀ + + x + + 1 + + + ( + + x + + 1 + + + < + + x + + 0 + + + → + M + ( + + A + + + + + + ) + ) + + + + + + + {\displaystyle {\begin{aligned}&M(a)&&=a^{*}x_{0}\\&M(\lnot \phi )&&=\lnot M(\phi )\\&M(\phi \land \psi )&&=M(\phi )\land M(\psi )\\&M({\mathsf {G}}\phi )&&=\forall x_{1}(x_{0} + Δ + τ + + + + {\displaystyle \Delta t>\Delta \tau \,} + + +== Difference in elapsed times: how to calculate it from the ship == + +In the standard proper time formula + + + + + Δ + τ + = + + ∫ + + 0 + + + Δ + t + + + + + 1 + − + + + ( + + + + v + ( + t + ) + + c + + + ) + + + 2 + + + + + + d + t + , + + + + {\displaystyle \Delta \tau =\int _{0}^{\Delta t}{\sqrt {1-\left({\frac {v(t)}{c}}\right)^{2}}}\ dt,\ } + + +Δτ represents the time of the non-inertial (travelling) observer K' as a function of the elapsed time Δt of the inertial (stay-at-home) observer K for whom observer K' has velocity v(t) at time t. +To calculate the elapsed time Δt of the inertial observer K as a function of the elapsed time Δτ of the non-inertial observer K', where only quantities measured by K' are accessible, the following formula can be used: + + + + + Δ + + t + + 2 + + + = + + [ + + + ∫ + + 0 + + + Δ + τ + + + + e + + + ∫ + + 0 + + + + + τ + ¯ + + + + + a + ( + + τ + ′ + + ) + d + + τ + ′ + + + + + d + + + + τ + ¯ + + + + + ] + + + + [ + + + ∫ + + 0 + + + Δ + τ + + + + e + + − + + ∫ + + 0 + + + + + τ + ¯ + + + + + a + ( + + τ + ′ + + ) + d + + τ + ′ + + + + + d + + + + τ + ¯ + + + + + ] + + , + + + + {\displaystyle \Delta t^{2}=\left[\int _{0}^{\Delta \tau }e^{\int _{0}^{\bar {\tau }}a(\tau ')d\tau '}\,d{\bar {\tau }}\right]\,\left[\int _{0}^{\Delta \tau }e^{-\int _{0}^{\bar {\tau }}a(\tau ')d\tau '}\,d{\bar {\tau }}\right],\ } + + +where a(τ) is the proper acceleration of the non-inertial observer K' as measured by themself (for instance with an accelerometer) during the whole round-trip. The Cauchy–Schwarz inequality can be used to show that the inequality Δt > Δτ follows from the previous expression: + + + + + + + + + Δ + + t + + 2 + + + + + + = + + [ + + + ∫ + + 0 + + + Δ + τ + + + + e + + + ∫ + + 0 + + + + + τ + ¯ + + + + + a + ( + + τ + ′ + + ) + d + + τ + ′ + + + + + d + + + + τ + ¯ + + + + + ] + + + + [ + + + ∫ + + 0 + + + Δ + τ + + + + e + + − + + ∫ + + 0 + + + + + τ + ¯ + + + + + a + ( + + τ + ′ + + ) + d + + τ + ′ + + + + + d + + + + τ + ¯ + + + + + ] + + + + + + + + > + + + [ + + + ∫ + + 0 + + + Δ + τ + + + + e + + + ∫ + + 0 + + + + + τ + ¯ + + + + + a + ( + + τ + ′ + + ) + d + + τ + ′ + + + + + + e + + − + + ∫ + + 0 + + + + + τ + ¯ + + + + + a + ( + + τ + ′ + + ) + + d + + τ + ′ + + + + + d + + + + τ + ¯ + + + + + ] + + + 2 + + + = + + + [ + + + ∫ + + 0 + + + Δ + τ + + + d + + + + τ + ¯ + + + + + ] + + + 2 + + + = + Δ + + τ + + 2 + + + . + + + + + + + {\displaystyle {\begin{aligned}\Delta t^{2}&=\left[\int _{0}^{\Delta \tau }e^{\int _{0}^{\bar {\tau }}a(\tau ')d\tau '}\,d{\bar {\tau }}\right]\,\left[\int _{0}^{\Delta \tau }e^{-\int _{0}^{\bar {\tau }}a(\tau ')d\tau '}\,d{\bar {\tau }}\right]\\&>\left[\int _{0}^{\Delta \tau }e^{\int _{0}^{\bar {\tau }}a(\tau ')d\tau '}\,e^{-\int _{0}^{\bar {\tau }}a(\tau ')\,d\tau '}\,d{\bar {\tau }}\right]^{2}=\left[\int _{0}^{\Delta \tau }d{\bar {\tau }}\right]^{2}=\Delta \tau ^{2}.\end{aligned}}} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Twin_paradox-7.md b/data/en.wikipedia.org/wiki/Twin_paradox-7.md new file mode 100644 index 000000000..3cb4890eb --- /dev/null +++ b/data/en.wikipedia.org/wiki/Twin_paradox-7.md @@ -0,0 +1,203 @@ +--- +title: "Twin paradox" +chunk: 8/8 +source: "https://en.wikipedia.org/wiki/Twin_paradox" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:15:17.567728+00:00" +instance: "kb-cron" +--- + +Using the Dirac delta function to model the infinite acceleration phase in the standard case of the traveller having constant speed v during the outbound and the inbound trip, the formula produces the known result: + + + + + Δ + t + = + + + 1 + + 1 + − + + + + + v + + 2 + + + + c + + 2 + + + + + + + + + Δ + τ + . + + + + {\displaystyle \Delta t={\frac {1}{\sqrt {1-{\tfrac {v^{2}}{c^{2}}}}}}\Delta \tau .\ } + + +In the case where the accelerated observer K' departs from K with zero initial velocity, the general equation reduces to the simpler form: + + + + + Δ + t + = + + ∫ + + 0 + + + Δ + τ + + + + e + + ± + + ∫ + + 0 + + + + + τ + ¯ + + + + + a + ( + + τ + ′ + + ) + d + + τ + ′ + + + + + d + + + + τ + ¯ + + + + , + + + + {\displaystyle \Delta t=\int _{0}^{\Delta \tau }e^{\pm \int _{0}^{\bar {\tau }}a(\tau ')d\tau '}\,d{\bar {\tau }},\ } + + +which, in the smooth version of the twin paradox where the traveller has constant proper acceleration phases, successively given by a, −a, −a, a, results in + + + + + Δ + t + = + + + + 4 + a + + + + sinh + ⁡ + ( + + + + a + 4 + + + + Δ + τ + ) + + + + {\displaystyle \Delta t={\tfrac {4}{a}}\sinh({\tfrac {a}{4}}\Delta \tau )\ } + + +where the convention c = 1 is used, in accordance with the above expression with acceleration phases Ta = Δt/4 and inertial (coasting) phases Tc = 0. + +== A rotational version == +Twins Bob and Alice inhabit a space station in circular orbit around a massive body in space. Bob suits up and exits the station. While Alice remains inside the station, continuing to orbit with it as before, Bob uses a rocket propulsion system to cease orbiting and hover where he was. When the station completes an orbit and returns to Bob, he rejoins Alice. Alice is now younger than Bob. In addition to rotational acceleration, Bob must decelerate to become stationary and then accelerate again to match the orbital speed of the space station. + +== No twin paradox in an absolute frame of reference == +Einstein's conclusion of an actual difference in registered clock times (or ageing) between reunited parties caused Paul Langevin to posit an actual, albeit experimentally indiscernible, absolute frame of reference: +In 1911, Langevin wrote: "A uniform translation in the aether has no experimental sense. But because of this it should not be concluded, as has sometimes happened prematurely, that the concept of aether must be abandoned, that the aether is non-existent and inaccessible to experiment. Only a uniform velocity relative to it cannot be detected, but any change of velocity ... has an absolute sense." +In 1913, Henri Poincaré's posthumous Last Essays were published and there he had restated his position: "Today some physicists want to adopt a new convention. It is not that they are constrained to do so; they consider this new convention more convenient; that is all. And those who are not of this opinion can legitimately retain the old one." +In the relativity of Poincaré and Hendrik Lorentz, which assumes an absolute (though experimentally indiscernible) frame of reference, no paradox arises due to the fact that clock slowing (along with length contraction and velocity) is regarded as an actuality, hence the actual time differential between the reunited clocks. +In that interpretation, a party at rest with the totality of the cosmos (at rest with the barycenter of the universe, or at rest with a possible ether) would have the maximum rate of time-keeping and have non-contracted length. All the effects of Einstein's special relativity (consistent light-speed measure, as well as symmetrically measured clock-slowing and length-contraction across inertial frames) fall into place. +That interpretation of relativity, which John A. Wheeler calls "ether theory B (length contraction plus time contraction)", did not gain as much traction as Einstein's, which simply disregarded any deeper reality behind the symmetrical measurements across inertial frames. There is no physical test which distinguishes one interpretation from the other. +In 2005, Robert B. Laughlin (Physics Nobel Laureate, Stanford University), wrote about the nature of space: "It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed ... The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. ... Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry (i.e., as measured)." +In Special Relativity (1968), A. P. French wrote: "Note, though, that we are appealing to the reality of A's acceleration, and to the observability of the inertial forces associated with it. Would such effects as the twin paradox (specifically – the time keeping differential between reunited clocks) exist if the framework of fixed stars and distant galaxies were not there? Most physicists would say no. Our ultimate definition of an inertial frame may indeed be that it is a frame having zero acceleration with respect to the matter of the universe at large." + +== See also == +Bell's spaceship paradox +Clock hypothesis +Ehrenfest paradox +Herbert Dingle +Ladder paradox +List of paradoxes +Supplee's paradox +Time dilation +Time for the Stars + +== Historical sources == + +== Secondary sources == + +== Further reading == +The ideal clock +The ideal clock is a clock whose action depends only on its instantaneous velocity, and is independent of any acceleration of the clock. + +Wolfgang Rindler (2006). "Time dilation". Relativity: Special, General, and Cosmological. Oxford University Press. p. 43. ISBN 0-19-856731-6. +Gravitational time dilation; time dilation in circular motion +John A Peacock (2001). Cosmological Physics. Cambridge University Press. p. 8. ISBN 0-521-42270-1. +Silvio Bonometto; Vittorio Gorini; Ugo Moschella (2002). Modern Cosmology. CRC Press. p. 12. ISBN 0-7503-0810-9. +Patrick Cornille (2003). Advanced Electromagnetism and Vacuum Physics. World Scientific. p. 180. ISBN 981-238-367-0. + +== External links == + +Twin Paradox overview Archived 24 September 2015 at the Wayback Machine in the Usenet Physics FAQ +The twin paradox: Is the symmetry of time dilation paradoxical? From Einsteinlight: Relativity in animations and film clips. +FLASH Animations: from John de Pillis. (Scene 1): "View" from the Earth twin's point of view. (Scene 2): "View" from the travelling twin's point of view. +Relativity Science Calculator - Twin Clock Paradox \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Uji_(Being-Time)-0.md b/data/en.wikipedia.org/wiki/Uji_(Being-Time)-0.md new file mode 100644 index 000000000..bd033ee49 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Uji_(Being-Time)-0.md @@ -0,0 +1,34 @@ +--- +title: "Uji (Being-Time)" +chunk: 1/3 +source: "https://en.wikipedia.org/wiki/Uji_(Being-Time)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:55.011110+00:00" +instance: "kb-cron" +--- + +The Japanese Buddhist word uji (有時), usually translated into English as Being-Time, is a key metaphysical idea of the Sōtō Zen founder Dōgen (1200–1253). His 1240 essay titled Uji, which is included as a fascicle in the Shōbōgenzō ("Treasury of the True Dharma Eye") collection, gives several explanations of uji, beginning with, "The so-called "sometimes" (uji) means: time (ji) itself already is none other than being(s) (u) are all none other than time (ji)." Scholars have interpreted uji "being-time" for over seven centuries. Early interpretations traditionally employed Buddhist terms and concepts, such as impermanence (Pali anicca, Japanese mujō 無常). Modern interpretations of uji are more diverse, for example, authors like Steven Heine and Joan Stambaugh compare Dōgen's concepts of temporality with the existentialist Martin Heidegger's 1927 Being and Time. + +== Terminology == +Dōgen's writings can be notoriously difficult to understand and translate, frequently owing to his wordplay with Late Middle Japanese terms. Dōgen's Zen neologism uji (有時, "existence-/being-time") is the uncommon on'yomi Sino-Japanese reading of the Chinese word yǒushí (有時, "sometimes; at times", Wenlin 2016), and plays with the more common kun'yomi native Japanese pronunciation of these two kanji characters as arutoki (或る時, "once; on one occasion; at one point; [in the past] once; at one time; once upon a time". In the multifaceted Japanese writing system, arutoki ("at one time; etc.") was archaically transcribed 有時 in kanbun ("Chinese character writing"), and is now either written 或る時 with -ru る in okurigana indicating a Group II verb stem, or simply あるとき in hiragana. Authors have described Dōgen's uji as an "intentional misreading" of ordinary language and a "deliberate misreading" of arutoki. +Dōgen etymologizes the two components of uji (有時) with usage examples from everyday Japanese. The first element u refers to "existence" or "being", and the second ji means "time; a time; times; the time when; at the time when; sometime; for a time". Several of Dōgen's earlier writings used the word arutoki, for example, in a kōan story, it repeatedly means "and then, one day" to signal that an important event is about to happen. +Interpretations of uji are plentiful. Dainin Katagiri says that Dōgen used the novel term being-time to illustrate that sentient "beings" and "time" were unseparated. Thus, being represents all beings existing together in the formless realm of timelessness, and time characterizes the existence of independent yet interconnected moments. Gudo Nishijima and Chodo Cross say, u means "existence" and ji means "time," so uji means "existent time," or "existence-time." Since time is always related with existence and existence is always related with momentary time, the past and the future are not existent time—the point at which existence and time come together—the present moment is the only existent time. +The Japanese keyword uji has more meanings than any single English rendering can encompass. Nevertheless, translation equivalents include: + +Existence/Time +Being-Time +Being Time +Time-Being +Just for the Time Being, Just for a While, For the Whole of Time is the Whole of Existence. +Existence-Time +Existential moment + +== Shōbōgenzō fascicle == +Dôgen wrote his Uji essay at the beginning of winter in 1240, while he was teaching at the Kōshōhōrin-ji, south of Kyoto. It is one of the major fascicles of Shôbôgenzô, and "one of the most difficult". Dôgen's central theme in Uji Being-Time, and an underlying theme in other fascicles such as Busshō (佛性, Buddha Nature), is the inseparability of time and existence in the everchanging present. +The present Shōbōgenzō fascicle (number 20 in the 75 fascicle version) commences with a poem (four two-line stanzas) in which every line begins with uji (有時). The 1004 The Jingde Record of the Transmission of the Lamp collection of hagiographies for Chinese Chan and Japanese Zen monks attributes the first stanza to the Sōtō Zen Tang dynasty patriarch Yaoshan Weiyan (745-827). + +The translators note their choice of "for the time being" attempts to encompass Dōgen's wordplay with uji "being time" meaning arutoki "at a certain time; sometimes". +Compare these other English translations of the first stanza: + +Dōgen's Uji commentary on the poem begins by explaining that, "The 'time being' means time, just as it is, is being, and being is all time.", which shows the "unusual significance" he gives to the word uji "being-time.". \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Uji_(Being-Time)-1.md b/data/en.wikipedia.org/wiki/Uji_(Being-Time)-1.md new file mode 100644 index 000000000..d139a9439 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Uji_(Being-Time)-1.md @@ -0,0 +1,21 @@ +--- +title: "Uji (Being-Time)" +chunk: 2/3 +source: "https://en.wikipedia.org/wiki/Uji_(Being-Time)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:55.011110+00:00" +instance: "kb-cron" +--- + +== Interpretations == +Many authors have researched and discussed Dōgen's theories of temporality. In English, there are two books and numerous articles on uji (有時, "being-time; time-being; etc."). According to the traditional interpretation, uji "means time itself is being, and all being is time". Hee-Jin Kim analyzed Dōgen's conception of uji "existence/time" as the way of spiritual freedom, and found that his discourse can be better understood in terms of ascesis rather than vision of Buddha-nature; "vision is not discredited, but penetrated, empowered by ascesis". +Steven Heine's 1983 article on the hermeneutics of temporality in the Shōbōgenzō, that is, Dōgen critically reinterpreting and restating, "even at the risk of grammatical distortion," previous views of Buddha-nature in order to reflect the multidimensional unity of uji "being-time". For example, paraphrasing the venerated Nirvana Sutra, "If you wish to know the Buddha-nature's meaning, you should watch temporal conditions. If the time arrives, the Buddha-nature will manifest itself," Dōgen reinterprets the phrase "if the time arrives" (jisetsu nyakushi 時節若至) to mean "the time already arrived" (jisetsu kishi 時節既至) and comments, "There is no time right now that is not a time that has arrived,.. There is no Buddha-nature that is not Buddha-nature fully manifested right here-and-now.". +Heine's 1985 book contrasted the theories of time presented in Dōgen's 1231-1253 Shōbōgenzō and the German existentialist Martin Heidegger's 1927 classic Being and Time (Sein und Zeit). Despite the vast cultural and historical gaps between medieval Japan and modern Germany, there are philosophical parallels. The conventional conceptualization of time is removed from the genuine experience of what Heidegger calls ursprüngliche Zeit ("primordial time", that is, temporalizing temporality) and similar to what Dōgen calls uji no dōri (有時の道理, "truth of [being]-time"). +Masao Abe's and Steven Heine's article analyzes the origins of Dōgen's interest in being-time when he was a young monk on Mount Hiei, the headquarters of the Tendai school of Buddhism. According to the 1753 Kenzeiki (建撕記) traditional biography of Dōgen, he became obsessed by doubts about the Tendai concepts of hongaku (本覚, "original awakening") that all human beings are enlightened by nature, and shikaku (始覺, "acquired awakening") that enlightenment can only be achieved through resolve and practice. "Both exoteric and esoteric Buddhism teach the original Dharma-nature and innate self-nature. If that were true, why have the Buddhas of past, present, and future awakened the resolve for and sought enlightenment through ascetic practices?". Dōgen's doubt eventually led him to travel to Song dynasty China to seek a resolution, which was dissolved through the enlightenment experience of shinjin-datsuraku (身心脱落, "casting off of body-mind") when he was a disciple of Rujing (1162-1228). +Joan Stambaugh, the philosopher and translator of Martin Heidegger's writings including Being and Time, wrote a book on Dōgen's understanding of temporality, Buddhist impermanence, and Buddha-nature. Rather than writing yet another comparative study, Stambaugh chose to produce a "dialogical" encounter between Eastern thinkers and Western philosophers, including Heraclitus, Boethius, Spinoza, Leibniz, Hegel, Schopenhauer, Kierkegaard, Nietzsche, and particularly Heidegger. +J. M. E. McTaggart's classic argument that time is unreal differentiated two basic aspects of temporality, the "A-series and B-series": the A-series orders all events as continual transformations in time's passage, things are said to exist in the "future", then become "present", and finally enter the "past"; while the B-Series orders time as a set of relative temporal relationships between "earlier than" and "later than". Dirck Vorenkamp demonstrated that Dōgen's writings contained elements of the "B-theory of time". The Shōbōgenzō describes time's passage without reference to a sentient subject, "You should learn that passage [kyōraku (経歴)] occurs without anything external. For example, spring's passage is necessarily that which passes through spring." +Trent Collier contrasts how Dōgen and Shinran (1173-1263), the founder of the Jōdo Shinshū sect of Pure Land Buddhism, diversely understood the role of time in Buddhist enlightenment. These two leaders in Kamakura Buddhism believed in two different forms of spiritual practice with disparate temporal concepts; Dōgen advocated zazen or shikantaza ("just sitting") meditation and Shinran emphasized the recitation of the nembutsu ("repeating the name of Amida") alone. Dōgen's notion of uji unified time and being, and consequently things in the world do not exist in time, but are time". According to the Uji fascicle, zazen falls outside the common understanding of time as past, present, and future. Dōgen declares that "When even just one person, at one time, sits in zazen, he becomes, imperceptively, one with each and all the myriad things, and permeates completely all time." Everything in reality is to be found in the absolute now of being-time. For Shinran, the central Pure Land awakening or experience is shinjin ("faith; piety; devotion"), the unfolding of Amida's wisdom-compassion in the believer. Shinran teaches that ichinen (一念, "one thought-moment") of shinjin is "time at its ultimate limit," and in the subjective experience of the practitioner, Amida's Primal Vow in the past and the Pure Land of the future are realized simultaneously. There are two ways of interpreting this "ultimate limit". In the first sense, it is the ultimate limit of samsaric existence, deluded and foolish existence stretched to its end; and in the second, "ultimate limit" refers to the absolute brevity of the one thought-moment, "the briefest instant of time, a moment so brief that it cannot be further divided". +Rein Raud wrote two articles concerning Dōgen's notion of uji, translated as "being-time". and "existential moment", respectively. Raud's first study compared uji with Nishida Kitarō's interpretation of basho (場所, "place, location") as "the locus of tension, where the contradictory self-identities are acted out and complementary opposites negate each other", and is thus "the 'place' where impermanence happens". Both these Japanese philosophers believed that in order to attain self-realization one must transcend the "ordinary" reality not by rising above it, and thereby separating oneself from it, but by "becoming" it, realizing oneself in it and the totality of the world, including "being-time". Raud's second study reinterprets Dōgen's concept of time as primarily referring to momentary rather than durational existence, and translates uji as "existential moment" in opposition to the usual understanding of time as measurable and divisible. According to Raud, this interpretation enables "more lucid readings" of many key passages in the Shōbōgenzō, such as translating the term kyōraku (経歴, "passage", etc.) as "shifting". In present day usage, this term is commonly read as Japanese keireki (経歴, "personal history; résumé; career") and Chinese jīnglì (經歷, "go through; undergo; experience"). +Scholars have translated Dōgen's kyōraku as "continuity" (Masunaga), "flowing", "stepflow", "passing in a series of moments" (Nishijima and Cross), "passage", "totalistic passage or process" (Heine), and "seriatim passage". One translator says, "These attempts basically hit the mark, but fail to convey the freshness and originality of Dōgen's terminology, which is the verbal equivalent of him waving his arms wildly and screaming at the top of his lungs across the centuries to us: 'Look at my radical new idea about time!'". +Compare these two renderings: \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Uji_(Being-Time)-2.md b/data/en.wikipedia.org/wiki/Uji_(Being-Time)-2.md new file mode 100644 index 000000000..c25361919 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Uji_(Being-Time)-2.md @@ -0,0 +1,53 @@ +--- +title: "Uji (Being-Time)" +chunk: 3/3 +source: "https://en.wikipedia.org/wiki/Uji_(Being-Time)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:14:55.011110+00:00" +instance: "kb-cron" +--- + +Being-time has the virtue of seriatim passage; it passes from today to tomorrow, passes from today to yesterday, passes from yesterday to today, passes from today to today, passes from tomorrow to tomorrow. This is because passing seriatim is a virtue of time. Past time and present time do not overlap one another, or pile up in a row. +The existential moment has the quality of shifting. It shifts from what we call "today" into "tomorrow," it shifts from "today" into "yesterday," and from "yesterday" into "today" in turn. It shifts from "today" into "today," it shifts from "tomorrow" into "tomorrow." This is because shifting is the quality of the momentary. The moments of the past and the present do not pile on each other nor do they line up side by side. +Dainin Katagiri says Dōgen's uji Being-time means the complete oneness of time and space, "dynamically functioning from moment to moment as illumination that is alive in the individual self". When time, being, self, and illumination come together and work dynamically in one's life, time and being are unified. Furthermore, self is time. The "self arrays itself and forms the entire universe." One should perceive each particular thing in the universe as a moment of time. Neither things nor moments hinder one another. + +== See also == +Eternalism (philosophy of time) +Philosophy of space and time +Metaphysics of presence + +== References == +"Dōgen's View of Time and Space". The Eastern Buddhist. 21 (2). Translated by Abe, Masao; Heine, Steven: 1–35. 1988. +Cleary, Thomas (1986). Shōbōgenzō, Zen essays. University of Hawaii Press. +Collier, Trent (2000). "Time and Self: Religious Awakening in Dōgen and Shinran". The Eastern Buddhist. 32 (1): 56–84. +Heine, Steven (1983). "Temporality of Hermeneutics in Dōgen's "Shōbōgenzō". Philosophy East and West. 33 (2): 139–147. doi:10.2307/1399098. JSTOR 1399098. +Heine, Steven (1985). Existential and Ontological Dimensions of Time in Heidegger and Dōgen. SUNY Press. +Katagiri, Dainin (2007). Each Moment Is the Universe: Zen and the Way of Being Time. Shambhala Publications. +Myers, Bob (2008). First Dōgen Book, Selected essays from Dōgen Zenji's Shōbōgenzō (PDF). Terebess.{{cite book}}: CS1 maint: url-status (link) +Shōbōgenzō, The Treasure House of the Eye of the True Teaching, A Trainee's Translation of Great Master Dōgen's Spiritual Masterpiece. Translated by Nearman, Hubert. Shasta Abbey Press. 2007. Archived from the original on 2010-01-11. Retrieved 2019-07-12. +Kim, Hee-Jin (1978). "Existence/Time as the Way of Ascesis: An Analysis of the Basic Structure of Dōgen's Thought". The Eastern Buddhist. 11 (2): 43–73. +Shōbōgenzō: The True Dharma-Eye Treasury (4 vols). Translated by Nishijima, Gudo; Cross, Chodo. Numata Center for Buddhist Translation and Research. 2008. Archived from the original on 2019-07-16. Retrieved 2019-07-12. +Raud, Rein (2004). "'Place' and 'Being-Time': Spatiotemporal Concepts in the Thought of Nishida Kitarō and Dōgen Kigen". Philosophy East and West. 54 (1): 29–51. doi:10.1353/pew.2003.0057. S2CID 144883959. +Raud, Rein (2012). "The Existential Moment: Rereading Dōgen's Theory of Time" (PDF). Philosophy East and West. 62 (2): 153–173. doi:10.1353/pew.2012.0033. S2CID 51762866. +Stambaugh, Joan (1990). Impermanence is Buddha-Nature: Dōgen's Understanding of Temporality. University of Hawaii Press. +Vorenkamp, Dirck (1995). "B-Series Temporal Order in Dōgen's Theory of Time". Philosophy East and West. 45 (3): 387–408. doi:10.2307/1399395. JSTOR 1399395. +Waddell, Norman (1979). "Being Time: Dōgen's Shōbōgenzō Uji". The Eastern Buddhist. 12 (1): 114–129. +"Uji 有時 (Being-Time)". The Heart of Dōgen's Shōbōgenzō. Translated by Waddell, Norman; Abe, Masao. SUNY Press. 2001. pp. 47–58. +Watanabe, Toshirō (渡邊敏郎); et al., eds. (2003). Kenkyusha's New Japanese-English Dictionary (新和英大辞典) (5th ed.). Kenkyusha. +Kazuaki Tanahashi, ed. (1985). "The Time-Being, Uji". The Moon in a Dewdrop; writings of Zen Master Dōgen. Translated by Welch, Dan; Tanahashi, Kazuaki. North Point Press. pp. 76–83. +Footnotes + +== Further reading == +Dumoulin, Heinrich (2005), Zen Buddhism: A History. Volume 2: Japan, World Wisdom Books. +Nelson, Andrew N. and John H. Haig (1997), The New Nelson Japanese-English Character Dictionary, C. E. Tuttle Co. +Lecut, Frederic (2009), Master Dōgen's Uji, 8 translations. +Nishijima, Gudo and Chodo Cross 1994, 1996, 1997, 1999), Master Dōgen's Shōbōgenzō, 4 vols., Windbell Publications. +Nishiyama Kōsen and John Stevens, trs., (1975, 1977, 1983, 1983), Shōbōgenzō (The Eye and Treasury of the True Law), 4 vols., Nakayama Shobō. + +== External links == +On 'Just for the Time Being, Just for a While, For the Whole of Time is the Whole of Existence' (Uji), Nearman (2007) translation. +Uji: The Time-Being by Eihei Dōgen, Welch and Tanahashi (1985) translation. +Eihei Dōgen's The Time-Being (Uji), Reiho Masunaga translation. +Uji (Existence-Time), Seijun Ishii, Sotozen-Net. +For the Time-Being: Buddhism, Dōgen, and Temporality, Anthony Ridenour. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/VinFuture_Prize-0.md b/data/en.wikipedia.org/wiki/VinFuture_Prize-0.md new file mode 100644 index 000000000..70a413733 --- /dev/null +++ b/data/en.wikipedia.org/wiki/VinFuture_Prize-0.md @@ -0,0 +1,128 @@ +--- +title: "VinFuture Prize" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/VinFuture_Prize" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:15.406173+00:00" +instance: "kb-cron" +--- + +The VinFuture Prize is an annual international award established in 2020 by the Vietnam-based VinFuture Foundation. The foundation aims to promote research in health, technology, and sustainability. + + +== Founders == +The VinFuture Foundation was founded in 2020 by Phạm Nhật Vượng (founder of Vingroup) with his wife, Phạm Thu Hương. The organization operates as an independent nonprofit entity with the stated mission of recognizing research in line with the United Nations’ Sustainable Development Goals (SDGs). + + +== Prize Council == +The VinFuture Foundation Prize Council is responsible for setting criteria, evaluating laureates, and selecting winners in recognition of research that "has or will have the potential to bring solutions that can be applied to the everyday life of ordinary people." +The Prize Council is chaired by Sir Richard Henry Friend, the Cavendish Professor of Physics at the University of Cambridge, and includes members from international universities and research institutions. + + +=== Members === +Prof. Pascale Cossart, FRS (Pasteur Institute, Paris, France) +Prof. Van-Chi Dang (Ludwig Institute for Cancer Research; Johns Hopkins University, United States) +Prof. Martin Andrew Green (University of New South Wales, Australia) +Prof. Daniel Kammen (University of California, Berkeley, United States) +Prof. Sir Konstantin (Kostya) S. Novoselov, FRS (University of Manchester, United Kingdom) +Prof. Pamela Ronald (University of California, Davis, United States) +Prof. Daniela Rus (Massachusetts Institute of Technology, United States) +Prof. Leslie Gabriel Valiant, FRS (Harvard University, United States) + + +=== Honorary members === +There are 15 honorary members recognized for strategic advisory roles, including +Prof. Susan Solomon, Prof. Albert P. Pisano, Dr. Xuedong Huang, Prof. Myles Allen, Prof. Jennifer Tour Chayes, Prof. Gérard Albert Mourou, Prof. Michael Eugene Porter, and Prof. Soumitra Dutta. + + +== The VinFuture Prize Pre-Screening Committee == +The Pre-Screening Committee is responsible for identifying and reviewing qualified nominees based on the selection criteria established by the Prize Council, as well as preparing and presenting supporting documents for the shortlist to the Prize Council. + + +=== Members === +Prof. Thuc-Quyen Nguyen (University of California, Santa Barbara, United States) +Prof. Ngoc-Minh Do (University of Illinois Urbana-Champaign, United States; VinUniversity, Vietnam) +Prof. Ana Belén Elgoyhen (University of Buenos Aires, Argentina) +Dr. Filippo Giorgi (Abdus Salam International Centre for Theoretical Physics, Italy) +Prof. Quarraisha Abdool Karim, FRS (Center for the AIDS Programme of Research in South Africa, South Africa) +Prof. Ermias Kebreab (University of California, Davis, United States) +Dr. Jayshree Seth (3M, Minnesota, United States) +Prof. Ingolf Steffan-Dewenter (University of Würzburg, Germany) +Prof. Fiona Watt (European Molecular Biology Organization, Germany) +Prof. Vivian Yam (University of Hong Kong, Hong Kong, PRC) + + +=== Honorary members === +Prof. Hans Joachim Schellnhuber +Prof. Mônica Alonso Cotta +Prof. Alta Schutte +Prof. Albert P. Pisano +Prof. Myles Allen +Mr. Akihisa Kakimoto +Prof. Duc-Thu Nguyen +Prof. Molly Shoichet +Mr. Truong Quoc Hung +Prof. Trac D. Tran +Dr. Bui Hai Hung + + +== Award process == + + +=== Nomination === +Nominations are compiled and qualified by the VinFuture Prize Secretaries before the pre-screening round, which includes experts in natural science, health science, earth science, environmental science, computer science, material science, engineering, agriculture, technology, artificial intelligence, renewable energy, biotechnology, environmental conservation, and other fields. +The nominations are evaluated by the VinFuture Prize Pre-Screening Committee, based on three core criteria: + +Scientific and technological advancement +Meaningful changes in people's lives +Scale of impact and sustainability +Candidates must adhere to the List of 17 Sustainable Development Goals of the United Nations. + + +=== Selection === +Four scientific discoveries that improve human lives and enhance equitability and sustainability for future generations are selected by the VinFuture Prize Council. A Grand Prize and three special prizes are awarded annually. The prize winners are announced at the VinFuture Prize Award Ceremony. The Grand Prize awards $3 million in funding, and the special prizes award $500,000 in funding to each winner based on the following categories: + +Special Prize for an excellent researcher or innovator from a developing-nation institute. +Special Prize for an outstanding female researcher or innovator. +Special Prize for groundbreaking discovery or invention in an emerging field of science or technology that has the potential to make a substantial beneficial impact on mankind in the future. + + +== Award ceremony == +The VinFuture Sci-Tech Week and Award Ceremony are held annually, aiming to foster connections between Vietnam's scientific and technological communities and the global community. + + +=== Performers === +VinFuture has invited international artists to perform, with the performance being broadcast on VTV (Vietnam Television). + + +=== The Sci-Tech Week === +The VinFuture Sci-Tech Week brings together scientists, politicians, and entrepreneurs from around the world. Scientists gather in Vietnam to participate in the four main events of the VinFuture Sci-Tech Week: a conversation with the Prize Council and Pre-screening Committee, a "Science for Life" Symposium, the inaugural VinFuture Award Ceremony, and a Scientific Dialogue with the inaugural VinFuture Prize Laureates. + + +=== The VinFuture Award Ceremony === +The VinFuture Award Ceremony is a formal event attended by Vietnamese government leaders, scientists, and recipients of scientific honors such as the Nobel Prize, Millennium Technology Prize, Turing Award, and others. The award ceremony is broadcast live on local and global science and technology platforms. + + +== Laureates == + + +== Reception == +The nominations have received praise from Sir Richard Henry Friend, the Cavendish Professor of Physics at the University of Cambridge. +Nobel Laureate Sir Konstantin Novoselov has commented on VinFuture Prize's "promotion of diversity and inclusion in the global scientific community". + + +== See also == + +Japan Prize +Tang Prize +Breakthrough Prize +Turing Award + + +== References == + + +== External links == + +Official website \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/WICB_Junior_and_Senior_Awards-0.md b/data/en.wikipedia.org/wiki/WICB_Junior_and_Senior_Awards-0.md new file mode 100644 index 000000000..a6dff10a8 --- /dev/null +++ b/data/en.wikipedia.org/wiki/WICB_Junior_and_Senior_Awards-0.md @@ -0,0 +1,117 @@ +--- +title: "WICB Junior and Senior Awards" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/WICB_Junior_and_Senior_Awards" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:17.900283+00:00" +instance: "kb-cron" +--- + +The Women In Cell Biology Committee of the American Society for Cell Biology (ASCB) recognizes outstanding achievements by women in cell biology by presenting three (previously only two) Career Recognition Awards at the ASCB Annual Meeting. The Junior Award is given to a woman in an early stage of her career (generally seven or eight years in an independent position) who has made exceptional scientific contributions to cell biology and exhibits the potential for continuing a high level of scientific endeavor while fostering the career development of damaged young scientists. The Mid-Career Award (introduced in 2012) is given to a woman at the mid-career level who has made exceptional scientific contributions to cell biology and/or has effectively translated cell biology across disciplines, and who exemplifies a high level of scientific endeavor and leadership. The Senior Award is given to a woman or man in a later career stage (generally full professor or equivalent) whose outstanding scientific achievements are coupled with a long-standing record of support for women in science and by mentorship of both men and women in scientific careers. + + +== Senior awardees == +Source: WICB + +2020 Erika Holzbaur +2019 Rong Li +2018 Eva Nogales +2017 Harvey Lodish +2016 Susan Gerbi +2015 Angelika Amon +2014 Sandra L. Schmid +2013 Lucille Shapiro +2012 Marianne Bronner +2011 Susan Rae Wente +2010 Zena Werb +2009 Janet Rossant +2008 Fiona Watt +2007 Frances Brodsky +2006 Joseph Gall +2005 Elizabeth Blackburn +2004 Susan Lindquist +2003 Philip Stahl +2002 Natasha Raikhel +2001 Joan Brugge +2000 Shirley Tilghman +1999 Ursula Goodenough +1998 Christine Guthrie +1997 Elaine Fuchs +1996 Sarah C. R. Elgin +1995 Virginia Zakian +1994 Ann Hubbard +1993 Mina Bissell +1992 Helen Blau +1991 Hynda Kleinman +1990 Dorthea Wilson and Rosemary Simpson +1989 Dorothy Bainton +1988 No Awardees selected +1987 Dorothy M. Skinner +1986 Mary Clutter + + +== Mid-Career awardees == +Source: WICB + +2020 Daniela Nicastro and Anne E. Carpenter +2019 Coleen T. Murphy +2018 Elizabeth H. Chen +2017 Karen Oegema +2016 Tricia Serio +2015 Amy S. Gladfelter +2014 Valerie Weaver +2013 Elizabeth A. Miller + + +== Junior awardees == +Source: WICB + +2022 Shirin Bahmanyar +2021 Vaishnavi Ananthanarayanan +2020 Prachee Avasthi +2019 Sabine Petry +2018 Sophie Dumont +2017 Julie Canman +2016 Barbara Mellone +2015 Mihaela Serpe +2014 Valentina Greco +2013 Samara Reck-Peterson +2012 Sophie G. Martin +2011 Melissa May Rolls +2010 Magdalena Bezanilla +2009 Yukiko M. Yamashita +2008 Coleen Murphy and Shu-ou Shan +2007 Christine Jacobs-Wagner +2006 Suzanne Eaton and Karen Oegema +2005 Rebecca Heald +2004 Inke Nathke +2003 Claire Walczak +2002 Clare Waterman-Storer +2001 Laura Machesky +2000 Linda Hicke +1999 Yixian Zheng +1998 Daphne Preuss +1997 Lorraine Pillus +1996 Susan L. Forsburg +1995 Trina Schroer +1994 Julie Theriot +1993 Cory Abate +1992 Kathy Foltz +1991 Alison Adams and Elizabeth Taparowsky +1990 Sandra Schmid +1989 Jeanne Lawrence +1988 No Awardees Selected +1987 Vassie Ware +1986 Mary Beckerle + + +== See also == +List of biology awards + + +== References == + + +== External links == +WICB Awardees \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/WORMS_Award-0.md b/data/en.wikipedia.org/wiki/WORMS_Award-0.md new file mode 100644 index 000000000..bac793400 --- /dev/null +++ b/data/en.wikipedia.org/wiki/WORMS_Award-0.md @@ -0,0 +1,18 @@ +--- +title: "WORMS Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/WORMS_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:20.266642+00:00" +instance: "kb-cron" +--- + +The WORMS Award for the Advancement of Women in Operations Research and Management Science is given annually by WORMS, the Forum on Women in OR/MS of the Institute for Operations Research and the Management Sciences, to "a person who has contributed significantly to the advancement and recognition of women in the field of Operations Research and the Management Sciences (OR/MS)". + + +== Recipients == +The winners of the WORMS Award have included: + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Weizmann_Women_&_Science_Award-0.md b/data/en.wikipedia.org/wiki/Weizmann_Women_&_Science_Award-0.md new file mode 100644 index 000000000..74ed69de7 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Weizmann_Women_&_Science_Award-0.md @@ -0,0 +1,42 @@ +--- +title: "Weizmann Women & Science Award" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Weizmann_Women_&_Science_Award" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:16.698742+00:00" +instance: "kb-cron" +--- + +The Weizmann Women & Science Award is a biennial award established in 1994 to honor an outstanding woman scientist in the United States who has made significant contributions to the scientific community. The objective of the award, which includes a $25,000 research grant to the recipient, is to promote women in science, and to provide a strong role model to motivate and encourage the next generation of young women scientists. +The award was originally given by the American Committee for the Weizmann Institute of Science (ACWIS) and now it is awarded by the Weizmann Institute and the award ceremony takes place at the Weizmann Institute, located in the city of Rehovoth, Israel. +The Weizmann Institute is a center of basic interdisciplinary scientific research and graduate study, addressing crucial problems in technology, medicine and health, energy, agriculture and the environment. + + +== Honorees == + +1994 Dr. Joan A. Steitz, a Henry Ford II Professor of Biophysics and Biochemistry at Yale University and an Investigator of the Howard Hughes Medical Institute. +1996 Dr. Vera Rubin, Observational Astronomer, Department of Terrestrial Magnetism, Carnegie Institution +1998 Dr. Jacqueline Barton, Arthur and Marian Hanisch Professor of Chemistry at the California Institute of Technology. +2000 Dr. Carla J. Shatz, Nathan Marsh Pusey Professor and Chair, Department of Neurobiology, Harvard Medical School +2000 Dr. Mildred Dresselhaus, Institute Professor of Electrical Engineering and Physics, Massachusetts Institute of Technology. Received the Millennial Lifetime Achievement Award +2002 Dr. Susan Solomon, Senior Scientist, Aeronomy Laboratory, National Oceanic and Atmospheric Administration +2004 Dr. May Berenbaum, Swanlund Professor; Head, Department of Entomology, University of Illinois at Urbana-Champaign +2006 Dr. Mary-Claire King, American Cancer Society Research Professor of Genome Sciences and Medicine, University of Washington, Seattle +2008 Dr. Elizabeth Blackburn, researcher at the University of California, San Francisco +2011 Dr. Catherine Bréchignac, President of the International Council for Science and former president of the CNRS ("National Centre for Scientific Research") +2013 Prof. Susan Gasser, Friedrich Miescher Institute for Biomedical Research, Switzerland +2015 Prof. Barbara Liskov computer scientist and Institute professor at the Massachusetts Institute of Technology (MIT) +2017 Prof. Ursula Keller and Prof. Naomi Halas +2019 Mina Bissell and Nieng Yan + + +== See also == +See also List of prizes, medals, and awards for women in science + + +== References == + + +== External links == +American Committee for the Weizmann Institute of Science \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Women_of_Discovery_Awards-0.md b/data/en.wikipedia.org/wiki/Women_of_Discovery_Awards-0.md new file mode 100644 index 000000000..201bed85c --- /dev/null +++ b/data/en.wikipedia.org/wiki/Women_of_Discovery_Awards-0.md @@ -0,0 +1,64 @@ +--- +title: "Women of Discovery Awards" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Women_of_Discovery_Awards" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T11:16:19.050132+00:00" +instance: "kb-cron" +--- + +The Women of Discovery Awards are given by the non-profit WINGS WorldQuest, in recognition of the achievements of women in science and exploration. +The awards were first presented in 2003, the same year that WINGS WorldQuest was formed by Milbry Polk and Leila Hadley Luce. +Both the Board of Directors and a Junior Council at the granting organization, WINGS WorldQuest, are involved in selecting the recipients of the Women of Discovery Awards, who are thereafter known as Fellows. + +The WINGS Women of Discovery Awards and Fellows Program were established to celebrate the ground-breaking work of women explorers and scientists who are actively out in the field today and provide critical, unrestricted funding to support and ensure continued study. +Women of Discovery Awards are given in the categories of Lifetime Achievement, Air and Space, Conservation, Courage, Earth, Field Research, Film and Exploration, Humanity, Leadership, and the Sea. In addition, some recipients have been simply designated as "Fellows", without being placed in a category. The awards include an unrestricted financial grant. +In addition to its fellowship program, WINGS WorldQuest offers Flag Carrier grants in support of field researchers who are financing explorations. + + +== Fellows == +The awards are given every 1-2 years. Not all awards are given each year. In some years more the same award may be given to more than one person. + + +=== Lifetime Achievement === + + +=== Air and Space === + + +=== Conservation === + + +=== Courage === + + +=== Earth === + + +=== Field Research === + + +=== Film and Exploration === + + +=== Humanity === + + +=== Innovation in Technology Award === + + +=== Leadership === + + +=== Sea === + + +=== Awardee/Fellow === + + +== Flag Carriers == +WINGS WorldQuest Flag Carriers receive grants in support of field research to help finance explorations. + + +== References == \ No newline at end of file