---
title: "Scientific law"
chunk: 2/6
source: "https://en.wikipedia.org/wiki/Scientific_law"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:45:43.771670+00:00"
instance: "kb-cron"
---

== Properties ==
Scientific laws are typically conclusions based on repeated scientific experiments and observations over many years and which have become accepted universally within the scientific community. A scientific law is "inferred from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present". The production of a summary description of our environment in the form of such laws is a fundamental aim of science.
Several general properties of scientific laws, particularly when referring to laws in physics, have been identified. Scientific laws are:

True, at least within their regime of validity. By definition, there have never been repeatable contradicting observations.
Universal. They appear to apply everywhere in the universe.
Simple. They are typically expressed in terms of a single mathematical equation.
Absolute. Nothing in the universe appears to affect them.
Stable. Unchanged since first discovered (although they may have been shown to be approximations of more accurate laws),
All-encompassing. Everything in the universe apparently must comply with them (according to observations).
Generally conservative of quantity.
Often expressions of existing homogeneities (symmetries) of space and time.
Typically theoretically reversible in time (if non-quantum), although time itself is irreversible.
Broad. In physics, laws exclusively refer to the broad domain of matter, motion, energy, and force itself, rather than more specific systems in the universe, such as living systems, e.g. the mechanics of the human body.
The term "scientific law" is traditionally associated with the natural sciences, though the social sciences also contain laws. For example, Zipf's law is a law in the social sciences which is based on mathematical statistics. In these cases, laws may describe general trends or expected behaviors rather than being absolutes.
In natural science, impossibility assertions come to be widely accepted as overwhelmingly probable rather than considered proved to the point of being unchallengeable. The basis for this strong acceptance is a combination of extensive evidence of something not occurring, combined with an underlying theory, very successful in making predictions, whose assumptions lead logically to the conclusion that something is impossible. While an impossibility assertion in natural science can never be absolutely proved, it could be refuted by the observation of a single counterexample. Such a counterexample would require that the assumptions underlying the theory that implied the impossibility be re-examined.
Some examples of widely accepted impossibilities in physics are perpetual motion machines, which violate the law of conservation of energy, exceeding the speed of light, which violates the implications of special relativity, the uncertainty principle of quantum mechanics, which asserts the impossibility of simultaneously knowing both the position and the momentum of a particle, and Bell's theorem: no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

== Laws as consequences of mathematical symmetries ==

Some laws reflect mathematical symmetries found in nature (e.g. the Pauli exclusion principle reflects identity of electrons, conservation laws reflect homogeneity of space, time, and Lorentz transformations reflect rotational symmetry of spacetime). Many fundamental physical laws are mathematical consequences of various symmetries of space, time, or other aspects of nature. Specifically, Noether's theorem connects some conservation laws to certain symmetries. For example, conservation of energy is a consequence of the shift symmetry of time (no moment of time is different from any other), while conservation of momentum is a consequence of the symmetry (homogeneity) of space (no place in space is special, or different from any other). The indistinguishability of all particles of each fundamental type (say, electrons, or photons) results in the Dirac and Bose quantum statistics which in turn result in the Pauli exclusion principle for fermions and in Bose–Einstein condensation for bosons. Special relativity uses rapidity to express motion according to the symmetries of hyperbolic rotation, a transformation mixing space and time. Symmetry between inertial and gravitational mass results in general relativity.
The inverse square law of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of space.
One strategy in the search for the most fundamental laws of nature is to search for the most general mathematical symmetry group that can be applied to the fundamental interactions.

== Laws of physics ==

=== Conservation laws ===

==== Conservation and symmetry ====

Conservation laws are fundamental laws that follow from the homogeneity of space, time and phase, in other words symmetry.

Noether's theorem: Any quantity with a continuously differentiable symmetry in the action has an associated conservation law.
Conservation of mass was the first law to be understood since most macroscopic physical processes involving masses, for example, collisions of massive particles or fluid flow, provide the apparent belief that mass is conserved. Mass conservation was observed to be true for all chemical reactions. In general, this is only approximative because with the advent of relativity and experiments in nuclear and particle physics: mass can be transformed into energy and vice versa, so mass is not always conserved but part of the more general conservation of mass–energy.
Conservation of energy, momentum and angular momentum for isolated systems can be found to be symmetries in time, translation, and rotation.
Conservation of charge was also realized since charge has never been observed to be created or destroyed and only found to move from place to place.

==== Continuity and transfer ====
Conservation laws can be expressed using the general continuity equation (for a conserved quantity) can be written in differential form as:

  
    
      
        
          
            
              ∂
              ρ
            
            
              ∂
              t
            
          
        
        =
        −
        ∇
        ⋅
        
          J
        
      
    
    {\displaystyle {\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {J} }
  