Physical Laws
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Scientific laws or laws of science are statements, based on repeated
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...
s or
observation Observation is the active acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data via the use of scientific instruments. The ...
s, that describe or
predict A prediction (Latin ''præ-'', "before," and ''dicere'', "to say"), or forecast, is a statement about a future event or data. They are often, but not always, based upon experience or knowledge. There is no universal agreement about the exact ...
a range of
natural phenomena Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are p ...
. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of
natural science Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and repeatab ...
(
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
,
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
,
astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
,
geoscience Earth science or geoscience includes all fields of natural science related to the planet Earth. This is a branch of science dealing with the physical, chemical, and biological complex constitutions and synergistic linkages of Earth's four spheres ...
,
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
). Laws are developed from data and can be further developed through
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
; in all cases they are directly or indirectly based on
empirical evidence Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented. Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing the law does not change. As with other kinds of scientific knowledge, scientific laws do not express absolute certainty, as mathematical
theorems In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the ...
or identities do. A scientific law may be contradicted, restricted, or extended by future observations. A law can often be formulated as one or several statements or
equation In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in ...
s, so that it can predict the outcome of an experiment. Laws differ from
hypotheses A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous obser ...
and
postulates An axiom, postulate, or assumption is a statement (logic), statement that is taken to be truth, true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that whi ...
, which are proposed during the scientific process before and during validation by experiment and observation. Hypotheses and postulates are not laws, since they have not been verified to the same degree, although they may lead to the formulation of laws. Laws are narrower in scope than
scientific theories A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation ...
, which may entail one or several laws. Science distinguishes a law or theory from facts. Calling a law a
fact A fact is a datum about one or more aspects of a circumstance, which, if accepted as true and proven true, allows a logical conclusion to be reached on a true–false evaluation. Standard reference works are often used to check facts. Scient ...
is
ambiguous Ambiguity is the type of meaning (linguistics), meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations wikt:plausible#Adjective, plausible. A common aspect of ambiguity is uncertainty. It ...
, an
overstatement Hyperbole (; adj. hyperbolic ) is the use of exaggeration as a rhetorical device or figure of speech. In rhetoric, it is also sometimes known as auxesis (literally 'growth'). In poetry and oratory, it emphasizes, evokes strong feelings, and cre ...
, or an
equivocation In logic, equivocation ("calling two different things by the same name") is an informal fallacy resulting from the use of a particular word/expression in multiple senses within an argument. It is a type of ambiguity that stems from a phrase havin ...
. The nature of scientific laws has been much discussed in
philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
, but in essence scientific laws are simply empirical conclusions reached by scientific method; they are intended to be neither laden with
ontological In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality. Ontology addresses questions like how entities are grouped into categories and which of these entities exis ...
commitments nor statements of logical absolutes.


Overview

A scientific law always applies to a
physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment. The environment is ignored except for its effects on the ...
under repeated conditions, and it implies that there is a causal relationship involving the elements of the system. Factual and well-confirmed statements like "Mercury is liquid at standard temperature and pressure" are considered too specific to qualify as scientific laws. A central problem in the
philosophy of science Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultim ...
, going back to
David Hume David Hume (; born David Home; 7 May 1711 NS (26 April 1711 OS) – 25 August 1776) Cranston, Maurice, and Thomas Edmund Jessop. 2020 999br>David Hume" ''Encyclopædia Britannica''. Retrieved 18 May 2020. was a Scottish Enlightenment philo ...
, is that of distinguishing causal relationships (such as those implied by laws) from principles that arise due to
constant conjunction In philosophy, constant conjunction is a relationship between two events, where one event is invariably followed by the other: if the occurrence of A is always followed by B, A and B are said to be ''constantly conjoined''. A critical philosophica ...
. Laws differ from
scientific theories A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation ...
in that they do not posit a mechanism or explanation of phenomena: they are merely distillations of the results of repeated observation. As such, the applicability of a law is limited to circumstances resembling those already observed, and the law may be found to be false when extrapolated.
Ohm's law Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
only applies to linear networks;
Newton's law of universal gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distanc ...
only applies in weak gravitational fields; the early laws of
aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...
, such as
Bernoulli's principle In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematici ...
, do not apply in the case of
compressible flow Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the r ...
such as occurs in
transonic Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but transonic ...
and
supersonic Supersonic speed is the speed of an object that exceeds the speed of sound ( Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...
flight;
Hooke's law In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring (device), spring by some distance () Proportionality (mathematics)#Direct_proportionality, scales linearly with respect to that ...
only applies to
strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...
below the
elastic limit In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and wi ...
;
Boyle's law Boyle's law, also referred to as the Boyle–Mariotte law, or Mariotte's law (especially in France), is an experimental gas law that describes the relationship between pressure and volume of a confined gas. Boyle's law has been stated as: The ...
applies with perfect accuracy only to the ideal gas, etc. These laws remain useful, but only under the specified conditions where they apply. Many laws take
mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
forms, and thus can be stated as an equation; for example, the
law of conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that ...
can be written as \Delta E = 0, where E is the total amount of energy in the universe. Similarly, the
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amoun ...
can be written as \mathrmU=\delta Q-\delta W\,, and
Newton's second law Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion ...
can be written as F = . While these scientific laws explain what our senses perceive, they are still empirical (acquired by observation or scientific experiment) and so are not like mathematical theorems which can be proved purely by mathematics. Like theories and hypotheses, laws make predictions; specifically, they predict that new observations will conform to the given law. Laws can be
falsified Falsifiability is a standard of evaluation of scientific theories and hypotheses that was introduced by the philosopher of science Karl Popper in his book ''The Logic of Scientific Discovery'' (1934). He proposed it as the cornerstone of a sol ...
if they are found in contradiction with new data. Some laws are only approximations of other more general laws, and are good approximations with a restricted domain of applicability. For example,
Newtonian dynamics In physics, Newtonian dynamics (also known as Newtonian mechanics) is the study of the dynamics of a particle or a small body according to Newton's laws of motion. Mathematical generalizations Typically, the Newtonian dynamics occurs in a thre ...
(which is based on Galilean transformations) is the low-speed limit of special relativity (since the Galilean transformation is the low-speed approximation to the Lorentz transformation). Similarly, the Newtonian gravitation law is a low-mass approximation of general relativity, and
Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
is an approximation to quantum electrodynamics at large distances (compared to the range of weak interactions). In such cases it is common to use the simpler, approximate versions of the laws, instead of the more accurate general laws. Laws are constantly being tested experimentally to increasing degrees of precision, which is one of the main goals of science. The fact that laws have never been observed to be violated does not preclude testing them at increased accuracy or in new kinds of conditions to confirm whether they continue to hold, or whether they break, and what can be discovered in the process. It is always possible for laws to be invalidated or proven to have limitations, by repeatable experimental evidence, should any be observed. Well-established laws have indeed been invalidated in some special cases, but the new formulations created to explain the discrepancies generalize upon, rather than overthrow, the originals. That is, the invalidated laws have been found to be only close approximations, to which other terms or factors must be added to cover previously unaccounted-for conditions, e.g. very large or very small scales of time or space, enormous speeds or masses, etc. Thus, rather than unchanging knowledge, physical laws are better viewed as a series of improving and more precise generalizations.


Properties

Scientific laws are typically conclusions based on repeated scientific
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...
s and
observations Observation is the active acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data via the use of scientific instruments. The ...
over many years and which have become accepted universally within the
scientific community The scientific community is a diverse network of interacting scientists. It includes many " sub-communities" working on particular scientific fields, and within particular institutions; interdisciplinary and cross-institutional activities are als ...
. A scientific law is "
inferred Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that i ...
from particular facts, applicable to a defined group or class of
phenomena A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfried W ...
, 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 Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...
. Several general properties of scientific laws, particularly when referring to laws in
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, 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 Conservatism is a cultural, social, and political philosophy that seeks to promote and to preserve traditional institutions, practices, and values. The central tenets of conservatism may vary in relation to the culture and civilization i ...
of quantity. * Often expressions of existing homogeneities (
symmetries Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
) of
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
and time. * Typically theoretically reversible in time (if non-
quantum In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...
), 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 A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
in the universe, such as
living systems Living systems are open self-organizing life forms that interact with their environment. These systems are maintained by flows of information, energy and matter. In the last few decades, some scientists have proposed that a general living systems ...
, i.e. the
mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...
of the
human body The human body is the structure of a Human, human being. It is composed of many different types of Cell (biology), cells that together create Tissue (biology), tissues and subsequently organ systems. They ensure homeostasis and the life, viabi ...
. The term "scientific law" is traditionally associated with the
natural sciences Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and repeatab ...
, though the
social sciences Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soci ...
also contain laws.
Andrew S. C. Ehrenberg Andrew Ehrenberg (1 May 1926 – 25 August 2010) was a statistician and marketing scientist. For over half a century, he made contributions to the methodology of data collection, analysis and presentation, and to understanding buyer behaviour a ...
(1993),
Even the Social Sciences Have Laws
,
Nature Nature, in the broadest sense, is the physics, physical world or universe. "Nature" can refer to the phenomenon, phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. ...
, 365:6445 (30), page 385.
For example, Zipf's law is a law in the social sciences which is based on
mathematical statistics Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical an ...
. 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 A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be s ...
, 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 A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "John Smith is not a lazy student" is a ...
. 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 Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
are
perpetual motion machines Perpetual motion is the motion of bodies that continues forever in an unperturbed system. A perpetual motion machine is a hypothetical machine that can do work infinitely without an external energy source. This kind of machine is impossible, a ...
, which violate the
law of conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that ...
, exceeding the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, which violates the implications of
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
, the
uncertainty principle In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
of
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, 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 In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulated ...
reflects identity of electrons, conservation laws reflect
homogeneity Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
of
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
, time, and
Lorentz transformations In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...
reflect rotational symmetry of
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
). Many fundamental physical laws are mathematical consequences of various
symmetries Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
of space, time, or other aspects of nature. Specifically,
Noether's theorem Noether's theorem or Noether's first theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in ...
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 than any other). The indistinguishability of all particles of each fundamental type (say, electrons, or photons) results in the
Dirac Distributed Research using Advanced Computing (DiRAC) is an integrated supercomputing facility used for research in particle physics, astronomy and cosmology in the United Kingdom. DiRAC makes use of multi-core processors and provides a variety of ...
and
Bose Bose may refer to: * Bose (crater), a lunar crater * ''Bose'' (film), a 2004 Indian Tamil film starring Srikanth and Sneha * Bose (surname), a surname (and list of people with the name) * Bose, Italy, a ''frazioni'' in Magnano, Province of Biella ...
quantum statistics which in turn result in the
Pauli exclusion principle In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulated ...
for
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
s and in
Bose–Einstein condensation Bose–Einstein may refer to: * Bose–Einstein condensate ** Bose–Einstein condensation (network theory) * Bose–Einstein correlations * Bose–Einstein statistics In quantum statistics, Bose–Einstein statistics (B–E statistics) describe ...
for
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
s. The rotational symmetry between time and
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
coordinate axes (when one is taken as imaginary, another as real) results in
Lorentz transformations In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...
which in turn result in
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
theory. Symmetry between
inertial In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration ...
and gravitational
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
results in
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
. The
inverse square law In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understoo ...
of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
. 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 In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of energy, conservation of linear momentum, co ...
are fundamental laws that follow from the homogeneity of space, time and
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
, in other words ''symmetry''. *
Noether's theorem Noether's theorem or Noether's first theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in ...
: Any quantity with a continuously differentiable symmetry in the action has an associated conservation law. *
Conservation of mass In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass can ...
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 In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
,
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
and
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
for isolated systems can be found to be symmetries in time, translation, and rotation. *
Conservation of charge In physics, charge conservation is the principle that the total electric charge in an isolated system never changes. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is alwa ...
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 A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. S ...
(for a conserved quantity) can be written in differential form as: :\frac=-\nabla \cdot \mathbf where ρ is some quantity per unit volume, J is the
flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...
of that quantity (change in quantity per unit time per unit area). Intuitively, the
divergence In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the ...
(denoted ∇•) of a vector field is a measure of flux diverging radially outwards from a point, so the negative is the amount piling up at a point; hence the rate of change of density in a region of space must be the amount of flux leaving or collecting in some region (see the main article for details). In the table below, the fluxes flows for various physical quantities in transport, and their associated continuity equations, are collected for comparison. : More general equations are the
convection–diffusion equation The convection–diffusion equation is a combination of the diffusion equation, diffusion and convection (advection equation, advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferr ...
and
Boltzmann transport equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of Thermodynamic equilibrium, equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics ( ...
, which have their roots in the continuity equation.


Laws of classical mechanics


Principle of least action

Classical mechanics, including
Newton's laws Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion ...
,
Lagrange's equations In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Lo ...
,
Hamilton's equations Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta ...
, etc., can be derived from the following principle: : \delta \mathcal = \delta\int_^ L(\mathbf, \mathbf, t) dt = 0 where \mathcal is the
action Action may refer to: * Action (narrative), a literary mode * Action fiction, a type of genre fiction * Action game, a genre of video game Film * Action film, a genre of film * ''Action'' (1921 film), a film by John Ford * ''Action'' (1980 fil ...
; the integral of the
Lagrangian Lagrangian may refer to: Mathematics * Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier ** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...
: L(\mathbf, \mathbf, t) = T(\mathbf, t)-V(\mathbf, \mathbf, t) of the physical system between two times ''t''1 and ''t''2. The kinetic energy of the system is ''T'' (a function of the rate of change of the
configuration Configuration or configurations may refer to: Computing * Computer configuration or system configuration * Configuration file, a software file used to configure the initial settings for a computer program * Configurator, also known as choice board ...
of the system), and
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
is ''V'' (a function of the configuration and its rate of change). The configuration of a system which has ''N''
degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...
is defined by
generalized coordinates In analytical mechanics, generalized coordinates are a set of parameters used to represent the state of a system in a configuration space. These parameters must uniquely define the configuration of the system relative to a reference state.,p. 3 ...
q = (''q''1, ''q''2, ... ''qN''). There are generalized momenta conjugate to these coordinates, p = (''p''1, ''p''2, ..., ''pN''), where: :p_i = \frac The action and Lagrangian both contain the dynamics of the system for all times. The term "path" simply refers to a curve traced out by the system in terms of the
generalized coordinates In analytical mechanics, generalized coordinates are a set of parameters used to represent the state of a system in a configuration space. These parameters must uniquely define the configuration of the system relative to a reference state.,p. 3 ...
in the configuration space, i.e. the curve q(''t''), parameterized by time (see also
parametric equation In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric obj ...
for this concept). The action is a ''
functional Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional sy ...
'' rather than a ''
function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...
'', since it depends on the Lagrangian, and the Lagrangian depends on the path q(''t''), so the action depends on the ''entire'' "shape" of the path for all times (in the time interval from ''t''1 to ''t''2). Between two instants of time, there are infinitely many paths, but one for which the action is stationary (to the first order) is the true path. The stationary value for the ''entire continuum'' of Lagrangian values corresponding to some path, ''not just one value'' of the Lagrangian, is required (in other words it is ''not'' as simple as "differentiating a function and setting it to zero, then solving the equations to find the points of
maxima and minima In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given ran ...
etc", rather this idea is applied to the entire "shape" of the function, see
calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...
for more details on this procedure). Notice ''L'' is ''not'' the total energy ''E'' of the system due to the difference, rather than the sum: :E=T+V The following general approaches to classical mechanics are summarized below in the order of establishment. They are equivalent formulations. Newton's is commonly used due to simplicity, but Hamilton's and Lagrange's equations are more general, and their range can extend into other branches of physics with suitable modifications. : From the above, any equation of motion in classical mechanics can be derived. ;Corollaries in mechanics *
Euler's laws of motion In classical mechanics, Euler's laws of motion are equations of motion which extend Newton's laws of motion for point particle to rigid body motion. They were formulated by Leonhard Euler about 50 years after Isaac Newton formulated his laws. O ...
*
Euler's equations (rigid body dynamics) In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to th ...
;Corollaries in
fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...
Equations describing fluid flow in various situations can be derived, using the above classical equations of motion and often conservation of mass, energy and momentum. Some elementary examples follow. *
Archimedes' principle Archimedes' principle (also spelled Archimedes's principle) states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimede ...
*
Bernoulli's principle In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematici ...
* Poiseuille's law *
Stokes's law In 1851, George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid. Stokes' law is derived by s ...
*
Navier–Stokes equations In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...
*
Faxén's law In fluid dynamics, Faxén's laws relate a sphere's velocity \mathbf and angular velocity \mathbf to the forces, torque, stresslet and flow it experiences under low Reynolds number (creeping flow) conditions. First law Faxen's first law was introduc ...


Laws of gravitation and relativity

Some of the more famous laws of nature are found in
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
's theories of (now)
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
, presented in his ''
Philosophiae Naturalis Principia Mathematica Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
'', and in
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
's
theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
.


Modern laws

;
Special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
The two postulates of special relativity are not "laws" in themselves, but assumptions of their nature in terms of ''relative motion''. They can be stated as "the laws of physics are the same in all
inertial frames In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration ...
" and "the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
is constant and has the same value in all inertial frames". The said postulates lead to the
Lorentz transformations In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...
– the transformation law between two
frame of reference In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both mathema ...
s moving relative to each other. For any
4-vector In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a ...
:A' =\Lambda A this replaces the
Galilean transformation 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 rotatio ...
law from classical mechanics. The Lorentz transformations reduce to the Galilean transformations for low velocities much less than the speed of light ''c''. The magnitudes of 4-vectors are invariants - ''not'' "conserved", but the same for all inertial frames (i.e. every observer in an inertial frame will agree on the same value), in particular if ''A'' is the
four-momentum In special relativity, four-momentum (also called momentum-energy or momenergy ) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is ...
, the magnitude can derive the famous invariant equation for mass-energy and momentum conservation (see
invariant mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, ...
): : E^2 = (pc)^2 + (mc^2)^2 in which the (more famous) mass-energy equivalence ''E'' = ''mc''2 is a special case. ;
General relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
General relativity is governed by the
Einstein field equation In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...
s, which describe the curvature of space-time due to mass-energy equivalent to the gravitational field. Solving the equation for the geometry of space warped due to the mass distribution gives the
metric tensor In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows ...
. Using the geodesic equation, the motion of masses falling along the geodesics can be calculated. ;
Gravitomagnetism Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain ...
In a relatively flat spacetime due to weak gravitational fields, gravitational analogues of Maxwell's equations can be found; the GEM equations, to describe an analogous ''
gravitomagnetic field Gravitoelectromagnetism, abbreviated GEM, refers to a set of Analogy, formal analogies between the equations for electromagnetism and General relativity, relativistic gravitation; specifically: between Maxwell's field equations and an approxima ...
''. They are well established by the theory, and experimental tests form ongoing research.Gravitation and Inertia, I. Ciufolini and J.A. Wheeler, Princeton Physics Series, 1995, :


Classical laws

Kepler's Laws, though originally discovered from planetary observations (also due to
Tycho Brahe Tycho Brahe ( ; born Tyge Ottesen Brahe; generally called Tycho (14 December 154624 October 1601) was a Danish astronomer, known for his comprehensive astronomical observations, generally considered to be the most accurate of his time. He was k ...
), are true for any ''
central force In classical mechanics, a central force on an object is a force that is directed towards or away from a point called center of force. : \vec = \mathbf(\mathbf) = \left\vert F( \mathbf ) \right\vert \hat where \vec F is the force, F is a vecto ...
s''. :


Thermodynamics

: *
Newton's law of cooling In the study of heat transfer, Newton's law of cooling is a physical law which states that The rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its environment. The law is frequently q ...
*
Fourier's law Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its ''thermal conductivity'', and is denoted . Heat spontaneously flows along a tem ...
*
Ideal gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...
, combines a number of separately developed gas laws; **
Boyle's law Boyle's law, also referred to as the Boyle–Mariotte law, or Mariotte's law (especially in France), is an experimental gas law that describes the relationship between pressure and volume of a confined gas. Boyle's law has been stated as: The ...
**
Charles's law Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is: When the pressure on a sample of a dry gas is held constant, the Kelvin t ...
**
Gay-Lussac's law Gay-Lussac's law usually refers to Joseph-Louis Gay-Lussac's law of combining volumes of gases, discovered in 1808 and published in 1809. It sometimes refers to the proportionality of the volume of a gas to its absolute temperature at constant pr ...
**
Avogadro's law Avogadro's law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) or Avogadro-Ampère's hypothesis is an experimental gas law relating the volume of a gas to the amount of substance of gas present. The law is a specific c ...
, into one :now improved by other
equations of state In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or intern ...
*
Dalton's law Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This empirical law was observed by Jo ...
(of partial pressures) *
Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerne ...
* Carnot's theorem *
Kopp's law Kopp's law can refer to either of two relationships discovered by the German chemist Hermann Franz Moritz Kopp (1817–1892). #Kopp found "that the molecular heat capacity of a solid compound is the sum of the atomic heat capacities of the elemen ...


Electromagnetism

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
give the time-evolution of the
electric Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...
and
magnetic Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particle ...
fields due to
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
and
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
distributions. Given the fields, the
Lorentz force In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
law is the
equation of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Verla ...
for charges in the fields. : These equations can be modified to include
magnetic monopole In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magneti ...
s, and are consistent with our observations of monopoles either existing or not existing; if they do not exist, the generalized equations reduce to the ones above, if they do, the equations become fully symmetric in electric and magnetic charges and currents. Indeed, there is a duality transformation where electric and magnetic charges can be "rotated into one another", and still satisfy Maxwell's equations. ;Pre-Maxwell laws These laws were found before the formulation of Maxwell's equations. They are not fundamental, since they can be derived from Maxwell's Equations. Coulomb's Law can be found from Gauss' Law (electrostatic form) and the Biot–Savart Law can be deduced from Ampere's Law (magnetostatic form). Lenz' Law and Faraday's Law can be incorporated into the Maxwell-Faraday equation. Nonetheless they are still very effective for simple calculations. *
Lenz's law Lenz's law states that the direction of the electric current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes changes in the initial magnetic field. It is named after p ...
*
Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
*
Biot–Savart law In physics, specifically electromagnetism, the Biot–Savart law ( or ) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the ...
;Other laws *
Ohm's law Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
* Kirchhoff's laws *
Joule's law Joule effect and Joule's law are any of several different physical effects discovered or characterized by English physicist James Prescott Joule. These physical effects are not the same, but all are frequently or occasionally referred to in the lite ...


Photonics

Classically,
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
is based on a
variational principle In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those func ...
: light travels from one point in space to another in the shortest time. *
Fermat's principle Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. In its original "strong" form, Fermat's principle states that the path taken by a ray between two given points is the pat ...
In
geometric optics Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
laws are based on approximations in Euclidean geometry (such as the
paraxial approximation In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens). A paraxial ray is a ray which makes a small angle (''θ'') to the optica ...
). *
Law of reflection Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface. The law of reflection states that a reflected ray of light emerges from the reflecting surface at the same angle to the surfa ...
*
Law of refraction Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
,
Snell's law Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
In
physical optics In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effec ...
, laws are based on physical properties of materials. *
Brewster's angle Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with ''no reflection''. When ''unpolarized'' light ...
*
Malus's law A polarizer or polariser is an optical filter that lets light waves of a specific polarization pass through while blocking light waves of other polarizations. It can filter a beam of light of undefined or mixed polarization into a beam of well ...
*
Beer–Lambert law The Beer–Lambert law, also known as Beer's law, the Lambert–Beer law, or the Beer–Lambert–Bouguer law relates the attenuation of light to the properties of the material through which the light is travelling. The law is commonly applied t ...
In actuality, optical properties of matter are significantly more complex and require quantum mechanics.


Laws of quantum mechanics

Quantum mechanics has its roots in
postulates An axiom, postulate, or assumption is a statement (logic), statement that is taken to be truth, true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that whi ...
. This leads to results which are not usually called "laws", but hold the same status, in that all of quantum mechanics follows from them. One postulate that a particle (or a system of many particles) is described by a
wavefunction A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
, and this satisfies a quantum wave equation: namely the
Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the ...
(which can be written as a non-relativistic wave equation, or a
relativistic wave equation In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the con ...
). Solving this wave equation predicts the time-evolution of the system's behaviour, analogous to solving Newton's laws in classical mechanics. Other postulates change the idea of physical observables; using quantum operators; some measurements can't be made at the same instant of time (
Uncertainty principle In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
s), particles are fundamentally indistinguishable. Another postulate; the
wavefunction collapse In quantum mechanics, wave function collapse occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an ''observat ...
postulate, counters the usual idea of a measurement in science. :


Radiation laws

Applying electromagnetism, thermodynamics, and quantum mechanics, to atoms and molecules, some laws of
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
and light are as follows. *
Stefan–Boltzmann law The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths ...
*
Planck's law In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature , when there is no net flow of matter or energy between the body and its environment. At ...
of black-body radiation *
Wien's displacement law Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck r ...
*
Radioactive decay law Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...


Laws of chemistry

Chemical laws are those laws of nature relevant to
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
. Historically, observations led to many empirical laws, though now it is known that chemistry has its foundations in
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
. ; Quantitative analysis The most fundamental concept in chemistry is the
law of conservation of mass In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass can ...
, which states that there is no detectable change in the quantity of matter during an ordinary
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
. Modern physics shows that it is actually
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
that is conserved, and that energy and mass are related; a concept which becomes important in
nuclear chemistry Nuclear chemistry is the sub-field of chemistry dealing with radioactivity, nuclear processes, and transformations in the nuclei of atoms, such as nuclear transmutation and nuclear properties. It is the chemistry of radioactive elements such as t ...
.
Conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
leads to the important concepts of equilibrium,
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
, and
kinetics Kinetics ( grc, κίνησις, , kinesis, ''movement'' or ''to move'') may refer to: Science and medicine * Kinetics (physics), the study of motion and its causes ** Rigid body kinetics, the study of the motion of rigid bodies * Chemical ki ...
. Additional laws of chemistry elaborate on the law of conservation of mass.
Joseph Proust Joseph Louis Proust (26 September 1754 – 5 July 1826) was a French chemist. He was best known for his discovery of the law of definite proportions in 1794, stating that chemical compounds always combine in constant proportions. Life Joseph L. ...
's
law of definite composition In chemistry, the law of definite proportions, sometimes called Proust's law, or law of constant composition states that a given chemical compound always contains its component elements in fixed ratio (by mass) and does not depend on its source an ...
says that pure chemicals are composed of elements in a definite formulation; we now know that the structural arrangement of these elements is also important.
Dalton Dalton may refer to: Science * Dalton (crater), a lunar crater * Dalton (program), chemistry software * Dalton (unit) (Da), the atomic mass unit * John Dalton, chemist, physicist and meteorologist Entertainment * Dalton (Buffyverse), minor cha ...
's
law of multiple proportions In chemistry, the law of multiple proportions states that if two elements form more than one compound, then the ratios of the masses of the second element which combine with a fixed mass of the first element will always be ratios of small whole ...
says that these chemicals will present themselves in proportions that are small whole numbers; although in many systems (notably
biomacromolecules ''Biomacromolecules'' is a peer-reviewed scientific journal published since 2000 by the American Chemical Society. It is abstracted and indexed in Chemical Abstracts Service, Scopus, EBSCOhost, PubMed, and Science Citation Index Expanded. , the ...
and
minerals In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. (2 ...
) the ratios tend to require large numbers, and are frequently represented as a fraction. The law of definite composition and the law of multiple proportions are the first two of the three laws of
stoichiometry Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equal ...
, the proportions by which the chemical elements combine to form chemical compounds. The third law of stoichiometry is the
law of reciprocal proportions The law of reciprocal proportions also called law of equivalent proportions or law of permanent ratios is one of the basic laws of stoichiometry. It relates the proportions in which elements combine across a number of different elements. It was fir ...
, which provides the basis for establishing
equivalent weight In chemistry, equivalent weight (also known as gram equivalent) is the mass of one equivalent, that is the mass of a given substance which will combine with or displace a fixed quantity of another substance. The equivalent weight of an element is ...
s for each chemical element. Elemental equivalent weights can then be used to derive
atomic weights Relative atomic mass (symbol: ''A''; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a give ...
for each element. More modern laws of chemistry define the relationship between energy and its transformations. ;
Reaction kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in wh ...
and equilibria * In equilibrium, molecules exist in mixture defined by the transformations possible on the timescale of the equilibrium, and are in a ratio defined by the intrinsic energy of the molecules—the lower the intrinsic energy, the more abundant the molecule.
Le Chatelier's principle Le Chatelier's principle (pronounced or ), also called Chatelier's principle (or the Equilibrium Law), is a principle of chemistry used to predict the effect of a change in conditions on chemical equilibria. The principle is named after French c ...
states that the system opposes changes in conditions from equilibrium states, i.e. there is an opposition to change the state of an equilibrium reaction. * Transforming one structure to another requires the input of energy to cross an energy barrier; this can come from the intrinsic energy of the molecules themselves, or from an external source which will generally accelerate transformations. The higher the energy barrier, the slower the transformation occurs. * There is a hypothetical intermediate, or ''transition structure'', that corresponds to the structure at the top of the energy barrier. The
Hammond–Leffler postulate Hammond's postulate (or alternatively the Hammond–Leffler postulate), is a hypothesis in physical organic chemistry which describes the geometric structure of the transition state in an organic chemical reaction. First proposed by George Hammon ...
states that this structure looks most similar to the product or starting material which has intrinsic energy closest to that of the energy barrier. Stabilizing this hypothetical intermediate through chemical interaction is one way to achieve
catalysis Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
. * All chemical processes are reversible (law of
microscopic reversibility The principle of microscopic reversibility in physics and chemistry is twofold: * First, it states that the microscopic detailed dynamics of particles and fields is time-reversible because the microscopic equations of motion are symmetric with respe ...
) although some processes have such an energy bias, they are essentially irreversible. * The reaction rate has the mathematical parameter known as the
rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction. For a reaction between reactants A and B to form product C the reaction rate is often found to have the f ...
. The
Arrhenius equation In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 18 ...
gives the temperature and
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
dependence of the rate constant, an empirical law. ;
Thermochemistry Thermochemistry is the study of the heat energy which is associated with chemical reactions and/or phase changes such as melting and boiling. A reaction may release or absorb energy, and a phase change may do the same. Thermochemistry focuses on ...
*
Dulong–Petit law The Dulong–Petit law, a thermodynamic law proposed by French physicists Pierre Louis Dulong and Alexis Thérèse Petit, states that the classical expression for the molar specific heat capacity of certain chemical elements is constant for tempe ...
*
Gibbs–Helmholtz equation The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs free energy of a system as a function of temperature. It was originally presented in an 1882 paper entitled " Die Thermodynamik chemischer Vorgange ...
* Hess's law ;Gas laws * Raoult's law *
Henry's law In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formulat ...
;Chemical transport *
Fick's laws of diffusion Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second law which in turn is identical to the diffusion equ ...
*
Graham's law Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham (chemist), Thomas Graham in 1848.Keith J. Laidler and John M. Meiser, ''Physical Chemistry'' (Benjamin/Cummings 1982), pp.&n ...
*
Lamm equation The Lamm equationO Lamm: (1929) "Die Differentialgleichung der Ultrazentrifugierung"'' Arkiv för matematik, astronomi och fysik'' 21B No. 2, 1–4 describes the sedimentation and diffusion of a solute under ultracentrifugation in traditional s ...


Laws of biology


Ecology

*
Competitive exclusion principle In ecology, the competitive exclusion principle, sometimes referred to as Gause's law, is a proposition that two species which compete for the same limited resource cannot coexist at constant population values. When one species has even the sligh ...
or Gause's law


Genetics

*
Mendelian laws Mendelian inheritance (also known as Mendelism) is a type of biology, biological Heredity, inheritance following the principles originally proposed by Gregor Mendel in 1865 and 1866, re-discovered in 1900 by Hugo de Vries and Carl Correns, an ...
(Dominance and Uniformity, segregation of genes, and Independent Assortment) *
Hardy–Weinberg principle In population genetics, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele and genotype frequencies in a population will remain constant from generation to generation in t ...


Natural selection

Whether or not
Natural Selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Charle ...
is a “law of nature” is controversial among biologists.Byerly HC: Natural selection as a law: Principles and processes. Am Nat. 1983; 121(5): 739–745.
Henry Byerly Henry Clement Byerly (August 7, 1935 – December 28, 2016) was an American philosopher known for his work in philosophy of science, logic and evolutionary theory. He was Professor Emeritus at the University of Arizona, where he taught from 1967 ...
, an American philosopher known for his work on evolutionary theory, discussed the problem of interpreting a principle of natural selection as a law. He suggested a formulation of natural selection as a framework principle that can contribute to a better understanding of evolutionary theory. His approach was to express relative fitness, the propensity of a
genotype The genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the alleles or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a ...
to increase in proportionate representation in a competitive environment, as a function of adaptedness (adaptive design) of the organism.


Laws of Earth Sciences


Geography

*
Arbia's law of geography Arbia’s law of geography states, "Everything is related to everything else, but things observed at a coarse spatial resolution are more related than things observed at a finer resolution." Originally proposed as the 2nd law of geography, this is ...
*
Tobler's first law of geography The First Law of Geography, according to Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." This first law is the foundation of the fundamental concepts of spatial dependence and spatia ...
*
Tobler's second law of geography The second law of geography, according to Waldo Tobler, is "the phenomenon external to a geographic area of interest affects what goes on inside." Background Tobler's second law of geography, "the phenomenon external to a geographic area of inte ...


Geology

*
Archie's law In petrophysics, Archie's law relates the ''in-situ'' electrical conductivity (C) of a porous rock to its porosity (\phi\,\!) and fluid saturation (S_w) of the pores: :C_t = \frac C_w \phi^m S_w^n Here, \phi\,\! denotes the porosity, C_t th ...
*
Buys-Ballot's law In meteorology, Buys Ballot's law () may be expressed as follows: In the Northern Hemisphere, if a person stands with their back to the wind, the atmospheric pressure is low to the left, high to the right. This is because wind travels counterc ...
*
Birch's law Birch's law, discovered by the geophysicist Francis Birch, establishes a linear relation between compressional wave velocity and density of rocks and minerals: : v_\mathrm = a( \bar M ) + b \rho where \, \bar M \, is the mean atomic mass in fo ...
*
Byerlee's law In rheology, Byerlee's law, also known as Byerlee's friction law concerns the shear stress (τ) required to slide one rock over another. The rocks have macroscopically flat surfaces, but the surfaces have small asperities that make them "rough." F ...
*
Principle of original horizontality The principle of original horizontality states that layers of sediment are originally deposited horizontally under the action of gravity. It is a relative dating technique. The principle is important to the analysis of folded and tilted strata. ...
*
Law of superposition The law of superposition is an axiom that forms one of the bases of the sciences of geology, archaeology, and other fields pertaining to geological stratigraphy. In its plainest form, it states that in undeformed stratigraphic sequences, the ...
*
Principle of lateral continuity The principle of lateral continuity states that layers of sediment initially extend laterally in all directions; in other words, they are laterally continuous. As a result, rocks that are otherwise similar, but are now separated by a valley or oth ...
*
Principle of cross-cutting relationships Cross-cutting relationships is a principle of geology that states that the geologic feature which cuts another is the younger of the two features. It is a relative dating technique in geology. It was first developed by Danish geological pioneer ...
*
Principle of faunal succession The principle of faunal succession, also known as the law of faunal succession, is based on the observation that sedimentary rock strata contain fossilized flora and fauna, and that these fossils succeed each other vertically in a specific, rel ...
*
Principle of inclusions and components The law of included fragments is a method of relative dating in geology. Essentially, this law states that clasts in a rock are older than the rock itself. One example of this is a xenolith, which is a fragment of country rock that fell into pas ...
*
Walther's law In geology, a facies ( , ; same pronunciation and spelling in the plural) is a body of rock with specified characteristics, which can be any observable attribute of rocks (such as their overall appearance, composition, or condition of formatio ...


Other fields

Some
mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of th ...
s and
axiom An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or f ...
s are referred to as laws because they provide logical foundation to empirical laws. Examples of other observed phenomena sometimes described as laws include the
Titius–Bode law The Titius–Bode law (sometimes termed just Bode's law) is a formulaic prediction of spacing between planets in any given solar system. The formula suggests that, extending outward, each planet should be approximately twice as far from the Sun as ...
of planetary positions, Zipf's law of linguistics, and
Moore's law Moore's law is the observation that the number of transistors in a dense integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empir ...
of technological growth. Many of these laws fall within the scope of uncomfortable science. Other laws are pragmatic and observational, such as the
law of unintended consequences In the social sciences, unintended consequences (sometimes unanticipated consequences or unforeseen consequences) are outcomes of a purposeful action that are not intended or foreseen. The term was popularised in the twentieth century by Ameri ...
. By analogy, principles in other fields of study are sometimes loosely referred to as "laws". These include
Occam's razor Occam's razor, Ockham's razor, or Ocham's razor ( la, novacula Occami), also known as the principle of parsimony or the law of parsimony ( la, lex parsimoniae), is the problem-solving principle that "entities should not be multiplied beyond neces ...
as a principle of philosophy and the
Pareto principle The Pareto principle states that for many outcomes, roughly 80% of consequences come from 20% of causes (the "vital few"). Other names for this principle are the 80/20 rule, the law of the vital few, or the principle of factor sparsity. Manage ...
of economics.


History

The observation and detection of underlying regularities in nature date from
prehistoric Prehistory, also known as pre-literary history, is the period of human history between the use of the first stone tools by hominins 3.3 million years ago and the beginning of recorded history with the invention of writing systems. The use of ...
times - the recognition of cause-and-effect relationships implicitly recognises the existence of laws of nature. The recognition of such regularities as independent scientific laws ''
per se Per se may refer to: * ''per se'', a Latin phrase meaning "by itself" or "in itself". * Illegal ''per se'', the legal usage in criminal and antitrust law * Negligence ''per se'', legal use in tort law *Per Se (restaurant) Per Se is a New Ameri ...
'', though, was limited by their entanglement in
animism Animism (from Latin: ' meaning 'breath, Soul, spirit, life') is the belief that objects, places, and creatures all possess a distinct Spirituality, spiritual essence. Potentially, animism perceives all things—Animal, animals, Plant, plants, Ro ...
, and by the attribution of many effects that do not have readily obvious causes—such as physical phenomena—to the actions of
gods A deity or god is a supernatural being who is considered divine or sacred. The ''Oxford Dictionary of English'' defines deity as a god or goddess, or anything revered as divine. C. Scott Littleton defines a deity as "a being with powers greater ...
, spirits,
supernatural being Supernatural refers to phenomena or entities that are beyond the laws of nature. The term is derived from Medieval Latin , from Latin (above, beyond, or outside of) + (nature) Though the corollary term "nature", has had multiple meanings si ...
s, etc. Observation and speculation about nature were intimately bound up with metaphysics and morality. In Europe, systematic theorizing about nature (''
physis Fusis, Phusis or Physis (; grc, φύσις ) is a Greek philosophical, theological, and scientific term, usually translated into English—according to its Latin translation "natura"—as "nature". The term originated in ancient Greek philosophy, ...
'') began with the early Greek philosophers and scientists and continued into the
Hellenistic In Classical antiquity, the Hellenistic period covers the time in Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in ...
and
Roman imperial The Roman Empire ( la, Imperium Romanum ; grc-gre, Βασιλεία τῶν Ῥωμαίων, Basileía tôn Rhōmaíōn) was the post-Roman Republic, Republican period of ancient Rome. As a polity, it included large territorial holdings aro ...
periods, during which times the intellectual influence of
Roman law Roman law is the law, legal system of ancient Rome, including the legal developments spanning over a thousand years of jurisprudence, from the Twelve Tables (c. 449 BC), to the ''Corpus Juris Civilis'' (AD 529) ordered by Eastern Roman emperor J ...
increasingly became paramount.
The formula "law of nature" first appears as "a live metaphor" favored by Latin poets
Lucretius Titus Lucretius Carus ( , ;  – ) was a Roman poet and philosopher. His only known work is the philosophical poem ''De rerum natura'', a didactic work about the tenets and philosophy of Epicureanism, and which usually is translated into E ...
,
Virgil Publius Vergilius Maro (; traditional dates 15 October 7021 September 19 BC), usually called Virgil or Vergil ( ) in English, was an ancient Roman poet of the Augustan period. He composed three of the most famous poems in Latin literature: t ...
,
Ovid Pūblius Ovidius Nāsō (; 20 March 43 BC – 17/18 AD), known in English as Ovid ( ), was a Roman poet who lived during the reign of Augustus. He was a contemporary of the older Virgil and Horace, with whom he is often ranked as one of the th ...
,
Manilius The gens Manilia was a plebeian family at ancient Rome. Members of this gens are frequently confused with the Manlii, Mallii, and Mamilii. Several of the Manilii were distinguished in the service of the Republic, with Manius Manilius obtaining ...
, in time gaining a firm theoretical presence in the prose treatises of
Seneca Seneca may refer to: People and language * Seneca (name), a list of people with either the given name or surname * Seneca people, one of the six Iroquois tribes of North America ** Seneca language, the language of the Seneca people Places Extrat ...
and
Pliny Pliny may refer to: People * Pliny the Elder (23–79 CE), ancient Roman nobleman, scientist, historian, and author of ''Naturalis Historia'' (''Pliny's Natural History'') * Pliny the Younger (died 113), ancient Roman statesman, orator, w ...
. Why this Roman origin? According to istorian and classicist DarynLehoux's persuasive narrative, the idea was made possible by the pivotal role of codified law and
forensic Forensic science, also known as criminalistics, is the application of science to Criminal law, criminal and Civil law (legal system), civil laws, mainly—on the criminal side—during criminal investigation, as governed by the legal standard ...
argument in Roman life and culture.

For the Romans . . . the place par excellence where ethics, law, nature, religion and politics overlap is the
law court A court is any person or institution, often as a government institution, with the authority to adjudicate legal disputes between parties and carry out the administration of justice in civil, criminal, and administrative matters in accordance w ...
. When we read Seneca's ''Natural Questions'', and watch again and again just how he applies standards of evidence, witness evaluation, argument and proof, we can recognize that we are reading one of the great Roman rhetoricians of the age, thoroughly immersed in forensic method. And not Seneca alone. Legal models of scientific judgment turn up all over the place, and for example prove equally integral to
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
's approach to verification, where the mind is assigned the role of magistrate, the senses that of disclosure of evidence, and dialectical reason that of the law itself.
The precise formulation of what are now recognized as modern and valid statements of the laws of nature dates from the 17th century in Europe, with the beginning of accurate experimentation and the development of advanced forms of mathematics. During this period,
natural philosophers Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics, that is, nature and the physical universe. It was dominant before the development of modern science. From the ancient wor ...
such as
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
(1642-1727) were influenced by a
religious Religion is usually defined as a social system, social-cultural system of designated religious behaviour, behaviors and practices, morality, morals, beliefs, worldviews, religious text, texts, sacred site, sanctified places, prophecy, prophecie ...
view - stemming from medieval concepts of
divine law Divine law is any body of law that is perceived as deriving from a transcendent source, such as the will of God or godsin contrast to man-made law or to secular law. According to Angelos Chaniotis and Rudolph F. Peters, divine laws are typically ...
- which held that God had instituted absolute, universal and immutable physical laws. In chapter 7 of ''The World'',
René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...
(1596-1650) described "nature" as matter itself, unchanging as created by God, thus changes in parts "are to be attributed to nature. The rules according to which these changes take place I call the 'laws of nature'." The modern
scientific method The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific m ...
which took shape at this time (with
Francis Bacon Francis Bacon, 1st Viscount St Alban (; 22 January 1561 – 9 April 1626), also known as Lord Verulam, was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England. Bacon led the advancement of both ...
(1561-1626) and
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
(1564-1642)) contributed to a trend of separating science from
theology Theology is the systematic study of the nature of the divine and, more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing the ...
, with minimal speculation about
metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
and ethics. (
Natural law Natural law ( la, ius naturale, ''lex naturalis'') is a system of law based on a close observation of human nature, and based on values intrinsic to human nature that can be deduced and applied independently of positive law (the express enacte ...
in the political sense, conceived as universal (i.e., divorced from sectarian religion and accidents of place), was also elaborated in this period by scholars such as
Grotius Hugo Grotius (; 10 April 1583 – 28 August 1645), also known as Huig de Groot () and Hugo de Groot (), was a Dutch humanist, diplomat, lawyer, theologian, jurist, poet and playwright. A teenage intellectual prodigy, he was born in Delft ...
(1583-1645),
Spinoza Baruch (de) Spinoza (born Bento de Espinosa; later as an author and a correspondent ''Benedictus de Spinoza'', anglicized to ''Benedict de Spinoza''; 24 November 1632 – 21 February 1677) was a Dutch philosopher of Portuguese-Jewish origin, b ...
(1632-1677), and
Hobbes Thomas Hobbes ( ; 5/15 April 1588 – 4/14 December 1679) was an English philosopher, considered to be one of the founders of modern political philosophy. Hobbes is best known for his 1651 book ''Leviathan'', in which he expounds an influent ...
(1588-1679).) The distinction between
natural law Natural law ( la, ius naturale, ''lex naturalis'') is a system of law based on a close observation of human nature, and based on values intrinsic to human nature that can be deduced and applied independently of positive law (the express enacte ...
in the political-legal sense and law of nature or physical law in the scientific sense is a modern one, both concepts being equally derived from ''
physis Fusis, Phusis or Physis (; grc, φύσις ) is a Greek philosophical, theological, and scientific term, usually translated into English—according to its Latin translation "natura"—as "nature". The term originated in ancient Greek philosophy, ...
'', the Greek word (translated into Latin as ''natura'') for ''nature''. Some modern philosophers, e.g.
Norman Swartz Norman Swartz (born 1939) is an American philosopher and professor emeritus (retired 1998) of philosophy, Simon Fraser University. He is the author or co-author of multiple books and multiple articles on the Internet Encyclopedia of Philosophy. He ...
, use "physical law" to mean the laws of nature as they truly are and not as they are inferred by scientists. See Norman Swartz, ''The Concept of Physical Law'' (New York: Cambridge University Press), 1985. Second edition available onlin


See also


References


Further reading

* John D. Barrow, John Barrow (1991). ''Theories of Everything: The Quest for Ultimate Explanations''. () * *
Francis Bacon Francis Bacon, 1st Viscount St Alban (; 22 January 1561 – 9 April 1626), also known as Lord Verulam, was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England. Bacon led the advancement of both ...
(1620). ''
Novum Organum The ''Novum Organum'', fully ''Novum Organum, sive Indicia Vera de Interpretatione Naturae'' ("New organon, or true directions concerning the interpretation of nature") or ''Instaurationis Magnae, Pars II'' ("Part II of The Great Instauration ...
''. * * Daryn Lehoux (2012). ''What Did the Romans Know? An Inquiry into Science and Worldmaking''. University of Chicago Press. () * * *


External links


Physics Formulary
a useful book in different formats containing many or the physical laws and formulae.
Eformulae.com
website containing most of the formulae in different disciplines. *
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Eac ...

"Laws of Nature"
by John W. Carroll. * Baaquie, Belal E

Core Curriculum,
National University of Singapore The National University of Singapore (NUS) is a national public research university in Singapore. Founded in 1905 as the Straits Settlements and Federated Malay States Government Medical School, NUS is the oldest autonomous university in the c ...
. * Francis, Erik Max
"The laws list".Physics
Alcyone Systems * Pazameta, Zoran
"The laws of nature".
Committee for the scientific investigation of Claims of the Paranormal The Committee for Skeptical Inquiry (CSI), formerly known as the Committee for the Scientific Investigation of Claims of the Paranormal (CSICOP), is a program within the US non-profit organization Center for Inquiry (CFI), which seeks to "prom ...
. *
The Internet Encyclopedia of Philosophy The ''Internet Encyclopedia of Philosophy'' (''IEP'') is a scholarly online encyclopedia, dealing with philosophy, philosophical topics, and philosophers. The IEP combines open access publication with peer reviewed publication of original pape ...

"Laws of Nature"
– By
Norman Swartz Norman Swartz (born 1939) is an American philosopher and professor emeritus (retired 1998) of philosophy, Simon Fraser University. He is the author or co-author of multiple books and multiple articles on the Internet Encyclopedia of Philosophy. He ...

"Laws of Nature"
''In Our Time'', BBC Radio 4 discussion with Mark Buchanan, Frank Close and Nancy Cartwright (Oct. 19, 2000) {{Authority control Causality * Metaphysics of science Philosophy of science Principles Laws in science Scientific method