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 cause-and-effect by demonstrating what outcome occurs whe ...
s or
observation
Observation in the natural sciences is an act or instance of noticing or perceiving and the acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the percep ...
s, that describe or
predict a range of
natural phenomena
Nature is an inherent character or constitution, particularly of the ecosphere or the universe as a whole. In this general sense nature refers to the laws, elements and phenomena of the physical world, including life. Although humans are part ...
. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of
natural science
Natural science or empirical 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 ...
(
physics
Physics is the scientific study of matter, its Elementary particle, 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 whi ...
,
chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
,
astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
,
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 and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...
). Laws are developed from data and can be further developed through
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
; in all cases they are directly or indirectly based on
empirical evidence
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law.
There is no general agreement on how the ...
. 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 laws 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 mathematical 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 ...
s, so that it can predict the outcome of an experiment. Laws differ from
hypotheses
A hypothesis (: hypotheses) is a proposed explanation for a phenomenon. A scientific method, scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educ ...
and
postulates
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 ...
, 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, which may entail one or several laws. Science distinguishes a law or theory from facts. Calling a law a
fact
A fact is a truth, true data, datum about one or more aspects of a circumstance. Standard reference works are often used to Fact-checking, check facts. Science, Scientific facts are verified by repeatable careful observation or measurement by ...
is
ambiguous
Ambiguity is the type of meaning in which a phrase, statement, or resolution is not explicitly defined, making for several interpretations; others describe it as a concept or statement that has no real reference. A common aspect of ambiguit ...
, 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 or expression in multiple senses within an argument.
It is a type of ambiguity that stems from a phrase ...
. The nature of scientific laws has been much discussed in
philosophy
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
, but in essence scientific laws are simply empirical conclusions reached by the scientific method; they are intended to be neither laden with
ontological
Ontology is the philosophical study of being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of reality and every ...
commitments nor statements of logical
absolutes.
Social science
Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of societies and the relationships among members within those societies. The term was formerly used to refer to the ...
s such as
economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
have also attempted to formulate scientific laws, though these generally have much less predictive power.
Overview
A scientific law always applies to a
physical system
A physical system is a collection of physical objects under study. The collection differs from a set: all the objects must coexist and have some physical relationship.
In other words, it is a portion of the physical universe chosen for analys ...
under repeated conditions, and it implies that there is a causal relationship involving the elements of the system.
Factual
A fact is a truth, true data, datum about one or more aspects of a circumstance. Standard reference works are often used to Fact-checking, check facts. Science, Scientific facts are verified by repeatable careful observation or measurement by ...
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 the branch of philosophy concerned with the foundations, methods, and implications of science. Amongst its central questions are the difference between science and non-science, the reliability of scientific theories, ...
, going back to
David Hume
David Hume (; born David Home; – 25 August 1776) was a Scottish philosopher, historian, economist, and essayist who was best known for his highly influential system of empiricism, philosophical scepticism and metaphysical naturalism. Beg ...
, 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 philosophic ...
.
Laws differ from
scientific theories 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 electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...
only applies to linear networks;
Newton's law of universal gravitation
Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is Proportionality (mathematics)#Direct proportionality, proportional to the product ...
only applies in weak gravitational fields; the early laws of
aerodynamics
Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...
, such as
Bernoulli's principle
Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. For example, for a fluid flowing horizontally Bernoulli's principle states that an increase in the speed occurs simultaneously with a decrease i ...
, 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 compressibility, compressible, flows are usually treated as being incompressible flow, incom ...
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 speed, supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach numb ...
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 by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of ...
only applies to
strain 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 w ...
;
Boyle's law
Boyle's law, also referred to as the Boyle–Mariotte law or Mariotte's law (especially in France), is an empirical gas laws, gas law that describes the relationship between pressure and volume of a confined gas. Boyle's law has been stated as:
...
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 a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
forms, and thus can be stated as an equation; for example, the
law of conservation of energy
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. In the case of a closed system, the principle says that the total amount of energy within the sy ...
can be written as
, where
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 in the context of thermodynamic processes. For a thermodynamic process affecting a thermodynamic system without transfer of matter, the law distinguishes two ...
can be written as
, and
Newton's second law
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows:
# A body re ...
can be written as
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 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 (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 scientific law, law of physics that calculates the amount of force (physics), force between two electric charge, electrically charged particles at rest. This electric for ...
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. This, 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 cause-and-effect by demonstrating what outcome occurs whe ...
s and
observations
Observation in the natural sciences is an act or instance of noticing or perceiving and the acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perceptio ...
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 "working group, sub-communities" working on particular scientific fields, and within particular institutions; interdisciplinary and cross-institutional acti ...
. A scientific law is "
inferred
Inferences are steps in logical 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 ...
from particular facts, applicable to a defined group or class of
phenomena
A phenomenon ( phenomena), sometimes spelled phaenomenon, is an observable Event (philosophy), event. The term came into its modern Philosophy, philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be ...
, 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 discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
.
Several general properties of scientific laws, particularly when referring to laws in
physics
Physics is the scientific study of matter, its Elementary particle, 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 whi ...
, 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 and ideology that seeks to promote and preserve traditional institutions, customs, and values. The central tenets of conservatism may vary in relation to the culture and civiliza ...
of quantity.
* Often expressions of existing homogeneities (symmetries
Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...
) of space
Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...
and time.[
* Typically theoretically reversible in time (if non-]quantum
In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...
), 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 is exp ...
in the universe, such as living systems
Living systems are life forms (or, more colloquially known as living things) treated as a system. They are said to be open self-organizing and said to interact with their environment. These systems are maintained by flows of information, energy an ...
, e.g. the mechanics
Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...
of the human body
The human body is the entire 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 (biology), organs and then Organ system, org ...
.
The term "scientific law" is traditionally associated with the natural sciences
Natural science or empirical 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 ...
, though the social sciences
Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of society, societies and the Social relation, relationships among members within those societies. The term was former ...
also contain laws. For example, Zipf's law
Zipf's law (; ) is an empirical law stating that when a list of measured values is sorted in decreasing order, the value of the -th entry is often approximately inversely proportional to .
The best known instance of Zipf's law applies to the ...
is a law in the social sciences which is based on mathematical statistics
Mathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques that are commonly used in statistics inc ...
. 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 systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...
, 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 "student John Smith is not lazy" is a c ...
. 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 scientific study of matter, its Elementary particle, 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 whi ...
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 indefinitely without an external energy source. This kind of machine is impossible ...
, which violate the law of conservation of energy
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. In the case of a closed system, the principle says that the total amount of energy within the sy ...
, exceeding the speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
, which violates the implications of special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity,
"On the Ele ...
, the uncertainty principle
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position a ...
of quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
, which asserts the impossibility of simultaneously knowing both the position and the momentum of a particle, and Bell's theorem
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measuremen ...
: 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 (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that o ...
reflects identity of electrons, conservation laws reflect homogeneity
Homogeneity and heterogeneity are concepts relating to the Uniformity (chemistry), uniformity of a Chemical substance, substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, ...
of space
Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...
, 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 ...
reflect rotational symmetry of spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
). Many fundamental physical laws are mathematical consequences of various symmetries
Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...
of space, time, or other aspects of nature. Specifically, Noether's theorem
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems (see Noether's second theorem) published by the mat ...
connects some conservation laws to certain symmetries. For example, conservation of energy is a consequence of the shift symmetry of time (no moment of time is different from any other), while conservation of momentum is a consequence of the symmetry (homogeneity) of space (no place in space is special, or different from any other). The indistinguishability of all particles of each fundamental type (say, electrons, or photons) results in the Dirac and Bose quantum statistics which in turn result in the Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that o ...
for fermion
In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...
s and in Bose–Einstein condensation 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 half odd-intege ...
s. Special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity,
"On the Ele ...
uses rapidity
In special relativity, the classical concept of velocity is converted to rapidity to accommodate the limit determined by the speed of light. Velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velo ...
to express motion according to the symmetries of hyperbolic rotation
In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is ''not'' a rotation or shear mapping.
For a fixed positive real number , th ...
, a transformation mixing space
Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...
and time. Symmetry between inertial
In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative ...
and gravitational mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
results in general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
.
The inverse square law
In science, an inverse-square law is any scientific law stating that the observed "intensity" of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cau ...
of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of space
Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...
.
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 mass-energy, conservation of linear momen ...
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 mathematica ...
, in other words ''symmetry''.
* Noether's theorem
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems (see Noether's second theorem) published by the mat ...
: 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 the mass of the system must remain constant over time.
The law implies that mass can neith ...
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
The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be Conservation law, ''conserved'' over time. In the case of a Closed system#In thermodynamics, closed system, the principle s ...
, momentum
In Newtonian mechanics, momentum (: momenta or momentums; 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. ...
and angular momentum
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...
for isolated systems can be found to be symmetries in time, translation, and rotation.
* Conservation of charge was also realized since charge has never been observed to be created or destroyed and only found to move from place to place.
Continuity and transfer
Conservation laws can be expressed using the general continuity equation
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 ...
(for a conserved quantity) can be written in differential form as:
:
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 in physics. For transport phe ...
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 rate that the vector field alters the volume in an infinitesimal neighborhood of each point. (In 2D this "volume" refers to ...
(denoted ∇⋅) of a vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space \mathbb^n. A vector field on a plane can be visualized as a collection of arrows with given magnitudes and dire ...
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 parabolic partial differential equation that combines the diffusion equation, diffusion and convection (advection equation, advection) equations. It describes physical phenomena where particles, energy, or o ...
and Boltzmann transport equation, 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 physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows:
# A body re ...
, Lagrange's equations
In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the d'Alembert principle of virtual work. It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his presentation to the ...
, Hamilton's equations
In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (gene ...
, etc., can be derived from the following principle:
:
where is the action
Action may refer to:
* Action (philosophy), something which is done by a person
* Action principles the heart of fundamental physics
* Action (narrative), a literary mode
* Action fiction, a type of genre fiction
* Action game, a genre of video gam ...
; the integral of the Lagrangian
:
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 of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity ...
is ''V'' (a function of the configuration and its rate of change). The configuration of a system which has ''N'' degrees of freedom
In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...
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. 397 ...
q = (''q''1, ''q''2, ... ''qN'').
There are generalized momenta conjugate to these coordinates, p = (''p''1, ''p''2, ..., ''pN''), where:
:
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. 397 ...
in the configuration space, i.e. the curve q(''t''), parameterized by time (see also parametric equation
In mathematics, a parametric equation expresses several quantities, such as the coordinates of a point (mathematics), point, as Function (mathematics), functions of one or several variable (mathematics), variables called parameters.
In the case ...
for this concept).
The action is a '' functional'' 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-orie ...
'', 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 maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum, they may be defined either within a given range (the ''local'' or ''relative ...
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 Function (mathematics), functions
and functional (mathematics), functionals, to find maxima and minima of f ...
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:
:
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
* 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 ...
Corollaries in fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them.
Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...
:
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 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. Archimedes' principle is a law of physics fun ...
* Bernoulli's principle
Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. For example, for a fluid flowing horizontally Bernoulli's principle states that an increase in the speed occurs simultaneously with a decrease i ...
* Poiseuille's law
* Stokes' law
In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. It was derived by George Gabriel Stokes in 1851 by solving the S ...
* Navier–Stokes equations
The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician Georg ...
* 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 () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
's theories of (now) classical mechanics
Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...
, presented in his ''Philosophiae Naturalis Principia Mathematica
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, value, mind, and language. It is a rational and critical inquiry that reflects on ...
'', and in Albert Einstein
Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
's theory of relativity
The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical ph ...
.
Modern laws
Special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity,
"On the Ele ...
:
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 an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative ...
" and "the speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
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 ...
– 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 (mathematics), origin, orientation (geometry), orientation, and scale (geometry), scale have been specified in physical space. It ...
s moving relative to each other. For any 4-vector
In special relativity, a four-vector (or 4-vector, sometimes Lorentz 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 vect ...
:
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 rotati ...
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 i ...
, 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, ...
):
:
in which the (more famous) mass–energy equivalence
In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame. The two differ only by a multiplicative constant and the units of measurement. The principle is described by the physicist Albert Einstei ...
is a special case.
General relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
:
General relativity is governed by the Einstein field equations
In the General relativity, 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#In general relativity and cosmology, matter within it. ...
, 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.
Gravitoelectromagnetism :
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''. They are well established by the theory, and experimental tests form ongoing research.
:
Classical laws
Kepler's laws, though originally discovered from planetary observations (also due to Tycho Brahe
Tycho Brahe ( ; ; born Tyge Ottesen Brahe, ; 14 December 154624 October 1601), generally called Tycho for short, was a Danish astronomer of the Renaissance, known for his comprehensive and unprecedentedly accurate astronomical observations. He ...
), 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.
\mathbf(\mathbf) = F( \mathbf )
where F is a force vector, ''F'' is a scalar valued force function (whose abso ...
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 frequentl ...
* Fourier's law
Thermal conduction is the diffusion of thermal energy (heat) within one material or between materials in contact. The higher temperature object has molecules with more kinetic energy; collisions between molecules distributes this kinetic energy ...
* 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 empirical gas laws, gas law that describes the relationship between pressure and volume of a confined gas. Boyle's law has been stated as:
...
** 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 ...
** 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. However, it sometimes refers to the proportionality of the volume of a gas to its Thermodynamic temperature ...
** 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 cas ...
, into one
: now improved by other equations of state
In physics and chemistry, 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 internal energy. Most mod ...
* 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 John ...
(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; it was devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G ...
* 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, Electrical network, electr ...
give the time-evolution of the electric
Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...
and magnetic
Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, m ...
fields due to electric charge
Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...
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 (hydr ...
distributions. Given the fields, the Lorentz force
In electromagnetism, the Lorentz force is the force exerted on a charged particle by electric and magnetic fields. It determines how charged particles move in electromagnetic environments and underlies many physical phenomena, from the operation ...
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. More specifically, the equations of motion describe the behavior of a physical system as a set of mathem ...
for charges in the fields.
:
These equations can be modified to include magnetic monopole
In particle physics, a magnetic monopole is a hypothetical 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 "magnetic charge". ...
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's law (electrostatic form) and the Biot–Savart law can be deduced from Ampere's law (magnetostatic form). Lenz's 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 Electromagnetic induction, induced in a Electrical conductor, conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes changes in t ...
* Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental scientific law, law of physics that calculates the amount of force (physics), force between two electric charge, electrically charged particles at rest. This electric for ...
* 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 electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...
* 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 optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...
is based on a variational principle
A variational principle is a mathematical procedure that renders a physical problem solvable by the calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions. For example, the pr ...
: 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 geometrical optics, ray optics and physical optics, wave optics. Fermat's principle states that the path taken by a Ray (optics), ray between two given ...
In geometric optics
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician ...
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 that 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 surf ...
* Law of refraction
Snell's law (also known as the Snell–Descartes law, the 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 th ...
, Snell's law
Snell's law (also known as the Snell–Descartes law, the 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 th ...
In physical optics
In physics, physical optics, or wave optics, is the branch of optics that studies Interference (wave propagation), interference, diffraction, Polarization (waves), polarization, and other phenomena for which the ray approximation of geometric opti ...
, laws are based on physical properties of materials.
* Brewster's angle
* Malus's law
* Beer–Lambert law
The Beer–Bouguer–Lambert (BBL) extinction law is an empirical relationship describing the attenuation in intensity of a radiation beam passing through a macroscopically homogenous medium with which it interacts. Formally, it states that the ...
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 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 ...
. This leads to results which are not usually called "laws", but hold the same status, in that all of quantum mechanics follows from them. These postulates can be summarized as follows:
* The state of a physical system, be it a particle or a system of many particles, is described by a wavefunction
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
.
* Every physical quantity is described by an operator acting on the system; the measured quantity has a probabilistic nature.
* The wavefunction
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
obeys the Schrödinger equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...
. Solving this wave equation predicts the time-evolution of the system's behavior, analogous to solving Newton's laws in classical mechanics.
* Two identical particles
In quantum mechanics, indistinguishable particles (also called identical or indiscernible particles) are particles that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to, ...
, such as two electrons, cannot be distinguished from one another by any means. Physical systems are classified by their symmetry properties.
These postulates in turn imply many other phenomena, e.g., uncertainty principle
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position a ...
s and the Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that o ...
.
:
Radiation laws
Applying electromagnetism, thermodynamics, and quantum mechanics, to atoms and molecules, some laws of electromagnetic radiation
In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
and light are as follows.
* Stefan–Boltzmann law
The Stefan–Boltzmann law, also known as ''Stefan's law'', describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Lu ...
* Planck's law
In physics, Planck's law (also Planck radiation 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 ...
of black-body radiation
* Wien's displacement law
In physics, 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 ...
* Radioactive decay law
Laws of chemistry
Chemical laws are those laws of nature relevant to chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
. Historically, observations led to many empirical laws, though now it is known that chemistry has its foundations in quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
.
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 the mass of the system must remain constant over time.
The law implies that mass can neith ...
, 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 chemistry, chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an Gibbs free energy, ...
. Modern physics shows that it is actually energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
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
The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be Conservation law, ''conserved'' over time. In the case of a Closed system#In thermodynamics, closed system, the principle s ...
leads to the important concepts of equilibrium
Equilibrium may refer to:
Film and television
* ''Equilibrium'' (film), a 2002 science fiction film
* '' The Story of Three Loves'', also known as ''Equilibrium'', a 1953 romantic anthology film
* "Equilibrium" (''seaQuest 2032'')
* ''Equilibr ...
, thermodynamics
Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
, and kinetics.
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 people, French chemist. He was best known for his discovery of the law of definite proportions in 1797, stating that chemical compounds always combine in constant proportions.
...
's law of definite composition
In chemistry, the law of definite proportions, sometimes called Proust's law or the law of constant composition, states that a given
chemical compound contains its constituent elements in a fixed ratio (by mass) and does not depend on its source ...
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's law of multiple proportions
In chemistry, the law of multiple proportions states that in compounds which contain two particular chemical elements, the amount of Element A per measure of Element B will differ across these compounds by ratios of small whole numbers. For inst ...
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 cur ...
and minerals
In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid substance with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. (2011): M ...
) 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 () is the relationships between the masses of reactants and Product (chemistry), products before, during, and following chemical reactions.
Stoichiometry is based on the law of conservation of mass; the total mass of reactants must ...
, 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 f ...
, which provides the basis for establishing equivalent weight
In chemistry, equivalent weight ( more precisely, equivalent mass) 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 ...
s for each chemical element. Elemental equivalent weights can then be used to derive atomic weights 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 different from chemical thermodynamics, which deals with the direction in which a ...
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
In chemistry, Le Chatelier's principle (pronounced or ) is a principle used to predict the effect of a change in conditions on chemical equilibrium. Other names include Chatelier's principle, Braun–Le Chatelier principle, Le Chatelier–Braun p ...
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 S. Ham ...
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 increase in rate of a chemical reaction due to an added substance known as a catalyst (). Catalysts are not consumed by the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycles quick ...
.
* 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 () is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants.
For a reaction between ...
. 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 188 ...
gives the temperature and activation energy
In the Arrhenius model of reaction rates, activation energy is the minimum amount of energy that must be available to reactants for a chemical reaction to occur. The activation energy (''E''a) of a reaction is measured in kilojoules per mole (k ...
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 to calculate 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 Vorgänge" ...
* Hess's law
Gas laws :
* Raoult's law
Raoult's law ( law) is a relation of physical chemistry, with implications in thermodynamics. Proposed by French chemist François-Marie Raoult in 1887, it states that the partial pressure of each component of an ideal mixture of ''liquids'' is ...
* 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 at equilibrium to its partial pressure above the liquid. The proportionality factor is called Henry's law constant ...
Chemical transport :
* Fick's laws of diffusion
Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second ...
* Graham's law
Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham in 1848. Keith J. Laidler and John M. Meiser, ''Physical Chemistry'' (Benjamin/Cummings 1982), pp. 18–19 Graham fou ...
* Lamm equation
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 slig ...
or Gause's law
Genetics
* Mendelian laws (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 frequency, allele and genotype frequencies in a population will remain constant from generation ...
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 Heredity, heritable traits characteristic of a population over generation ...
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, 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
* Tobler's second law of geography
Geology
* Archie's law
In petrophysics, Archie's law is a purely empirical law relating the measured electrical conductivity of a porous rock to its porosity and fluid saturation. It is named after Gus Archie (1907–1978) and laid the foundation for modern well l ...
* Buys Ballot's law
* Birch's law
* Byerlee's law
* 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, reli ...
* 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 pass ...
* Walther's law
Other fields
Some mathematical
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
theorem
In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...
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 ...
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 simply Bode's law) is a formulaic prediction of spacing between planets in any given planetary system. The formula suggests that, extending outward, each planet should be approximately twice as far from the S ...
of planetary positions, Zipf's law
Zipf's law (; ) is an empirical law stating that when a list of measured values is sorted in decreasing order, the value of the -th entry is often approximately inversely proportional to .
The best known instance of Zipf's law applies to the ...
of linguistics, and Moore's law
Moore's law is the observation that the Transistor count, number of transistors in an integrated circuit (IC) doubles about every two years. Moore's law is an observation and Forecasting, projection of a historical trend. Rather than a law of ...
of technological growth. Many of these laws fall within the scope of uncomfortable science Uncomfortable science, as identified by statistician John Tukey, comprises situations in which there is a need to draw an inference from a limited sample of data, where further samples influenced by the same cause system will not be available. Mor ...
. 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, more colloquially called knock-on effects) are outcomes of a purposeful action that are not intended or foreseen. The term was po ...
. By analogy, principles in other fields of study are sometimes loosely referred to as "laws". These include Occam's razor
In philosophy, Occam's razor (also spelled Ockham's razor or Ocham's razor; ) is the problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements. It is also known as the principle o ...
as a principle of philosophy and the Pareto principle of economics.
History
The observation and detection of underlying regularities in nature date from prehistoric
Prehistory, also called pre-literary history, is the period of human history between the first known use of stone tools by hominins million years ago and the beginning of recorded history with the invention of writing systems. The use o ...
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 Amer ...
'', though, was limited by their entanglement in animism
Animism (from meaning 'breath, spirit, life') is the belief that objects, places, and creatures all possess a distinct spiritual essence. Animism perceives all things—animals, plants, rocks, rivers, weather systems, human handiwork, and in ...
, 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 considered to be sacred and worthy of worship due to having authority over some aspect of the universe and/or life. The ''Oxford Dictionary of English'' defines ''deity'' as a God (male deity), god or god ...
, spirits, supernatural being
Supernatural phenomena or entities are those beyond the Scientific law, laws of nature. The term is derived from Medieval Latin , from Latin 'above, beyond, outside of' + 'nature'. Although the corollary term "nature" has had multiple meanin ...
s, etc. Observation and speculation about nature were intimately bound up with metaphysics and morality.
In Europe, systematic theorizing about nature (''physis
Physis (; ; pl. physeis, φύσεις) 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, a ...
'') began with the early Greek philosophers and scientists and continued into the Hellenistic
In classical antiquity, the Hellenistic period covers the time in Greek history after Classical Greece, between the death of Alexander the Great in 323 BC and the death of Cleopatra VII in 30 BC, which was followed by the ascendancy of the R ...
and Roman imperial 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 (), to the (AD 529) ordered by Eastern Roman emperor Justinian I.
Roman law also den ...
increasingly became paramount.The formula "law of nature" first appears as "a live metaphor" favored by Latin poets Lucretius
Titus Lucretius Carus ( ; ; – October 15, 55 BC) 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, which usually is t ...
, Virgil
Publius Vergilius Maro (; 15 October 70 BC21 September 19 BC), usually called Virgil or Vergil ( ) in English, was an ancient Rome, ancient Roman poet of the Augustan literature (ancient Rome), Augustan period. He composed three of the most fa ...
, Ovid
Publius Ovidius Naso (; 20 March 43 BC – AD 17/18), known in English as Ovid ( ), was a Augustan literature (ancient Rome), Roman poet who lived during the reign of Augustus. He was a younger contemporary of Virgil and Horace, with whom he i ...
, Manilius, in time gaining a firm theoretical presence in the prose treatises of Seneca and Pliny. 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 combines principles of law and science to investigate criminal activity. Through crime scene investigations and laboratory analysis, forensic scientists are able to link suspects to evidence. An example is determining the time and ...
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
Law is a set of rules that are created and are law enforcement, enforceable by social or governmental institutions to regulate behavior, with its precise definition a matter of longstanding debate. It has been variously described as a Socia ...
. 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 (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...
'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, while ignoring any supernatural influence. It was dominant before the developme ...
such as Isaac Newton
Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
(1642–1727) were influenced by a religious
Religion is a range of social- cultural systems, including designated behaviors and practices, morals, beliefs, worldviews, texts, sanctified places, prophecies, ethics, or organizations, that generally relate humanity to supernatural ...
view – stemming from medieval concepts of divine law
Divine law is any body of law that is perceived as deriving from a Transcendence (religion), 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, di ...
– which held that God had instituted absolute, universal and immutable physical laws. In chapter 7 of ''The World'', René Descartes
René Descartes ( , ; ; 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 Modern science, science. Mathematics was paramou ...
(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 evidence, empirical method for acquiring knowledge that has been referred to while doing science since at least the 17th century. Historically, it was developed through the centuries from the ancient and ...
which took shape at this time (with Francis Bacon
Francis Bacon, 1st Viscount St Alban (; 22 January 1561 – 9 April 1626) was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England under King James I. Bacon argued for the importance of nat ...
(1561–1626) and Galileo
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...
(1564–1642)) contributed to a trend of separating science from theology
Theology is the study of religious belief from a Religion, religious perspective, with a focus on the nature of divinity. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itse ...
, with minimal speculation about metaphysics
Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...
and ethics. (Natural law
Natural law (, ) is a Philosophy, philosophical and legal theory that posits the existence of a set of inherent laws derived from nature and universal moral principles, which are discoverable through reason. In ethics, natural law theory asserts ...
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 Hugo de Groot () or Huig de Groot (), was a Dutch humanist, diplomat, lawyer, theologian, jurist, statesman, poet and playwright. A teenage prodigy, he was born in Delft an ...
(1583–1645), Spinoza
Baruch (de) Spinoza (24 November 163221 February 1677), also known under his Latinized pen name Benedictus de Spinoza, was a philosopher of Portuguese-Jewish origin, who was born in the Dutch Republic. A forerunner of the Age of Enlightenmen ...
(1632–1677), and Hobbes
Thomas Hobbes ( ; 5 April 1588 – 4 December 1679) was an English philosopher, best known for his 1651 book ''Leviathan'', in which he expounds an influential formulation of social contract theory. He is considered to be one of the founders ...
(1588–1679).)
The distinction between natural law
Natural law (, ) is a Philosophy, philosophical and legal theory that posits the existence of a set of inherent laws derived from nature and universal moral principles, which are discoverable through reason. In ethics, natural law theory asserts ...
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
Physis (; ; pl. physeis, φύσεις) 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, a ...
'', the Greek word (translated into Latin as ''natura'') for ''nature''.[
Some modern philosophers, e.g. Norman Swartz, 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
*
*
* Francis Bacon
Francis Bacon, 1st Viscount St Alban (; 22 January 1561 – 9 April 1626) was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England under King James I. Bacon argued for the importance of nat ...
(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 Instauratio ...
''.
*
*
*
*
*
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'') is a freely available online philosophy resource published and maintained by Stanford University, encompassing both an online encyclopedia of philosophy and peer-reviewed original publication ...
"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 university, national Public university, public research university in Singapore. It was officially established in 1980 by the merging of the University of Singapore and Nanyang University ...
.
* 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 Internet Encyclopedia of Philosophy
"Laws of Nature"
– By Norman Swartz
*
{{Authority control
Causality
*
Metaphysics of science
Philosophy of science
Principles
Laws in science
Scientific method