Scientific law

"Laws of the universe" redirects here. For the anime film series, seeThe Laws of the Universe.

Scientific lawsorlaws of scienceare statements, based onrepeatedexperimentsorobservations,that describe orpredicta range ofnatural phenomena.The termlawhas diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields ofnatural science(physics,chemistry,astronomy,geoscience,biology). Laws are developed from data and can be further developed throughmathematics;in all cases they are directly or indirectly based onempirical evidence.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, asmathematical lawsdo. A scientific law may be contradicted, restricted, or extended by future observations.

A law can often be formulated as one or several statements orequations,so that it can predict the outcome of an experiment. Laws differ fromhypothesesandpostulates,which are proposed during thescientific processbefore 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 thanscientific theories,which may entail one or several laws.Science distinguishes a law or theory from facts.Calling a law afactisambiguous,anoverstatement,or anequivocation.The nature of scientific laws has been much discussed inphilosophy,but in essence scientific laws are simply empirical conclusions reached by scientific method; they are intended to be neither laden withontologicalcommitments nor statements of logicalabsolutes.

Overview

A scientific law always applies to aphysical systemunder repeated conditions, and it implies that there is a causal relationship involving the elements of the system.Factualand 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 thephilosophy of science,going back toDavid Hume,is that of distinguishing causal relationships (such as those implied by laws) from principles that arise due toconstant conjunction.

Laws differ fromscientific theoriesin 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 lawonly applies to linear networks;Newton's law of universal gravitationonly applies in weak gravitational fields; the early laws ofaerodynamics,such asBernoulli's principle,do not apply in the case ofcompressible flowsuch as occurs intransonicandsupersonicflight;Hooke's lawonly applies tostrainbelow theelastic limit;Boyle's lawapplies with perfect accuracy only to the ideal gas, etc. These laws remain useful, but only under the specified conditions where they apply.

Many laws takemathematicalforms, and thus can be stated as an equation; for example, thelaw of conservation of energycan be written as$\Delta E=0$,where$E$is the total amount of energy in the universe. Similarly, thefirst law of thermodynamicscan be written as$\mathrm {d} U=\delta Q-\delta W\,$,andNewton's second lawcan be written as$\textstyle F={\frac {dp}{dt}}.$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 befalsifiedif 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, theNewtonian gravitation lawis a low-mass approximation of general relativity, andCoulomb's lawis an approximation to quantum electrodynamics at large distances (compared to the range of weak interactions). In such cases it is common to use the simpler, approximate versions of the laws, instead of the more accurate general laws.

Laws are constantly being tested experimentally to increasing degrees of precision, which is one of the main goals of science. The fact that laws have never been observed to be violated does not preclude testing them at increased accuracy or in new kinds of conditions to confirm whether they continue to hold, or whether they break, and what can be discovered in the process. It is always possible for laws to be invalidated or proven to have limitations, by repeatable experimental evidence, should any be observed. Well-established laws have indeed been invalidated in some special cases, but the new formulations created to explain the discrepancies generalize upon, rather than overthrow, the originals. That is, the invalidated laws have been found to be only close approximations, to which other terms or factors must be added to cover previously unaccounted-for conditions, e.g. very large or very small scales of time or space, enormous speeds or masses, etc. Thus, rather than unchanging knowledge, physical laws are better viewed as a series of improving and more precise generalizations.

Properties

Scientific laws are typically conclusions based on repeated scientificexperimentsandobservationsover many years and which have become accepted universally within thescientific community.A scientific law is "inferredfrom particular facts, applicable to a defined group or class ofphenomena,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 ofscience.

Several general properties of scientific laws, particularly when referring to laws inphysics,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).
• Generallyconservativeof quantity.
• Often expressions of existing homogeneities (symmetries) ofspaceand time.
• Typically theoretically reversible in time (if non-quantum), althoughtime itself is irreversible.
• Broad. In physics, laws exclusively refer to the broad domain of matter, motion, energy, and force itself, rather than more specificsystemsin the universe, such asliving systems,e.g. themechanicsof thehuman body.

The term "scientific law" is traditionally associated with thenatural sciences,though thesocial sciencesalso contain laws.For example,Zipf's lawis a law in the social sciences which is based onmathematical statistics.In these cases, laws may describe general trends or expected behaviors rather than being absolutes.

In natural science,impossibility assertionscome 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 underlyingtheory,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 singlecounterexample.Such a counterexample would require that the assumptions underlying the theory that implied the impossibility be re-examined.

Some examples of widely accepted impossibilities inphysicsareperpetual motion machines,which violate thelaw of conservation of energy,exceeding thespeed of light,which violates the implications ofspecial relativity,theuncertainty principleofquantum mechanics,which asserts the impossibility of simultaneously knowing both the position and the momentum of a particle, andBell's theorem:no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

Laws as consequences of mathematical symmetries

Main article:Symmetry (physics)

Some laws reflect mathematical symmetries found in nature (e.g. thePauli exclusion principlereflects identity of electrons, conservation laws reflecthomogeneityofspace,time, andLorentz transformationsreflect rotational symmetry ofspacetime). Many fundamental physical laws are mathematical consequences of varioussymmetriesof space, time, or other aspects of nature. Specifically,Noether's theoremconnects 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 theDiracandBosequantum statistics which in turn result in thePauli exclusion principleforfermionsand inBose–Einstein condensationforbosons.Special relativityusesrapidityto express motion according to the symmetries ofhyperbolic rotation,a transformation mixingspaceand time. Symmetry betweeninertialand gravitationalmassresults ingeneral relativity.

Theinverse square lawof interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality ofspace.

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

Main article:Symmetry (physics)

Conservation lawsare fundamental laws that follow from the homogeneity of space, time andphase,in other wordssymmetry.

• Noether's theorem:Any quantity with a continuously differentiable symmetry in the action has an associated conservation law.
• Conservation of masswas 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 ofmass–energy.
• Conservation of energy,momentumandangular momentumfor isolated systems can be found to besymmetries in time,translation, and rotation.
• Conservation of chargewas 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 generalcontinuity equation(for a conserved quantity) can be written in differential form as:

${\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {J}$

whereρis some quantity per unit volume,Jis thefluxof that quantity (change in quantity per unit time per unit area). Intuitively, thedivergence(denoted ∇⋅) of avector fieldis 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.

Physics, conserved quantity	Conserved quantityq	Volume densityρ(ofq)	FluxJ(ofq)	Equation
Hydrodynamics,fluids	m=mass(kg)	ρ= volumemass density(kg m−3)	ρu,where u=velocity fieldof fluid (m s−1)	${\frac {\partial \rho }{\partial t}}=-\nabla \cdot (\rho \mathbf {u} )$
Electromagnetism,electric charge	q= electric charge (C)	ρ= volume electriccharge density(C m−3)	J= electriccurrent density(A m−2)	${\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {J}$
Thermodynamics,energy	E= energy (J)	u= volumeenergy density(J m−3)	q=heat flux(W m−2)	${\frac {\partial u}{\partial t}}=-\nabla \cdot \mathbf {q}$
Quantum mechanics,probability	Ψ|2d3r=probability distribution	Ψ|2=probability density function(m−3), Ψ =wavefunctionof quantum system	j=probability current/flux	${\frac {\partial |\Psi |^{2}}{\partial t}}=-\nabla \cdot \mathbf {j}$

More general equations are theconvection–diffusion equationandBoltzmann transport equation,which have their roots in the continuity equation.

Laws of classical mechanics

Principle of least action

Main article:Principle of least action

Classical mechanics, includingNewton's laws,Lagrange's equations,Hamilton's equations,etc., can be derived from the following principle:

$\delta {\mathcal {S}}=\delta \int _{t_{1}}^{t_{2}}L(\mathbf {q},\mathbf {\dot {q}},t)\,dt=0$

where${\mathcal {S}}$is theaction;the integral of theLagrangian

$L(\mathbf {q},\mathbf {\dot {q}},t)=T(\mathbf {\dot {q}},t)-V(\mathbf {q},\mathbf {\dot {q}},t)$

of the physical system between two timest₁andt₂.The kinetic energy of the system isT(a function of the rate of change of theconfigurationof the system), andpotential energyisV(a function of the configuration and its rate of change). The configuration of a system which hasNdegrees of freedomis defined bygeneralized coordinatesq= (q₁,q₂,...q_N).

There aregeneralized momentaconjugate to these coordinates,p= (p₁,p₂,...,p_N), where:

$p_{i}={\frac {\partial L}{\partial {\dot {q}}_{i}}}$

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 thegeneralized coordinatesin theconfiguration space,i.e. the curveq(t), parameterized by time (see alsoparametric equationfor this concept).

The action is afunctionalrather than afunction,since it depends on the Lagrangian, and the Lagrangian depends on the pathq(t), so the action depends on theentire"shape" of the path for all times (in the time interval fromt₁tot₂). 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 theentire continuumof Lagrangian values corresponding to some path,not just one valueof the Lagrangian, is required (in other words it isnotas simple as "differentiating a function and setting it to zero, then solving the equations to find the points ofmaxima and minimaetc ", rather this idea is applied to the entire" shape "of the function, seecalculus of variationsfor more details on this procedure).

NoticeLisnotthe total energyEof the system due to the difference, rather than the sum:

$E=T+V$

The followinggeneral 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.

Laws of motion
Principle of least action: ${\mathcal {S}}=\int _{t_{1}}^{t_{2}}L\,\mathrm {d} t\,\!$
TheEuler–Lagrange equationsare: ${\frac {\mathrm {d} }{\mathrm {d} t}}\left({\frac {\partial L}{\partial {\dot {q}}_{i}}}\right)={\frac {\partial L}{\partial q_{i}}}$ Using the definition of generalized momentum, there is the symmetry: $p_{i}={\frac {\partial L}{\partial {\dot {q}}_{i}}}\quad {\dot {p}}_{i}={\frac {\partial L}{\partial {q}_{i}}}$	Hamilton's equations ${\dfrac {\partial \mathbf {p} }{\partial t}}=-{\dfrac {\partial H}{\partial \mathbf {q} }}$ ${\dfrac {\partial \mathbf {q} }{\partial t}}={\dfrac {\partial H}{\partial \mathbf {p} }}$ The Hamiltonian as a function of generalized coordinates and momenta has the general form: $H(\mathbf {q},\mathbf {p},t)=\mathbf {p} \cdot \mathbf {\dot {q}} -L$
	Hamilton–Jacobi equation $H\left(\mathbf {q},{\frac {\partial S}{\partial \mathbf {q} }},t\right)=-{\frac {\partial S}{\partial t}}$
Newton's laws Newton's laws of motion They are low-limit solutions torelativity.Alternative formulations of Newtonian mechanics areLagrangianandHamiltonianmechanics. The laws can be summarized by two equations (since the 1st is a special case of the 2nd, zero resultant acceleration): $\mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},\quad \mathbf {F} _{ij}=-\mathbf {F} _{ji}$ wherep= momentum of body,Fij= forceonbodyibybodyj,Fji= forceonbodyjbybodyi. For adynamical systemthe two equations (effectively) combine into one: ${\frac {\mathrm {d} \mathbf {p} _{\mathrm {i} }}{\mathrm {d} t}}=\mathbf {F} _{\text{E}}+\sum _{\mathrm {i} \neq \mathrm {j} }\mathbf {F} _{\mathrm {ij} }$ in whichFE= resultant external force (due to any agent not part of system). Bodyidoes not exert a force on itself.

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)

Corollaries influid mechanics

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
• Bernoulli's principle
• Poiseuille's law
• Stokes' law
• Navier–Stokes equations
• Faxén's law

Laws of gravitation and relativity

Some of the more famous laws of nature are found inIsaac Newton's theories of (now)classical mechanics,presented in hisPhilosophiae Naturalis Principia Mathematica,and inAlbert Einstein'stheory of relativity.

Modern laws

Special relativity

The two postulates of special relativity are not "laws" in themselves, but assumptions of their nature in terms ofrelative motion.

They can be stated as "the laws of physics are the same in allinertial frames"and" thespeed of lightis constant and has the same value in all inertial frames ".

The said postulates lead to theLorentz transformations– the transformation law between twoframe of referencesmoving relative to each other. For any4-vector

$A'=\Lambda A$

this replaces theGalilean transformationlaw from classical mechanics. The Lorentz transformations reduce to the Galilean transformations for low velocities much less than the speed of lightc.

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 ifAis thefour-momentum,the magnitude can derive the famous invariant equation for mass–energy and momentum conservation (seeinvariant mass):

$E^{2}=(pc)^{2}+(mc^{2})^{2}$

in which the (more famous)mass–energy equivalenceE=mc²is a special case.

General relativity

General relativity is governed by theEinstein field equations,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 themetric tensor.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; theGEM equations,to describe an analogousgravitomagnetic field.They are well established by the theory, and experimental tests form ongoing research.

Einstein field equations(EFE): $R_{\mu \nu }+\left(\Lambda -{\frac {R}{2}}\right)g_{\mu \nu }={\frac {8\pi G}{c^{4}}}T_{\mu \nu }\,\!$ where Λ =cosmological constant,Rμν=Ricci curvature tensor,Tμν=stress–energy tensor,gμν=metric tensor	Geodesic equation: ${\frac {{\rm {d}}^{2}x^{\lambda }}{{\rm {d}}t^{2}}}+\Gamma _{\mu \nu }^{\lambda }{\frac {{\rm {d}}x^{\mu }}{{\rm {d}}t}}{\frac {{\rm {d}}x^{\nu }}{{\rm {d}}t}}=0\,$ where Γ is aChristoffel symbolof thesecond kind,containing the metric.
GEM Equations Ifgthe gravitational field andHthe gravitomagnetic field, the solutions in these limits are: $\nabla \cdot \mathbf {g} =-4\pi G\rho \,\!$ $\nabla \cdot \mathbf {H} =\mathbf {0} \,\!$ $\nabla \times \mathbf {g} =-{\frac {\partial \mathbf {H} }{\partial t}}\,\!$ $\nabla \times \mathbf {H} ={\frac {4}{c^{2}}}\left(-4\pi G\mathbf {J} +{\frac {\partial \mathbf {g} }{\partial t}}\right)\,\!$ whereρis themass densityandJis the mass current density ormass flux.
In addition there is thegravitomagnetic Lorentz force: $\mathbf {F} =\gamma (\mathbf {v} )m\left(\mathbf {g} +\mathbf {v} \times \mathbf {H} \right)$ wheremis therest massof the particlce and γ is theLorentz factor.

Classical laws

Main articles:Kepler's laws of planetary motionandNewton's law of gravitation

Kepler's laws, though originally discovered from planetary observations (also due toTycho Brahe), are true for anycentral forces.

Newton's law of universal gravitation: For two point masses: $\mathbf {F} ={\frac {Gm_{1}m_{2}}{\left|\mathbf {r} \right|^{2}}}\mathbf {\hat {r}} \,\!$ For a non uniform mass distribution of local mass densityρ(r) of body of VolumeV,this becomes: $\mathbf {g} =G\int _{V}{\frac {\mathbf {r} \rho \,\mathrm {d} {V}}{\left|\mathbf {r} \right|^{3}}}\,\!$	Gauss's law for gravity: An equivalent statement to Newton's law is: $\nabla \cdot \mathbf {g} =4\pi G\rho \,\!$
Kepler's 1st Law:Planets move in an ellipse, with the star at a focus $r={\frac {\ell }{1+e\cos \theta }}\,\!$ where $e={\sqrt {1-(b/a)^{2}}}$ is theeccentricityof the elliptic orbit, of semi-major axisaand semi-minor axisb,andℓis the semi-latus rectum. This equation in itself is nothing physically fundamental; simply thepolar equationof anellipsein which the pole (origin of polar coordinate system) is positioned at a focus of the ellipse, where the orbited star is.
Kepler's 2nd Law:equal areas are swept out in equal times (area bounded by two radial distances and the orbital circumference): ${\frac {\mathrm {d} A}{\mathrm {d} t}}={\frac {\left|\mathbf {L} \right|}{2m}}\,\!$ whereLis the orbital angular momentum of the particle (i.e. planet) of massmabout the focus of orbit,
Kepler's 3rd Law:The square of the orbital time periodTis proportional to the cube of the semi-major axisa: $T^{2}={\frac {4\pi ^{2}}{G\left(m+M\right)}}a^{3}\,\!$ whereMis the mass of the central body (i.e. star).

Thermodynamics

Laws of thermodynamics
First law of thermodynamics:The change in internal energy dUin a closed system is accounted for entirely by the heat δQabsorbed by the system and the work δWdone by the system: $\mathrm {d} U=\delta Q-\delta W\,$ Second law of thermodynamics:There are many statements of this law, perhaps the simplest is "the entropy of isolated systems never decreases", $\Delta S\geq 0$ meaning reversible changes have zero entropy change, irreversible process are positive, and impossible process are negative.	Zeroth law of thermodynamics:If two systems are inthermal equilibriumwith a third system, then they are in thermal equilibrium with one another. $T_{A}=T_{B}\,,T_{B}=T_{C}\Rightarrow T_{A}=T_{C}\,\!$ Third law of thermodynamics: As the temperatureTof a system approaches absolute zero, the entropySapproaches a minimum valueC:asT→ 0,S→C.
For homogeneous systems the first and second law can be combined into theFundamental thermodynamic relation: $\mathrm {d} U=T\,\mathrm {d} S-P\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,\!$
Onsager reciprocal relations:sometimes called theFourth Law of Thermodynamics $\mathbf {J} _{u}=L_{uu}\,\nabla (1/T)-L_{ur}\,\nabla (m/T);$ $\mathbf {J} _{r}=L_{ru}\,\nabla (1/T)-L_{rr}\,\nabla (m/T).$

• Newton's law of cooling
• Fourier's law
• Ideal gas law,combines a number of separately developed gas laws;
  • Boyle's law
  • Charles's law
  • Gay-Lussac's law
  • Avogadro's law,into one

now improved by otherequations of state

• Dalton's law(of partial pressures)
• Boltzmann equation
• Carnot's theorem
• Kopp's law

Electromagnetism

Maxwell's equationsgive the time-evolution of theelectricandmagneticfields due toelectric chargeandcurrentdistributions. Given the fields, theLorentz forcelaw is theequation of motionfor charges in the fields.

Maxwell's equations Gauss's lawfor electricity $\nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}$ Gauss's law for magnetism $\nabla \cdot \mathbf {B} =0$ Faraday's law $\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}$ Ampère's circuital law(with Maxwell's correction) $\nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +{\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} }{\partial t}}\$

Lorentz forcelaw: $\mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)$

Quantum electrodynamics(QED):Maxwell's equations are generally true and consistent with relativity - but they do not predict some observed quantum phenomena (e.g. light propagation asEM waves,rather thanphotons,seeMaxwell's equationsfor details). They are modified in QED theory.

These equations can be modified to includemagnetic monopoles,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
• Coulomb's law
• Biot–Savart law

Other laws

• Ohm's law
• Kirchhoff's laws
• Joule's law

Photonics

Classically,opticsis based on avariational principle:light travels from one point in space to another in the shortest time.

• Fermat's principle

Ingeometric opticslaws are based on approximations in Euclidean geometry (such as theparaxial approximation).

• Law of reflection
• Law of refraction,Snell's law

Inphysical optics,laws are based on physical properties of materials.

• Brewster's angle
• Malus's law
• Beer–Lambert law

In actuality, optical properties of matter are significantly more complex and require quantum mechanics.

Laws of quantum mechanics

Quantum mechanics has its roots inpostulates.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 awavefunction.
• Every physical quantity is described by anoperatoracting on the system; the measured quantity has aprobabilistic nature.
• Thewavefunctionobeys theSchrödinger equation.Solving this wave equation predicts the time-evolution of the system's behavior, analogous to solving Newton's laws in classical mechanics.
• Twoidentical particles,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 principlesand thePauli exclusion principle.

Quantum mechanics,Quantum field theory Schrödinger equation(general form):Describes the time dependence of a quantum mechanical system. $i\hbar {\frac {d}{dt}}\left|\psi \right\rangle ={\hat {H}}\left|\psi \right\rangle$ TheHamiltonian(in quantum mechanics)His aself-adjoint operatoracting on the state space,$|\psi \rangle$(seeDirac notation) is the instantaneousquantum state vectorat timet,positionr,iis the unitimaginary number,ħ=h/2πis thereduced Planck constant.	Wave–particle duality Planck–Einstein law:theenergyofphotonsis proportional to thefrequencyof the light (the constant is thePlanck constant,h). $E=h\nu =\hbar \omega$ De Broglie wavelength:this laid the foundations of wave–particle duality, and was the key concept in theSchrödinger equation, $\mathbf {p} ={\frac {h}{\lambda }}\mathbf {\hat {k}} =\hbar \mathbf {k}$ Heisenberg uncertainty principle:Uncertaintyin position multiplied by uncertainty inmomentumis at least half of thereduced Planck constant,similarly for time andenergy; $\Delta x\,\Delta p\geq {\frac {\hbar }{2}},\,\Delta E\,\Delta t\geq {\frac {\hbar }{2}}$ The uncertainty principle can be generalized to any pair of observables – see main article.
Wave mechanics Schrödinger equation(original form): $i\hbar {\frac {\partial }{\partial t}}\psi =-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi +V\psi$
Pauli exclusion principle:No two identicalfermionscan occupy the same quantum state (bosonscan). Mathematically, if two particles are interchanged, fermionic wavefunctions are anti-symmetric, while bosonic wavefunctions are symmetric: $\psi (\cdots \mathbf {r} _{i}\cdots \mathbf {r} _{j}\cdots )=(-1)^{2s}\psi (\cdots \mathbf {r} _{j}\cdots \mathbf {r} _{i}\cdots )$ whereriis the position of particlei,andsis thespinof the particle. There is no way to keep track of particles physically, labels are only used mathematically to prevent confusion.

Radiation laws

Applying electromagnetism, thermodynamics, and quantum mechanics, to atoms and molecules, some laws ofelectromagnetic radiationand light are as follows.

• Stefan–Boltzmann law
• Planck's lawof black-body radiation
• Wien's displacement law
• Radioactive decay law

Laws of chemistry

Main article:Chemical law

Chemical lawsare those laws of nature relevant tochemistry.Historically, observations led to many empirical laws, though now it is known that chemistry has its foundations inquantum mechanics.

Quantitative analysis

The most fundamental concept in chemistry is thelaw of conservation of mass,which states that there is no detectable change in the quantity of matter during an ordinarychemical reaction.Modern physics shows that it is actuallyenergythat is conserved, and thatenergy and mass are related;a concept which becomes important innuclear chemistry.Conservation of energyleads to the important concepts ofequilibrium,thermodynamics,andkinetics.

Additional laws of chemistry elaborate on the law of conservation of mass.Joseph Proust'slaw of definite compositionsays 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'slaw of multiple proportionssays that these chemicals will present themselves in proportions that are small whole numbers; although in many systems (notablybiomacromoleculesandminerals) 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 ofstoichiometry,the proportions by which the chemical elements combine to form chemical compounds. The third law of stoichiometry is thelaw of reciprocal proportions,which provides the basis for establishingequivalent weightsfor each chemical element. Elemental equivalent weights can then be used to deriveatomic weightsfor each element.

More modern laws of chemistry define the relationship between energy and its transformations.

Reaction kineticsandequilibria

• 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 principlestates 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, ortransition structure,that corresponds to the structure at the top of the energy barrier. TheHammond–Leffler postulatestates 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 achievecatalysis.
• All chemical processes are reversible (law ofmicroscopic reversibility) although some processes have such an energy bias, they are essentially irreversible.
• The reaction rate has the mathematical parameter known as therate constant.TheArrhenius equationgives the temperature andactivation energydependence of the rate constant, an empirical law.

Thermochemistry

• Dulong–Petit law
• Gibbs–Helmholtz equation
• Hess's law

Gas laws

• Raoult's law
• Henry's law

Chemical transport

• Fick's laws of diffusion
• Graham's law
• Lamm equation

Laws of biology

Main article:Biological rules

Ecology

• Competitive exclusion principleor Gause's law

Genetics

• Mendelian laws(Dominance and Uniformity, segregation of genes, and Independent Assortment)
• Hardy–Weinberg principle

Natural selection

Whether or notNatural Selectionis a “law of nature” is controversial among biologists.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 relativefitness,the propensity of agenotypeto increase in proportionate representation in a competitive environment, as a function ofadaptedness(adaptive design) of the organism.

Laws of Earth sciences

Geography

• Arbia's law of geography
• Tobler's first law of geography
• Tobler's second law of geography

Geology

• Archie's law
• Buys Ballot's law
• Birch's law
• Byerlee's law
• Principle of original horizontality
• Law of superposition
• Principle of lateral continuity
• Principle of cross-cutting relationships
• Principle of faunal succession
• Principle of inclusions and components
• Walther's law

Other fields

Somemathematicaltheoremsandaxiomsare referred to as laws because they provide logical foundation to empirical laws.

Examples of other observed phenomena sometimes described as laws include theTitius–Bode lawof planetary positions,Zipf's lawof linguistics, andMoore's lawof technological growth. Many of these laws fall within the scope ofuncomfortable science.Other laws are pragmatic and observational, such as thelaw of unintended consequences.By analogy, principles in other fields of study are sometimes loosely referred to as "laws". These includeOccam's razoras a principle of philosophy and thePareto principleof economics.

History

The observation and detection of underlying regularities in nature date fromprehistorictimes – the recognition of cause-and-effect relationships implicitly recognises the existence of laws of nature. The recognition of such regularities as independent scientific lawsper se,though, was limited by their entanglement inanimism,and by the attribution of many effects that do not have readily obvious causes—such as physical phenomena—to the actions ofgods,spirits,supernatural beings,etc. Observation and speculation about nature were intimately bound up with metaphysics and morality.

In Europe, systematic theorizing about nature (physis) began with the earlyGreek philosophers and scientistsand continued into theHellenisticandRoman imperialperiods, during which times the intellectual influence ofRoman lawincreasingly became paramount.

The formula "law of nature" first appears as "a live metaphor" favored by Latin poetsLucretius,Virgil,Ovid,Manilius,in time gaining a firm theoretical presence in the prose treatises ofSenecaandPliny.Why this Roman origin? According to [historian and classicist Daryn] Lehoux's persuasive narrative,the idea was made possible by the pivotal role of codified law andforensicargument in Roman life and culture.

For the Romans... the place par excellence where ethics, law, nature, religion and politics overlap is thelaw court.When we read Seneca'sNatural 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 toPtolemy'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 philosopherssuch asIsaac Newton(1642–1727) were influenced by areligiousview – stemming from medieval concepts ofdivine law– which held that God had instituted absolute, universal and immutable physical laws.In chapter 7 ofThe World,René Descartes(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 modernscientific methodwhich took shape at this time (withFrancis Bacon(1561–1626) andGalileo(1564–1642)) contributed to a trend ofseparating sciencefromtheology,with minimal speculation aboutmetaphysicsand ethics. (Natural lawin 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 asGrotius(1583–1645),Spinoza(1632–1677), andHobbes(1588–1679).)

The distinction betweennatural lawin the political-legal sense and law of nature or physical law in the scientific sense is a modern one, both concepts being equally derived fromphysis,the Greek word (translated into Latin asnatura) fornature.

See also

• Empirical research
• Empirical statistical laws
• Formula
• List of laws
• Law (principle)
• Nomology
• Philosophy of science
• Physical constant
• List of scientific laws named after people
• Theory

Further reading

• Barrow, John D.(1992).Theories of Everything: The Quest for Ultimate Explanations.Ballantine Books.ISBN0-449-90738-4.
• Dilworth, Craig (2007). "Appendix IV. On the nature of scientific laws and theories".Scientific progress: a study concerning the nature of the relation between successive scientific theories(4th ed.). Dordrecht: Springer Verlag.ISBN978-1-4020-6353-4.
• Francis Bacon(1620).Novum Organum.
• Hanzel, Igor (1999).The concept of scientific law in the philosophy of science and epistemology: a study of theoretical reason.Dordrecht [u.a.]: Kluwer.ISBN978-0-7923-5852-7.
• Lehoux, Daryn (2012-02-28).What Did the Romans Know? An Inquiry into Science and Worldmaking.Chicago, Ill.: University of Chicago Press.ISBN978-0-226-47114-3.
• Nagel, Ernest (1984). "5. Experimental laws and theories".The structure of science problems in the logic of scientific explanation(2nd ed.). Indianapolis: Hackett.ISBN978-0-915144-71-6.
• R. Penrose (2007).The Road to Reality.Vintage books.ISBN978-0-679-77631-4.
• Swartz, Norman (20 February 2009)."Laws of Nature".Internet encyclopedia of philosophy.Retrieved7 May2012.

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:"Laws of Nature"by John W. Carroll.
• Baaquie, Belal E."Laws of Physics: A Primer".Core Curriculum,National University of Singapore.
• Francis, Erik Max."The laws list"..Physics.Alcyone Systems
• Pazameta, Zoran."The laws of nature".Archived2014-02-26 at theWayback MachineCommittee for the scientific investigation of Claims of the Paranormal.
• The Internet Encyclopedia of Philosophy."Laws of Nature"– ByNorman Swartz
• Mark Buchanan; Frank Close; Nancy Cartwright; Melvyn Bragg (host) (Oct 19, 2000)."Laws of Nature".In Our Time.BBC Radio 4.