This is a list of physical laws discovered by science. Bolded items are categories for the entries indented underneath instead of individual laws.

Most significant laws in science are conservation laws:

• Conservation of energy law
• Conservation of momentum law
• Conservation of angular momentum law
• Charge conservation law

These fundamental laws follow from homogeneity of space, time and phase (see Emmy Noether theorem).

Other less significant (=non fundamental) laws are the mathematical consequences of the above conservation laws for derivative physical quantities (mathematically defined as force, pressure, temperature, density, force fields, etc):

• Boyle's Law (pressure and volume of ideal gas)
• Charles & Gay-Lussac (gases expand equally with the same change of temperature)
• Ideal Gas Law $PV\; =\; \backslash \; nRT$
• Dulong-Petit law (specific heat capacity at constant volume)

  $c\_V\; =\; \backslash frac\{3R\}\; \{M\}$

Einstein

• Energy of photons - Energy equals Planck's constant multiplied by the frequency of the light.

  $E\; \backslash \; =\; hf$

Special Relativity

• Constancy of the speed of light

• Lorentz transformations - Transformations of Cartesian coordinates between relatively moving reference frames.

  $x\text{'}\; =\; (x\; -\; vt)\; /\; \backslash sqrt\{1\; -\; v^2/c^2\}$

  $y\text{'}\; =\; y$

  $z\text{'}\; =\; z$

  $t\text{'}\; =\; (t\; -\; vx/c^2)\; /\; \backslash sqrt\{1\; -\; v^2/c^2\}$

• Law of force - Force equals mass times acceleration divided by the square root of one minus the ratio squared of the object's velocity to the speed of light.

  $F\; =\; ma\; /\; \backslash sqrt(\{1\; -\; v^2/c^2\})^3$

• Mass-energy equivalence

  $\backslash \; E\; =\; mc^2$ (Energy = mass × speed of light²)

General Relativity

• Energy-momentum (including mass via E=mc²) curves spacetime.

  This is described by the Einstein field equations:

  $R\_\{ab\}\; -\; \{1\; \backslash over\; 2\}R\backslash ,g\_\{ab\}\; =\; \{8\; \backslash pi\; G\; \backslash over\; c^4\}\; T\_\{ab\}.$

  $R\_\{ab\}$ is the Ricci tensor, $R$ is the Ricci scalar, $g\_\{ab\}$ is the metric tensor, $T\_\{ab\}$ is the stress-energy tensor, and the constant is given in terms of $\backslash pi$ (pi), $c$ (the speed of light) and $G$ (the gravitational constant).

  • Laws of Kepler (planetary motion)

Beer-Lambert (light absorption)

Newton

• Newton's laws of motion - Replaced with relativity

  *1. Law of Inertia

  *2. $\backslash \; F\; =\; ma$ Force equals mass times acceleration.

  *3. $F\_\{ab\}=-F\_\{ba\}$ Force of a on b equals the negative force of b on a, or for every action there is an equal and opposite reaction.

• Law of heat conduction
• General law of gravitation - Gravitational force between two objects equals the gravitational constant times the product of the masses divided by the distance between them squared.

  $F\_g\; =\; G\; \backslash frac\{m\_1m\_2\}\; \{r^2\}$

  This law is really just the low limit solution of Einstein's field equations and is not accurate with modern high precision gravitational measurements.

  • Coulomb's law - Force between any two charges is equal to the absolute value of the multiple of the charges divided by 4 pi times the vacuum permittivity times the distance squared between the two charges.

$F\; =\; \backslash frac\{\backslash left|q\_1\; q\_2\backslash right|\}\{4\; \backslash pi\; \backslash epsilon\_0\; r^2\}$

• Ohm's Law

$$

V = I \cdot R

• Kirchhoff's circuit laws (current and voltage laws)
• Kirchhoff's law of thermal radiation
• Maxwell's equations (electric and magnetic fields):

{| border="1" style="margin-left: 3em;"

Name	Partial Differential form
Gauss's law :	$\backslash nabla\; \backslash cdot\; \backslash mathbf\{D\}\; =\; \backslash rho$
Gauss's law for magnetism:	$\backslash nabla\; \backslash cdot\; \backslash mathbf\{B\}\; =\; 0$
Faraday's law of induction:	$\backslash nabla\; \backslash times\; \backslash mathbf\{E\}\; =\; -\backslash frac\{\backslash partial\; \backslash mathbf\{B\}\}\; \{\backslash partial\; t\}$
Ampere's law + Maxwell's extension:	$\backslash nabla\; \backslash times\; \backslash mathbf\{H\}\; =\; \backslash mathbf\{J\}\; +\; \backslash frac\{\backslash partial\; \backslash mathbf\{D\}\}\; \{\backslash partial\; t\}$

• Navier-Stokes equations of fluid dynamics

$-\backslash nabla\; p\; +$

\mu \left( \nabla^2 \mathbf{u} + {1 \over 3} \nabla (\nabla \cdot \mathbf{u} ) \right) + \rho \mathbf{u} = \rho \left( { \partial\mathbf{u} \over \partial t} + \mathbf{u} \cdot \nabla \mathbf{u} \right)

• Poiseuille's law (voluminal laminar stationary flow of incompressible uniform viscous liquid through a cylindrical tube with the constant circular cross-section)

$\backslash Phi\_\{V\}\; =\; \{\backslash pi\; r^\{4\}\backslash over\; 8\; \backslash eta\}\; \{\; \backslash triangle\; p^\{\backslash star\}\; \backslash over\; l\}$

Radiation laws

• Planck's law of black body radiation (spectral density in a radiation of a black-body)

• Wien's law (wavelength of the peak of the emission of a black body) :λ₀T = k_w
• Stefan-Boltzmann law (total radiation from a black body)

  $j^\{\backslash star\}\; =\; \backslash sigma\; T^4$

Thermodynamics

• zeroth law of thermodynamics

  $A\; \backslash sim\; B\; \backslash wedge\; B\; \backslash sim\; C\; \backslash Rightarrow\; A\; \backslash sim\; C$

• first law of thermodynamics

  $\backslash Delta\; U\; =\; Q\; +\; W$

• second law of thermodynamics

  $e\; =\; \backslash frac\; \{Q\_H\; -\; Q\_C\}\; \{Q\_H\}\; =\; 1\; -\; \backslash frac\; \{Q\_C\}\; \{Q\_H\}$

• third law of thermodynamics

  $e\_T\; =\; \backslash frac\; \{T\_H\; -\; T\_C\}\; \{T\_H\}\; =\; 1\; -\; \backslash frac\; \{T\_C\}\; \{T\_H\}$

• Onsager reciprocal relations - sometimes called the Fourth Law of Thermodynamics

  $\backslash mathbf\{J\}\_\{u\}\; =\; L\_\{uu\}\backslash ,\; \backslash nabla(1/T)\; -\; L\_\{ur\}\backslash ,\; \backslash nabla(m/T)\; \backslash !$; and

  $\backslash mathbf\{J\}\_\{r\}\; =\; L\_\{ru\}\backslash ,\; \backslash nabla(1/T)\; -\; L\_\{rr\}\backslash ,\; \backslash nabla(m/T)\; \backslash !$.

• Buys-Ballot's law (wind travels counterclockwise around low pressure systems in the Northern Hemisphere)

Quantum Mechanics

• Heisenberg Uncertainty Principle - Uncertainty in position multiplied by uncertainty in momentum is equal to or greater than Dirac's constant divided by 2.

  $\backslash Delta\; x\; \backslash Delta\; p\; \backslash ge\; \backslash frac\{\backslash hbar\}\{2\}$

• De Broglie hypothesis - Laid the foundations of particle-wave duality and was the key idea in the Schrödinger equation.

  $\backslash lambda\; =\; \backslash frac\; \{hc\}\{mc^2\}\; =\; \backslash frac\; \{h\}\{mc\}\; =\; \backslash frac\; \{h\}\{p\}$

• Schrödinger equation - Describes the time dependence of a quantum mechanical system.

  $H(t)\; \backslash left|\; \backslash psi\; (t)\; \backslash right\backslash rangle\; =\; i\; \backslash hbar\; \{\backslash partial\backslash over\backslash partial\; t\}\; \backslash left|\; \backslash psi\; (t)\; \backslash right\backslash rangle$

  The Hamiltonian H(t) is a self-adjoint operator acting on the state space, $\backslash psi\; (t)$ is the instantaneous state vector at time t, i is the unit imaginary number, $\backslash hbar$ is Planck's constant divided by 2π

It is thought that the successful integration of Einstein's field equations with the uncertainty principle and Schrödinger equation, something no one has achieved so far with a testable theory, will lead to a theory of quantum gravity, the most basic physical law sought after today.

See also

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• Scientific laws named after people

Science-related lists

قائمة القوانين العلمية | Lijst van natuurwetten | seznam fizikalnih zakonov | Liste des lois scientifiques