List of laws in science

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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:

• Energy conservation law
• Momentum conservation law
• Angular momentum conservation 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 <math>PV = \ nRT</math>
• Dulong-Petit law (specific heat capacity at constant volume)

  <math> c_V = \frac{3R} {M}</math>

Einstein

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

  <math> E \ = hf </math>

Special Relativity

• Constancy of the speed of light
• Lorentz transformations - Transformations of Cartesian coordinates between relatively moving reference frames.

  <math>x' = (x - vt) / \sqrt{1 - v^2/c^2}</math>

  <math>y' = y</math>

  <math>z' = z</math>

  <math>t' = (t - vx/c^2) / \sqrt{1 - v^2/c^2}</math>

• 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.

  <math>F = ma / \sqrt({1 - v^2/c^2})^3</math>

• Mass-energy equivalence

  <math> \ E = mc^2 </math> (Energy = mass × speed of light²)

General Relativity

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

  This is described by the Einstein field equations:

  <math>R_{ab} - {1 \over 2}R\,g_{ab} = {8 \pi G \over c^4} T_{ab}.</math>

  <math>R_{ab}</math> is the Ricci tensor, <math>R</math> is the Ricci scalar, <math>g_{ab}</math> is the metric tensor, <math>T_{ab}</math> is the stress-energy tensor, and the constant is given in terms of <math>\pi</math> (pi), <math>c</math> (the speed of light) and <math>G</math> (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. <math> \ F = ma </math> Force equals mass times acceleration.

  *3. <math>F_{ab}=-F_{ba}</math> 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.

  <math> F_g = G \frac{m_1m_2} {r^2} </math>

  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.

<math> F = \frac{\left|q_1 q_2\right|}{4 \pi \epsilon_0 r^2} </math>

• Ohm's Law

<math>

V = I \cdot R </math>

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

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

• Navier-Stokes equations of fluid dynamics

<math>-\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) </math>

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

<math> \Phi_{V} = {\pi r^{4}\over 8 \eta} { \triangle p^{\star} \over l}</math>

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)

  <math> j^{\star} = \sigma T^4</math>

Thermodynamics

• zeroth law of thermodynamics

<math>A \sim B \wedge B \sim C \Rightarrow A \sim C</math>

• first law of thermodynamics

<math>\mathrm{d}U=\delta Q-\delta W\,</math>,

• second law of thermodynamics
• third law of thermodynamics
• Onsager reciprocal relations - sometimes called the Fourth Law of Thermodynamics

  <math> \mathbf{J}_{u} = L_{uu}\, \nabla(1/T) - L_{ur}\, \nabla(m/T) \!</math>; and

  <math> \mathbf{J}_{r} = L_{ru}\, \nabla(1/T) - L_{rr}\, \nabla(m/T) \!</math>.

• 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.

  <math>\Delta x \Delta p \ge \frac{\hbar}{2} </math>

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

  <math> H(t) \left| \psi (t) \right\rangle = i \hbar {\partial\over\partial t} \left| \psi (t) \right\rangle</math>

  The Hamiltonian H(t) is a self-adjoint operator acting on the state space, <math>\psi (t)</math> is the instantaneous state vector at time t, i is the unit imaginary number, <math>\hbar</math> 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

• Scientific laws named after peoplear:قائمة القوانين العلمية

nl:Lijst van natuurwetten sl:seznam fizikalnih zakonov fr:Liste des lois scientifiques