Laws of science

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In science, there are a specific number of established scientific laws, or physical laws as they are sometimes called, that are considered absolute and inarguable facts of the physical world. Laws of science may, however, be disproved if new facts or evidence arise to contradict them. A "law" differs from those as hypotheses, theories, postulates, and principles, etc., in that a law is a general statement about nature that is considered proven beyond doubt. Conservative estimates indicate that there are 18 basic physical laws in the universe: ^[1]

Fluid mechanics

Archimedes’ principle

Force, mass, and inertia

Heat, energy, and temperature

Quantum mechanics

Heisenberg’s uncertainty principle

Others, such as Roger Penrose with his 2004 book The Road to Reality – a complete guide to the laws of the universe, argues that there are a large number of established laws of science. Some laws, such as Descartes’ first law of nature, have become obsolete. A rough outline of the basic laws in science is as follows:

1 Conservation laws
2 Gas laws
3 Einstein's laws
4 Newton's laws
5 Electromagnetic laws
6 Thermodynamic laws
7 Quantum laws
8 Other laws
9 References
10 See also

[edit] Conservation laws

Most significant laws in science are conservation laws:

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

[edit] Gas laws

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 $PV = \ nRT$

[edit] Einstein's laws

Einstein

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

$E \ = hf$

Special Relativity

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

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

$y' = y$

$z' = z$

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

$F = ma / \sqrt({1 - v^2/c^2})^3$
Mass-energy equivalence

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

General Relativity

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

This is described by the Einstein field equations:

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

$R a b$ is the Ricci tensor, $R$ is the Ricci scalar, $g a b$ is the metric tensor, $T a b$ is the stress-energy tensor, and the constant is given in terms of $π$ (pi), $c$ (the speed of light) and $G$ (the gravitational constant).

[edit] Newton's laws

Newton

Newton's laws of motion - Replaced with relativity

*1. Law of Inertia

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

*3. $F a b = - F b a$ 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.

$F_g = G \frac{m_1m_2} {r^2}$

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

[edit] Electromagnetic laws

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.

$F = \frac{\left|q_1 q_2\right|}{4 \pi \epsilon_0 r^2}$

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):

Name	Partial Differential form
Gauss's law :	$\nabla \cdot \mathbf{D} = \rho$

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

[edit] Thermodynamic laws

Thermodynamics

Zeroth law of thermodynamics

$A \sim B \wedge B \sim C \Rightarrow A \sim C$
First law of thermodynamics

$\mathrm{d}U=\delta Q-\delta W\,$
Second law of thermodynamics

$\int \frac{\delta Q}{T} \ge 0$
Third law of thermodynamics

$T \Rightarrow 0, S \Rightarrow C$
Onsager reciprocal relations - sometimes called the Fourth Law of Thermodynamics

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

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

[edit] Quantum laws

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.

$\Delta x \Delta p \ge \frac{\hbar}{2}$
De Broglie hypothesis - Laid the foundations of particle-wave duality and was the key idea in the Schrödinger equation.

$\lambda = \frac {hc}{mc^2} = \frac {h}{mc} = \frac {h}{p}$
Schrödinger equation - Describes the time dependence of a quantum mechanical system.

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

The Hamiltonian H(t) is a self-adjoint operator acting on the state space, $ψ(t)$ is the instantaneous state vector at time t, i is the unit imaginary number, $\hbar$ 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.

[edit] Other laws

Navier-Stokes equations of fluid dynamics

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

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

$\Phi_{V} = {\pi r^{4}\over 8 \eta} { \triangle p^{\star} \over l}$

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)

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