Laws of science

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The laws of science are various established scientific laws, or physical laws as they are sometimes called, that are considered universal and invariable facts of the physical world. Laws of science may, however, be disproved if new facts or evidence contradicts them. A "law" differs from hypotheses, theories, postulates, principles, etc., in that a law is an analytic statement, usually with an empirically determined constant. A theory may contain a set of laws, or a theory may be implied from an empirically determined law.

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

[edit] Overview

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:

[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.

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

$y' = y$

$z' = z$

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

E=mc² where m=m₀/sqrt(1-(v²/c²)

[edit] Newton's laws

Newton

Newton's laws of motion - Replaced with relativity

*1. Law of Inertia

*2. $\ F = d(\vec p)/dt$ Although it implies $\ F = ma$ , that is not necessarily true.

*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] Chemical laws

Main article: Chemical law

Chemical laws are those laws of nature relevant to chemistry. The most fundamental concept in chemistry is the law of conservation of mass, which states that there is no detectable change in the quantity of matter during an ordinary chemical reaction. Modern physics shows that it is actually energy that is conserved, and that energy and mass are related; a concept which becomes important in nuclear chemistry. Conservation of energy leads to the important concepts of equilibrium, thermodynamics, and kinetics.

Additional laws of chemistry elaborate on the law of conservation of mass. Joseph Proust's law of definite composition 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 says that these chemicals will present themselves in proportions that are small whole numbers (i.e. 1:2 O:H in water); although in many systems (notably biomacromolecules and minerals) the ratios tend to require large numbers, and are frequently represented as a fraction. Such compounds are known as non-stoichiometric compounds

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

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.
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 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.
All chemical processes are reversible (law of microscopic reversibility) although some processes have such an energy bias, they are essentially irreversible.

[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:	$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$
Ampère'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)

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