विज्ञान के नियम

एक मोटे अनुमान के अनुसार ब्रह्माण्ड में कोई १८ मूल भौतिक नियम होंगे।^[1]

संरक्षन के नियम विज्ञान में सर्वाधिक महत्त्व रखते हैं।

• [[द्रव्य की अविनाशिता का नियम

   द्रव्यमान संरक्षण का नियम(Conservation of mass)

• उर्जा संरक्षण का नियम (Conservation of energy)
• संवेग संरक्षण का नियम
• कोणीय संवेग के संरक्षण का नियम
• आवेश के संरक्षण का नियम

ये मूल नियम स्पेस, समय एवं कला (phase) की समांगता (homogeneity) के परिणाम हैं। एमी नीदर का प्रमेय (Emmy Noether theorem) देखिये।

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 ${\displaystyle PV=\ nRT}$

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

${\displaystyle E\ =hf}$

Special Relativity

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

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

  ${\displaystyle y'=y}$

  ${\displaystyle z'=z}$

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

• Mass-energy equivalence

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

General Relativity

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

  This is described by the Einstein field equations:

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

  ${\displaystyle R_{ab}}$ is the Ricci tensor, ${\displaystyle R}$ is the Ricci scalar, ${\displaystyle g_{ab}}$ is the metric tensor, ${\displaystyle T_{ab}}$ is the stress-energy tensor, and the constant is given in terms of ${\displaystyle \pi }$ (pi), ${\displaystyle c}$ (the speed of light) and ${\displaystyle G}$ (the gravitational constant).

  ${\displaystyle \ E=mc^{2}}$ where ${\displaystyle m={\frac {m_{0}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}$

• Newton's laws of motion - Replaced by relativity

1. Law of Inertia
2. ${\displaystyle \ F=d({\vec {p}})/dt}$ . Although it implies ${\displaystyle \ F=ma}$ , that is not necessarily true.
3. ${\displaystyle F_{ab}=-F_{ba}}$ . 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.

• ${\displaystyle F_{g}=G{\frac {m_{1}m_{2}}{r^{2}}}}$
• This law is really just the low limit solution of Einstein's field equations and is not accurate with modern high precision gravitational measurements.

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.

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.

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

${\displaystyle F={\frac {\left|q_{1}q_{2}\right|}{4\pi \epsilon _{0}r^{2}}}}$

• Ohm's Law

${\displaystyle V=I\cdot R}$

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

Thermodynamics

• Zeroth law of thermodynamics

  If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with one another.

• First law of thermodynamics

  The change in energy dU in a system is accounted for entirely by the heat δQ absorbed by the system and the work δW done by the system:

  ${\displaystyle \mathrm {d} U=\delta Q-\delta W\,}$

• Second law of thermodynamics

  ${\displaystyle \int {\frac {\delta Q}{T}}\geq 0}$

• Third law of thermodynamics

  As the temperature T of a system approaches absolute zero, the entropy S approaches a minimum value C: as T → 0, S → C.

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

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

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

क्वाण्टम यांत्रिकी

• हाइजेनबर्ग का अनिश्चितता का सिद्धान्त - स्थिति की अनिश्चितता एवं संवेग की अनिश्चितता का गुणनफल 'परिवर्तित (reduced) प्लैंक नियतांक' के आधे के बराबर या उससे अधिक होता है।

  ${\displaystyle \Delta x\Delta p\geq {\frac {\hbar }{2}}}$

• Matter wavelength - Laid the foundations of particle-wave duality and was the key idea in the Schrödinger equation.

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

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

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

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

• Navier-Stokes equations of fluid dynamics

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

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

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

• 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)

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

• Laws of Kepler (planetary motion)
• Beer-Lambert (light absorption)
• Dulong-Petit law (specific heat capacity at constant volume)

  ${\displaystyle c_{V}={\frac {3R}{M}}}$

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

• भौतिक नियम (Physical law) - यहाँ इस पर भी चर्चा है कि 'नियम' किसे कहा जाय।
• व्यक्तियों के नाम से प्रसिद्ध वैज्ञानिक नियम

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