Conservation law

Encyclopedia

In physics

, a

does not change as the system evolves.

One particularly important physical result concerning conservation laws is Noether's Theorem

, which states that there is a one-to-one correspondence between conservation laws and differentiable symmetries of physical systems

. For example, the conservation of energy follows from the time-invariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum.

A partial listing of conservation laws that are said to be

There are also

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, a

**conservation law**states that a particular measurable property of an isolated physical systemPhysical system

In physics, the word system has a technical meaning, namely, it is the portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which in analysis is ignored except for its effects on the system. The cut between system and the world is a free...

does not change as the system evolves.

One particularly important physical result concerning conservation laws is Noether's Theorem

Noether's theorem

Noether's theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918...

, which states that there is a one-to-one correspondence between conservation laws and differentiable symmetries of physical systems

Symmetry in physics

In physics, symmetry includes all features of a physical system that exhibit the property of symmetry—that is, under certain transformations, aspects of these systems are "unchanged", according to a particular observation...

. For example, the conservation of energy follows from the time-invariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum.

A partial listing of conservation laws that are said to be

**exact laws**, or more precisely*have never been shown to be violated:*- Conservation of mass-energy
- Conservation of linear momentum
- Conservation of angular momentum
- Conservation of electric chargeCharge conservationIn physics, charge conservation is the principle that electric charge can neither be created nor destroyed. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved...
- Conservation of color chargeColor chargeIn particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
- Conservation of weak isospinWeak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
- Conservation of probability densityProbability currentIn quantum mechanics, the probability current is a mathematical quantity describing the flow of probability density. Intuitively; if one pictures the probability density as an inhomogeneous fluid, then the probability current is the rate of flow of this fluid...
- CPT symmetryCPT symmetryCPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...

(combining charge, parity and time conjugation) - Lorentz symmetry

There are also

**approximate**conservation laws. These are approximately true in particular situations, such as low speeds, short time scales, or certain interactions.- Conservation of massConservation of massThe law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass of an isolated system will remain constant over time...

(applies for non-relativistic speeds and when there are no nuclear reactionNuclear reactionIn nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...

s) - Conservation of baryon number (See chiral anomalyChiral anomalyA chiral anomaly is the anomalous nonconservation of a chiral current. In some theories of fermions with chiral symmetry, the quantization may lead to the breaking of this chiral symmetry. In that case, the charge associated with the chiral symmetry is not conserved.The non-conservation happens...

) - Conservation of lepton numberLepton numberIn particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0...

(In the Standard ModelStandard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

) - Conservation of flavor (violated by the weak interactionWeak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

) - Conservation of parityParity (physics)In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
- Invariance under Charge conjugation
- Invariance under time reversalT-symmetryT Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...
- CP symmetry, the combination of charge and parity conjugation (equivalent to time reversal if CPT holds)

## See also

- Charge conservationCharge conservationIn physics, charge conservation is the principle that electric charge can neither be created nor destroyed. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved...
- Conserved quantityConserved quantityIn mathematics, a conserved quantity of a dynamical system is a function H of the dependent variables that is a constant along each trajectory of the system. A conserved quantity can be a useful tool for qualitative analysis...

- Some kinds of helicity are conserved in dissipationless limit: hydrodynamical helicity, magnetic helicityMagnetic helicityIn plasma physics, magnetic helicity is the extent to which a magnetic field "wraps around itself". It is a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field...

, cross-helicity.

- Some kinds of helicity are conserved in dissipationless limit: hydrodynamical helicity, magnetic helicity
- Continuity equationContinuity equationA continuity equation in physics is a differential equation that describes the transport of a conserved quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described...
- Noether's theoremNoether's theoremNoether's theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918...
- Philosophy of physicsPhilosophy of physicsIn philosophy, the philosophy of physics studies the fundamental philosophical questions underlying modern physics, the study of matter and energy and how they interact. The philosophy of physics begins by reflecting on the basic metaphysical and epistemological questions posed by physics:...
- Symmetry in physicsSymmetry in physicsIn physics, symmetry includes all features of a physical system that exhibit the property of symmetry—that is, under certain transformations, aspects of these systems are "unchanged", according to a particular observation...
- Totalitarian principleTotalitarian principleIn quantum mechanics, Gell-Mann's Totalitarian Principle states: "Everything not forbidden is compulsory." Physicist Murray Gell-Mann borrowed this expression from T.H...

## External links

- Conservation Laws — an online textbook