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In physics, a 'conservation law' states that a particular measurable property of an isolated physical system does not change as the system evolves.
Any particular conservation law is a mathematical identity to certain symmetry of a physical system.
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 energy

★ Conservation of linear momentum

★ Conservation of angular momentum

★ Conservation of electric charge

★ Conservation of color charge

★ Conservation of probability
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 mass (applies for low speeds)

★ Conservation of baryon number (See chiral anomaly)

★ Conservation of lepton number (In the Standard Model)

★ Conservation of flavor (violated by the weak interaction)

★ Conservation of parity

★ CP symmetry

Contents

Global and local conservation laws

Philosophy of conservation laws

See also

References

External links

Global and local conservation laws

A conserved property of a physical system may be conserved either locally, or just globally. To be conserved locally, the property must flow from one place to another, and not just disappear one place and reappear another. On the other hand, if the conserved quantity is allowed to appear somewhere else, but with the total amount of the conserved quantity remaining the same, then we have a global conservation law.
A local symmetry has mediator particles and fields, like the electromagnetic field (photon) for the electric charge, which stems from a local U(1)-symmetry, the gauge freedom of the electrodynamics. There is a corresponding force, the Coulomb-force.
The angular momentum stems from a global rotation symmetry, and there is no interaction between two rotating bodies, which have their own angular momentum.

Philosophy of conservation laws

Noether's theorem expresses the equivalence which exists between conservation laws and the invariance of physical laws with respect to certain transformations (typically called "symmetries") for systems which obey the Principle of least action and hence having a Lagrangian and a Hamiltonian (See Classical mechanics, Hamiltonian mechanics for details). For instance, translational time invariance implies that energy is conserved, translational invariance of space implies that momentum is conserved, and rotational invariance implies that angular momentum is conserved.
Thus, philosophically conservation laws can be considered as a statement that nothing depends on certain quantity (say, on location in space, or location in time, etc.).
''Things that remain unchanged, in the midst of change''
The idea that some things remain unchanged throughout the evolution of the universe has been motivating philosophers and scientists alike throughout history.
Quantities that are conserved, the ''invariants'', seem to preserve what some would like to call 'physical reality' and seem to be more fundamental than many other physical quantities. These laws bring a great deal of simplicity into the structure of a physical theory. They are the ultimate basis for most solutions of the equations of physics.

See also

★ Continuity equation

★ Philosophy of physics

★ Noether's theorem

References

★ Stenger, Victor J., 2000. ''Timeless Reality: Symmetry, Simplicity, and Multiple Universes''. Prometheus Books. Chpt. 12 is a gentle introduction to symmetry, invariance, and conservation laws.

External links

★ Conservation Laws — an online textbook