Conservation law

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.

Conservation Laws

A partial listing of conservation laws that are said to be exact laws, or more precisely have never been shown to be inexact:

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

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, time invariance implies that energy is conserved, translation invariance implies that momentum is conserved, and rotation invariance implies that angular momentum is conserved.

Things that remain unchanged, in the midst of change

The idea that some things remain unchanging throughout the evolution of the universe has been motivating philosophers and scientists alike for a long time.

In fact, quantities that are conserved, the invariants, seem to preserve what some would like to call some kind of a 'physical reality' and seem to have a more meaningful existence 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.

Reference

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

Conservation laws

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