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Conservation law
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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. The following list is a partial listing of conservation laws that have never been shown to be inexact (actually though, in General relativity energy, momentum and angular momentum are not conserved in general because a general curved spacetime manifold would not possess Killing symmetries for translations or rotations):

There are also approximate conservation laws (i.e. true approximately for short time scales) in particle physics like those of baryon number (which is NOT really conserved, if for nothing else but chiral anomaly, speculations about GUT theories aside) and strangeness (which is violated by the weak interaction!).

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") (This only applies to systems describable by a Lagrangian). There is an analogous theorem for Hamiltonian mechanics. 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.

Some conservation laws hold in many circumstances, but exceptions to them have been observed. (If a quantity isn't conserved, in what sense is it a conservation law???) Such is the violation of parity conservation; apparently the universe has "handedness" (right versus left).

Philosophy of Conservation Laws

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 one 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.