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 is a partial listing of conservation laws that 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.
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.
Philosophy of Conservation Laws
- 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 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.