The converse of Noether's theorem does not turn out to be true in general. Noether showed that if there is a symmetry in the system then there is a correspondi

The converse of Noether's theorem does not turn out to be true in general. Noether showed that if there is a symmetry in the system then there is a corresponding conservation law. But the existence of a conserved quantity does not (in general) imply the existence of some symmetry in the physical system. (I should note that there are more careful ways to get something that looks like the converse of Noether's theorem, but the literature is fairly complicated -- you have to distinguish between trivial conservation laws and non-trivial conservation laws. Here's one answer online: http://physics.stackexchange.com/questions/24596/is-the-converse-of-noethers-first-theorem-true-every-conservation-law-has-a-sy http://physics.stackexchange.com/questions/24596/is-the-conv...)