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There isn't a Noether conservation law corresponding to reflective symmetry, is there? The situation where Noether's theorem applies is where you have a smooth
by gjm11 11y ago
There isn't a Noether conservation law corresponding to reflective symmetry, is there? The situation where Noether's theorem applies is where you have a smooth family of symmetries, with one of them being the identity (i.e., the trivial symmetry where you don't change anything at all), but reflections don't fit that pattern.
On the other hand, if the laws of physics are invariant under reflections then they are also invariant under rotations because you can make rotations out of reflections. So you could say that conservation of angular momentum is the corresponding conservation law. But (so far as anyone knows, I think) the laws of physics really are rotation-invariant and conservation of angular momentum really does hold.
- JadeNB 11y ago> On the other hand, if the laws of physics are invariant under reflections then they are also invariant under rotations because you can make rotations out of reflections. So you could say that conservation of angular momentum is the corresponding conservation law. This is an interesting idea, but, I think, too weak. It is true that every rotation is a composition of two reflections, but there's such an important difference between rotations (orientation-preserving) and reflections (orientation-reversing) that I think one shouldn't say that invariance under the former implies anything about invariance under the latter.