Noether's theorem relates continuous symmetries in the time evolution of a system to a conserved value. Many conserved values, such as conservation of momentum, can be described via this theorem. I'm interested in whether there is a meaningful conserved value for a cyclic time symmetry, $t^\prime = t + \tau$, where $\tau$ is not an infintessimal perturbation.
From what I can tell, that symmetry is not a continuous symmetry, so I should not be able to apply Nother's thorem. However, intuitively things like standing waves feel like there's a conservation law that governs them (less general than conservation of energy or momentum). Of course, feelings are not the same as mathematical truths. Is there a clever mathematical way to treat a cyclic time symmetry which permits the application of Nother's theorem or a related corollary, or is this simply a perfect example of what Nother's theorem can't speak to?
