Ada Lovelace Day

The memory of some system wit hysteresis implies some change of internal state and is not at issue with the kind of time invariance Noether's law refers to. Unless you use rules/laws that abstract away that internal state to get a description of what is going on, then you end up with a system that might not conserve energy (via exchanging it with whatever you abstracted away). Otherwise, "repeat an experiment at a different time" implies setting up everything the same, including the same starting point in whatever hysteresis effect you are dealing with.

Thanks - it's now (still) clear as mud :) I wonder how this handles hysteresis.

I didn't have a chance to read the wikipedia article beyond seeing it had an introduction section. Her theorem basically amounts to there being an equivalence between certain kinds of symmetries in laws of physics and laws that state something is conserved. For example, the idea that an experiment should act the same anywhere if you recreate the same conditions, i.e. just moving everything from empty point A to empty point B, mathematically implies that momentum is conserved. Rotational symmetry, that turning things to point in a different direction doesn't change things, implies conservation of angular momentum, and being able to repeat an experiment at a different time implies conservation of energy. As long as some really basic laws of physics (basically an extension of Newton's laws) are true, then conservation of energy and the time symmetry will always be a pair, with violation of the former implying violation of the latter.

You're right: I'm confused forwards and backwards.