# What goes wrong, theoretically, when we reverse time?

(Please bear with me if this is a stupid question; I'm not a physicist, just a curious student.)

I know that Noether's Theorem links symmetries to conserved quantities: the fact that the laws of physics work anywhere in space, for example, is linked to conservation of linear momentum.

In particular, if the direction of time were reversed (we replaced all the $$t$$s with $$-t$$s), we would have a "conservation of entropy". But the second law of thermodynamics says that entropy isn't conserved. Therefore, the laws of physics aren't symmetric under time-reversal.

This seems strange, because the laws of physics are symmetric under time-translation (this gets us conservation of energy, which does seem to be true).

So my question is: what law of physics breaks under time-reversal that doesn't break under time-translation?

• "if the direction of time were reversed [...] we would have a conservation of entropy" - This is not true. The theoretical derivation of the entropy increase (at least the one that I've seen) is time symmetrical with the minimal entropy at the present moment. The actual steady entropy increase is not a theoretical law that you could "reverse", but an experimental fact. So your question may be based on a poor assumption. Theory and experiment are different. You can silently lift a cup from a saucer, but cannot put it back down without a sound, even though in theory this is time reversible. – safesphere Jan 29 at 21:22
• Possible duplicate: physics.stackexchange.com/q/185264/2451 – Qmechanic Jan 30 at 9:05