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(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?

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    $\begingroup$ "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. $\endgroup$
    – safesphere
    Jan 29, 2019 at 21:22
  • $\begingroup$ Possible duplicate: physics.stackexchange.com/q/185264/2451 $\endgroup$
    – Qmechanic ♦
    Jan 30, 2019 at 9:05

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Time reversal symmetry is a discrete symmetry, whereas spatial translation is a continuous one. I can do a very big or very small spatial translation, but time reversal isn't like that; it's more like the two states of a light switch. Noether's theorem gets conservation laws from continuous symmetries only. Indeed, time translation is a continuous symmetry that gives us energy conservation (well, Hamiltonian conservation if we're being pedantic, but 9 times out of 10 that's as good as the same thing).

It's not clear to me why entropy, in particular, is what you expected to be conserved, but I think your reasoning is probably based on the direction-of-time concept. For what it's worth, the question of why there's a direction of time at all, with entropy increasing along it, is something physicists debate to this day.

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The Weak Nuclear Force throws off a lot of symmetries. Time reversal among them T-Reversal. Time reversals

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