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If you look at canonical derivations of the time reversal operator in quantum mechanics, it is always assumed that time reversal is a symmetry operation and therefore Wigner's theorem applies. But how do we know that time reversal is a symmetry operation? Is this an assumption? If so, what is it based on?

My intuition says that nature has an arrow of time and therefore time reversal should not be a symmetry transformation.

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  • $\begingroup$ First consider why your intuition says that nature has an arrow of time. Do you apply that to classical mechanics as well? Be suspicious of 'intuition', since nothing says that yours and mine are the same at all (much less the same as Wigner's). $\endgroup$ – Jon Custer Jul 27 '17 at 13:45
  • $\begingroup$ I consider nature having an arrow of time because there are dozens of processes which only happen in one direction of time. If there was no arrow of time, then i can't see, how these processes can be explained. But maybe i didn't understand your comment correctly. Was your intention to allude to the fluctuation theorem which solves loschmidt's paradoxon? $\endgroup$ – psicolor Jul 27 '17 at 15:26
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    $\begingroup$ No, simpler than that. Consider classical mechanics - there is complete time reversal symmetry (what goes up must come down). In the transition to standard quantum mechanics, what is changed? Now, if you want to talk about the transition from classical to quantum thermodynamics, that is a different kettle of fish, but as written you question does not seem to go in that direction. $\endgroup$ – Jon Custer Jul 27 '17 at 15:48

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