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I have read at this Phys.SE post (What exactly is the physical picture of Time Reversal Symmetry) that even though classical mechanics are time reversible, a system will never spontaneously revert its direction thanks to the existence of conservation laws.

Could someone explain this?

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veronika
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    Where exactly did you read that? A system will not "spontaneously revert" its direction simply because classical systems are deterministic and will not "spontaneously" do anything. Time reversibility means that time reversal of any solution is also a solution to the same equations of motion (but with different initial state). Classical conservation laws derive from continuous symmetries of a system, discrete symmetries give "selection rules". – Conifold Feb 25 '17 at 22:17
  • -1. You should always provide a link instead of saying "I have read somewhere that..." The context of your question is important for understanding what you mean. – sammy gerbil Feb 25 '17 at 23:03
  • @Conifold Thanks for the comment and the link I edited the question – veronika Feb 26 '17 at 06:29
  • @sammygerbil ok,ok i edited the question – veronika Feb 26 '17 at 06:31

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Time reversible does not mean you can reverse time, and thus direction of motion, at any time you'd like. You have to also reverse initial conditions. Thus, when you start your model, you change all t to -t, not in the middle of it.

If you did reverse direction of motion and time you will have reversed momentum and violate the laws of momentum conservation.

The idea on time reversal is to have everything go backward from the beginning. All those laws and eom's then hold.

Bob Bee
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