According to time-reversal symmetry, if I reversed time, the laws of physics would still hold up, so if I dropped a ball to the ground, then in reverse order all of the light and sound and frictional heating that it created would combine in one spot to basically kick the ball into my hand from the ground. Let's say I'm pushing two dice forward on a table by pushing one with my finger and letting it push the other— how would this work in reverse? What causes the second die to move with the first? Why is the first one moving, anyway? (Ignore air displacement- for the purposes of this question, we're in a vacuum)

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    $\begingroup$ I believe time reversal symmetry works for certain physical laws, but not to the observable universe due to the Second law of Thermodynamics. $\endgroup$ – Ed Yablecki Jan 4 '16 at 22:24
  • $\begingroup$ @EdYablecki: The second law of thermodynamics is the definition of temperature. In most physical situations there is no temperature because the system is not even near equilibrium. Contrary to popular belief statistical mechanics doesn't give us an argument against time reversal. It actually requires a poorly understood and most likely unprovable axiom to force irreversibility into statistical mechanics. $\endgroup$ – CuriousOne Jan 5 '16 at 2:53
  • $\begingroup$ The reason why you don't see time reversal symmetry in physics is because it doesn't work for open systems. In open systems the outgoing and incoming solutions are not equivalent. In closed systems, however, this distinction does not exist, since everything gets reflected at the boundaries of the system. $\endgroup$ – CuriousOne Jan 5 '16 at 2:55
  • $\begingroup$ Ordinarily finger pushes die 1, which pushes die 2. In reverse -- die 2 pushes die 1, which pushes finger. What 'causes' die 2 to move? Just as you said, the culmination of heat and sound waves that were produced by the die in the original situation. $\endgroup$ – user66309 Jan 6 '16 at 22:30

Not all laws of physics would be invariant under time reversal so you you should first specify which law you are interested in. Let us assume it is the Newton's Second Law, which is time reversal invariant. This means that the "reverse movement" of a system of particles is acceptable, as long as it does not violate any fundamental principle. For example a dice moving freely in a friction-less horizontal plane could reverse its movement according to the Newton's Second Law . It does not happens though because momentum should be conserved. You should not talk about light and sound and whatever combining to push your dice upwards as long as you are interested only in the Newton's second law time reversibility. On the other hand, for systems with many particles, a gas for example, we can have zero momentum, zero angular momentum and so on. However we don't see the time reversal, admitted my mechanics, because it would violate second law of thermodynamics, which, by the way is not a definition of temperature as mentioned above.


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