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?
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.
