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If laws of physics are time symmetric, is motion forwards and backwards in time only defined in terms of increase or decrease in entropy (low entropy is past and High entropy is future)? If it is so, would reversing a particular process (broken egg reassembling itself) count as reversing it's time? If not what constitutes backward/forward motion in time?

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The standard model is not symmetric under time reversal. In particular, the weak interactions violate this (it is often referred to as CP violation, but this is equivalent by CPT invariance). This discovery was awarded the 1980 Nobel prize in physics.

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    $\begingroup$ This is not the reason there is a macroscopic arrow of time though $\endgroup$
    – J Kusin
    Dec 11, 2020 at 6:45
  • $\begingroup$ @JKusin This is breaking of time-reversal at a fundamental level. Your argument about its equivalence to CP breaking somehow invalidating this fact make no sense. I also will not parrot some vague statement about entropy when for any closed Hamiltonian system entropy is a conserved quantity, as follows from Liouville's theorem. $\endgroup$ Dec 11, 2020 at 20:16
  • $\begingroup$ "Time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe." That plainly states the weak force is not the or a reason for the "physical basis for arrow of time". en.wikipedia.org/wiki/T-symmetry You must look to initial conditons i.e. Big Bang to get the second law from totally symmetric laws (CPT) $\endgroup$
    – J Kusin
    Dec 12, 2020 at 0:46
  • $\begingroup$ @JKusin You can cite wikipedia all you like, it doesn't make this assertion more sensible. Time-reversal is broken. The fact that this is equivalent to the breaking of some other symmetry is irrelevant. $\endgroup$ Dec 12, 2020 at 1:41
  • $\begingroup$ Fine then read this link.springer.com/article/10.1007/s10838-016-9342-z Time-assymetry of any physical law is not a sufficient conditon for the arrow of time $\endgroup$
    – J Kusin
    Dec 12, 2020 at 6:24
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Macroscopic arrow emerges due to two things essentialy.

(1) "The current consensus hinges upon the Boltzmann-Shannon identification of the logarithm of phase space volume with the negative of Shannon information, and hence to entropy. In this notion, a fixed initial state of a macroscopic system corresponds to relatively low entropy because the coordinates of the molecules of the body are constrained. As the system evolves in the presence of dissipation, the molecular coordinates can move into larger volumes of phase space, becoming more uncertain, and thus leading to increase in entropy."

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(2) "Time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe."

The laws of physics ARE completely time symmetric via the CPT theorem. A single arrow arises/emerges from symmetrical laws because we hypothesize a very low entropy initial condition (2) for a macroscopic system (1).

The macroscopic system in question is the environment/universe, and it's entropy is always increasing or staying the same with (1) + (2). A subsystem can lower it's entropy, but I wouldn't call it going back in time, even though that isn't a totally wrong notion due to how we equate forward in time with an incease in entropy of the environment.

Both quotes from here: https://en.wikipedia.org/wiki/T-symmetry

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If laws of physics are time symmetric

There are many tests to check if physical law not gets broken under some symmetry operations, including but not limited to :

  • Translation in space
  • Translation in time
  • Rotation through a fixed angle
  • Uniform velocity in a straight line (Lorentz transformation)
  • Reversal of time
  • Reflection of space
  • Interchange of identical atoms or identical particles
  • Quantum-mechanical phase
  • Matter-antimatter (charge conjugation)

Credit goes to Feynman lectures. Thus physical law does not necessary have to be time-symmetric (but usually it is). Sometimes time symmetry may be broken and/or others, depends on exact law. For example, charge conjugation symmetry must be broken for some law(s), because now we are living in a universe which is dominated mainly by matter. Antimatter amounts are minuscule. But in the beginning of universe all laws were C-symmetric, because these matter/antimatter amounts were more or less equal.

would reversing a particular process (broken egg reassembling itself) count as reversing it's time?

Basically, yes. Making an entropy constantly decreasing for some process, it means a reversed time arrow for that process. Easiest way to visualize this is to see movie backwards. In the backwards movie view mode, you exactly reverse time arrow of a scene.

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