Microscopically, there is no time arrow.
No. There is weak force.
Myth: The arrow of time is a consequence of CP-symmetry violation.
The weak nuclear interactions violate the CP symmetry which is equivalent to saying that they violate the T symmetry. Is it the reason why eggs don’t unbreak? Of course not. There are two basic ways to see why. First, the weak interactions much like all other interactions preserve the CPT symmetry – there is extensive theoretical as well as experimental evidence supporting this assertion. And the CPT symmetry would be enough to show that eggs break as often as unbreak. More precisely, eggs break as often as mirror anti-eggs unbreak. ;-)
— Myths about the arrow of time
— Lubos Motl
Weak force’s T-symmetry-violation has nothing to do with the time arrow.
In other words, microscopic time arrow has nothing to do with the macroscopic time arrow.
— Me@2020-03-21 07:56:01 PM
About T-violation and the arrow of time: the simple answer is that the weak interactions are perfectly unitary, even if they are not T-invariant. They don’t affect the entropy in any way, so they don’t help with the arrow of time.
A bit more carefully: if you did want to explain the arrow of time using microscopic dynamics, you would have to argue that there exist more solutions to the equations of motion in which entropy grows than solutions in which entropy decreases. But CPT invariance is enough to guarantee that that’s not true. For any trajectory (or ensemble of trajectories, or evolution of a distribution function) in which the entropy changes in one way, there is another trajectory (or set…) in which the entropy changes in precisely the opposite way: the CPT conjugate. Such laws of physics do not in and of themselves pick out what we think of as the arrow of time.
People talk about the “arrow of time of the weak interactions,” but ask yourself: in which direction does it point? There just isn’t any direct relationship to entropy.
— Sean Carroll
2020.03.21 Saturday (c) All rights reserved by ACHK