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First of all, I'm not major in physics and the question might seems stupid, as I'm layman studying for my self-interest and I really don't know much about it. I only think it might open some understanding if I just start to ask some questions. So please correct me if I'm wrong.

If I understand it correctly, kaon has two decay pathways that give rise to different pions under complex transformation. This is considered as CP violation.

As I learned from Wikipedia, CPT symmetry appears that if a process violates CP symmetry, then it will violate T symmetry also. Thus, the kaon case also violates T symmetry, and this might happen to other particles other than kaon.

Now imagine a fictional "mirror" universe, where all the matters are antimatters and vice versa. Will the time arrow in this universe in the opposite direction with the time arrow in our universe? How can we tell that?

Please correct me if I'm wrong and give me some explanations regarding this problems in layman terms, and also some formal formulations, if any, so I can relate the formal materials and the layman analogy. Thanks!

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Time is a variable like space, and in a self contained universe each physicist in his/her universe will define as positive the direction given by the arrow of time in thermodynamics, so reversal in the two universes would not mean anything.

As the arrow of time is defined by classical physics, thermodynamics, the two universes are independent so no time can be checked. The term "universe" includes everything that is, so there will be no way to communicate between an antimatter universe and ours.

I can imagine an elaborate model might be made of two, a matter and an antimatter, universes, but it will depend on how this is hypothesized, to see if there is an overlap that might be studied. Imo it is science fiction, not physics.

Now if one hypothesizes that this, our one universe in the beginning split into a matter part and an antimatter part, there are a lot of other things to check than CP violation. In any case it will mean that CP violation predictions for calculations of lifetimes etc will be going the opposite way for the two parts, but time would have the same direction since there would have been a thermodynamic connection before the split.

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