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- The weak interactions are different going forward and going backwards in time. But how can we know this, since we can’t actually reverse time?

In Sean Carroll's lectures Mysteries of Modern Physics: Time, he talks about the the CPLEAR experiment, which showed that the weak interactions are different going forward and going backwards in time. But it seems like there is a big assumption: reversing a particle interaction means that it is happening backwards in time. But it isn't, no time reversal is actually happening. How do we know that if we could actually reverse time, we would see kaons turning into anti-kaons at the same rate?