It's been a few years since my physics degree. But I've been wondering: if you look at pictures of collisions at CERN, isn't it obvious which way time flows - simply on a probability basis? The likelihood of a huge cascade reversing into a proton and antiproton is vanishingly small. CPT seems violated to me. Am I missing something?
This may not be the answer you’re looking for, but your sense of what is probable may have something to do with the way in which you categorize the states. Sure, it’s more likely to end up with a huge cascade, but there are many many different outcomes which you would call a “huge cascade”. The probability of one specific cascade, with a particular distribution of energy between all the particles, is also vanishingly small. The notion of many similar final states is encapsulated in the notion of “density of states”. CPT symmetry, on the other hand relates to the matrix element, or “amplitude” for a given process. Fermi’s golden rule tells us that the rate for a given process is the matrix element times the density of states.