Liouville’s Theorem says that if you know that the state of the universe has to be one of the states in a set A, and then as time passes you run each universe in that set forwards, so that now you know that the universe is in set A’, then the “volume” of sets A and A’ has to be the same.
I don’t know what Liouville’s Theorem is, but this sounds like an objection to not being able to run time backwards.
Liouville’s Theorem says that if you know that the state of the universe has to be one of the states in a set A, and then as time passes you run each universe in that set forwards, so that now you know that the universe is in set A’, then the “volume” of sets A and A’ has to be the same.