In physics we have the CPT-theorem which guarantees time-reversal symmetry of dynamical evolution (although in some edge cases we will also have to reverse parity and charge).
It seems clear enough that the Schroedinger equation on its own determines past states as well as it determines future states. However, how does the so-called "Measurement Process" fit into this, where we place Psi discontinuously into an eigenstate? Do people ignore this when they say physics is reversible? Does CPT refer only to pure Schroedinger evolution? Or is "placing into an eigenstate" an idealization?