The laws of physics are invariant under CPT transformations reversing time, inverting space and flipping charges. Almost so. The collapse of the wave function is the odd man out. Can the time direction of the collapse of the wave function be reversed so that the collapse happened in the past?
The collapse presupposed the Schroedinger picture. Can a collapse occur in the Heisenberg picture, with the projection operator $P$ replaced with $UPU^{1}$?
The collapse is a non-unitary operation. It cannot be reversed (undone). Typically, we establish contact between the studied system and a macroscopic body (apparatus) that we are unable to describe by a wave-function. Also, we are not able to describe rigorously the process that follows this contact. The projection transformation done by such an apparatus on the wave-function is an irreversible truncation of the wave-function. Therefore the expression $UPU^{-1}$ is not correct because U is a unitary transformation, and this is not our case.
