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The Schrödinger equation does obey T-symmetry, so the time evolution of a state would obey it.. the fact that the measurement collapses a wave function at some later time doesn’t imply that time has a preferred direction
For instance if you start in a position eigenstate, let it evolve in time, and then measure the momentum.. there’s no reason why you can’t run time backwards and go from a p to an x eigenstate instead.. they are both valid physical processes
Do there are valid physical process which instantaneously change a particle from an eigenstate into a superposition state?
one could say when you measure the position then it’s “instantaneously” in a superposition or eigenstates
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