Notes:
Einstein thought that surely God would know what path the photon had taken. He claimed therefore that quantum physics was incomplete. That we should add something so that we would get a so called local realistic model. That is the photon decided locally at the mirror where to go and after the passage of the half transparant mirror the photon had decided a or b.
Bell proved in the sixties that ALL local realistic models in specific experiments, where correlations between two particles were measured, would result in different outcomes than the outcomes predicted by quantum theory.
The crucial experiments have been done an qp was confirmed and all local realistic theories were rejected. So the measurement really is a crucial element in the formalism.
IT doesn’t just show us the result of an earlier process but it has an ‘active’ contributon.
Finally analysis of this situation shows clearly that some connectedness between far apart parts of the system is going on.