Quantum Mechanics Thought Experiment If a photon approaches a filter with a 0.5 chance of passing through, we have no way of knowing whether it will pass or not. All we know is that if we do the experiment many times, it will pass through 50% of the time.
So, a thought experiment: if we were able to watch a photon pass through the filter, and then if we could rewind time somehow and replay the scene so that all conditions in the universe were identical - does quantum theory have anything to say currently about whether we would see:
(A) the photon pass through every time the scenario was replayed.
(B) the photon pass through 50% of the time, just as if you repeated the experiment in the real world.
Or is the answer just, "we don't know"?
 A: I jump into this question with some trepidation, given that the premise is wildly speculative. But it’s interesting to think about because such an experiment might be able to distinguish between certain classes of quantum mechanics interpretations, which in reality are indistinguishable.
Rephrasing your question: Is the randomness inherent to quantum mechanics fundamental, or simply apparent? Probably most interpretations of QM come down on the side of fundamental randomness. At least one, however, says that QM only seems random (due to the complexity of the universe), and there is additional invisible information (“hidden variables”) that would “explain” every quantum event and reveal them to be deterministic if only we had access to it.
Both of the above classes of QM interpretations predict precisely the same results of experiments in our universe because, as far as we know, there’s no way for us to rewind time and repeatedly measure the outcome of the same quantum event. The best we can do is attempt to replicate an experiment, but there’s no way to ensure that everything is exactly the same.
But suppose we could? Physics would have the tool to resolve one of its greatest interpretational mysteries.
Edit: The Transactional Interpretation of Quantum Mechanics (TIQM) is an interesting case. It would appear to occupy a third category, in which despite the lack of hidden variables, quantum randomness is only apparent. From John Cramer’s book on the subject, The Quantum Handshake (2016), Section 5.4 “The Mechanism of Transaction Formation”, pp. 66-67,

Thus, mutual offer/confirmation perturbations of emitter and absorber acting on each other create a frequency-matched pair of dipole resonators as mixed states, and this dynamically unstable system either exponentially avalanches to the formation of a complete transaction, or it disappears when a competing transaction forms. In a universe full of particles, this process does not occur in isolation, and both emitter and absorber are also randomly perturbed by waves from other systems that can randomly drive the exponential instability in either direction. This is the source of randomness in quantum processes.

So if time could be rewound (a particularly apt thought experiment for this interpretation), Cramer would seem to suggest that the same random perturbations would occur (because they are due to the state of reality), thus resulting in the same outcomes. That is, in TIQM, situation (A) is true.
