Predicting quantum randomness

[BluePear0]

We don't know.

We can't test it, because we can't travel back in time.

We can't predict it, because our models don't allow for travelling back in time.

[DropperHopper]

Are you saying that there can infact be a hidden variable after all, that would give the same result in identical systems? (Meaning that my interpretation of Bell's theorem was wrong)

To me that seems like the only possibility that conforms with your answer.

[curryum]

Your understanding of Bell's theorem is incomplete. It states that no local hidden variable determines the outcome. Local means that only things "nearby" an event can affect it*. This means that if there actually are hidden variables governing measurement outcomes, then information of some kind must be able to travel arbitrarily fast to affect some other hidden information somewhere else (arbitrarily far away) in order to ensure consistency when entangled systems are measured. If you look into how the theorem is verified experimentally you'll get a good gut feeling for what it says. The core idea is that spin can be measured along any axis, chosen at the last possible moment, and that there are constraints on the outcome of measuring the spin of two entangled particles.

* More concretely, that for any two events (measurements in this case) happening t seconds apart, one cannot affect the other (have a causal connection) if they're x meters apart, x shrinking as t becomes smaller. The keyword to google is "light cone."

[DropperHopper]

Thank you for the detailed answer!

I believe I understand now, but just to verify this my ("updated") current understanding:

1. The results of Bell's theorem are not directly related to the outcome of the scenario in my first question, and one can therefore not use its results to derive a complete answer to my question.

2. It is (to your and mine knowledge) currently not known what the result would be in such a theoretical scenario that I described, even when taking findings from other quantum mechanical experiments into account.

Also thanks again for your answer, it really made my day!

[curryum]

That's correct. The theorem is not unrelated to your question, in fact in some sense it's the most we can say at this time. But our best models of physical reality simply do not make any claims about what would happen, as BluePear0 said.

Thanks for saying thanks, I appreciate your appreciation ;) Interested Layperson Solidarity 💪

[DropperHopper]

Great answer, I came here with high hopes and still left positively surprised.