True randomness in QM

[Alex K]

I think it goes too far to say that the consensus is that #2 true randomness is at the bottom of Quantum uncertainty. There is a consensus to use something like the Copenhagen interpretation (or should I say prescription) for all practical calculations in order to not get bogged down with metaphysical questions. That means that virtually everyone, for pragmatic reasons, uses a prescription to calculate results which does not contain rhe additional information (so called hidden variables) which would uniquely determine the result of a measurement involving quantum uncertainty. I believe people don't necessarily choose to do that because they believe in their hearts that there must be true randomness at the bottom of QM, but rather because it makes no difference for the result of any calculation if we included a (usually more complicated) deterministic description with hidden variables : we don't know the values of these hidden variables anyways, and they are constructed precisely such that ignorance of the hidden variable reproduces the same statistical distribution as true quantum randomness. Someone who "believes" in a deterministic interpretation of qm will generally still use the copenhagen or similar prescriptions to calculate concrete results because it is simple.

Doesn't Bell's theorem rule out hidden variables?

No, it's only a statement about the properties of the hidden variables. The fact that the Bell inequalities are obviously violated in Nature only rules out local theories of hidden variables - This means that one cannot write down a quantum theory in which the hidden variables are a property of, say, individual particles only, without running afoul of observations. If you for example make an experiment where two quantum randomly polarized, but entangled photons are sent out in opposite directions and send them to two far apart polarization detectors, a hidden variable which deterministically determines the outcome of the polarization measurement on one side must depend on the setting of the polarimeter (or an equivalent value) on the other side. That's exactly the kind of game Bell plays in his papers.

And if we theoretically were to replay the universe many times would the outcomes be the exact same? If so, doesn't that imply that true randomness doesn't exist?

That question is kind of equivalent to the question whether true randomness exists - or in other words, whether the state of the universe at one point in time uniquely determines its future development. It is not known.