> Neither Heisenberg's uncertainty principle nor Bell's inequality exclude the possibility, however small, that the Universe, including all observers inhabiting it, is in principle computable by a completely deterministic computer program...
Either I'm confused (definitely possible) or this is sort of implicitly equivocating between two different senses of "determinism". There are experiments we can perform that appear to demonstrate quantum randomness. Though it may sound superficially plausible that any particular such random outcome is actually the deterministic output of a hidden pseudorandom number generator, that hypothesis is ruled out by Bell's theorem.
What Bell's theorem can't rule out is the hypothesis that not only any individual quantum measurement, but the sum total of everything that happens in the universe including the experimenters' choices of what actions to take during the experiment, is all part of a single deterministic causal path for the whole universe, that just so happens to play out in such a way that we never see anything that visibly contradicts Bell's theorem. This can't really be empirically falsified, but there are various philosophy-of-science reasons to be a priori skeptical of it (depending on which philosophers of science you ask, of course).
Though it may sound superficially plausible that any particular such random outcome is actually the deterministic output of a hidden pseudorandom number generator, that hypothesis is ruled out by Bell's theorem.
As far as I understand Bell's theorem only rules out the hypothesis that the random outcomes are the deterministic output of a hidden pseudorandom number generator that obeys locality. There could be a deterministic, non local process that generates the "quantum randomness", and this could be detectable if it exists.
Any true non-local effect would however clash with the observation that the universe obeys the theory of relativity. Quantum mechanics can handle this by switching to quantum field theory, but non-local theories such an Bohmian mechanics cannot.
Bells theorem rules out only local hidden variables. Quantum mechanics itself works around the issue not because of indeterminism, but because wave function collapses everywhere at once in a non local way.
But perhaps we do not even need to abandon locality, if we modify it a bit. There is no good reason to believe that space at short distances should be similar to Euclidean space, one interesting hypothesis is that space is more like a graph, and entangled particles in addition to the normal long path through the graph are also connected directly, which allows measurement on one of them to change the state of the other.
I'm not a theoretical physicist, but I've heard in informal conversations with some that one idea being explored more now is that perhaps space itself is just a statistical emergent property of entanglement.
Leonard Susskind has several interesting lectures about it which can be found by searching for ER=EPR, but i hope the final theory would explain more of the strange behaviors of quantum mechanics, something like the theory outlined in https://blog.stephenwolfram.com/2015/12/what-is-spacetime-re...
Yes, the idea is that the particles themselves are connected to each other like two ends of a wormhole, so the signal about applied measurement doesn't have to take the 3km long path outside, but can directly go from one entangled particle to the other.
Entanglement would allow to send information if it was possible to clone quantum states https://en.wikipedia.org/wiki/No-communication_theorem#Some_.... If we are looking for a hidden variable theory, we need an explanation for no-cloning theorem independently from entanglement issue, so this does not add any additional restriction.
Either I'm confused (definitely possible) or this is sort of implicitly equivocating between two different senses of "determinism". There are experiments we can perform that appear to demonstrate quantum randomness. Though it may sound superficially plausible that any particular such random outcome is actually the deterministic output of a hidden pseudorandom number generator, that hypothesis is ruled out by Bell's theorem.
What Bell's theorem can't rule out is the hypothesis that not only any individual quantum measurement, but the sum total of everything that happens in the universe including the experimenters' choices of what actions to take during the experiment, is all part of a single deterministic causal path for the whole universe, that just so happens to play out in such a way that we never see anything that visibly contradicts Bell's theorem. This can't really be empirically falsified, but there are various philosophy-of-science reasons to be a priori skeptical of it (depending on which philosophers of science you ask, of course).