As Bell wrote "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local"(https://en.wikipedia.org/wiki/Bell%27s_theorem). Therefore, if a quantum mechanical local theory is postulated, it has been proven that no hidden variable can exist; isn't this philosophically impossible to prove that no hidden variable exists? I mean, if we cannot see inside a bottle, in the same way that we cannot see a hidden variable, then how can we say if anything is there or not?

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    Bell's argument isn't against the existence of hidden variables, but rather the viability of hidden variables as an explanation. (This is a good question, just not up for writing an answer at the moment.)
    – Nat
    Feb 25 '20 at 19:03
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    Also worth noting Bell's argument is not about hidden variables theories in general, it's specifically about "local" hidden variables theories where there can be no faster than light influences. It does not rule out hidden variables theories that violate this condition like Bohmian mechanics, that's why he says of hidden variables theories that "if it agrees with quantum mechanics it will not be local" (meaning he does accept the possibility of non-local hidden variables theories that agree with observed results of quantum mechanics).
    – Hypnosifl
    Feb 25 '20 at 19:19
  • BTW I gave a simple analogy to explain one of Bell's inequalities and why it can't be violated in a local hidden variables theory in this answer on the physics stackexchange.
    – Hypnosifl
    Feb 25 '20 at 19:30
  • Thank you for your comments. I think I get it now: all Bell says is that no hidden variable is needed to be assumed to complete a local quantum mechanical theory, and this argument doesn't mean that no hidden variable can exist; it just means that even if they do, it doesn't matter to us. Feb 26 '20 at 13:54
  • Glad to see you're still attacking the metaphysical implications of quantum theory!
    – J D
    Feb 26 '20 at 17:06

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