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Bell's inequality is a no-go theorem contrasting crucial correlations of physical observables in QM to those of the world as described by classical mechanics, essentially local hidden variables theories serving as a viable "explanation" of QM: QM inevitably violates these inequalities, as observed. Further use for the CHSH inequality generalization.

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Bell's theorem for dummies, how does it work?

I will attempt to answer questions 1-3 as best I can. The others, I defer to the other excellent answers here provided. Before I start: "The inequalities between the two hypotheses rise when the part …
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