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Loosely speaking, the Bell theorem says that any theory making the same measurable predictions as QM must necessarily be "nonlocal" in the Bell sense. (Here Bell locality is different from other notions of locality such as signal locality or locality of the Lagrangian. By the Bell theorem, I mean not only the original Bell inequality and its close cousin CHSH inequality, but also the results such as GHZ theorem and Hardy theorem which involve only equalities, not inequalities.) However, any such theorem actually uses some additional assumptions, so many people argue that it is some of those additional assumptions, not locality, that is violated by QM (and by Nature). The aim of this thread is to make a list of all these additional assumptions that are necessary to prove the Bell theorem. An additional aim is to make the list of assumptions that are used in some

- macroscopic realism (macroscopic measurement outcomes are objective, i.e. not merely a subjective experience of an agent)

- statistical independence of the choice of parameters (the choices of which observables will be measured by different apparatuses are not mutually correlated)

- Reichenbach common cause principle (if two phenomena are correlated, then the correlation is caused either by their mutual influence or by a third common cause)

- no causation backwards in time

- determinism (unnecessary because some versions of the theorem use only probabilistic reasoning)

- Kolmogorov probability axioms (unnecessary because the GHZ theorem uses only perfect correlations, i.e. does not use probabilistic reasoning at all)

- hidden/additional variables (unnecessary because some versions of the theorem, e.g. those by Mermin in Am. J. Phys., use only directly perceptible macroscopic phenomena)

- microscopic realism (unnecessary for the same reason as hidden/additional variables)

*but not all*versions of the theorem, so are not really necessary. The following list of necessary and unnecessary assumptions is supposed to be preliminary, so I invite others to supplement and correct the list.**Necessary assumptions:**- macroscopic realism (macroscopic measurement outcomes are objective, i.e. not merely a subjective experience of an agent)

- statistical independence of the choice of parameters (the choices of which observables will be measured by different apparatuses are not mutually correlated)

- Reichenbach common cause principle (if two phenomena are correlated, then the correlation is caused either by their mutual influence or by a third common cause)

- no causation backwards in time

**Unnecessary assumptions:**- determinism (unnecessary because some versions of the theorem use only probabilistic reasoning)

- Kolmogorov probability axioms (unnecessary because the GHZ theorem uses only perfect correlations, i.e. does not use probabilistic reasoning at all)

- hidden/additional variables (unnecessary because some versions of the theorem, e.g. those by Mermin in Am. J. Phys., use only directly perceptible macroscopic phenomena)

- microscopic realism (unnecessary for the same reason as hidden/additional variables)

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