0 Einstein and Bell , von Mises and Kolmogorov : reality and locality , frequency and probability Andrei Khrennikov

We perform analysis of Bell's arguments (and their generalizations) on the basis of the frequency approach to probability theory (R. von Mises, 1919). This analysis demonstrated that there are no physical arguments which support the existence of 'probability dis-tributions' which were formally used in all investigations based on the conventional (Kolmogorov, 1933) approach to probability theory. In fact, probability distributions may fluctuate from run to run (no collectives). This chaos on the microlevel need not contradict to the stabilization of frequencies for physical observables. We discuss the relation to the completeness of quantum mechanics (and the efficiency of detectors). If micro-reality is also statistically stable (as the macro-reality), then the only root of the violation of Bell's inequality (or CHSH inequality) is the dependence of collectives corresponding to two different measurement devices. Such a dependence implies the violation of the factorization rule for the simultaneous probability distribution. Formally this rule coincides with the well known BCHS locality condition (or outcome independence condition). However, von Mises' approach implies completely different interpretation of dependence. It is not a dependence of events, but it is a dependence of collectives (merely via the same preparation procedure).