Nonlocality as well as rejection of realism are only sufficient (but non-necessary!) conditions for violation of Bell’s inequality

In this review we remind the viewpoint that violation of Bell’s inequality might be interpreted not only as an evidence of the alternative – either nonlocality or “death of reality” (under the assumption the quantum mechanics is incomplete). Violation of Bell’s type inequalities is a well known sufficient condition of probabilistic incompatibility of random variables – impossibility to realize them on a single probability space. Thus, in fact, we should take into account an additional interpretation of violation of Bell’s inequality – a few pairs of random variables (two-dimensional vector variables) involved in the EPR–Bohm experiment are incompatible. They could not be realized on a single Kolmogorov probability space. Thus, one can choose between: (a) completeness of quantum mechanics; (b) nonlocality; (c) “ death of reality”; (d) non-Kolmogorovness. In any event, violation of Bell’s inequality has a variety of possible interpretations. Hence, it could not be used to obtain the definite conclusion on the relation between quantum and classical models.