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Advanced Science Letters

What Does Probability Theory Tell Us About Bell's Inequality?

Andrei Yu. Khrennikov

Published Dec 1, 2009• 4 citations
Publisher

Abstract

In this paper we would like to stress that, besides two commonly discussed conditions inducing violation of Bell's inequality—nonlocality and death of realism—there is the third condition having th ...
DOI
10.1166/asl.2009.1051

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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 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 derive the unique conclusion on the relation between quantum and classical models.