Bell's inequality: Physics meets Probability

Details Bell's inequality: Physics meets Probability Bell's inequality: Physics meets Probability

2007-09-25

arxiv.org/abs/0709.3909v2

Information Science 179, N. 5, 492-504 (2009)

Physics

Quantum Physics

Legget's inequality and experiment of S. Gr\"oblacher, T. Paterik, R. Kaltenbaek, C. Brukner, M. Zukowski, A. Aspelmeyer, and

Scientific paper

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.

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