5. Andrei Khrennikov, Event Independence, Collective Independence, EPR‐Bohm Experiment, and Incompleteness of Quantum Mechanics

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Volume 16: Pages 196-199, 2003

Event Independence, Collective Independence, EPRBohm Experiment, and Incompleteness of Quantum Mechanics

Andrei Khrennikov

International Center for Mathematical Modeling in Physics and Cognitive Sciences, University of Växjö, Växjö, S35195, Sweden

We study the notion of independence in the EPRBohm framework by means of a comparative analysis of this notion in both the conventional and frequency approaches to probability theory. The importance of such an analysis is that it allows us to demonstrate that the Bell inequalities were obtained using totally unjustified assumptions (e.g., the BellClauserHorne factor ability condition). The frequency approach also allows us to demonstrate that GillWeihsZeilingerZukowski's arguments based on the experimenter's freedom to choose settings to support Bell's theorem are not justified by the structure of the EPRBohm experiment either. Finally, our analysis leads us to support Einstein's original point of view, according to which quantum mechanics is simply not a complete theory.

Keywords: EPRBohm experiment, Bell's inequality, BellClauserHorne factorability condition, Kolmogorov's and von Mises's approaches to probability, event independence, collective independence, HessPhilipp model

Received: May 31, 2002; Published online: December 15, 2008