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The Bell Theorem as a Special Case of a Theorem of Bass

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Abstract

The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found 10 years earlier by Bass and stated in full generality by Vorob’ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequalities. We show that these precise conditions differ significantly from the definition of objective local variable spaces and as an application that the Bell inequalities may be violated even for objective local random variables.

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Authors and Affiliations

  1. Department of Electrical Engineering and Department of Physics, Beckman Institute, University of Illinois, Urbana, Il, 61801, USA

    Karl Hess

  2. Department of Statistics and Department of Mathematics, Beckman Institute, University of Illinois, Urbana, Il, 61801, USA

    Walter Philipp

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  1. Karl Hess
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  2. Walter Philipp
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Correspondence to Karl Hess.

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Hess, K., Philipp, W. The Bell Theorem as a Special Case of a Theorem of Bass. Found Phys 35, 1749–1767 (2005). https://doi.org/10.1007/s10701-005-6520-y

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  • DOI: https://doi.org/10.1007/s10701-005-6520-y

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