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arXiv:1304.0532 · Foundations of Physics

Strong Constraints on Models that Explain the Violation of Bell Inequalities with Hidden Superluminal Influences

Valerio Scarani, Jean-Daniel Bancal, Antoine Suárez, Nicolas Gisin

Published Mar 4, 2014• 33 citations
arXivHTMLPDF
DOI
10.1007/s10701-014-9785-1

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We discuss models that attempt to provide an explanation for the violation of Bell inequalities at a distance in terms of hidden influences.These models reproduce the quantum correlations in most situations, but are restricted to produce local correlations in some configurations.The argument presented in (Bancal et al.Nat Phys 8:867, 2012) applies to all of these models, which can thus be proved to allow for faster-than-light communication.In other words, the signalling character of these models cannot remain hidden.
John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.
John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.