Simple refutation of Joy Christian's simple refutation of Bell's simple theorem

Richard David Gill

Published Mar 7, 2012• 5 citations

Abstract

I point out a simple algebraic error in Joy Christian’s refutation of Bell’s theorem. In substituting the result of multiplying some derived bivectors with one another by consultation of their multiplication table, he confuses the generic vectors which he used to define the table, with other specific vectors having a special role in the paper, which had been introduced earlier. The result should be expressed in terms of the derived bivectors which indeed do follow this multiplication table. When correcting this calculation, the result is not the singlet correlation any more. Moreover, curi-ously, his normalized correlations are independent of the number of measurements and certainly do not require letting n converge to infinity. At the same time, his unnormalized or raw correlations are identically equal to −1, independently of the number of measurements! Correctly computed, his standardized correlations are the bivectors −a · b − a ∧ b, and they find their origin entirely in his normalization or standardization factors. I conclude that his research program has been set up around an elaborately hidden but trivial mistake.

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In a series of very interesting papers [1-7], Joy Christian constructed a counterexample to Bell's theorem. This counterexample does not have the same assumptions as the original Bell's theorem, and therefore it does not represent a genuine disproof in a strict mathematical sense. However, assuming the physical relevance of the new assumptions, the counterexample is shown to be a contextual hidden variable theory. If Bell's theorem's importance is to rule out contextual hidden variable theories obeying relativistic locality, then Joy Christian's counterexample achieves its aim. If however contextual hidden variables theories are not considered genuine physically theories and Bell's theorem's importance stems from its ability to be experimentally confirmed, then Joy Christian's counterexample does not diminish the importance of Bell's theorem. The implications of Joy Christian's counterexample are discussed in the context of information theory. Version 2 note: Subsequent analysis disproved the mathematical consistency of Joy Christian's model. This paper was based on the assumption of the mathematical validity of the model. Except for the addition of this note, the content of this paper was not modified in any other way.

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