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Does Geometric Algebra Provide a Loophole to Bell’s Theorem?

Mathematical Institute, Faculty of Science, Leiden University, Rapenburg 70, 2311 EZ Leiden, The Netherlands
Entropy 2020, 22(1), 61; https://doi.org/10.3390/e22010061
Received: 21 October 2019 / Revised: 27 December 2019 / Accepted: 30 December 2019 / Published: 31 December 2019
(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)
In 2007, and in a series of later papers, Joy Christian claimed to refute Bell’s theorem, presenting an alleged local realistic model of the singlet correlations using techniques from geometric algebra (GA). Several authors published papers refuting his claims, and Christian’s ideas did not gain acceptance. However, he recently succeeded in publishing yet more ambitious and complex versions of his theory in fairly mainstream journals. How could this be? The mathematics and logic of Bell’s theorem is simple and transparent and has been intensely studied and debated for over 50 years. Christian claims to have a mathematical counterexample to a purely mathematical theorem. Each new version of Christian’s model used new devices to circumvent Bell’s theorem or depended on a new way to misunderstand Bell’s work. These devices and misinterpretations are in common use by other Bell critics, so it useful to identify and name them. I hope that this paper can serve as a useful resource to those who need to evaluate new “disproofs of Bell’s theorem”. Christian’s fundamental idea is simple and quite original: he gives a probabilistic interpretation of the fundamental GA equation a · b = ( a b + b a ) / 2 . After that, ambiguous notation and technical complexity allows sign errors to be hidden from sight, and new mathematical errors can be introduced. View Full-Text
Keywords: Bell’s theorem; geometric algebra; Clifford algebra; quantum information Bell’s theorem; geometric algebra; Clifford algebra; quantum information
MDPI and ACS Style

Gill, R.D. Does Geometric Algebra Provide a Loophole to Bell’s Theorem? Entropy 2020, 22, 61.

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