Does Geometric Algebra provide a loophole to Bell's Theorem? (with corrections)

TL;DR

This paper critically examines Joy Christian's claims of refuting Bell's theorem using Geometric Algebra, highlighting mathematical errors and misunderstandings in his models that have persisted despite multiple refutations.

Contribution

The paper analyzes and clarifies the mathematical and logical flaws in Christian's models, providing a resource to evaluate future disproofs of Bell's theorem.

Findings

Christian's models contain hidden sign errors.

His interpretations rely on misunderstandings of Bell's work.

Repeated attempts to refute Bell's theorem are flawed due to mathematical inaccuracies.

Abstract

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 = (ab + ba)/2. After that, ambiguous notation and technical complexity allow sign errors to be hidden from sight, and new mathematical errors can be introduced.