Abstract
I point out critical errors in the paper "Dr. Bertlmann's Socks in a Quaternionic World of Ambidextral Reality" by Joy~Christian, published in IEEE Access. Christian's model does not generate the singlet correlations but in fact simply reproduces the Bertlmann effect. John Bell's friend and colleague Reinhold Bertlmann of CERN, in his younger days, always wore one pink and one blue sock, at random. The moment you saw his left foot, you knew what colour sock would be on his right foot. Action at a distance? As John Bell liked to explain, quantum entanglement cannot be explained away in such an easy way. Yet Christian's model assigns the two particles of the EPR-B experiment an equal and opposite spin at the source, the choice being determined by a fair coin toss. However they are measured, these spins are recovered. Christian's computer simulation works by not actually simulating his model at all but by almost directly tracing the negative cosine built into his computer algebra package. Bell's theorem has not been disproved. Debate as to what it means for the foundations of physics as well as for quantum information engineering (quantum communication, computation) is more lively today than ever before. Christian's paper, alas, does not contribute to the debate, but distracts from it. A possible role for Geometric Algebra is still wide open and deserves further investigation, informed by a proper understanding of the mathematical content of Bell's theorem.
Highlights
Bell’s 1964 theorem [1] states that the conventional framework of quantum mechanics is incompatible with a physical principle called local realism
Christian [8] claims in a recent article in IEEE ACCESS to have a counterexample
His other recent articles [6] and [7], the last of which was published in IEEE ACCESS, make the same claim
Summary
Bell’s 1964 theorem [1] states that the conventional framework of quantum mechanics is incompatible with a physical principle called local realism. Bell’s theorem is a cornerstone of modern quantum information theory, and of quantum computing. His other recent articles [6] and [7], the last of which was published in IEEE ACCESS, make the same claim They have the common purpose of disproving Bell’s theorem by giving a local realistic model, which in a nutshell means a classical physical model, which reproduces quantum correlations. Christian’s idea that quantum correlations are explained by the geometry of space might seem appealing, but his work lends no support to this idea. Anyway, such an explanation would not be ‘‘local’’ in any meaningful sense. Bell does not take account of the geometry of space because his argument, on the side of local realism, does not depend on it in any way whatsoever
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