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arXiv:quant-ph/0212085

A Local Mathematical Model for EPR-Experiments

Walter Philipp, K. Hess

Published Dec 13, 2002• 1 citation
arXivHTMLPDF

Abstract

In this paper we give a detailed and simplified version of our original mathematical model published first in the Proceedings of the National Academy of Science. We hope that this will clarify some misinterpretations of our original paper.
DOI
10.48550/arxiv.quant-ph/0212085

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I was very enthusiastic about our findings and wanted to publish them in a prestigious journal. I knew that this was not going to be easy, because neither Walter nor I were known experts in this particular area of mathematical physics, and any referee who saw that we tried to refute Bell would probably have a negative reaction to it. This is why I called my friend Federico Capasso and asked him to help. I had known Federico since many years. He was one of the top researchers at Bell Laboratories and now professor of applied physics at Harvard. Federico and I had hadmany spirited discussions about research topics and had become very good friends. Federico’s research area is solid state physics. He is a great expert in the area of light detectors, including the photodetectors that are used in the EPRB experiments, and he is the “father” of the quantum cascade laser. He knew about EPRB experiments and the Bell theorem. He also knew that I would not be calling him if I was not convinced about having important results. After presenting my case, I asked Federicowhether hewould, as amember of the National Academy of Sciences, sponsor a paper for PNAS, the proceedings of this National Academy and a very prestigious journal. I was at that time not yet a member of the academy myself. Any member of the academy could communicate annually a small number of papers to PNAS, determine the referees, and be involved in the publication process in the role of a guest editor. If the referee reports were good, such a paper would be printed with very high probability. For academymembers, this was a wonderful way to publish their own research and also to sponsor deserving research of young scientists as well as research on somewhat risky but highly interesting topics.
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.
A new formulation of the EPR argument is presented, one which uses John Bell’s mathematically precise local causality condition in place of the looser locality assumption which was used in the original EPR paper and on which Niels Bohr seems to have based his objection to the EPR argument. The new formulation of EPR helps clarify the relation between this argument and Bell’s Theorem. The relation between these two arguments — in particular, the role of EPR as part one of Bell’s two‐part argument for nonlocality — is also discussed in detail.