Gill Richard David
Mathematical Institute, Faculty of Science, Leiden University, Rapenburg 70, 2311 EZ Leiden, The Netherlands.
Entropy (Basel). 2019 Dec 31;22(1):61. doi: 10.3390/e22010061.
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.
2007年以及在随后的一系列论文中，乔伊·克里斯蒂安声称反驳了贝尔定理，他运用几何代数（GA）技术提出了一个所谓的单重态关联的局域实在模型。几位作者发表论文反驳他的观点，克里斯蒂安的想法未被接受。然而，他最近成功地在相当主流的期刊上发表了其理论更具野心和复杂的版本。这怎么可能呢？贝尔定理的数学和逻辑简单明了，并且已经被深入研究和辩论了五十多年。克里斯蒂安声称对一个纯数学定理有一个数学反例。克里斯蒂安模型的每个新版本都使用新手段来规避贝尔定理，或者依赖于一种新的误解贝尔工作的方式。这些手段和误解在其他反驳贝尔定理的人当中很常见，所以识别并命名它们是有用的。我希望本文能为那些需要评估新的“贝尔定理证伪”的人提供一个有用的参考。克里斯蒂安的基本思想简单且颇为新颖：他对基本的几何代数方程a·b = (ab + ba)/2给出了一种概率解释。在此之后，模糊的符号表示和技术复杂性使得符号错误得以隐藏，并且可能引入新的数学错误。
