A Critical Review of Works Pertinent to the Einstein-Bohr Debate and Bell’s Theorem

• Published in: Symmetry (Basel) 2022-01, Vol.14 (1), p.163
• Main Author: Hess, Karl
• Format: Article
• Language: English
• Subjects: Atoms & subatomic particles; Bell; CHSH; Combinatorial analysis; EPRB; Experiments; Mathematical analysis; Probability; Quantum entanglement; Quantum physics; Quantum theory; Random variables; Theorems; Theory of relativity
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym14010163

This review is related to the Einstein-Bohr debate and to Einstein–Podolsky–Rosen’s (EPR) and Bohm’s (EPRB) Gedanken-experiments as well as their realization in actual experiments. I examine a significant number of papers, from my minority point of view and conclude that the well-known theorems of Bell and Clauser, Horne, Shimony and Holt (CHSH) deal with mathematical abstractions that have only a tenuous relation to quantum theory and the actual EPRB experiments. It is also shown that, therefore, Bell-CHSH cannot be used to assess the nature of quantum entanglement, nor can physical features of entanglement be used to prove Bell-CHSH. Their proofs are, among other factors, based on a statistical sampling argument that is invalid for general physical entities and processes and only applicable for finite “populations”; not for elements of physical reality that are linked, for example, to a time-like continuum. Bell-CHSH have, furthermore, neglected the subtleties of the theorem of Vorob’ev that includes their theorems as special cases. Vorob’ev found that certain combinatorial-topological cyclicities of classical random variables form a necessary and sufficient condition for the constraints that are now known as Bell-CHSH inequalities. These constraints, however, must not be linked to the observables of quantum theory nor to the actual EPRB experiments for a variety of reasons, including the existence of continuum-related variables and appropriate considerations of symmetry.