Dr. Bertlmann's Socks in a Quaternionic World of Ambidextral Reality

Joy Christian
2020 IEEE Access  
Unlike our basic theories of space and time, quantum mechanics is not a locally causal theory. Moreover, it is widely believed that any hopes of restoring local causality within any realistic theory have been undermined by Bell's theorem and the experimental investigations it has inspired. In this pedagogical paper, John S. Bell's amusing example of Dr. Bertlmann's socks to illustrate the results of these experiments is reconsidered, first within a toy model of a two-dimensional one-sided world
more » ... of a non-orientable Möbius strip, and then within a real world of three-dimensional quaternionic sphere, S 3 , which results from an addition of a single point to IR 3 at infinity. In the latter quaternionic world, which happens to be the spatial part of a solution of Einstein's field equations of general relativity, the singlet correlations between a pair of entangled fermions can be understood as classically as those between Dr. Bertlmann's colorful socks. INDEX TERMS Bell's theorem, determinism, EPR argument, Friedmann-Robertson-Walker spacetime, geometric algebra, local causality, local realism, quantum mechanics, quaternions, Möbius topology. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.
doi:10.1109/access.2020.3031734 fatcat:elf7nd65hnd5vdjgatczlne5gu