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

TL;DR

This paper explores how quantum entanglement correlations can be understood classically using a quaternionic model of space, extending Bell's socks analogy to a three-dimensional quaternionic sphere related to general relativity.

Contribution

It introduces a quaternionic geometric framework to interpret quantum correlations classically, bridging quantum mechanics and general relativity.

Findings

Quantum correlations modeled as classical within quaternionic space

Extension of Bell's socks analogy to three-dimensional quaternionic sphere

Connection between entanglement and spacetime geometry

Abstract

In this pedagogical paper, John S. Bell's amusing example of Dr. Bertlmann's socks is reconsidered, first within a toy model of a two-dimensional one-sided world of a non-orientable M\"obius strip, and then within a real world of three-dimensional quaternionic sphere, S^3, which results from an addition of a single point to R^3 at infinity. In the 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.