Resurrecting the Prospect of Supplementary Variableswith the Principle of Local Realism

Abstract

I produce a coherent mathematical formulation of the supplementary variables structure for Aspect’s experimental test of Bell’s inequality as devised by Clauser, Horne, Shimony, and Holt, a formalization which has been widely considered to be impossible. Contrary to Aspect’s understanding, it is made clear that a supplementary variable formulation can represent any tendered probability distribution whatsoever. This includes both the QM distribution and the “naive distribution”, which he had suggested as a foil. It has long been known that quantum theory does not support a complete distribution for the components of the thought experiment that underlies the inequality. However, further than that, here I identify precisely the bounding polytope of distributions that do cohere with both its explicit premises and with the prospect of supplementary variables. In this context, it is found once again that every distribution within this polytope respects the conditions of Bell’s inequality, and that the famous evaluation of the gedankenexpectation defying it as 22 is mistaken. The argument is relevant to all subsequent embellishments of experimental methodology post Aspect, designed to block seven declared possible loopholes. The probabilistic prognostications of quantum theory are not denied, nor are the experimental observations. However, their inferential implications have been misrepresented.