A Classical Model of EPR Experiment with Quantum Mechanical Correlations and Bell Inequalities

Abstract

Despite considerable amounts of literature in recent years, one of the difficulties with the interpretation of Bell’s inequalities has been the lack of explicit models of hidden variables with which to compare classical and quantum correlations and to test the assumptions underlying their derivation. It is now generally believed that the so-called “local-realistic” hidden variable (HV) theories are ruled out by experiment [1,2]. In this paper, we present a simple classical model of correlated events which can in principle be realized experimentally, and which exhibits the same correlations as those obtained in spin1/2 correlation experiments. Our model is local in the sense of Bell, but is not in conflict with Bell’s inequalities, because as we shall see the normalization of the correlation function is performed in different ways in our model and in the derivation of these inequalities.

A simple model of a classical break-up process is given in which the correlation E(a, b) of the components A and B of the spins of the two subsystems along directions a and b gives precisely the quantum mechanical result —cosa • b). The model is “local”, but the normalization procedure of correlation functions in terms of “hidden variables” is different from that used in deriving Bell’s inequalities. A discretization procedure of the classical spins is then given which reproduces fully the dichotomous quantum mechanical results both for probabilities and for correlation functions. This procedure illustrates particularly clearly the difference between quantum and classical spins and provides a possible intuitive picture for the notion of the “reduction of the wave function”.

This article is reprinted with permission from Physics Letters, 105A, 9, 458–462, copyright © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division), Holland.