Accardi contra Bell (cum mundi) : the impossible coupling

Abstract

An experimentally observed violation of Bell s inequality is supposed to show the failure of local realism to deal with quantum reality. However, finite statistics and the time sequential nature of real experiments still allows a loophole for local realism. We show that the randomised design of the Aspect experiment closes this loophole. Our main tool is van de Geer s (2000) supermartingale version of the classical Bernstein (1924) inequality guaranteeing, at the root n scale, a not-heavier-than-Gaussian tail of the distribution of a sum of bounded supermartingale differences. The results are used to specify a protocol for a public bet between the author and L. Accardi, who in recent papers (Accardi and Regoli, 2000a,b, 2001) has claimed to have produced a suite of computer programmes, to be run on a network of computers, which will simulate a violation of Bell s inequalites. At a sample size of thirty thousand, both error probabilities are guaranteed smaller than one in a million, provided we adhere to the sequential randomized design.