ABSTRACT

Accardi contra Bell

Richard Gill, September 19, 2001

In recent preprints, L. Accardi has claimed that he can construct a deterministic classical system, satisfying locality constraints, which violates the inequalities of Bell. In fact a computer simulation programme can be downloaded from his webpage

http://volterra.mat.uniroma2.it

This is only the most recent contribution to a nearly fourty year old controversy, as to what the elementary probabilistic inequality, concerning four 0/1-valued random variables X1, X2, Y1, Y2 :

Pr(X1=Y2) <= Pr(X1=Y1) + Pr(X2=Y1) + Pr(X2=Y2)

has to say about the experimentally confirmed prediction of quantum mechanics, that certain counts in an experiment with polarized photons can satisfy:

N12 >> N11 + N21 + N22 .

I have bet Luigi Accardi 1500 Euro, that his computer programme cannot be written according to certain specifications, reflecting the spatial structure of the experiment with the photons. I will explain the background to this bet, and use some martingale theory to show why even time-dependence cannot be used to escape Bell's inequality.

Draft paper:

http://www.math.uu.nl/people/gill/Temp/constance.pdf

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Martijn Pistorius (pistorius@math.uu.nl)

Last Updated: September 17, 2001