Accardi contra Bell (cum mundi) : The Impossible Coupling

• An experimeotally observed violation of Bell's inequality i.s suppooed to show the failuro of local realism to deal with quantum roality. However, finite statistics and the Lime sequential nature of real experiments still allows a loophole for local roalism. We show that the raodomised design of the Aspect experiment closes this loophole. Our main tool is van de Geer's (1995, 2000) martingale version of the classical Bernstein (1924) incquality guaranteeing, at the  root n scale, a not-beavier-than-Gaussian tail of the distribution of a sum of bouoded supermartingale dilferences. The results are used to specify a protocol for a public bet between the author and L. Accardi, who in recont papers (Aocardi and Regal.i, 2000a, b, 2001; Accardi, lmafuku and Regoli, 2002) has claimed to have produced a suite of computer programmes, to be run on a network of computers, wbich will simulate a violation of Bell's inequalites. At a sarnple size of twenty five thousand, botb error probabilities are guaranteed smaller than about one in a million, provided we adhere to tho sequential randomized design while Accardi aims for tbe greatest possible violation allowed by quantum mechanics.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

MATHEMATICS

MATEMATIK

Publication and Content Type

vet (subject category)

kap (subject category)