A logical loophole in the derivation of the Bell inequalities

Gerrit Coddens (1)

1 LSI - Laboratoire des Solides Irradiés - Irradiated Solids Laboratory

The Bell inequalities are based on a tacit assumption of a COMMON probability distribution that precludes their application to the experiments of Aspect et al. The basic ideas of this argument have already been given in references [1,2], but the present presentation recollects them in a clearer and more concise way. We show that the intuitive idea that it would be easy enough to define such a common probability distribution (and this way make up for the hiatus in the traditional proof) is wrong. We discuss two such intuitive repair scenarios, one based on Cartesian products of sets and one based on unions of sets. Both lead to an impasse for reasons that intially might have escaped our attention. When we change strategies to avoid an error in the first scenario, another error pops up in an entirely different place within the second scenario. Perhaps it is possible to invent yet other scenarios, such that the polemics could go on. But it cannot be anybody's task to imagine all possible attempts to repair the logical loophole and then rebut them one by one. That would be a reversal of the charge of proof. In the situation as it stands, the proof of the Bell inequalities is wrong due to the absence of an existence proof for the tacitly assumed common probability distribution. We discuss also a number of mathematical and physical hints which strongly suggest that the error is absolutely lethal and that no repair scenario will ever be able to provide us with the missing existence proof. This logical loophole is much more fundamental than the experimental loopholes which have currently received much interest due to the ingenious efforts of experimentalists to close them.

Mots clés: quantum mechanics; Bell inequalities

Domaines: Physique mathématique [math-ph]

Gerrit Coddens. A logical loophole in the derivation of the Bell inequalities. 2018. ⟨cea-01737341v6⟩