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Removing the last obstacle to the Einstein-Fine resolution of the EPR-Bell problem

László E. Szabó

Published Feb 10, 2000• 0 citations
OpenAlex

Abstract

In the real spin-correlation experiments the detection/emission inefficiency is usually ascribed to independent random detection errors, and treated by the enhancement hypothesis. In Fine's prism model the detection inefficiency is an effect not only of the random errors in the analyzer + detector equipment, but is also the manifestation of a pre-settled (hidden) property of the particles.

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EPR Paradox, Bell Inequalities and Peculiarities of Quantum Correlations

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In the real spin-correlation experiments the detection/emission inefficiency is usually ascribed to independent random detection errors, and treated by the enhancement hypothesis. In Fine's prism model the detection inefficiency is an effect not only of the random errors in the analyzer + detector equipment, but is also the manifestation of a pre-settled (hidden) property of the particles.
We discuss supplementary (or hidden) variables in spin-measuring equipments in EPR-Bell experiment. This theme was considered in a Bell's later work. We generalize it. First, we show why the original supplementary variable λλλ is not to be regarded to include supplementary variables in spin-measuring equipments (why supplementary variables should be introduced additionally in spin-measuring equipments) Next, we show the followings. When the supplementary variables introduced in spin-measuring equipments have local correlations, the Bell inequality is recovered. On the other hand, when they have nonlocal correlations, the Bell inequality is not recovered. This fact is in accord with the fact that the Bell inequality is derived for local realistic models.
A recent analysis by de Barros and Suppes of experimentally realizable GHZ correlations supports the conclusion that these correlations cannot be explained by introducing local hidden variables. We show, nevertheless, that their analysis does not exclude local hidden variable models in which the inefficiency in the experiment is an effect not only of random errors in the detector equipment, but is also the manifestation of a pre-set, hidden property of the particles ("prism models"). Indeed, we present an explicit prism model for the GHZ scenario; that is, a local hidden variable model entirely compatible with recent GHZ experiments.
Subtraction of ``accidentals'' in Einstein-Podolsky-Rosen experiments frequently changes results compatible with local realism into ones that appear to demonstrate non-locality. The validity of the procedure depends on the unproven assumption of the independence of emission events. Other possible sources of bias include enhancement, imperfect synchronisation, over-reliance on rotational invariance, and the well-known detection loophole. Investigation of existing results may be more fruitful than attempts at loophole-free Bell tests, improving our understanding of light.
Some years ago Szab\'o and Fine proposed a {\it local} hidden variable theory for the GHZ experiment based on the assumption that "the detection efficiency is not (only) the effect of random errors in the detector equipment, but it is a more fundamental phenomenon, the manifestation of a predetermined hidden property of the particles". Szab\'o and Fine, however, did not provide a general approach to quantum phenomena which avoids nonlocality. Such an approach, based on the same assumption, was instead recently supplied by some of us and called {\it extended semantic realism} ({\it ESR}) model. We show here that one can extract from the ESR model several local finite models referring to the specific physical situation considered in the GHZ experiment, and that these models can be converted into the toy models for the GHZ experiment worked out by Szab\'o and Fine.