Physics – Mathematical Physics
Scientific paper
2011-11-17
Physics
Mathematical Physics
12 pages, 2 figures. Enhanced and reorganized, minor corr. calculations
Scientific paper
Experimental tests of Bell inequalities often require supplementary assumptions; in particular inhomogeneous inequalities (like the Clauser-Horne one) require the so-called "no-enhancement" (NEN) hypothesis. In this paper, by extending an already well known Local Hidden Variables (LHV) model for the Clauser-Horne-Shimony-Holt inequality to account for the probabilities of detection when the polarizers are removed, we show that, not only (i) the phenomenon of "variable detection probability" (VDP) can be straightforwardly included the in the usual LHV framework for homogeneous Bell inequalities, but, (ii) the violation of the non-genuine version (non-genuine $\equiv$ involving supplementary assumptions) of an inhomogeneous inequality appears as the most natural consequence of that phenomenon, for the particular cases where the NEN hypothesis is broken, what we call "enhancement" (ENH). Our treatment focuses on LHV's as mere mathematical constructions, with the aim of exposing as clearly as possible the relevancy of the role of VDP and ENH within the framework of Bell inequalities. This "pre-quantum" perspective is nevertheless supplemented with the minimum references to QM and other additional material (see Appendix) that we judge necessary to illustrate their physical implications, as well as the coherence of the whole picture.
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