Bell's inequalities

Abstract

Assumed data streams from a delayed choice gedanken experiment must satisfy a Bell's identity independently of locality assumptions. The violation of Bell's inequality by assumed correlations of identical form among these data streams implies that they cannot all result from statistically equivalent variables of a homogeneous process. This is consistent with both the requirements of arithmetic and distinctions between commuting and noncommuting observables in quantum mechanics. Neglect of these distinctions implies a logical loophole in the conventional interpretation of Bell's inequalities.

Bell's inequality violation due to misidentification of spatially non-stationary random processes

“…Sica [10,11] emphasized that Bell's inequalities are limits of arithmetic inequalities that must be satisfied by any cross-correlations of three or four finite data-lists (as appropriate), with data restricted to ± 1. Further, since experimental data are inherently finite, such data arranged in appropriate lists cannot violate the Bell inequality, no matter how exotic the statistics.…”

“…2, the next section of the introduction will review an alternative derivation of the Bell inequality [10,11] in order to clarify the concepts used in this paper, which depart from those usually encountered in discussions of this subject.…”

“…It has been shown [11] that the violation of Bell inequality (4) by three correlations of the form (1) indicates that the single correlation actually observed cannot result from a stochastic process that is spatially stationary in second order correlations, i.e. one that is wide sense stationary, since triple data sets from all such processes and their resulting correlations must always satisfy (3).…”

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“…It has recently been shown [1,2] that Bell's inequalities depend on only one of the several assumptions historically employed in their derivation: namely, that cross correlations are performed among three or four lists of data, as appropriate to the inequality, each datum restricted to ± 1. Bell's inequalities are identically satisfied by such data lists independently of the physical assumptions usually believed to underlie them.…”

“…Bell's inequalities are identically satisfied by such data lists independently of the physical assumptions usually believed to underlie them. From closely related reasoning [2], it follows that Bell's inequality necessarily constrains the single function characterizing the correlation of periodic, spatially stationary stochastic processes, and that such processes cannot produce the cosine correlation of the singlet state.…”