Bell's inequalities I: An explanation for their experimental violation

TL;DR

This paper presents derivations of Bell's inequalities as arithmetic identities independent of statistical assumptions, clarifying their experimental violation and proposing procedures to test their validity.

Contribution

It introduces explicit, data-based derivations of Bell's inequalities and describes procedures to verify their conditions experimentally.

Findings

Bell's inequalities are arithmetic identities, not statistical, and cannot be violated if conditions are met.

Experimental procedures are proposed to ensure data validity for testing inequalities.

Measured correlations cannot all be negative cosine functions under valid conditions.

Abstract

Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and thus cannot be violated by data that meets the conditions for their validity. Two experimentally performable procedures are described to meet these conditions. Once such data are acquired, it follows that the measured correlations cannot all equal a negative cosine of angular differences. The relation between this finding and the predictions of quantum mechanics is discussed in a companion paper.