Breakdown of Bell's Theorem for incompatible measurements

TL;DR

This paper critically examines Bell's theorem, demonstrating that its assumptions are unjustified for incompatible measurements and providing classical counterexamples that challenge its foundational claims.

Contribution

The paper refutes the core proposition of Bell's theorem for incompatible measurements and introduces classical counterexamples, challenging the theorem's assumptions and conclusions.

Findings

Bell's proposition is refuted by classical counterexamples.

Assumptions in Bell's theorem are unjustified for incompatible measurements.

Criticism based on standard sampling arguments is shown to be false.

Abstract

Bell's theorem contains the proposition that the Einstein-Podolsky-Rosen (EPR) theory (hypothesis) of the existence of elements of reality together with Einstein locality permits a mathematical description of EPR experiments by functions that are all defined on one common probability space. This proposition leads in turn to restrictions for possible experimental outcomes that Bell expressed in terms of his well known inequalities and that Vorob'ev and others had investigated before Bell. Summarizing several previous publications and adding new material, the above proposition is refuted by Einstein-local counterexamples from classical physics and shown to involve additional assumptions that can not be justified for mutually exclusive (incompatible) measurements and experiments. Moreover, criticism of our work by Mermin who invoked "standard sampling arguments" is shown to be false.