A Note on Bell's Theorem Logical Consistency

TL;DR

This paper argues that counterfactual definiteness is an unnecessary, inconsistent assumption in Bell's theorem, and presents a revised derivation showing it is irrelevant to Bell inequalities and their implications.

Contribution

It offers a new perspective by demonstrating that counterfactual definiteness is neither necessary nor consistent, and provides a coherent Bell inequality derivation excluding this assumption.

Findings

Counterfactual definiteness is incompatible with falsifiability.

Bell inequalities can be derived without assuming counterfactual definiteness.

Counterfactual reasoning is an incongruent application in quantum physics.

Abstract

Counterfactual definiteness is supposed to underlie the Bell theorem. An old controversy exists among those who reject the theorem implications by rejecting counterfactual definiteness and those who claim that, since it is a direct consequence of locality, it cannot be independently rejected. We propose a different approach for solving this contentious issue by realizing that counterfactual definiteness is an unnecessary and inconsistent assumption. Counterfactual definiteness is not equivalent to realism or determinism neither it follows from locality. It merely reduces to an incongruent application of counterfactual reasoning. Being incompatible with falsifiability, it constitutes an unjustified assumption that goes against the scientific method's rigor. Correct formulations of the Bell theorem's bases show it is absent either as a fundamental hypothesis or as a consequence of something else. Most importantly, we present a coherent Bell inequality derivation carefully devised to show explicitly and convincingly the absence of incompatible experiments or counterfactual reasoning. Thus, even admitting that counterfactual definiteness could be a consistent assumption, the necessary conclusion is that it is irrelevant for the inequality formulation and can be safely ignored when discussing Bell's inequality philosophical and physical implications.