The GHSZ argument: a gedankenexperiment requiring more denken

TL;DR

This paper critically reexamines the GHSZ thought experiment, identifying a logical error in their claim of inconsistency in local realism, which may impact the understanding of quantum entanglement and hidden variables.

Contribution

The paper reveals a fundamental logical flaw in the GHSZ argument, challenging its conclusion of inconsistency in local realism and clarifying the role of symmetries in the problem.

Findings

Identifies a logical error in the GHSZ argument

Shows the contradiction arises from presuming contradictory premises

Suggests reevaluation of local realism and hidden variables in quantum mechanics

Abstract

I reassess the gedankenexperiment of Greenberger, Horne, Shimony and Zeilinger after twenty-five years, finding their influential claim to discovery of an inconsistency inherent in high dimensional formulations of local realism to arise from a fundamental error of logic. They manage this by presuming contradictory premises: that a specific linear combination of four angles involved in their proposed parallel experiments on two pairs of electrons equals both $\pi$ and $0$ at the same time. Ignoring this while presuming the contradictory implications of these two conditions, they introduce the contradiction themselves. The notation they use in their "derivation" is not sufficiently ornate to represent the entanglement in the double electron spin pair problem they design, confounding their error. The situation they propose actually motivates only an understanding of the full array of symmetries involved in their problem. In tandem with the error now recognized in the supposed defiance of Bell's inequality by quantum probabilities, my reassessment of their work should motivate a reevaluation of the current consensus outlook regarding the principle of local realism and the proposition of hidden variables.