The Contextual Modal Logic of a Wigner's Friend Generalization

TL;DR

This paper uses contextuality and modal logic to analyze a quantum thought experiment, showing that perceived contradictions are not logically accessible when these factors are considered.

Contribution

It introduces a logical framework incorporating contextuality to resolve apparent contradictions in quantum mechanics, specifically in the Frauchiger-Renner experiment.

Findings

The Frauchiger-Renner contradiction is avoided when contextuality is taken into account.

Modal logic can effectively model quantum contextuality.

Logical inconsistencies in quantum mechanics are not unavoidable when considering contextual properties.

Abstract

Quantum mechanics has been subject to logical scrutiny since its inception. The behavior of quantum systems, which are fundamentally dissimilar from classical systems, often appears to point to a logical inconsistency in quantum mechanics, allegedly leading to contradictions in the prediction of experimental measurements--though such contradictions have never materialized. A recent example of this type of inquiry into the logical well-posedness of quantum mechanics is the Frauchiger-Renner Gedankenexperiment, which purports to demonstrate that quantum mechanics is logically inconsistent. In this article, we show that by considering the property of contextuality in quantum systems--as predicted by the Kochen-Specker theorem--the supposed contradiction proposed by Frauchiger and Renner becomes logically inaccessible.