A relational perspective on the Wigner-Araki-Yanase theorem

TL;DR

This paper offers a new interpretation of the Wigner-Araki-Yanase theorem through a relational quantum mechanics perspective, emphasizing the dual role of measurement apparatuses in symmetry contexts.

Contribution

It introduces a relational view of the WAY theorem and analyzes models to highlight the importance of measurement apparatuses as physical reference systems.

Findings

Measurement apparatuses must serve as physical references in symmetry scenarios.

The relational interpretation clarifies the dual role of measurement devices.

Models demonstrate the necessity of reference systems in quantum measurements.

Abstract

We present a novel interpretation of the Wigner-Araki-Yanase (WAY) theorem based on a relational view of quantum mechanics. Several models are analysed in detail, backed up by general considerations, which serve to illustrate that the moral of the WAY theorem may be that in the presence of symmetry, a measuring apparatus must fulfil the dual purpose of both reflecting the statistical behaviour of the system under investigation, and acting as a physical reference system serving to define those quantities which must be understood as relative.