What Reference Frames Teach Us. Part I: About Symmetry Principles and Observability

TL;DR

This paper investigates the role of reference frames in General Relativity, revealing violations of symmetry principles and redefining the concept of partial observables as inherently relational and dynamical.

Contribution

It challenges traditional views on symmetry violations and redefines partial observables as relational and gauge-invariant through dynamical coupling.

Findings

Violation of Earman's SP1 principle in certain scenarios

Partial observables are inherently relational, not just gauge-invariant

Distinction between relational and gauge-invariant properties clarified

Abstract

This paper is an exploration of the nuanced realm of reference frames within the framework of General Relativity. Our analysis exposes a violation of Earman's SP1 principle in scenarios involving fields that are dynamically uncoupled, a common assumption for reference frames. Unlike other violations, we cannot foreclose it by eliminating background spacetime structure. Our analysis also leads us to challenge the conventional notion of partial observables as quantities that are associated with a measuring instrument and expressed within a coordinate system. Instead, we argue that a partial observable is inherently relational, even if gauge-variant, and needs dynamical coupling with other partial observables to form a bona-fide, gauge-invariant complete observables. This perspective allows us to distinguish between being relational and being gauge-invariant, two properties that are often conflated.