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

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.