Rethinking Symmetry Principles and Partial Observables With Reference Frames

Abstract

Dynamically uncoupled fields are a modelling device used in the literature on reference frames, classical and quantum. We argue that the device is not innocuous. First, uncoupled fields violate Earman's symmetry principle SP1---that every dynamical symmetry is a spacetime symmetry---and the violation, unlike the familiar Newtonian one, cannot be repaired by excising surplus spacetime structure: it arises from a deficit of dynamical structure, not an excess of spatiotemporal structure. This qualifies implicit assumptions of Earman's SP1, while leaving its diagnostic role intact. Second, uncoupled fields expose a lacuna in the partial/complete observables programme: only dynamically coupled fields can serve as bona-fide partial observables, so partial observability is derivative on complete observability. We then reinterpret the standard formalism for partial observables: qua measurable, a partial observable is a relational quantity expressed with respect to an uncoupled frame, and it remains gauge-variant. This reinterpretation vindicates Rovelli's claim that partial observables are individually measurable, against Thiemann and Adlam, and separates two properties easily conflated in the generally covariant formulations of theories: invariance under diffeomorphisms and invariance along the gauge flow.