Coordinates, observables and symmetry in relativity

Abstract

We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a ``point-coincidence'' between scalar fields that completely characterise a spacetime model, we also propose a natural generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.

37 pages

References in corpus (6)

• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Partial and Complete Observables for Canonical General Relativity
• The Hole Argument for Covariant Theories
• Events and observables in generally invariant spacetime theories
• Dirac Quantization of Parametrized Field Theory

Cited by in corpus (9)

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• Relational observables in Asymptotically safe gravity
• Cartan gravity, matter fields, and the gauge principle
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• The dressing field method for diffeomorphisms: a relational framework
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR
• Dynamical diffeomorphisms
• Observing Shape in Spacetime
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives