Coordinates, observables and symmetry in relativity

Details Coordinates, observables and symmetry in relativity Coordinates, observables and symmetry in relativity

2007-11-16

arxiv.org/abs/0711.2651v2

Annals of Physics 324 (2009) 1585-1611

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

37 pages

Scientific paper

10.1016/j.aop.2009.03.014

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.

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