On the recovery of geometrodynamics from two different sets of first principles

Details On the recovery of geometrodynamics from two different sets of first principles On the recovery of geometrodynamics from two different sets of first principles

2005-11-14

arxiv.org/abs/gr-qc/0511070v2

Stud.Hist.Philos.Mod.Phys.38:15,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Replaced by version Accepted by Studies in History and Philosophy of Modern Physics

Scientific paper

The conventional spacetime formulation of general relativity may be recast as a dynamics of spatial 3-geometries (geometrodynamics). Furthermore, geometrodynamics can be derived from first principles. I investigate two distinct sets of these: (i) Hojman, Kucha\v{r} and Teitelboim's, which presuppose that the spatial 3-geometries are embedded in spacetime. (ii) The 3-space approach of Barbour, Foster, \'{O} Murchadha and Anderson in which the spatial 3-geometries are presupposed but spacetime is not. I consider how the constituent postulates of the conventional approach to relativity emerge or are to be built into these formulations. I argue that the 3-space approach is a viable description of classical physics (fundamental matter fields included), and one which affords considerable philosophical insight because of its `relationalist' character. From these assumptions of less structure, it is also interesting that conventional relativity can be recovered (albeit as one of several options). However, contrary to speculation in the earlier 3-space approach papers, I also argue that this approach is not selective over which sorts of fundamental matter physics it admits. In particular, it does not imply the equivalence principle.

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