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

Abstract

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.