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ON THE RECOVERY OF GEOMETRODYNAMICS FROM TWO DIFFERENT SETS OF FIRST PRINCIPLES
, 2006
"... The conventional spacetime formulation of general relativity may be recast as a dynamics of spatial 3geometries (geometrodynamics). Furthermore, geometrodynamics can be derived from first principles. I investigate two distinct sets of these: (i) Hojman, Kuchaˇr and Teitelboim’s, which presuppose th ..."
Abstract

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The conventional spacetime formulation of general relativity may be recast as a dynamics of spatial 3geometries (geometrodynamics). Furthermore, geometrodynamics can be derived from first principles. I investigate two distinct sets of these: (i) Hojman, Kuchaˇr and Teitelboim’s, which presuppose that the spatial 3geometries are embedded in spacetime. (ii) The 3space approach of Barbour, Foster, Ó Murchadha and Anderson in which the spatial 3geometries 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 3space 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 3space 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.