2003/02/28 by E. Anderson, Edward Anderson · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1103/physrevd.68.104001
published as Phys.Rev.D68:104001,2003 · Revtex version; Journal-ref added
arxiv created 2003/11/03 · openalex publication_date 2003/11/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Wheeler asked how one might derive the Einstein-Hamilton-Jacobi equation from plausible first principles without any use of the Einstein field equations themselves. In addition to Hojman, Kucha\ifmmode \checkr\else \vr\fi and Teitelboim's ``seventh route to relativity'' partial answer to this, there is now a ``3-space'' partial answer due to Barbour, Foster and 'O Murchadha (BF'O) which principally differs in that general covariance is no longer presupposed. BF'O's formulation of the 3-space approach is based on best-matched actions such as the lapse-eliminated Baierlein-Sharp-Wheeler (BSW) action of general relativity (GR). These give rise to several branches of gravitational theories including GR on superspace and a theory of gravity on conformal superspace. This paper investigates the 3-space approach further, motivated both by the hierarchies of increasingly well-defined and weakened simplicity postulates present in all routes to relativity, and by the requirement that all the known fundamental matter fields be included. We further the study of configuration spaces of gravity-matter systems upon which BF'O's formulation leans. We note that in further developments the lapse-eliminated BSW actions used by BF'O become impractical and require generalization. We circumvent many of these problems by the equivalent use of lapse-uneliminated actions, which furthermore permit us to interpret BF'O's formulation within Kucha\ifmmode \checkr\else \vr\fi's generally covariant hypersurface framework. This viewpoint provides alternative reasons to BF'O's as to why the inclusion of bosonic fields in the 3-space approach gives rise to minimally coupled scalar fields, electromagnetism and Yang-Mills theory. This viewpoint also permits us to quickly exhibit further GR-matter theories admitted by the 3-space formulation. In particular, we show that the spin-(1)/(2) fermions of the theories of Dirac, Maxwell-Dirac and Yang-Mills-Dirac, all coupled to GR, are admitted by the generalized 3-space formulation we present. Thus all the known fundamental matter fields can be accommodated. This corresponds to being able to pick actions for all these theories which have less kinematics than suggested by the generally covariant hypersurface framework. For all these theories, Wheeler's thin sandwich conjecture may be posed, rendering them timeless in Barbour's sense.