Edward Anderson (Cambridge): Spaces of Spaces

Abstract:

John Archibald Wheeler asked that we study superspace: the space of 3-geometry configurations for GR (3-metrics quotiented by 3-diffeomorphisms). Moreover; Chris Isham has studied a far wider range of spaces of spaces; from the point of view of quantization. I here present:

a) classical preliminaries for this study. These do not only include the obvious classical dynamics precursors on these spaces but also the phrasing of stochastic theory thereupon (following e.g. several different works of David Kendall).

b) A relational and background independent analysis of the choices made in adopting such spaces of spaces; this is in the vein of my and Julian Barbour’s meanings of relational notions.

These considerations greatly generalize Wheeler’s questions about superspace.ξTwo particular points of focus areξ:

1) on the commonplace appearance of stratified manifolds as configurations.

2) On the lattice of topological spaces based on a fixed set.