Graph explorer

Spaces of Spaces

Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I consider furthmore generalized configuration spaces to all levels within the conventional `equipped sets' paradigm of mathematical structure used in fundamental Theoretical Physics. This covers A) the more familiar issue of topology change in the sense of topological manifolds (tied to cobordisms), including via pinched manifolds. B) The less familiar issue of not regarding as fixed the yet deeper levels of structure: topological spaces themselves (and their metric space subcase), collections of subsets and sets. Isham has previously presented quantization schemes for a number of these. I consider some classical preliminaries for this program, aside from the most obvious (classical dynamics for each). Rather, I provide I) to all levels Relational and Background Independence criteria, which have Problem of Time facets as consequences. I demonstrate that many of these issues descend all the way down, whilst also documenting at which level the ot