Problem of Time and Background Independence: the Individual Facets

Abstract

I lay out the problem of time facets as arising piecemeal from a number of aspects of background independence. Almost all of these already have simpler classical counterparts. This approach can be viewed as a facet by facet completion of the observation that Barbour-type relationalism is a background independent precursor to 2 of the 9 facets. That completion proceeds in an order dictated by the additional layers of mathematical structure required to support each. Moreover, the `nonlinear nature' of the interactions between the Problem of Time facets renders a joint study of them mandatory. The current article is none the less a useful prequel via gaining a conceptual understanding of each facet, prior to embarking on rendering some combinations of facets consistent and what further obstructions arise in attempting such joint considerations. See [20, 21, 26] for up to date studies of this more complicated joint version. I also identify new facets (threading based), subfacets (of observables and of reconstructions) and further source of variety from how far down the levels of mathematical structure these facets extend.