Problem of Time and Background Independence: the Individual Facets

TL;DR

This paper explores the multifaceted problem of time in background-independent theories, analyzing classical counterparts, and emphasizing the importance of understanding each facet individually before tackling their complex interactions.

Contribution

It provides a detailed, facet-by-facet conceptual analysis of the problem of time, including new facets and subfacets, and discusses the layered mathematical structures involved.

Findings

Classical counterparts of time facets are identified.

Interactions between facets are nonlinear and complex.

New threading-based facets and subfacets are introduced.

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.