Where to Apply Relationalism

TL;DR

This paper discusses the application of relationalism to the Problem of Time in quantum gravity, highlighting its classical advantages, potential impacts on various facets, and suggesting future research directions involving background independence.

Contribution

It evaluates the relevance of relationalism to the Problem of Time and proposes extending relational ideas to quantum gravity's background structures.

Findings

Relationalism addresses several classical facets of the Problem of Time.

Classical relational approaches are more tractable and offer insights for quantum cases.

Incorporating relational thinking into quantum gravity could extend background independence concepts.

Abstract

Relationalism -- along the lines developed by Barbour and collaborators in the past 3 decades -- can be considered an advance with 1/4 of the facets of the canonical approach's Problem of Time as identified by Isham and Kuchar. Indeed, almost all of the Problem of Time facets have classical counterparts, since they arise from consequences of demanding background independence rather than about combining GR and QM per se. Moreover the quantum version is harder, while the classical counterpart provides some suggestions through being more solvable. The suggestion then is to consider the effect of this advance on the Problem of Time as a whole, as opposed to repeating the same classical portion for a different redundancy group acting on the configuration space: shape dynamics. There are indeed some knock-on effects because the facets are notoriously not independent. The other facets do also however require distinct insights. Finally, I comment on the above being `metric' background independence, whereas quantum gravity usually assumes many other levels of background structures. Whilst Isham already wrote about this over two decades ago, it has largely not yet been incorporated into quantum gravity programs, and could well be a good area to extend and re-envigour by use of relational thinking.