Regarding the `Hole Argument' and the `Problem of Time'

TL;DR

This paper explores the formal and philosophical connections between the hole argument and the problem of time in general relativity, highlighting conceptual issues in canonical gravity and discussing implications for spacetime ontology debates.

Contribution

It provides a formal analysis linking the hole argument and the problem of time, and discusses philosophical implications for spacetime ontology and the relationalist/substantivalist debate.

Findings

Formal inadequacies underpin both the hole argument and the problem of time.

Resolving conceptual issues in canonical gravity can impact foundational debates.

The paper suggests a need for improved formal language in quantum gravity.

Abstract

The canonical formalism of general relativity affords a particularly interesting characterisation of the infamous hole argument. It also provides a natural formalism in which to relate the hole argument to the problem of time in classical and quantum gravity. In this paper, we examine the connection between these two much discussed problems in the foundations of spacetime theory along two interrelated lines. First, from a formal perspective, we consider the extent to which the two problems can and cannot be precisely and distinctly characterised. Second, from a philosophical perspective, we consider the implications of various responses to the problems, with a particular focus upon the viability of a `deflationary' attitude to the relationalist/substantivalist debate regarding the ontology of spacetime. Conceptual and formal inadequacies within the representative language of canonical gravity will be shown to be at the heart of both the canonical hole argument and the problem of time. Interesting and fruitful work at the interface of physics and philosophy relates to the challenge of resolving such inadequacies.