The hole argument and beyond: Part II: treating non-isomorphic spacetimes

Conference item

In this two-part paper we review, and then develop, the assessment of the hole argument for general relativity.

The review (in Part I) discussed how to compare points in isomorphic spacetimes, i.e. models of the theory. This second Part proposes a framework for making comparisons of non-isomorphic spacetimes. It combines two ideas we discussed in Part I—the philosophical idea of counterparts, and the idea of threading points between spacetimes other than by isomorphism—with the mathematics of fibre bundles.

We first recall the ideas from Part I (Section 1). Then in Section 2 and an Appendix, we define a fibre bundle whose fibres are isomorphic copies of a given spacetime or model, and discuss connections on this fibre bundle. This material proceeds on analogy with field-space formulations of gauge theories. Finally, in Section 3, we show how this fibre bundle gives natural expressions of the philosophical ideas of counterparts, and of threading.

Authors: Gomes, H; Butterfield, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Journal of Physics: Conference Series
• Volume: 2533
• Issue: 1
• Article number: 012003
• Publication date: 2023-06-30
• Acceptance date: 2023-06-09
• Event title: Tenth International Workshop on Decoherence, Information, Complexity and Entropy (DICE 2022)
• Event location: Castiglioncello, Italy
• Event website: https://osiris.df.unipi.it/~elze/DICE2022.html
• Event start date: 2022-09-19
• Event end date: 2022-09-23
• DOI: 10.1088/1742-6596/2533/1/012003
• ISSN: 1742-6596
• Language: English
• Keywords: FFR