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The Hole Argument and Beyond: Part II: Treating Non-isomorphic Spacetimes

Gomes, Henrique and Butterfield, Jeremy (2023) The Hole Argument and Beyond: Part II: Treating Non-isomorphic Spacetimes. [Preprint]

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Abstract

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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Gomes, Henriquegomes.ha@gmail.com0000-0002-9285-0090
Butterfield, Jeremyjb56@cam.ac.uk0000-0002-0215-5802
Additional Information: Forthcoming in the Journal of Physics: Proceedings of the DICE Conference, Castiglioncello, Italy, September 2022
Keywords: the hole argument, fibre bundles, comparing non-isomorphic spacetimes, spacetimes as counterparts, best-matching, relational connection-form
Subjects: General Issues > Determinism/Indeterminism
General Issues > Realism/Anti-realism
Specific Sciences > Physics > Relativity Theory
Depositing User: Jeremy Butterfield
Date Deposited: 26 Mar 2023 16:00
Last Modified: 26 Mar 2023 16:00
Item ID: 21912
Subjects: General Issues > Determinism/Indeterminism
General Issues > Realism/Anti-realism
Specific Sciences > Physics > Relativity Theory
Date: March 2023
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21912

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