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 | |||||||||
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| 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 |
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| 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 |
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| Date: | March 2023 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/21912 |
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