Madarász, J.X., Stannett, M. orcid.org/0000-0002-2794-8614 and Székely, G. (2022) Investigations of isotropy and homogeneity of spacetime in first-order logic. Annals of Pure and Applied Logic, 173 (9). 103153. ISSN 0168-0072
Abstract
We investigate the logical connection between (spatial) isotropy, homogeneity of space, and homogeneity of time within a general axiomatic framework. We show that isotropy not only entails homogeneity of space, but also, in Image 1, homogeneity of time. In turn, homogeneity of time implies homogeneity of space in general, and the converse also holds true in Image 2
An important innovation in our approach is that formulations of physical properties are simultaneously empirical and axiomatic (in the sense of first-order mathematical logic). In this case, for example, rather than presuppose the existence of spacetime metrics – together with all the continuity and smoothness apparatus that would entail – the basic logical formulas underpinning our work refer instead to the sets of (idealised) experiments that support the properties in question, e.g., isotropy is axiomatized by considering a set of experiments whose outcomes remain unchanged under spatial rotation. Higher-order constructs are not needed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | First-order logic; Relativity theory; Classical spacetime; Homogeneity; Isotropy; Axiomatization |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Funding Information: | Funder Grant number LONDON MATHEMATICAL SOCIETY 41508 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Jun 2022 13:17 |
Last Modified: | 29 Jun 2022 16:29 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.apal.2022.103153 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:187965 |