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The Geometry of Conventionality

Published online by Cambridge University Press:  01 January 2022

James Owen Weatherall  and
John Byron Manchak
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Abstract

There is a venerable position in the philosophy of space and time that holds that the geometry of spacetime is conventional, provided one is willing to postulate a “universal force field.” Here we ask a more focused question, inspired by this literature: in the context of our best classical theories of space and time, if one understands “force” in the standard way, can one accommodate different geometries by postulating a new force field? We argue that the answer depends on one’s theory. In Newtonian gravitation the answer is yes; in relativity theory, it is no.

Type
Research Article
Information
Philosophy of Science , Volume 81 , Issue 2 , April 2014 , pp. 233 - 247
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

This article was revised and reposted on January 21, 2015, with corrections to typesetting errors in several mathematical terms that should have had staggered indices. Corrections, detailed by page number in the original April 2014 article, are noted in the erratum published in the April 2015 issue.

†

The authors would like to thank David Malament, Erik Curiel, Arthur Fine, Thomas Ryckman, J. Brian Pitts, Jeremy Butterfield, Adam Caulton, Eleanor Knox, Hans Halvorson, and an anonymous referee for helpful comments on previous drafts of this article. Versions of this work have been presented to the Hungarian Academy of Sciences, to a seminar at the University of Pittsburgh, and at the seventeenth UK and European Meeting on the Foundations of Physics in Munich; we are grateful to the organizers of these events and for the insightful discussions that followed the talks.

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A correction has been issued for this article:

Erratum