Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T08:17:59.036Z Has data issue: false hasContentIssue false
  • English
  • Français

The Geometry of Conventionality

Published online by Cambridge University Press:  01 January 2022

James Owen Weatherall  and
John Byron Manchak
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.

References

Carnap, Rudolf. 1922. Der Raum. Berlin: Reuther & Reichard.Google Scholar
Carnap, Rudolf 1958. “Preface.” In Reichenbach 1958.Google Scholar
Carnap, Rudolf 1966. Philosophical Foundations of Physics. New York: Basic.Google Scholar
Friedman, Michael. 1983. Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science. Princeton, NJ: Princeton University Press.Google Scholar
Glymour, Clark. 1977. “The Epistemology of Geometry.” Noûs 11 (3): 227–51.CrossRefGoogle Scholar
Grünbaum, Adolf. 1963. Philosophical Problems of Space and Time. New York: Knopf.Google Scholar
Grünbaum, Adolf 1968. Geometry and Chronometry in Philosophical Perspective. Minneapolis: University of Minnesota Press.Google Scholar
Knox, Eleanor. 2013. “Newtonian Spacetime Structure in Light of the Equivalence Principle.” British Journal for the Philosophy of Science, forthcoming. doi:10.1093/bjps/axt037.CrossRefGoogle Scholar
Malament, David B. 1986. “A Modest Remark about Reichenbach, Rotation, and General Relativity.” Philosophy of Science 52 (4): 615–20.Google Scholar
Malament, David B. 2012. Topics in the Foundations of General Relativity and Newtonian Gravitation Theory. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Norton, John D. 1994. “Why Geometry Is Not Conventional.” In Semantical Aspects of Spacetime Theories, ed. Maier, U. and Schmidt, H.-J., 159–67. Mannheim: Wissenschaftsverlag.Google Scholar
Poincaré, Henri. 1905. Science and Hypothesis. New York: Scott.Google Scholar
Reichenbach, Hans. 1958. The Philosophy of Space and Time. New York: Dover.Google Scholar
Salmon, Wesley C. 1979. “The Philosophy of Hans Reichenbach.” In Hans Reichenbach: Logical Empiricist, ed. Salmon, Wesley C., 1–84. Boston: Reidel.CrossRefGoogle Scholar
Schlick, Moritz. 1920. Space and Time in Contemporary Physics. New York: Oxford University Press.Google Scholar
Sklar, Lawrence. 1974. Space, Time, and Spacetime. Berkeley: University of California Press.Google Scholar
Wald, Robert M. 1984. General Relativity. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Weatherall, James Owen. 2013. “Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?” Unpublished manuscript, University of California, Irvine.Google Scholar

A correction has been issued for this article:

Erratum