Abstract
It is generally acknowledged that the requirement that the laws of a spacetime theory be covariant under a general coordinate transformation is a restriction on the form but not the content of the theory. The prevalent view in the physics community holds that the substantive version of general covariance – exhibited, for example, by Einstein’s general theory of relativity – consists in the requirement that diffeomorphism invariance is a gauge symmetry of the theory. This conception of general covariance is explained and confronted by two challenges. One challenge claims, in effect, that substantive general covariance is not deserving of the name since, just as it is possible to rewrite any spacetime so that it satisfies formal general covariance, so it is also possible to rewrite the theory so that it satisfies the proffered version of substantive general covariance. The other challenge claims that the proffered version of substantive general covariance is not strong enough to guarantee the intended meaning of general covariance. Both challenges are discussed in terms of concrete examples. It is argued that both challenges fail but, at the same time, that they help to clarify what is at stake on the seemingly never ending dispute over the nature and status of general covariance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bain J.: 2004, ‘Theories of Newtonian Gravity and Empirical Indistinguishability’, Studies in History and Philosophy of Modern Physics, forthcoming.
Biezunski, M. (ed.): 1989, Œuvres Choisies d’Albert Einstein, Tome 4 (Correspondances Françaises), Editions CNRS, Paris.
L. Bombelli (1991) ‘Unimodular Relativity, General Covariance, Time, and the Ashtekar Variables’ R. Mann P. Wesson (Eds) Gravitation: A Banff Summer Institute World Scientific Singapore 221–232
J. D. Brown J. W. York (1989) ArticleTitle‘Jacobi’s Action and the Recovery of Time in General Relativity’ Physical Review D 40 3312–3318 Occurrence Handle10.1103/PhysRevD.40.3312
J. Christian (1997) ArticleTitle‘Exactly Soluble Sector of Quantum Gravity’ Physical Review D 56 4844–4877 Occurrence Handle10.1103/PhysRevD.56.4844
C. Duval H. Künzle (1984) ArticleTitle‘Minimal Gravitational Coupling in Newtonian Theory and the Covariant Schrödinger Equation’ General Relativity and Gravitation 4 333–347
Earman, J.: 2002, ‘Thoroughly Modern McTaggart: Or What McTaggart Would Have Said if He Had Learned the General Theory of Relativity’, Philosophers’ Imprint. http://www.philosophersimprint.org/
J. Earman (2003a) ‘Tracking Down Gauge: An Ode to the Constrained Hamiltonian Formalism’ K. Brading E. Castellani (Eds) Symmetries in Physics Cambridge University Press Cambridge 140–162
J. Earman (2003b) ArticleTitle‘The Cosmological Constant, the Fate of the Universe, Unimodular Gravity, and All That’ Studies in History and Philosophy of Modern Physics 34 559–577
A. Einstein (1916) ArticleTitle‘Grundlage der allgemeinen Relativitätstheorie’ Annalen der Physik 49 769–822
A. Einstein (1951) ‘Reply to Criticisms’ P. A. Schilpp (Eds) Albert Einstein: Philosopher-Scientist NumberInSeriesVol. 2 Harper and Row New York
M. Friedman (1983) Foundations of Space-Time Theories Princeton University Press Princeton, NJ
M. Henneaux C. Teitelboim (1989) ArticleTitle‘The Cosmological Constant and General Covariance’ Physics Letters B 222 195–199 Occurrence Handle10.1016/0370-2693(89)91251-3
M. Henneaux C. Teitelboim (1992) Quantization of Gauge Systems Princeton University Press Princeton, NJ
D. Howard (1999) ‘Point Coincidences and Pointer Coincidences: Einstein and the Invariant Content of Space-Time Theories’ H. Goenner J. Renn J. Ritter T. Sauer (Eds) The Expanding Worlds of General Relativity, Einstein Studies NumberInSeriesVol. 7 Birkhäuser Boston 463–500
C. J. Isham (1992) ‘Canonical Quantum Gravity and the Problem of Time’ L. A. Ibot M. A. Rodríguez (Eds) Integrable Systems, Quantum Groups, and Quantum Field Theories Kluwer Academic Boston 157–287
C. J. Isham K. Kuchař (1986a) ArticleTitle‘Representations of Spacetime Diffeomorphisms. I. Canonical Parametrized Field Theories’ Annals of Physics 164 316–333
C. J. Isham K. Kuchař (1986b) ArticleTitle‘Representations of Spacetime Diffeomorphisms. II. Canonical Geometrodynmamics’ Annals of Physics 164 288–315
E. Kretchmann (1915) ArticleTitle‘Über die prinzipielle Bestimmbarkeit der berechtigten Bezugssystemebelibiger Relativitätstheorien’ Annalen der Physik 48 907–942
E. Kretchmann (1917) ArticleTitle‘Über den physikalischen Sinn der Relativitütspostulate, A. Einsteins neue und seine ursprügliche Relativitätstheorie’ Annalen der Physik 53 575–614
K. Kuchař (1991) ArticleTitle‘Does an Unspecified Cosmological Constant Solve the Problem of Time in Quantum Gravity?’ Physical Review D 43 3332–3344
Kuchař, K.: 1992, ‘Time and the Interpretation of Quantum Gravity’, in G. Kunsatter, D. Vincent, and J.Williams (eds.), Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics, World Scientific, Singapore, pp. 211–314.
H. Künzle (1972) ArticleTitle‘Galelei and Lorentz Structures on Spacetime: Comparison of the Corresponding Geometry and Physics’ Annales de l’Institut Henri Poincaré Physique Théorique 41 363–384
Norton, J. D.: 1984, ‘How Einstein Found His Field Equations: 1912–1915’, reprinted in D. Howard and J. Stachel (eds.), Einstein and the History of General Relativity. Einstein Studies, Vol. I, Birkhäuser, Boston, 1986, pp. 101–159.
J. D. Norton (1993) ArticleTitle‘General Covariance and the Foundations of General Relativity: Eight Decades of Dispute’ Reports on Progress in Physics 56 791–858 Occurrence Handle10.1088/0034-4885/56/7/001
P. J. Olver (1993) Applications of Lie Groups to Differential Equations EditionNumber2 Springer- Verlag New York
C. Rovelli (1991) ArticleTitle‘What is an Observable in Classical and Quantum Gravity?’ Classical and Quantum Gravity 8 297–316
Rovelli, C.: 1998, ‘Loop Quantum Gravity’, Living Reviews in Relativity http://www.livingreviews.org/
R. Rynasiewicz (1999) ‘Kretchmann’s Analysis of General Covariance’ H. Goenner J. Renn J. Ritter T. Sauer (Eds) The Expanding Worlds of General Relativity Birkhäuser Boston 431–462
L. Smolin (2004) ArticleTitle‘Atoms of Space and Time’ Scientific American 290 IssueID1 66–75
R. Sorkin (2002) ArticleTitle‘An Example Relevant to the Kretchmann–Einstein Debate’ Modern Physics Letters A 17 695–700
P. Speziali (Eds) (1972) Albert Einstein–Michele Besso Correspondence 1903–1955 Hermann Paris
J. Stachel (1986) ’Einstein’s Search for General Covariance: 1912-1915’ D. Howard J. Stachel (Eds) Einstein and the History of General Relativity. Einstein Studies NumberInSeriesVol. I Birkhäuser Boston 63–100
J. Stachel (1993) ‘The Meaning of General Covariance: The Hole Story’ J. Earman A. I. Janis G. J. Massey N. Rescher (Eds) Philosophical Problems of the Internal and External Worlds University of Pittsburgh Press Pittsburgh, PA 129–160
W. G. Unruh (1989) ArticleTitle‘Unimodular Theory of Canonical Quantum Gravity’ Physical Review D 40 1048–1051
W. G. Unruh R. M. Wald (1989) ArticleTitle‘Time and the Interpretation of Canonical Quantum Gravity’ Physical Review D 40 2598–2614
R. M. Wald (1984) General Relativity University of Chicago Press Chicago, IL
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Earman, J. Two Challenges to the Requirement of Substantive General Covariance. Synthese 148, 443–468 (2006). https://doi.org/10.1007/s11229-004-6239-x
Issue Date:
DOI: https://doi.org/10.1007/s11229-004-6239-x