General-relativistic Spacetimes Are Not (so) Special

Authors

DOI:

https://doi.org/10.35588/cc.v6d7925

Keywords:

General relativity, Gauge symmetry, Spacetime, Diffeomorphism invariance, Quantum gravity

Abstract

The invariance under diffeomorphisms of general relativity is a formal property of the theory that is not present in other theories. Some authors, closely related to research in quantum gravity, have argued that this symmetry means that spacetime in general relativity cannot be interpreted like other spacetimes. More specifically, spacetime would be only a structure for representing “correlations.” This position is supported by three arguments: the gauge argument, relationalist arguments such as the hole argument, and the relationship with quantum gravity. In this article, I study this position and these arguments and reject them. The position I defend is that invariance under diffeomorphisms does not make the spacetimes of general relativity different in any deep sense, and that they should be interpreted analogously to other spacetimes. More precisely, spacetime, both in general relativity and other theories, is a set of events with a series of causal, geometric, and inertial relations.

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References

Chataignier, L., Hoehn, P. A., Lock, M. P. E., & Mele, F. M. (2024). Relational Dynamics with Periodic Clocks (arXiv:2409.06479). arXiv. https://doi.org/10.48550/arXiv.2409.06479

Dittrich, B., Hoehn, P. A., Koslowski, T. A., & Nelson, M. I. (2015). Chaos, Dirac observables and constraint quantization. https://arxiv.org/abs/1508.01947v1

Dittrich, B., Höhn, P. A., Koslowski, T. A., & Nelson, M. I. (2017). Can chaos be observed in quantum gravity? Physics Letters B, 769, 554–560. https://doi.org/10.1016/j.physletb.2017.02.038

Earman, J. (2002). Thoroughly Modern Mctaggart: Or, What Mctaggart Would Have Said If He Had Read the General Theory of Relativity. Philosophers’ Imprint, 2(3), 1–28.

Earman, J. (2006). The Implications of General Covariance for the Ontology and Ideology of Spacetime. Philosophy and Foundations of Physics, 1(C), 3–23. https://doi.org/10.1016/S1871-1774(06)01001-1

Earman, J., & Norton, J. (1987). What Price Spacetime Substantivalism? The Hole Story. Https://Doi.Org/10.1093/Bjps/38.4.515, 38(4), 515–525. https://doi.org/10.1093/BJPS/38.4.515

Isham, C. J. (1993). Canonical Quantum Gravity and the Problem of Time. In Integrable Systems, Quantum Groups, and Quantum Field Theories (pp. 157–287). Springer Netherlands. https://doi.org/10.1007/978-94-011-1980-1_6

Kretschmann, E. (1917). Über den Physikalischen Sinn der Relativitätspostulate. Annalen Der Physik, 53, 575–614.

Kuchař, K. V. (1991). The problem of time in canonical quantization of relativistic systems. In A. Ashtekar & J. Stachel (Eds.), Conceptual Problems of Quantum Gravity (p. 141). Birkhauser. https://philpapers.org/rec/KUCTPO-3

Kuchař, K. V. (1992). Time and interpretations of quantum gravity. In G. Kunstatter, D. Vincent, & J. Williams (Eds.), Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics. World Scientific Publishing Company. https://doi.org/10.1142/S0218271811019347

Kuchař, K. V. (1993). Canonical Quantum Gravity. General Relativity and Gravitation, 1992, 119.

Mozota Frauca, Á. (2023). Reassessing the problem of time of quantum gravity. General Relativity and Gravitation, 55(1), 21. https://doi.org/10.1007/s10714-023-03067-x

Mozota Frauca, Á. (2024a). GPS observables in Newtonian spacetime or why we do not need ‘physical’ coordinate systems. European Journal for Philosophy of Science, 14(4), 51. https://doi.org/10.1007/s13194-024-00611-7

Mozota Frauca, Á. (2024b). In Which Sense Can We Say That First-Class Constraints Generate Gauge Transformations? Philosophy of Physics. https://doi.org/10.31389/pop.48

Mozota Frauca, Á. (2024c). The Problem of Time for Non-Deparametrizable Models and Quantum Gravity. In F. Bianchini, V. Fano, & P. Graziani (Eds.), Current Topics in Logic and the Philosophy of Science. Papers from SILFS 2022 postgraduate conference. (Vol. 4). College Publications. https://philsci-archive.pitt.edu/24052/

Mozota Frauca, Á. (2025). Against Radical Relationalism: In Defense of the Ordinal Structure of Time. Foundations of Physics, 55(3), 37. https://doi.org/10.1007/s10701-025-00850-5

Norton, J. D., Pooley, O., & Read, J. (2023). The Hole Argument. In E. N. Zalta & U. Nodelman (Eds.), The Stanford Encyclopedia of Philosophy (Summer 2023). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/sum2023/entries/spacetime-holearg/

Pitts, J. B. (2014). A first class constraint generates not a gauge transformation, but a bad physical change: The case of electromagnetism. Annals of Physics, 351, 382–406. https://doi.org/10.1016/j.aop.2014.08.014

Pitts, J. B. (2018). Equivalent Theories and Changing Hamiltonian Observables in General Relativity. Foundations of Physics, 48(5), 579–590. https://doi.org/10.1007/s10701-018-0148-1

Pitts, J. B. (2022). First-Class Constraints, Gauge Transformations, de-Ockhamization, and Triviality: Replies to Critics, Or, How (Not) to Get a Gauge Transformation from a Second-Class Primary Constraint. https://doi.org/10.48550/arxiv.2212.02944

Pitts, J. B. (2024). Does a second-class primary constraint generate a gauge transformation? Electromagnetisms and gravities, massless and massive. Annals of Physics, 462, 169621. https://doi.org/10.1016/j.aop.2024.169621

Pons, J. M., & Salisbury, D. C. (2005). Issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity. Physical Review D, 71(12), 124012. https://doi.org/10.1103/PhysRevD.71.124012

Pons, J. M., Salisbury, D. C., & Sundermeyer, K. A. (2010). Observables in classical canonical gravity: Folklore demystified. Journal of Physics: Conference Series, 222(1), 012018. https://doi.org/10.1088/1742-6596/222/1/012018

Pooley, O. (2017). Background Independence, Diffeomorphism Invariance and the Meaning of Coordinates. In D. Lehmkuhl, G. Schiemann, & E. Scholz (Eds.), Towards a Theory of Spacetime Theories (pp. 105–143). Springer. https://doi.org/10.1007/978-1-4939-3210-8_4

Pooley, O., & Wallace, D. (2022). First-class constraints generate gauge transformations in electromagnetism (reply to Pitts). https://doi.org/10.48550/arxiv.2210.09063

Rickles, D. (2008). Chapter 7 Who’s Afraid of Background Independence? In D. Dieks (Ed.), Philosophy and Foundations of Physics (Vol. 4, pp. 133–152). Elsevier. https://doi.org/10.1016/S1871-1774(08)00007-7

Rovelli, C. (1991a). Quantum evolving constants. Reply to "Comment on `Time in quantum gravity: An hypothesis’ ". Physical Review D, 44(4), 1339. https://doi.org/10.1103/PhysRevD.44.1339

Rovelli, C. (1991b). Time in quantum gravity: An hypothesis. Physical Review D, 43(2), 442. https://doi.org/10.1103/PhysRevD.43.442

Rovelli, C. (1991c). What is observable in classical and quantum gravity? Classical and Quantum Gravity, 8(2), 297. https://doi.org/10.1088/0264-9381/8/2/011

Rovelli, C. (2004). Quantum Gravity. Cambridge University Press. https://doi.org/10.1017/CBO9780511755804

Rovelli, C. (2011). “Forget time” Essay written for the FQXi contest on the Nature of Time. Foundations of Physics, 41(9), 1475–1490. https://doi.org/10.1007/s10701-011-9561-4

Rovelli, C., & Vidotto, F. (2022). Philosophical Foundations of Loop Quantum Gravity. https://arxiv.org/abs/2211.06718v2

Thébault, K. P. Y. (2012). Three denials of time in the interpretation of canonical gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 43(4), 277–294. https://doi.org/10.1016/J.SHPSB.2012.09.001

Thébault, K. P. Y. (2021). The Problem of Time. In E. Knox & A. Wilson (Eds.), The Routledge Companion to Philosophy of Physics. Routledge. https://www.routledge.com/The-Routledge-Companion-to-Philosophy-of-Physics/Knox-Wilson/p/book/9781138653078#

Weatherall, J. O. (2021). Classical Spacetime Structure. In The Routledge Companion to Philosophy of Physics. Routledge.

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Submitted

2026-01-19

Published

2026-01-19

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Dossier: Philosophy and Foundations of Physics

How to Cite

General-relativistic Spacetimes Are Not (so) Special. (2026). Culturas Científicas, 6(1). https://doi.org/10.35588/cc.v6d7925

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