Skip to main content Accessibility help
×
Home
Hostname: page-component-66d7dfc8f5-g56fq Total loading time: 0.296 Render date: 2023-02-09T12:39:52.136Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Regarding the ‘Hole Argument’ and the ‘Problem of Time’

Published online by Cambridge University Press:  01 January 2022

Abstract

The canonical formalism of general relativity affords a particularly interesting characterization of the infamous hole argument. It also provides a natural formalism in which to relate the hole argument to the problem of time in classical and quantum gravity. Conceptual and formal inadequacies within the representative language of canonical gravity will be shown to be at the heart of both the canonical hole argument and the problem of time. Interesting and fruitful work at the interface of physics and philosophy relates to the challenge of resolving such inadequacies.

Type
Research Article
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

We are hugely indebted to Erik Curiel, Samuel Fletcher, Oliver Pooley, Bryan Roberts, and James Weatherall for discussion and written comments that were invaluable in the evolution of this article. We are also very appreciative of feedback from members of audiences in Berlin, Bristol, London, and Oxford. K. T. acknowledges the support of the Munich Center for Mathematical Philosophy, the Alexander von Humboldt Foundation, and the University of Bristol. S. G.’s work was supported by the Netherlands Organisation for Scientific Research (NWO; project 620.01.784).

References

Ambj⊘rn, Jan, Jurkiewicz, Jerzy, and Loll, Renate. 2001. “Dynamically Triangulating Lorentzian Quantum Gravity.” Nuclear Physics B 610 (1): 347–82.Google Scholar
Anderson, Edward. 2012. “Problem of Time in Quantum Gravity.” Annalen der Physik 524 (12): 757–86.CrossRefGoogle Scholar
Anderson, Edward, Barbour, Julian, Foster, Brendan Z., Kelleher, Bryan, and O’Murchadha, Niall. 2005. “The Physical Gravitational Degrees of Freedom.” Classical and Quantum Gravity 22:17951802.CrossRefGoogle Scholar
Anderson, Edward, Barbour, Julian, Foster, Brendan Z., and O’Murchadha, Niall. 2003. “Scale-Invariant Gravity: Geometrodynamics.” Classical and Quantum Gravity 20:1571.CrossRefGoogle Scholar
Arnowitt, R., Deser, S., and Misner, C. W.. 1960. “Canonical Variables for General Relativity.” Physical Review 117:15951602. http://link.aps.org/doi/10.1103/PhysRev.117.1595.CrossRefGoogle Scholar
Deser, S., and Misner, C. W. 1962. “The Dynamics of General Relativity.” In Gravitation: An Introduction to Current Research, ed. Witten, L., 227–65. New York: Wiley.Google Scholar
Baez, John C. 1998. “Spin Foam Models.” Classical and Quantum Gravity 15 (7): 1827–58.CrossRefGoogle Scholar
Barbour, Julian. 1994. “The Timelessness of Quantum Gravity.” Pt. 1, “The Evidence from the Classical Theory.” Classical and Quantum Gravity 11 (12): 2853–73.CrossRefGoogle Scholar
Barbour, Julian 2003. “Scale-Invariant Gravity: Particle Dynamics.” Classical and Quantum Gravity 20:1543–70.CrossRefGoogle Scholar
Barbour, Julian, and Foster, B. Z.. 2008. “Constraints and Gauge Transformations: Dirac’s Theorem Is Not Always Valid.” arXiv.org preprint.Google Scholar
Barbour, Julian, Koslowski, Tim, and Mercati, Flavio. 2014. “The Solution to the Problem of Time in Shape Dynamics.” Classical and Quantum Gravity 31 (15): 155001.CrossRefGoogle Scholar
Belot, G. 2007. “The Representation of Time and Change in Mechanics.” In Handbook of Philosophy of Physics, ed. Butterfield, J. and Earman, J., chap. 2. Amsterdam: Elsevier.Google Scholar
Belot, G., and Earman, J.. 1999. “From Metaphysics to Physics.” In From Physics to Philosophy, ed. Butterfield, J. and Pagnois, C., 166–86. Cambridge: Cambridge University Press.Google Scholar
Pagnois, C. 2001. “Pre-Socratic Quantum Gravity.” In Physics Meets Philosophy at the Planck Scale, ed. Callender, C. and Hugget, N.. Cambridge: Cambridge University Press.Google Scholar
Bergmann, Peter. 1949. “Non-linear Field Theories.” Physical Review 75 (4): 680–85.CrossRefGoogle Scholar
Blohmann, Christian, Fernandes, Marco Cezar Barbosa, and Weinstein, Alan. 2010. “Groupoid Symmetry and Constraints in General Relativity.” arXiv.org, arXiv:1003.2857.Google Scholar
Bombelli, Luca, Lee, Joohan, Meyer, David, and Sorkin, Rafael D. 1987. “Space-Time as a Causal Set.” Physical Review Letters 59 (5): 521–24.CrossRefGoogle ScholarPubMed
Brighouse, Carolyn. 1994. “Spacetime and Holes.” In PSA 1994: Proceedings of the 1994 Biennial Meeting of the Philosophy of Science Association, ed. Hull, David L. and Forbes, Micky, 117–25. East Lansing, MI: Philosophy of Science Association.Google Scholar
Butterfield, Jeremy. 1989. “The Hole Truth.” British Journal for the Philosophy of Science 40:128.CrossRefGoogle Scholar
Corichi, Alejandro. 2008. “On the Geometry of Quantum Constrained Systems.” Classical and Quantum Gravity 25 (13): 135013. http://stacks.iop.org/0264-9381/25/i=13/a=135013.CrossRefGoogle Scholar
Curiel, Erik. 2015. “On the Existence of Spacetime Structure.” British Journal for the Philosophy of Science, forthcoming.Google Scholar
Dirac, P. A. 1950. “Generalized Hamiltonian Dynamics.” Canadian Journal of Mathematics 2:129–48.CrossRefGoogle Scholar
Dirac, P. A. 1958. “The Theory of Gravitation in Hamiltonian Form.” Proceedings of the Royal Society of London A 246:333–43.Google Scholar
Dirac, P. A. 1964. Lectures on Quantum Mechanics. New York: Dover.Google Scholar
Dittrich, B. 2006. “Partial and Complete Observables for Canonical General Relativity.” Classical and Quantum Gravity 23:6155–84.CrossRefGoogle Scholar
Dittrich, B. 2007. “Partial and Complete Observables for Hamiltonian Constrained Systems.” General Relativity and Gravitation 39:18911927.CrossRefGoogle Scholar
Dittrich, Bianca, Hoehn, Philipp A., Koslowski, Tim A., and Nelson, Mike I.. 2015. “Chaos, Dirac Observables and Constraint Quantization.” arXiv.org. http://arxiv.org/abs/1508.01947.Google Scholar
Dowker, Fay. 2005. “Causal Sets and the Deep Structure of Spacetime.” In 100 Years of Relativity, Space-Time Structure: Einstein and Beyond, ed. Ashtekar, Abhay, 445–64. Hackensack, NJ: World Scientific.Google Scholar
Earman, J. 2002. “Thoroughly Modern McTaggart; or, What McTaggart Would Have Said if He Had Read the General Theory of Relativity.” Philosopher’s Imprint 2 (3): 128.Google Scholar
Earman, John, and Norton, John. 1987. “What Price Spacetime Substantivalism? The Hole Story.” British Journal for the Philosophy of Science 38 (4): 515–25.CrossRefGoogle Scholar
Geroch, R. 1970. “Domain of Dependence.” Journal of Mathematical Physics 11:437–49.CrossRefGoogle Scholar
Giulini, Domenico. 1999. “The Generalized Thin-Sandwich Problem and Its Local Solvability.” Journal of Mathematical Physics 40 (5): 2470–82.CrossRefGoogle Scholar
Giulini, Domenico, and Marolf, D.. 1999. “On the Generality of Refined Algebraic Quantization.” Classical and Quantum Gravity 16:2479–88.CrossRefGoogle Scholar
Gomes, H., Gryb, S., and Koslowski, T.. 2011. “Einstein Gravity as a 3D Conformally Invariant Theory.” Classical and Quantum Gravity 28 (4): 045005.CrossRefGoogle Scholar
Gryb, Sean, and Thébault, Karim P. Y.. 2012. “The Role of Time in Relational Quantum Theories.” Foundations of Physics 42 (9): 1210–38.CrossRefGoogle Scholar
Gryb, Sean, and Thébault, Karim P. Y. 2014. “Symmetry and Evolution in Quantum Gravity.” Foundations of Physics 44 (3): 305–48.CrossRefGoogle Scholar
Gryb, Sean, and Thébault, Karim P. Y. 2015a. “Schrodinger Evolution for the Universe: Reparametrization.” Classical and Quantum Gravity 33 (6): 065004.CrossRefGoogle Scholar
Gryb, Sean, and Thébault, Karim P. Y. 2015b. “Time Remains.” British Journal for the Philosophy of Science, forthcoming.Google Scholar
Henneaux, M., and Teitelboim, C.. 1992. Quantization of Gauge Systems. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Henson, Joe. 2006. “The Causal Set Approach to Quantum Gravity.” arXiv.org, arXiv:gr-qc/0601121.Google Scholar
Isham, C. 1992. “Canonical Quantum Gravity and the Problem of Time.” arXiv.org. http://arxiv.org/abs/grqc/9210011.CrossRefGoogle Scholar
Isham, C. J., and Kuchař, K. V.. 1985a. “Representations of Spacetime Diffeomorphisms.” Pt. 1, “Canonical Parametrized Field Theories.” Annals of Physics 164 (2): 288315.. http://www.sciencedirect.com/science/article/pii/0003491685900181.CrossRefGoogle Scholar
Isham, C. J., and Kuchař, K. V.. 1985b. “Representations of Spacetime Diffeomorphisms.” Pt. 2, “Canonical Geometrodynamics.” Annals of Physics 164 (2): 316–33.. http://www.sciencedirect.com/science/article/pii/0003491685900193.Google Scholar
Kuchař, K. 1991. “The Problem of Time in Canonical Quantization of Relativistic Systems.” In Conceptual Problems of Quantum Gravity, ed. Ashtekar, A. and Stachel, J.. Boston: Birkhäuser.Google Scholar
Lauscher, O., and Reuter, M.. 2001. “Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity.” Physical Review D 65 (2): 025013.Google Scholar
Loll, Renate. 2001. “Discrete Lorentzian Quantum Gravity.” Nuclear Physics B 94 (1): 96107.CrossRefGoogle Scholar
Maudlin, Tim. 1988. “The Essence of Space-Time.” In PSA 1988: Proceedings of the 1988 Biennial Meeting of the Philosophy of Science Association, ed. Fine, Arthur and Leplin, Jarrett, 8291. East Lansing, MI: Philosophy of Science Association.Google Scholar
Leplin, Jarrett 2002. “Thoroughly Muddled McTaggart; or, How to Abuse Gauge Freedom to Create Metaphysical Monostrosities.” Philosopher’s Imprint 2 (4): 119.Google Scholar
Norton, John D. 2015. “The Hole Argument.” In The Stanford Encyclopedia of Philosophy, ed. Zalta, Edward N.. Stanford, CA: Stanford University.Google Scholar
Perez, Alejandro. 2013. “The Spin Foam Approach to Quantum Gravity.” Living Reviews in Relativity 16 (3): 12052019.CrossRefGoogle ScholarPubMed
Pitts, J. Brian. 2014a. “Change in Hamiltonian General Relativity from the Lack of a Time-Like Killing Vector Field.” Studies in History and Philosophy of Modern Physics, forthcoming. http://philsci-archive.pitt.edu/10094/.CrossRefGoogle Scholar
Pitts, J. Brian 2014b. “A First Class Constraint Generates Not a Gauge Transformation, but a Bad Physical Change: The Case of Electromagnetism.” Annals of Physics 351:382406.CrossRefGoogle Scholar
Pons, J. M. 2005. “On Dirac’s Incomplete Analysis of Gauge Transformations.” Studies in History and Philosophy of Science B 36:491518.CrossRefGoogle Scholar
Pons, J. M., Salisbury, D. C., and Shepley, L. C.. 1997. “Gauge Transformations in the Lagrangian and Hamiltonian Formalisms of Generally Covariant Theories.” Physical Review D 55 (2): 658–68.Google Scholar
Pons, J. M., Salisbury, D. C., and Sundermeyer, K. A.. 2010. “Observables in Classical Canonical Gravity: Folklore Demystified.” Journal of Physics A 222 (1): 12018.Google Scholar
Pooley, Oliver. 2001. “Relationism Rehabilitated?” Pt. 2, “Relativity.” PhilSci, University of Pittsburgh. http://philsci-archive.pitt.edu/221/.Google Scholar
Pooley, Oliver 2006. “A Hole Revolution, or Are We Back Where We Started?Studies in History and Philosophy of Science B 37 (2): 372–80.Google Scholar
Pooley, Oliver 2013. “Substantivalist and Relationalist Approaches to Spacetime.” In The Oxford Handbook of Philosophy of Physics, ed. Batterman, Robert W.. New York: Oxford University Press.Google Scholar
Rickles, Dean P. 2005. “A New Spin on the Hole Argument.” Studies in History and Philosophy of Science B 36 (3): 415–34.Google Scholar
Rickles, Dean P. 2006. “Bringing the Hole Argument Back in the Loop: A Response to Pooley.” Studies in History and Philosophy of Science B 37 (2): 381–87.Google Scholar
Roberts, Bryan W. 2014. “Disregarding the ‘Hole Argument.’” arXiv.org, arXiv:1412.5289.Google Scholar
Rovelli, Carlo. 2002. “Partial Observables.” Physical Review D 65:124013.Google Scholar
Rovelli, Carlo 2004. Quantum Gravity. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Rovelli, Carlo 2014. “Why Gauge?Foundations of Physics 44 (1): 91104.CrossRefGoogle Scholar
Salisbury, Donald C. 2007. “Rosenfeld, Bergmann, Dirac and the Invention of Constrained Hamiltonian Dynamics.” arXiv.org. http://arxiv.org/abs/physics/0701299v1.Google Scholar
Salisbury, Donald C. 2010. “Léon Rosenfeld’s Pioneering Steps toward a Quantum Theory of Gravity.” Journal of Physics: Conference Series 222 (1): 012052.Google Scholar
Salisbury, Donald C. 2012. “Peter Bergmann and the Invention of Constrained Hamiltonian Dynamics.” In Einstein and the Changing Worldviews of Physics, ed. Lehner, Christoph and Renn, Jürgen, 247–57. Einstein Studies 12. Boston: Birkhäuser.Google Scholar
Stachel, John. 2014. “The Hole Argument and Some Physical and Philosophical Implications.” Living Reviews in Relativity, vol. 17.Google Scholar
Teitelboim, Claudio. 1973. “How Commutators of Constraints Reflect the Spacetime Structure.” Annals of Physics 79 (2): 542–57.CrossRefGoogle Scholar
Thébault, K. P. Y. 2011. “Symplectic Reduction and the Problem of Time in Nonrelativistic Mechanics.” PhilSci, University of Pittsburgh. http://philsci-archive.pitt.edu/8623/.Google Scholar
Thébault, K. P. Y. 2012. “Three Denials of Time in the Interpretation of Canonical Gravity.” Studies in History and Philosophy of Science B 43 (4): 277–94.Google Scholar
Thiemann, T. 2006. “The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity.” Classical and Quantum Gravity 23:2211–48.CrossRefGoogle Scholar
Thiemann, T. 2007. Modern Canonical Quantum General Relativity. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Weatherall, James Owen. 2016. “Regarding the ‘Hole Argument.’” British Journal for the Philosophy of Science, forthcoming.Google Scholar

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Regarding the ‘Hole Argument’ and the ‘Problem of Time’
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Regarding the ‘Hole Argument’ and the ‘Problem of Time’
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Regarding the ‘Hole Argument’ and the ‘Problem of Time’
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *