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Determinism and General Relativity

Published online by Cambridge University Press:  01 January 2022

Abstract

We investigate the fate of determinism in general relativity (GR), comparing the philosopher’s account with the physicist’s well-posed initial value formulations. The fate of determinism is interwoven with the question of what it is for a spacetime to be ‘physically reasonable’. A central concern is the status of global hyperbolicity, a putatively necessary condition for determinism in GR. While global hyperbolicity may fail to be true of all physically reasonable models, we analyze whether global hyperbolicity should be (i) imposed by fiat; (ii) established from weaker assumptions, as in cosmic censorship theorems; or (iii) justified by beyond-GR physics.

Type
Research Article
Copyright
Copyright 2021 by the Philosophy of Science Association. All rights reserved.

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Footnotes

We thank Gordon Belot, Juliusz Doboszewski, J. B. Manchak, the audience at PSA 2010 in Montreal, the New Directions group at Western University, and two anonymous referees for their valuable feedback and exchanges. We acknowledge partial support from the John Templeton Foundation (grants 61048 and 61387). Both authors contributed equally to this article.

References

Andersson, Lars. 2004. “The Global Existence Problem in General Relativity.” In The Einstein Equations and the Large Scale Behavior of Gravitational Fields, ed. Chruściel, Piotr and Friedrich, Helmut, 71120. Boston: Birkhäuser.CrossRefGoogle Scholar
Belnap, Nuel. 1992. “Branching SpaceTime.” Synthese 92:385434.CrossRefGoogle Scholar
Budic, Robert, and Sachs, Rainer K. 1976. “Deterministic SpaceTimes.” General Relativity and Gravitation 7:2129.CrossRefGoogle Scholar
Butterfield, Jeremy. 1989. “The Hole Truth.” British Journal for the Philosophy of Science 40:169–88.CrossRefGoogle Scholar
Choquet-Bruhat, Yvonne, and Geroch, Robert. 1969. “Global Aspects of the Cauchy Problem in General Relativity.” Communications in Mathematical Physics 14:329–35.CrossRefGoogle Scholar
Christodoulou, Demetrios. 2007. The Formation of Shocks in 3-Dimensional Fluids, vol. 2. Zurich: European Mathematical Society.CrossRefGoogle Scholar
Christodoulou, Demetrios, and Klainerman, Sergiu. 1993. The Global Nonlinear Stability of the Minkowski Space. Princeton, NJ: Princeton University Press.Google Scholar
Chruściel, Piotr T. 1991. On Uniqueness in the Large of Solutions of Einstein’s Equations (“Strong Cosmic Censorship”). Proceedings of the Centre for Mathematics and Its Applications, Australian National University 27. Canberra: Australian National University.Google Scholar
Chruściel, Piotr T., and Isenberg, James. 1993. “Nonisometric Vacuum Extensions of Vacuum Maximal Globally Hyperbolic Spacetimes.” Physical Review D 48 (4): 1616–28.Google ScholarPubMed
Dafermos, Mihalis, and Jonathan, Luk. 2017. “The Interior of Dynamical Vacuum Black Holes I: The C0-Stability of the Kerr Cauchy Horizon.” arXiv, Cornell University. .Google Scholar
Doboszewski, Juliusz. 2019. “Relativistic Spacetimes and Definitions of Determinism.” European Journal for Philosophy of Science 9:24.CrossRefGoogle Scholar
Doboszewski, Juliusz. 2020. “Epistemic Holes and Determinism in Classical General Relativity.” British Journal for the Philosophy of Science 71 (3): 1093–111.CrossRefGoogle Scholar
Earman, John. 1986. A Primer on Determinism. Dordrecht: Kluwer.CrossRefGoogle Scholar
Earman, John. 1995. Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes. New York: Oxford University Press.Google Scholar
Earman, John. 2004. “Determinism: What We Have Learned and What We Still Don’t Know.” In Determinism, Freedom, and Agency, ed. Campbell, Joseph K., O’Rourke, Michael, and Shier, David. Cambridge, MA: MIT Press.Google Scholar
Earman, John. 2008. “Pruning Some Branches from ‘Branching Spacetimes.’” In The Ontology of Spacetime II, ed. Dieks, Dennis, 187206. Amsterdam: Elsevier.CrossRefGoogle Scholar
Earman, John, and Norton, John. 1987. “What Price Spacetime Substantivalism? The Hole Story.” British Journal for the Philosophy of Science 38:515–25.CrossRefGoogle Scholar
Earman, John, Smeenk, Chris, and Wüthrich, Christian. 2009. “Do the Laws of Physics Forbid the Operation of Time Machines?Synthese 169:91124.CrossRefGoogle Scholar
Fletcher, Samuel C. 2012. “What Counts as a Newtonian System? The View from Norton’s Dome.” European Journal for Philosophy of Science 2:275–97.CrossRefGoogle Scholar
Fletcher, Samuel C. 2016. “Similarity, Topology, and Physical Significance in Relativity Theory.” British Journal for the Philosophy of Science 67:365–89.CrossRefGoogle Scholar
Friedman, John L. 2004. “The Cauchy Problem on Spacetimes That Are Not Globally Hyperbolic.” In The Einstein Equations and the Large Scale Behavior of Gravitational Fields, ed. Chruściel, Piotr and Friedrich, Helmut, 331–46. Boston: Birkhäuser.Google Scholar
Friedrich, Helmut, and Nagy, Gabriel. 1999. “The Initial Boundary Value Problem for Einstein’s Vacuum Field Equation.” Communications in Mathematical Physics 201:619–55.CrossRefGoogle Scholar
Friedrich, Helmut, and Rendall, Alan. 1999. “The Cauchy Problem for the Einstein Equations.” In Einstein’s Field Equations and Their Physical Implications, ed. Schmidt, Bernd G., 127223. Lecture Notes in Physics. Dordrecht: Springer.CrossRefGoogle Scholar
Gauntlett, Jerome P., Gutowski, Jan B., Hull, Christopher M., Pakis, Stathis, and Reall, Harvey S. 2003. “All Supersymmetric Solutions of Minimal Supergravity in Five Dimensions.” Classical and Quantum Gravity 20:4587–634.CrossRefGoogle Scholar
Geroch, Robert. 1977. “Prediction in General Relativity.” In Foundations of SpaceTime Theories, ed. Earman, John, Glymour, Clark, and Stachel, John, 8193. Minneapolis: University of Minnesota Press.Google Scholar
Geroch, Robert. 1996. “Partial Differential Equations of Physics.” In General Relativity: Proceedings of the Forty-Sixth Scottish Universities Summer School in Physics, Aberdeen, ed. Hall, Graham S. and Pulham, John R., 1960. Edinburgh: SUSSP.Google Scholar
Glymour, Clark. 1977. “Indistinguishable SpaceTimes and the Fundamental Group.” In Foundations of SpaceTime Theories, ed. Earman, John, Glymour, Clark, and Stachel, John, 5059. Minneapolis: University of Minnesota Press.Google Scholar
Hawking, Stephen W., and Ellis, George F. R. 1973. The Large Scale Structure of SpaceTime. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hawking, Stephen W., and Penrose, Roger. 1996. The Nature of Space and Time. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Holzegel, Gustav, Jonathan, Luk, Smulevici, Jacques, and Warnick, Claude. 2020. “Asymptotic Properties of Linear Field Equations in Anto-De Sitter Space.” Communications in Mathematical Physics 374:1125–78.CrossRefGoogle ScholarPubMed
Huggett, Nick, and Wüthrich, Christian. 2013. “Emergent Spacetime and Empirical (In)coherence.” Studies in the History and Philosophy of Modern Physics 44:276–85.CrossRefGoogle Scholar
Isenberg, James. 2015. “On Strong Cosmic Censorship.” Surveys in Differential Geometry 20 (1): 1736.CrossRefGoogle Scholar
Luc, Joanna, and Placek, Tomasz. 2020. “Interpreting Non-Hausdorff (Generalized) Manifolds in General Relativity.” Philosophy of Science 87 (1): 2142.CrossRefGoogle Scholar
Malament, David B. 1977. “Obervationally Indistinguishable SpaceTimes.” In Foundations of SpaceTime Theories, ed. Earman, John, Glymour, Clark, and Stachel, John, 6180. Minneapolis: University of Minnesota Press.Google Scholar
Malament, David B. 2008. “Norton’s Slippery Slope.” Philosophy of Science 75:799816.CrossRefGoogle Scholar
Malament, David B. 2012. Topics in the Foundations of General Relativity and Newtonian Gravitation Theory. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Manchak, John B. 2009. “Can We Know the Global Structure of Spacetime?Studies in History and Philosophy of Modern Physics 40:5356.CrossRefGoogle Scholar
Manchak, John B. 2011. “What Is a Physically Reasonable SpaceTime?Philosophy of Science 42:7476.Google Scholar
Manchak, John B. 2016. “Epistemic ‘Holes’ in SpaceTime.” Philosophy of Science 83 (2): 265–76.CrossRefGoogle Scholar
Manchak, John B. 2018. “Some ‘No-Hole’ Spacetime Properties Are Unstable.” Foundations of Physics 48:1539–45.CrossRefGoogle Scholar
McCall, Storrs. 1994. A Model of the Universe. Oxford: Clarendon.Google Scholar
Moncrief, Vincent, and Isenberg, James. 1983. “Symmetries of Cosmological Cauchy Horizons.” Communications in Mathematical Physics 89:387413.CrossRefGoogle Scholar
Moncrief, Vincent, and Isenberg, James. 2020. “Symmetries of Cosmological Cauchy Horizons with Non-closed Orbits.” Communications in Mathematical Physics 374 (1): 145–86.CrossRefGoogle Scholar
Müller, Thomas. 2013. “A Generalized Manifold Topology for Branching SpaceTimes.” Philosophy of Science 80:1089–100.CrossRefGoogle Scholar
Norton, John D. 2003. “Causation as Folk Science.” Philosophers’ Imprint 3:122.Google Scholar
Penrose, Roger. 1979. “Singularities and Time-Asymmetry.” In General Relativity: An Einstein Centenary Survey, ed. Hawking, Stephen W. and Israel, Werner, 581638. Cambridge: Cambridge University Press.Google Scholar
Placek, Tomasz, and Belnap, Nuel. 2012. “Indeterminism Is a Modal Notion: Branching Spacetimes and Earman’s Pruning.” Synthese 187:441–69.CrossRefGoogle Scholar
Rendall, Alan D. 2008. Partial Differential Equations in General Relativity, vol. 16 of Oxford Graduate Texts in Mathematics. Oxford: Oxford University Press.Google Scholar
Reula, Oscar, and Sarbach, Olivier. 2011. “The Initial-Boundary Value Problem in General Relativity.” International Journal of Modern Physics D 20:767–83.CrossRefGoogle Scholar
Ringström, Hans. 2009. The Cauchy Problem in General Relativity. Zurich: European Mathematical Society.CrossRefGoogle Scholar
Sarbach, Olivier, and Tiglio, Manuel. 2012. “Continuum and Discrete Initial-Boundary Value Problems and Einstein’s Field Equations.” Living Reviews in Relativity 15 (1): 9.CrossRefGoogle ScholarPubMed
Smeenk, Chris, and Wüthrich, Christian. 2011. “Time Travel and Time Machines.” In The Oxford Handbook of Time, ed. Callender, Craig, 577630. Oxford: Oxford University Press.Google Scholar
Stachel, John. 2014. “The Hole Argument and Some Physical and Philosophical Implications.” Living Reviews in Relativity 17 (1).CrossRefGoogle ScholarPubMed
Wald, Robert M. 1998. “Gravitational Collapse and Cosmic Censorship.” In Black Holes, Gravitational Radiation and the Universe: Essays in Honor of C. V. Vishveshwara, ed. Iyer, Bala R. and Bhawal, Biplab, 6985. Dordrecht: Kluwer.Google Scholar
Weatherall, James O. 2018. “Regarding the ‘Hole Argument.’British Journal for the Philosophy of Science 69:329–50.CrossRefGoogle Scholar
Wüthrich, Christian. 2011. “Can the World Be Shown to Be Indeterministic after All?” In Probabilities in Physics, ed. Beisbart, Claus and Hartmann, Stephan, 365–89. Oxford: Oxford University Press.Google Scholar
Wüthrich, Christian. Forthcoming. “Time Travelling in Emergent Spacetime.” In Hajnal Andréka and István Németi on the Unity of Science: From Computing to Relativity Theory through Algebraic Logic, ed. Judit Madarász and Gergely Székely. Dordrecht: Springer.Google Scholar
Xia, Zhihong. 1992. “The Existence of Noncollision Singularities in Newtonian Systems.” Annals of Mathematics 135:411–68.CrossRefGoogle Scholar

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