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Einstein Algebras and the Hole Argument

Published online by Cambridge University Press:  01 January 2022

Jonathan Bain
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Abstract

Einstein algebras have been suggested (Earman 1989) and rejected (Rynasiewicz 1992) as a way to avoid the hole argument against spacetime substantivalism. In this article, I debate their merits and faults. In particular, I suggest that a gauge-invariant interpretation of Einstein algebras that avoids the hole argument can be associated with one approach to quantizing gravity, and, for this reason, is at least as well motivated as sophisticated substantivalist and relationalist interpretations of the standard tensor formalism.

Type
Philosophy of Space and Time
Information
Philosophy of Science , Volume 70 , Issue 5: Proceedings of the 2002 Biennial Meeting of The Philosophy of Science Association. Part I: Contributed Papers , December 2003 , pp. 1073 - 1085
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

Thanks to Jeremy Butterfield for insightful comments on an earlier draft. Any remaining mistakes are, of course, those of the author.

References

Belot, Gordon, and Earman, John (2001), “Pre-Socratic Quantum Gravity”, in Callander, Craig and Huggett, Nick (eds.), Physics Meets Philosophy on the Planck Scale. Cambridge: Cambridge University Press, 213–255.CrossRefGoogle Scholar
Brighouse, Carolyn (1994), “Spacetime and Holes”, in Hull, David, Forbes, Micky and Burian, Richard M. (eds.), PSA 1994, Vol. 1. East Lansing: Philosophy of Science Association, 117–125.Google Scholar
Butterfield, Jeremy (1989), “The Hole Truth”, The Hole Truth 40:1–28.Google Scholar
Connes, Alain (1994), Noncommutative Geometry. San Diego, CA: Academic Press.Google Scholar
Connes, Alain, and Rovelli, Carlo (1994), “Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in Generally Covariant Quantum Theories”, Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in Generally Covariant Quantum Theories 11:2899–2917.Google Scholar
Demaret, Jaques, Heller, Michael, and Lambert, Dominique (1997), “Local and Global Properties of the World”, Local and Global Properties of the World 2:137–176.Google Scholar
Earman, John (1989), World Enough and Spacetime. Cambridge: MIT Press.Google Scholar
Earman, John, and Norton, John D. (1987), “What Price Spacetime Substantivalism? The Hole Story”, What Price Spacetime Substantivalism? The Hole Story 38:515–525.Google Scholar
Geroch, Robert (1972), “Einstein Algebras”, Einstein Algebras 26:271–275.Google Scholar
Heller, Michael, and Sasin, Wieslaw (1995), “Sheaves of Einstein Algebras”, Sheaves of Einstein Algebras 34:387–398.Google Scholar
Heller, Michael, and Sasin, Wieslaw (1996), “Noncommutative Structure of Singularities in General Relativity”, Noncommutative Structure of Singularities in General Relativity 37:5664–5671.Google Scholar
Heller, Michael, and Sasin, Wieslaw (1998), “Emergence of Time”, Emergence of Time 250:48–54.Google Scholar
Heller, Michael, and Sasin, Wieslaw (1999), “Noncommutative Unification of General Relativity and Quantum Mechanics”, Noncommutative Unification of General Relativity and Quantum Mechanics 38:1619–1642.Google Scholar
Hoefer, Carl (1996), “The Metaphysics of Space-Time Substantivalism”, The Metaphysics of Space-Time Substantivalism 43:5–27.Google Scholar
Leeds, Stephen (1995), “Holes and Determinism: Another Look”, Holes and Determinism: Another Look 62:425–437.Google Scholar
Liu, Chuang (1996), “Realism and Spacetime: Of Arguments against Metaphysical Realism and Manifold Realism”, Realism and Spacetime: Of Arguments against Metaphysical Realism and Manifold Realism 33:243–263.Google Scholar
Maudlin, Tim (1990), “Substances and Spacetime: What Aristotle Would Have Said to Einstein”, Substances and Spacetime: What Aristotle Would Have Said to Einstein 21:531–561.Google Scholar
Mundy, Brent (1992), “Space-Time and Isomorphism”, in Hull, David, Forbes, Micky, and Okruhlik, Kathleen (eds.), PSA 1992, Vol. 1. East Lansing: Philosophy of Science Association, 515–527.Google Scholar
Pooley, Oliver (2001), “Relationism Rehabilitated? II: Relativity”, preprint PITT-PHIL-SCI00000221<http://philsci-archive.pitt.edu/documents/disk0/00/00/02/21/index.html>>Google Scholar
Rynasiewicz, Robert (1992), “Rings, Holes, and Substantivalism: On the Program of Leibniz Algebras”, Rings, Holes, and Substantivalism: On the Program of Leibniz Algebras 59:572–589.Google Scholar