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The Hilbert Space of Quantum Gravity Is Locally Finite-Dimensional

Bao, Ning and Carroll, Sean M. and Singh, Ashmeet (2017) The Hilbert Space of Quantum Gravity Is Locally Finite-Dimensional. International Journal of Modern Physics D, 26 (12). Art. No. 1743013. ISSN 0218-2718. doi:10.1142/S0218271817430131.

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We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense, is defined on a finite-dimensional factor of a larger Hilbert space. Because quantum gravity potentially describes superpositions of different geometries, it is crucial that we associate Hilbert-space factors with spatial regions only on individual decohered branches of the universal wave function. We discuss some implications of this claim, including the fact that quantum-field theory cannot be a fundamental description of nature.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Bao, Ning0000-0002-3296-1039
Carroll, Sean M.0000-0002-4226-5758
Singh, Ashmeet0000-0002-4404-1416
Additional Information:© 2017 World Scientific Publishing Company. Received 26 May 2017; Accepted 11 September 2017; Published 10 October 2017. We thank Scott Aaronson, Steven Giddings, and John Preskill for helpful discussions. This research is funded in part by the Walter Burke Institute for Theoretical Physics at Caltech, by DOE grant DE-SC0011632, and by the Foundational Questions Institute. This essay received an Honorable Mention in the 2017 Essay Competition of the Gravity Research Foundation.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Foundational Questions Institute (FQXI)UNSPECIFIED
Subject Keywords:Quantum gravity; quantum foundations; decoherence
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Other Numbering System NameOther Numbering System ID
Issue or Number:12
Classification Code:PACS: 03.65.Aa, 04.60.−m, 03.65.Yz, 03.65.Ta
Record Number:CaltechAUTHORS:20170427-143158126
Persistent URL:
Official Citation:The Hilbert space of quantum gravity is locally finite-dimensional Ning Bao, Sean M. Carroll, and Ashmeet Singh International Journal of Modern Physics D 2017 26:12
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77018
Deposited By: Joy Painter
Deposited On:27 Apr 2017 21:40
Last Modified:15 Nov 2021 17:04

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