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Title: The Hilbert space of quantum gravity is locally finite-dimensional

Abstract

In this article, 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.

Authors:
 [1]; ORCiD logo [1];  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1598796
Grant/Contract Number:  
SC0011632
Resource Type:
Accepted Manuscript
Journal Name:
International Journal of Modern Physics D
Additional Journal Information:
Journal Volume: 26; Journal Issue: 12; Journal ID: ISSN 0218-2718
Publisher:
World Scientific
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Quantum gravity; quantum foundations; decoherence

Citation Formats

Bao, Ning, Carroll, Sean M., and Singh, Ashmeet. The Hilbert space of quantum gravity is locally finite-dimensional. United States: N. p., 2017. Web. doi:10.1142/S0218271817430131.
Bao, Ning, Carroll, Sean M., & Singh, Ashmeet. The Hilbert space of quantum gravity is locally finite-dimensional. United States. doi:10.1142/S0218271817430131.
Bao, Ning, Carroll, Sean M., and Singh, Ashmeet. Tue . "The Hilbert space of quantum gravity is locally finite-dimensional". United States. doi:10.1142/S0218271817430131. https://www.osti.gov/servlets/purl/1598796.
@article{osti_1598796,
title = {The Hilbert space of quantum gravity is locally finite-dimensional},
author = {Bao, Ning and Carroll, Sean M. and Singh, Ashmeet},
abstractNote = {In this article, 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.},
doi = {10.1142/S0218271817430131},
journal = {International Journal of Modern Physics D},
number = 12,
volume = 26,
place = {United States},
year = {2017},
month = {10}
}

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Cited by: 3 works
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    Works referencing / citing this record:

    How low can vacuum energy go when your fields are finite-dimensional?
    journal, October 2019

    • Cao, ChunJun; Chatwin-Davies, Aidan; Singh, Ashmeet
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