The Hilbert space of quantum gravity is locally finite-dimensional

Bao, Ning; Carroll, Sean M.; Singh, Ashmeet

doi:10.1142/S0218271817430131

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

Journal Article · Tue Oct 10 00:00:00 EDT 2017 · International Journal of Modern Physics D

DOI:https://doi.org/10.1142/S0218271817430131· OSTI ID:1598796

Bao, Ning ^[1];

^[1]; Singh, Ashmeet ^[1]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

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.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011632

OSTI ID:: 1598796

Journal Information:: International Journal of Modern Physics D, Vol. 26, Issue 12; ISSN 0218-2718

Publisher:: World ScientificCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 19 works

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Cited By (6)

Spacetime granularity from finite-dimensionality of local observable algebras Raasakka, Matti Classical and Quantum Gravity, Vol. 37, Issue 4 https://doi.org/10.1088/1361-6382/ab5eb0	journal	January 2020
Towards space from Hilbert space: finding lattice structure in finite-dimensional quantum systems Pollack, Jason; Singh, Ashmeet Quantum Studies: Mathematics and Foundations, Vol. 6, Issue 2 https://doi.org/10.1007/s40509-018-0176-8	journal	December 2018
How low can vacuum energy go when your fields are finite-dimensional? Cao, ChunJun; Chatwin-Davies, Aidan; Singh, Ashmeet International Journal of Modern Physics D, Vol. 28, Issue 14 https://doi.org/10.1142/s0218271819440061	journal	October 2019
Quantum-First Gravity Giddings, Steven B. Foundations of Physics, Vol. 49, Issue 3 https://doi.org/10.1007/s10701-019-00239-1	journal	February 2019
Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space Cao, ChunJun; Carroll, Sean M. arXiv https://doi.org/10.48550/arxiv.1712.02803	text	January 2017
Quantum-first gravity Giddings, Steven B. arXiv https://doi.org/10.48550/arxiv.1803.04973	text	January 2018

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