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Title: Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space

Abstract

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson’s “entanglement equilibrium” that the geometry should obey Einstein’s equation in the weak-field limit. Here, we also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

Authors:
;
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:
1431154
Alternate Identifier(s):
OSTI ID: 1501451
Grant/Contract Number:  
SC0011632
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 8; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS

Citation Formats

Cao, ChunJun, and Carroll, Sean M. Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.97.086003.
Cao, ChunJun, & Carroll, Sean M. Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space. United States. doi:10.1103/PhysRevD.97.086003.
Cao, ChunJun, and Carroll, Sean M. Tue . "Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space". United States. doi:10.1103/PhysRevD.97.086003.
@article{osti_1431154,
title = {Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space},
author = {Cao, ChunJun and Carroll, Sean M.},
abstractNote = {We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson’s “entanglement equilibrium” that the geometry should obey Einstein’s equation in the weak-field limit. Here, we also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.},
doi = {10.1103/PhysRevD.97.086003},
journal = {Physical Review D},
number = 8,
volume = 97,
place = {United States},
year = {2018},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.97.086003

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Cited by: 3 works
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