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Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space

Cao, ChunJun and Carroll, Sean M. (2018) Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space. Physical Review D, 97 (8). Art. No. 086003. ISSN 2470-0010. http://resolver.caltech.edu/CaltechAUTHORS:20171214-111114409

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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. 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.97.086003DOIArticle
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.97.086003PublisherArticle
http://arxiv.org/abs/1712.02803arXivDiscussion Paper
ORCID:
AuthorORCID
Carroll, Sean M.0000-0002-4226-5758
Additional Information:© 2017 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. Received 1 February 2018; published 3 April 2018. We thank Bartek Czech for the helpful comments on integral geometry that helped inspire this work. We also thank Aidan Chatwin-Davies, Junyu Liu, Spiros Michalakis, and Gunther Uhlmann for engaging and informing discussions. We thank the organizers of YITP long term workshop and QIQG3 at UBC Vancouver. This work is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, as well as by the Walter Burke Institute for Theoretical Physics at Caltech.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
SCOAP3UNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2017-069
Record Number:CaltechAUTHORS:20171214-111114409
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171214-111114409
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83922
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:14 Dec 2017 19:37
Last Modified:03 Apr 2018 17:03

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