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Entanglement Conservation, ER=EPR, and a New Classical Area Theorem for Wormholes

Remmen, Grant N. and Bao, Ning and Pollack, Jason (2016) Entanglement Conservation, ER=EPR, and a New Classical Area Theorem for Wormholes. Journal of High Energy Physics, 2016 (7). Art. No. 048. ISSN 1126-6708. doi:10.1007/JHEP07(2016)048.

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We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throat separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. This theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.

Item Type:Article
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URLURL TypeDescription Paper
Remmen, Grant N.0000-0001-6569-8866
Bao, Ning0000-0002-3296-1039
Pollack, Jason0000-0003-4754-4905
Additional Information:© 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: April 29, 2016; Accepted: June 27, 2016; Published: July 11, 2016. We thank Sean Carroll and Mukund Rangamani for useful discussions and comments. This research was supported in part by DOE grant DE-SC0011632 and by the Gordon and Betty Moore Foundation through Grant 776 to the Caltech Moore Center for Theoretical Cosmology and Physics. N.B. is supported by the DuBridge postdoctoral fellowship at the Walter Burke Institute for Theoretical Physics. G.N.R. is supported by a Hertz Graduate Fellowship and a NSF Graduate Research Fellowship under Grant No. DGE-1144469.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Gordon and Betty Moore Foundation776
Lee A. DuBridge FellowshipUNSPECIFIED
Fannie and John Hertz FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1144469
Subject Keywords:Classical Theories of Gravity, Black Holes, Models of Quantum Gravity, Gauge-gravity correspondence
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Issue or Number:7
Record Number:CaltechAUTHORS:20160622-105352946
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68581
Deposited By: Jacquelyn O'Sullivan
Deposited On:27 Jun 2016 18:18
Last Modified:11 Nov 2021 04:02

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