Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes
Abstract
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. In conclusion, this theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.
- Authors:
-
- California Inst. of Technology (CalTech), Pasadena, CA (United States)
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1326938
- Grant/Contract Number:
- SC0011632
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 7; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTRONOMY AND ASTROPHYSICS; Classical Theories of Gravity; Black Holes; Models of Quantum Gravity; Gauge-gravity correspondence
Citation Formats
Remmen, Grant N., Bao, Ning, and Pollack, Jason. Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes. United States: N. p., 2016.
Web. doi:10.1007/JHEP07(2016)048.
Remmen, Grant N., Bao, Ning, & Pollack, Jason. Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes. United States. https://doi.org/10.1007/JHEP07(2016)048
Remmen, Grant N., Bao, Ning, and Pollack, Jason. Mon .
"Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes". United States. https://doi.org/10.1007/JHEP07(2016)048. https://www.osti.gov/servlets/purl/1326938.
@article{osti_1326938,
title = {Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes},
author = {Remmen, Grant N. and Bao, Ning and Pollack, Jason},
abstractNote = {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. In conclusion, this theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.},
doi = {10.1007/JHEP07(2016)048},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2016,
place = {United States},
year = {Mon Jul 11 00:00:00 EDT 2016},
month = {Mon Jul 11 00:00:00 EDT 2016}
}
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