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

Journal Article · · Physical Review. D.
 [1];  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States)

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.

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:
1431154
Alternate ID(s):
OSTI ID: 1501451
Journal Information:
Physical Review. D., Vol. 97, Issue 8; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 24 works
Citation information provided by
Web of Science

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Cited By (9)

Quantum-First Gravity journal February 2019
The multiple realizability of general relativity in quantum gravity journal September 2019
Towards bulk metric reconstruction from extremal area variations journal August 2019
Black holes in the quantum universe journal November 2019
Von Neumann Entropy from Unitarity journal May 2019
Quantum-first gravity text January 2018
Von Neumann entropy from unitarity text January 2018
Towards Bulk Metric Reconstruction from Extremal Area Variations text January 2019
Black holes in the quantum universe text January 2019

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