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Published April 15, 2018 | Published + Submitted
Journal Article Open

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


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.

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.

Attached Files

Published - PhysRevD.97.086003.pdf

Submitted - 1712.02803.pdf


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