Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
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 this 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.
Cite
@article{arxiv.1712.02803,
title = {Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space},
author = {ChunJun Cao and Sean M. Carroll},
journal= {arXiv preprint arXiv:1712.02803},
year = {2018}
}
Comments
29 pages, 2 figures