  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.
