Entanglement Equilibrium and the Einstein Equation

TL;DR

This paper establishes a theoretical link between the Einstein equation and a maximal vacuum entanglement hypothesis, suggesting that Einstein's gravity can be derived from quantum entanglement principles in vacuum states.

Contribution

It demonstrates that the Einstein equation is equivalent to a stationarity condition of vacuum entanglement entropy for conformal quantum fields.

Findings

Einstein equation implies the maximal entanglement hypothesis.

Vacuum entanglement entropy is stationary if and only if Einstein's equation holds.

Results extend to nonconformal fields under a conjecture.

Abstract

A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy.