Gravitation and vacuum entanglement entropy

TL;DR

This paper explores how the entanglement entropy of quantum vacuum fluctuations relates to gravity, proposing that finite entropy due to UV physics implies Einstein's gravity, and vice versa, through thermodynamic arguments.

Contribution

It establishes a thermodynamic link between vacuum entanglement entropy and the emergence of gravity, highlighting the mutual influence of UV physics and spacetime dynamics.

Findings

Finite entanglement entropy suggests gravity via thermodynamics.

Gravity renders entanglement entropy finite.

Limitations in understanding corrections to Einstein gravity.

Abstract

The vacuum of quantum fields contains correlated fluctuations. When restricted to one side of a surface these have a huge entropy of entanglement that scales with the surface area. If UV physics renders this entropy finite, then a thermodynamic argument implies the existence of gravity. That is, the causal structure of spacetime must be dynamical and governed by the Einstein equation with Newton's constant inversely proportional to the entropy density. Conversely, the existence of gravity makes the entanglement entropy finite. This thermodynamic reasoning is powerful despite the lack of a detailed description of the dynamics at the cutoff scale, but it has its limitations. In particular, we should not expect to understand corrections to Einstein gravity in this way.