TL;DR

From Quantum Relative Entropy to the Semiclassical Einstein Equations

the paper in

Physical Review Letters​

From Quantum Relative Entropy to the Semiclassical Einstein Equations​

Philipp Dorau* and Albert Much†

Abstract​

We provide arguments indicating that the semiclassical Einstein equations follow from quantum relative entropy and its proportionality to an area variation. Using modular theory, we establish that the relative entropy between the vacuum state and coherent excitations of a scalar quantum field on a bifurcate Killing horizon is given by the energy flux across the horizon. Under the assumption of the Bekenstein-Hawking entropy-area formula, this energy flux is proportional to a variation in the surface area of the horizon cross section. The semiclassical Einstein equations follow automatically from this identification. Our approach provides a quantum field theoretic generalization of Jacobson’s thermodynamic derivation of the Einstein equations, replacing classical thermodynamic entropy with the well-defined quantum relative (Araki-Uhlmann) entropy. This suggests that quantum information plays a central role in what is often seen as a zeroth order approximation of a theory of quantum gravity, namely quantum field theory in curved spacetimes.
Phys. Rev. Lett. 136, 091602 – Published 2 March, 2026

DOI:https://doi.org/10.1103/lmq8-nsty

this means gravity isn't a fundamental force

if true what does this means to string theory and loop quantum gravity and other quantum gravity?

are there gravitons in these theories

Demystifier said:

In such a theory there may still be a graviton, but in such a theory it is a collective excitation analogous to a phonon (a quantum of sound), rather than a fundamental particle. Such theories are in spirit very different from loop quantum gravity and string theory, but there is no direct contradiction between them. Loop quantum gravity, and even string theory, may well be good effective theories, rather than the fundamental ones.

Einstein Equations from Quantum Relative Entropy imply that gravity is not fundamental field - perhaps conflict with Deur graviton self interaction and string theorywhich promises gravitons

could loop quantum gravity physicist used Einstein Equations from Quantum Relative Entropy with spinfoam to prove and show how loop quantum gravity gives you semiclassical Einstein equations

similar to Einstein Equations from Quantum Relative Entropy

Physical Review D​

Entanglement entropy in loop quantum gravity and geometrical area law​

Muxin Han*

Phys. Rev. D 113, 084045 – Published 20 April, 2026

DOI:https://doi.org/10.1103/8l48-qhks

Abstract

The nonfactorizing nature of the Hilbert space in loop quantum gravity (LQG) due to gauge invariance requires a generalized definition of entanglement entropy. This work employs the framework of von Neumann algebras to investigate the entanglement entropy in LQG. On a graph, the holonomy and flux operators within a region and on the boundary generate a nonfactor type I von Neumann algebra, which is used to define the entanglement entropy for LQG states. This algebraic formalism is applied to “fixed-area states”—superpositions of spin networks associated with a surface with a definite macroscopic area given by the LQG area spectrum. By maximizing the entropy, we derive a geometrical area law where the entanglement entropy is proportional to the area. In addition, we show that bulk entanglement can renormalize the area-law coefficient and produce logarithmic corrections. The results in this paper closely relate to LQG black hole entropy.

Entanglement entropy in loop quantum gravity and geometrical area law

Muxin Han*

From Quantum Relative Entropy to the Semiclassical Einstein Equations​

Philipp Dorau* and Albert Much†

together might show how

Semiclassical Einstein Equations from loop quantum gravity and geometrical area law​