If gravity is emergent, how does this affect string theory and loop quantum gravity?

[kodama]

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]

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.

 

[Demystifier]

Sabine also made a video on that paper:

 

[Roberto Pavani]

Thank you for posting this. My reading may be incomplete, but I see it primarily as a derivation of the Einstein equations from information-theoretic considerations, rather than a derivation of spacetime itself. The framework seems to start from a setting where local horizons, causal structure and spacetime geometry are already available, and then shows how the Einstein equations can follow from relative entropy under certain assumptions.

For that reason, I would personally view it as evidence that quantum information may underlie gravitational dynamics, rather than as a demonstration that spacetime and gravity are fully emergent.
The origin of spacetime structure itself, and of the cosmological constant, still seem to me to be open questions. But perhaps I am missing something, and these questions are simply beyond the scope of the present paper and left for future work.

 

[kodama]

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​

 

[danieltanfh95]

The derivation assumes the Bekenstein-Hawking entropy-area formula S=A/(4Gℏ)S=A/(4Gℏ), which is itself a semi-classical result. It comes from Hawking 1975 (QFT on curved spacetime plus Einstein equations to fix κκ) combined with the first law of BH mechanics (using the κ/8πGκ/8πG coefficient from Einstein specifically, change the gravitational Lagrangian and it becomes Wald entropy, not A/4GA/4G). So the entropy-area formula already encodes Einstein gravity. Deriving Einstein equations from that assumption is reformulation rather than foundation, and the same structural issue applies to Jacobson 1995, which this paper explicitly builds on.

The paper’s real contribution is a cleaner thermodynamic-style derivation using quantum relative entropy (Araki-Uhlmann) and modular theory instead of classical thermodynamic entropy, technically valuable, but reading it as “gravity is emergent from quantum information” overstates the ontological content, and more of a clickbait title.

 

[loop quantum gravity]

TL;DR: From Quantum Relative Entropy to the Semiclassical Einstein Equations

the paper in

Physical Review Letters​

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

What does it even mean that it's not fundamental force; if we recall that gravity field is exactly as acceleration field (inertial mass=gravitational mass). For a full quantum theory of gravity you must have the graviton with spin 2; it makes you wonder if gravity makes masses to gravitate then what does light can make to gravity itself. Einstein et al replaced "force" with geometry; we may have such a notion of quantum geometry it was a fad in the 1990's. I still think you can make a theory that is not relativistic and not quantum but yet in the appropriate limit it's Quantum and in the other limit it's relativistic.

Just like we do with plasma when we say that sometimes it reacts as a liquid sometimes as gas and sometimes neither of them, and thus it's considered the fourth state of matter. (I know I took a course on plasma which was awsome, I read most of Chen's book, who said math and physics is boring?!).

I wonder what would happen when the inertial mass won't equal the gravitational mass, obviously such a thing if it will ever occur will demand to rethink what is really constant in the universe...

 

[PeterDonis]

What does it even mean that it's not fundamental force

That it's emergent from something else.

gravity field is exactly as acceleration field (inertial mass=gravitational mass).

No, that's not what "gravity" is when we're talking about whether it's emergent or not. What we're talking about is "gravity" as spacetime curvature, i.e., tidal gravity. That's the invariant part that doesn't depend on the observer. Your "acceleration field" does--I can make it vanish by freely falling.

For a full quantum theory of gravity you must have the graviton with spin 2

This is believed to be an effective quantum theory of gravity at some level, but whether it actually will turn out to be physically relevant in any signfiicant regime is an open question. It might be that, by the time we get to a regime where quantum effects on the spacetime geometry are relevant at all, the spin-2 field effective theory already has broken down and we need something else. (We already know the theory is non-renormalizable so we expect it to only be an effective theory and to break down at some point anyway.)

I still think you can make a theory that is not relativistic and not quantum but yet in the appropriate limit it's Quantum and in the other limit it's relativistic.

Please note that personal speculation is off limits here.

I wonder what would happen when the inertial mass won't equal the gravitational mass, obviously such a thing if it will ever occur will demand to rethink what is really constant in the universe...

Same comment here.

 

[loop quantum gravity]

That it's emergent from something else.


No, that's not what "gravity" is when we're talking about whether it's emergent or not. What we're talking about is "gravity" as spacetime curvature, i.e., tidal gravity. That's the invariant part that doesn't depend on the observer. Your "acceleration field" does--I can make it vanish by freely falling.


This is believed to be an effective quantum theory of gravity at some level, but whether it actually will turn out to be physically relevant in any signfiicant regime is an open question. It might be that, by the time we get to a regime where quantum effects on the spacetime geometry are relevant at all, the spin-2 field effective theory already has broken down and we need something else. (We already know the theory is non-renormalizable so we expect it to only be an effective theory and to break down at some point anyway.)


Please note that personal speculation is off limits here.


Same comment here.

Thanks for clearing matters out. Well, as for being emergent or not it depends if we have an experiment that shows bijectively that emerges from something else. I read some say from entropy; In my UG lab classes we never calculated entropy directly. If we somehow can change the direction of increase in entropy to a decrease then the arrow of time will change its direction, and gravity will become anti gravity; but so are also the other three interactions; so does it mean entropy is the fundamental for all 4 intercations?

 

[PeterDonis]

as for being emergent or not it depends if we have an experiment that shows bijectively that emerges from something else.

"Emergent" is a theoretical concept. If we have a theory that says gravity is emergent, we can test the theory. But we can't just do an experiment and say "oh, that shows that gravity is emergent", without some theoretical framework to be tested.

I read some say from entropy

Please give a specific reference.

If we somehow can change the direction of increase in entropy to a decrease then the arrow of time will change its direction, and gravity will become anti gravity

I have no idea where you are getting this from. Do you have a reference? Please bear in mind, again, that personal speculation is off limits here.

 

[ohwilleke]

Thanks for clearing matters out. Well, as for being emergent or not it depends if we have an experiment that shows bijectively that emerges from something else. I read some say from entropy; In my UG lab classes we never calculated entropy directly.

There are emergent gravity theories that are intimately related to entropy concepts such as S. Shamari, A. Sheykhi, "Resolving Galactic and Cluster Dynamics Without Dark Matter: Tsallis Entropy as the Unique Foundation of Emergent Gravity" arXiv:2607.19435 (July 21, 2026) (see especially the papers cited therein, which are published, and the introductory materials, for a quick up to date review of the literature in the field, even though this pre-print from last week is not yet published). Probably the most widely cited article exploring this concept is Erik P. Verlinde, "Emergent Gravity and the Dark Universe" SciPost Phys. 2, 016 (2017) (also found at arXiv:1611.02269v2).

If we somehow can change the direction of increase in entropy to a decrease then the arrow of time will change its direction

One of a modest number of papers exploring this kind of idea is Latham Boyle, Kieran Finn, Neil Turok, "CPT-Symmetric Universe" Phys. Rev. Lett. 121, 251301 (2018) (also available at arXiv:1803.08928v3).

It does not really turn gravity into anti-gravity (and the equations of general relativity themselves do not really have a preferred time direction), instead, this hypothesis is primarily a way to explain the baryon asymmetry of the universe (i.e. why most of the stuff in the observable universe is matter rather than antimatter, even though at the particle physics level new particles are generally created in ways that exactly balance matter and antimatter components). This question is a hot one to resolve because there is currently no mechanism to produce the baryon asymmetry of the universe with Standard Model particle physics and general relativity from an idealized beginning (which admittedly is just a hypothesis itself) with equal amounts of matter and antimatter. This theory is attractive because it answers this question without proposing any new physics that would operate in our observable universe (since we can't directly observe the Big Bang itself, even though we can observe phenomena that arose very shortly after it from which we can make scientific inferences).

This hypothesis also has implications for cosmological inflation, in the view of some of the authors who argue that this concept disfavors cosmological inflation.

This article (and related articles by this and another independent group of researchers) proposes the Big Bang is a boundary between our universe, which is matter dominated and has time that due to entropy and the Second Law of Thermodynamics flows in the direction with which we are familiar, on one hand, and a universe "before" the Big Bang, which is anti-matter dominated and in which time flows in the opposite direction as in the part of the universe with which we are familiar due to entropy and the Second Law of Thermodynamics flowing again "away from the Big Bang" in time, on the other.

In this hypothesis, our universe is matter dominated because when matter-antimatter pairs of particles were created at the time of the Big Bang, the matter particles more often ended up on our side of the Big Bang, while the anti-matter particles more often ended up on the other side of the Big Bang.

 

[loop quantum gravity]

"Emergent" is a theoretical concept. If we have a theory that says gravity is emergent, we can test the theory. But we can't just do an experiment and say "oh, that shows that gravity is emergent", without some theoretical framework to be tested.


Please give a specific reference.


I have no idea where you are getting this from. Do you have a reference? Please bear in mind, again, that personal speculation is off limits here.

Does M theory and its companion F theory tell us if gravity is emergent or not?
I guess they would say that some sort of vibrating strings lead to gravity's emergence; no I don't have referneces at the top of my head right I just remember stuff, and granted my memory is not that strong.

 

[loop quantum gravity]

There are emergent gravity theories that are intimately related to entropy concepts such as S. Shamari, A. Sheykhi, "Resolving Galactic and Cluster Dynamics Without Dark Matter: Tsallis Entropy as the Unique Foundation of Emergent Gravity" arXiv:2607.19435 (July 21, 2026) (see especially the papers cited therein, which are published, and the introductory materials, for a quick up to date review of the literature in the field, even though this pre-print from last week is not yet published). Probably the most widely cited article exploring this concept is Erik P. Verlinde, "Emergent Gravity and the Dark Universe" SciPost Phys. 2, 016 (2017) (also found at arXiv:1611.02269v2).


One of a modest number of papers exploring this kind of idea is Latham Boyle, Kieran Finn, Neil Turok, "CPT-Symmetric Universe" Phys. Rev. Lett. 121, 251301 (2018) (also available at arXiv:1803.08928v3).

It does not really turn gravity into anti-gravity (and the equations of general relativity themselves do not really have a preferred time direction), instead, this hypothesis is primarily a way to explain the baryon asymmetry of the universe (i.e. why most of the stuff in the observable universe is matter rather than antimatter, even though at the particle physics level new particles are generally created in ways that exactly balance matter and antimatter components). This question is a hot one to resolve because there is currently no mechanism to produce the baryon asymmetry of the universe with Standard Model particle physics and general relativity from an idealized beginning (which admittedly is just a hypothesis itself) with equal amounts of matter and antimatter. This theory is attractive because it answers this question without proposing any new physics that would operate in our observable universe (since we can't directly observe the Big Bang itself, even though we can observe phenomena that arose very shortly after it from which we can make scientific inferences).

This hypothesis also has implications for cosmological inflation, in the view of some of the authors who argue that this concept disfavors cosmological inflation.

This article (and related articles by this and another independent group of researchers) proposes the Big Bang is a boundary between our universe, which is matter dominated and has time that due to entropy and the Second Law of Thermodynamics flows in the direction with which we are familiar, on one hand, and a universe "before" the Big Bang, which is anti-matter dominated and in which time flows in the opposite direction as in the part of the universe with which we are familiar due to entropy and the Second Law of Thermodynamics flowing again "away from the Big Bang" in time, on the other.

In this hypothesis, our universe is matter dominated because when matter-antimatter pairs of particles were created at the time of the Big Bang, the matter particles more often ended up on our side of the Big Bang, while the anti-matter particles more often ended up on the other side of the Big Bang.

Thanks for the reference if only I had the time to read it all. (I have quite a lot of books in maths and physics to be read; so it takes a lot of time).

 

[PeterDonis]

Does M theory and its companion F theory tell us if gravity is emergent or not?

The basic idea of string theory is that everything is emergent from the underlying string dynamics, including not just gravity but all of our current Standard Model of particle physics.

Unfortunately the string scale, where we might expect to see the underlying string dynamics, is about 20 orders of magnitude smaller than the smallest scales we can currently probe with experiments, so there's no expectation that we'll be able to test string theory by experiment any time soon. The one prediction string theorists have made that could be tested with our current technology was that the LHC would find evidence of supersymmetry, and that prediction is now notorious for its wrongness.

 

[loop quantum gravity]

The basic idea of string theory is that everything is emergent from the underlying string dynamics, including not just gravity but all of our current Standard Model of particle physics.

Unfortunately the string scale, where we might expect to see the underlying string dynamics, is about 20 orders of magnitude smaller than the smallest scales we can currently probe with experiments, so there's no expectation that we'll be able to test string theory by experiment any time soon. The one prediction string theorists have made that could be tested with our current technology was that the LHC would find evidence of supersymmetry, and that prediction is now notorious for its wrongness.

why is it notoriously wrong? I mean there are several SUSY theories and I think not all of them were bogged down by LHC, were they?
On another matter I gave a look at BFSS paper on M theory being suggested as a matrix theory, I think they tried to incoporate to M theory, RMT. As someone who took a course on Random Matrices (from the maths department), this stuff is amazingly hard. I cannot understand how did people could do these stuff back then without AI or even an AGI.

 

[PeterDonis]

why is it notoriously wrong?

Because the LHC found zero evidence of supersymmetry.

there are several SUSY theories and I think not all of them were bogged down by LHC, were they?

The prediction that is now notorious for its wrongness was not that any particular SUSY theory would be suggested by evidence from the LHC. It was simply that the LHC would find some kind of evidence for some kind of supersymmetry. It found none.

Of course string theorists were quick to shift their ground and start talking about SUSY theories that could not be ruled out based on no evidence of supersymmetry at the LHC energy scale. That just underscores the fact that string theory doesn't make useful predictions at all in any regime where we can currently do experiments.

 

[ohwilleke]

Does M theory and its companion F theory tell us if gravity is emergent or not?

Gravity is not emergent in M theory and F theory in the same sense that it is in entropic gravity theories, i.e. in M theory and F theory it is not the case that gravity flows logically from the other forces without a need for it to have a source of its own.

Indeed, in some versions of these theories that conceptualize them in terms of branes, the other forces are confined to a brane, while gravity is not, which helps explain why gravity is weak in relative terms of the particle scale. This treats gravity as something very distinct from the other forces rather than a something that flows logically from them.