I Gravitons and General Relativity

[Rick16]

I have problems understanding gravitons. I would understand them in the context of Newtonian gravitation. The Newtonian gravitational field is a force field and the gravitational interaction takes directly place between specific masses. It would therefore make sense to assume the existence of mediators for the interaction in this context.

The Einsteinian gravitational field, however, is not a force field. As I understand it, the field seems to be spacetime itself. In general relativity, gravitation is a geometric phenomenon and each mass just follows the curvature of spacetime, without direct interaction with other specific masses. I find it difficult to see why mediators would be needed in this picture. It even seems that gravitons would invalidate GR – not as an abstract mathematical model, but as a model of the physical reality. Is the reality of gravitation curved spacetime, or is it an exchange of particles? I don’t see how it can be both.

 

[PeterDonis]

each mass just follows the curvature of spacetime, without direct interaction with other specific masses.

That depends on what you consider to be "direct interaction".

First, in GR, spacetime curvature is caused by stress-energy. GR does not explain how this happens, in the sense of giving an underlying model. It just asserts that it happens.

Second, the way GR is normally presented in textbooks, when we say "mass just follows the curvature of spacetime", we are treating that mass as a test object--i.e., it does not cause any spacetime curvature on its own. But of course no real object is exactly a test object; all real objects have some stress-energy and cause some spacetime curvature, even if it's negligible in practical terms.

So in the real world, no mass just follows the curvature of spacetime created by some other mass, without contributing anything at all to spacetime curvature itself. And that means it is always possible to view GR in the real world as an effective theory that sits on top of some underlying model in which there is indeed an "interaction" of some sort between masses--the interaction just needs to obey the equivalence principle so that it looks at the classical level like spacetime curvature generated by stress-energy according to the Einstein Field Equation. See further comments below on that.

It even seems that gravitons would invalidate GR

No, they don't. What they do is give a possible underlying model for where curved spacetime comes from.

In the 1960s and early 1970s, a number of physicists, including Feynman and Deser, investigated the quantum field theory of a massless spin-2 field (which is what "graviton" translates to in QFT language), and found that the classical limit of this theory is...the Einstein Field Equation of GR. So on this view, what looks to us classically like curved spacetime generated by stress-energy, at the underlying quantum level is the quantum field of the graviton.

The main problem with this at the time was that the QFT in question is not renormalizable, which means that it can't be a fundamental theory by itself. But the current view of QFT in general seems to be that all of our known QFTs, such as the Standard Model of particle physics, are effective theories anyway, not fundamental. For an effective theory, non-renormalizability isn't really an issue, since you don't expect the theory to be valid to arbitrarily high energy scales anyway. So the "graviton" is simply the effective theory at that level for gravity/spacetime.

 

[Demystifier]

Is the reality of gravitation curved spacetime, or is it an exchange of particles? I don’t see how it can be both.

This question is often asked by lay people, so I think it deserves a particularly clear answer without math. I don't know how to answer it, without math, in a particularly clear way. If someone does, I believe it would make a very valuable insight article.

That being said, let me try to give such an answer anyway. The curvature of spacetime is not fixed, it changes. The change propagates at the speed of light. The change propagates in a similar way as light, indeed this propagation of change is called gravitational wave. But we know that light has both wave and particle properties, in a sense light is "both" wave and particle. More precisely, light is an entity which is neither classical wave nor classical particle, but a quantum object with some wave-like properties and some particle-like properties. To understand it better, one has to study quantum mechanics, which will not be studied here. Anyway, just like light is "both" wave and particle in this quantum-mechanical sense, so is the change of curvature. The quantum of gravity, namely the particle called graviton, is something very similar to the quantum of light, namely the particle called photon.

 

[mitchell porter]

I think the key thing is to understand how you get "particles" (or wavefunctions for particles, if you will) from a quantum field, specifically from superpositions of classical field states. If that makes sense to a person, it should be much easier to see how superpositions of curved space-time can correspond to graviton wavefunctions.

What I would like to see, is an exposition of the classic ideas of quantum gravity (like its nonrenormalizability) that stays in touch with an underlying geometric perspective all the way...

 

[Rick16]

Thank you for your answers. Very convincing. It did not occur to me that curvature could/should be produced by something. I thought if we know the cause and we know the effect, that is all we need to know. I did not think that there should be a link between cause and effect.

[Moderator's note: Deleted question here which has been spun off into a separate thread.]

 

[PeterDonis]

I still have this uneasiness about mediator particles in general.

This question, which is separate from the topic of this thread, has been spun off into its own thread in the quantum physics forum:

https://www.physicsforums.com/threads/quantum-fields-and-mediator-particles.1079270/

 

[Rick16]

There was a post here a couple of hours ago with a link to an article that I wanted to read. It has disappeared. What happened?

 

[Rick16]

In the 1960s and early 1970s, a number of physicists, including Feynman and Deser, investigated the quantum field theory of a massless spin-2 field (which is what "graviton" translates to in QFT language), and found that the classical limit of this theory is...the Einstein Field Equation of GR.

This is by the way highly intriguing. I am not yet ready to pursue it, but thank you for mentioning it.

 

[PeterDonis]

There was a post here a couple of hours ago with a link to an article that I wanted to read. It has disappeared. What happened?

It was deleted by the moderators because the linked article is not an acceptable reference for PF discussion.

 

[ohwilleke]

In the 1960s and early 1970s, a number of physicists, including Feynman and Deser, investigated the quantum field theory of a massless spin-2 field (which is what "graviton" translates to in QFT language), and found that the classical limit of this theory is...the Einstein Field Equation of GR. So on this view, what looks to us classically like curved spacetime generated by stress-energy, at the underlying quantum level is the quantum field of the graviton.

The main problem with this at the time was that the QFT in question is not renormalizable, which means that it can't be a fundamental theory by itself. But the current view of QFT in general seems to be that all of our known QFTs, such as the Standard Model of particle physics, are effective theories anyway, not fundamental. For an effective theory, non-renormalizability isn't really an issue, since you don't expect the theory to be valid to arbitrarily high energy scales anyway. So the "graviton" is simply the effective theory at that level for gravity/spacetime.

Worth noting that the same "in the classical limit" does not mean "identical" and that there were be qualitative differences between this kind of quantum gravity theory and classical GR, most obviously, that a graviton theory would be probabilistic, rather than deterministic, and would involve the localization of gravitational field energy into individual gravitons.

There was a recent paper that speculated that non-perturbative gravitational effects could solve the non-renormalizability issue.

In the peculiar manner by which physicists reckon descent, this article is by a "child" and "grandchild" of the late Stanley Deser. We begin by sharing reminiscences of Stanley from over 40 years. Then we turn to a problem which was dear to his heart: the prospect that gravity might nonperturbatively screen its own ultraviolet divergences and those of other theories. After reviewing the original 1960 work by ADM, we describe a cosmological analogue of the problem and then begin the process of implementing it in gravity plus QED.

R. P. Woodard and B. Yesilyurt, "The Other ADM" arXiv:2410.05213 (October 7, 2024).

The possibility of renormalizability is also suggested by the successes of the gravity as QCD squared paradigm, in which a renormalizable set of QCD type calculations seem to successfully reproduce expected quantum gravity results when transformed, which shouldn't be possible in a truly non-renormalizable theory.

 

[PeterDonis]

"in the classical limit" does not mean "identical"

I'm not sure what you mean by this. The fact that the classical limit of the QFT of the massless spin-2 field that I referred to is classical GR was established during the research effort I referred to.

there were be qualitative differences between this kind of quantum gravity theory and classical GR,

In the classical limit, those differences are assumed to be negligible and are ignored. If you're not ignoring them, you're not in the classical limit.

Again, I'm not sure what you think the issue is here.

 

[ohwilleke]

Again, I'm not sure what you think the issue is here. . . . If you're not ignoring them, you're not in the classical limit.

I am not saying that you are wrong.

I'm simply clarifying and emphasizing that the fact that the "classical limit" does not imply that GR and the massless spin-2 graviton (which couples in proportion to mass energy) are identical. They aren't just two identical mathematical statements expressed in different notation. In principle, at least, a massless spin-2 graviton theory could be distinguished with experiments from classical GR, because there would be some quantum gravity effects which would be absent in classical GR. A massless spin-2 graviton is not exactly classical GR, it just produces the same phenomena in the classical limit of this quantum gravity theory.

By analogy, the Standard Model's theory of electromagnetism, quantum electrodynamics, which is a quantum mechanical theory, is identical to the electromagnetism of the classical Maxwell's equations in the classical limit. But that doesn't mean that there are differences of practical importance between Maxwell's equations and QED.

For example, quantum tunneling, which is necessary for every transistor to work, and hence part of almost every computer and radio on the planet, is a phenomena found in QED that is not possible in QED's classical limit of Maxwell's equation.

The idea that everything that is not in the classical limit of a massless spin-2 graviton theory is not important in any real world circumstances is not at all an established point.

There are differences between the two when you don't restrict yourself to the classical limit of a massless spin-2 graviton theory, and there could be circumstances (e.g., Hawking radiation or black hole information conservation or black hole "no hair" theorems) where the differences between the massless spin-2 graviton theory and the classical limit might be important, and could be detectible. The could be others I'm not aware of, or that haven't yet been conceived and documented in the scientific literature.

Among other things, this is important because classical GR is theoretically inconsistent, in its classical formulation, with the Standard Model of Particle Physics, which is a quantum mechanical, non-classical theory, something that the massless spin-2 graviton quantum gravity approach seeks to address.

It is also important because some important features of GR are typically explained in reasoning that flows from qualitative features of classical GR (like the non-localization of gravitational field energy) which are not shared by a spin-2 massless graviton quantum gravity theory.

Even if you get the same observable result in many cases, you don't get there with the same kind of analysis and reasoning, in many cases.

For example, in classical GR, the self-interaction of the gravitational field with itself is embedded in the LHS of Einstein's Field Equations, while in a spin-2 massless graviton quantum gravity theory, gravitons are not just a carrier boson of, but a source of gravitational fields, just like all other particles. This structure of a massless spin-2 graviton theory is important and makes it a non-Abelian field theory, like QCD, but unlike QED which is an Abelian field theory. Even when the end result gives rise to the same predicted observables in the classical limit, the analysis and reasoning behind every instance in which there is gravitational field self-interaction is very different.

I'm not enough of an expert to know precisely all of the ways that a massless spin-2 graviton theory would differ from GR, in circumstances outside the classical limit, at least in less obvious respects than I have mentioned.

I have searched, so far in vain, for credible references spelling out those differences comprehensively.

But I have a hard time believing that nobody has ever written an article doing so, given the roughly half century that has elapsed since high profile scientists like Deser and Feynman started to seriously investigate the issue, since it is such an obvious question to ask.

For example, one of the more notable questions that I'd want to know the answer to is whether a massless spin-2 graviton theory would be in Minkowski space (like the rest of the Standard Model), with the apparent space-time curvature of classical GR actually being merely equivalent in effect to the gravitational effects of a massless spin-2 graviton, or if it operates in some different type of space, and if so, what kind - the same type of space-time as GR or something that differs from both the space-time of GR and the space-time of the Standard Model. The character of space-time is a very fundamental issue, so it would be helpful to know whether or not it is the same in a quantum gravity theory as a classical GR theory, as basic piece of context.

A BSM theory that has features that are present in a massless spin-2 graviton quantum gravity theory that are absent in classical GR might be more worth taking seriously than one that differs from or lacks those features. We'd like to think that at least some unsolved question in physics might be due to quantum gravity effects.

 

[PeterDonis]

the "classical limit" does not imply that GR and the massless spin-2 graviton (which couples in proportion to mass energy) are identical.

I agree that this is true. I'm not sure why it needs to be emphasized since the same is true for the classical limit of any quantum theory. Obviously the classical theory doesn't make all of the same predictions as the quantum theory. They're not the same theory.

I have a hard time believing that nobody has ever written an article doing so, given the roughly half century that has elapsed since high profile scientists like Deser and Feynman started to seriously investigate the issue, since it is such an obvious question to ask.

Unfortunately I'm not aware of such an article either. I think the fact that the theory was not renormalizable might have made the question seem not useful back in the 1960s and early 1970s when all that research was going on; the current understanding regarding effective field theories was not really in place then.

As for why nobody is investigating it now, this might be relevant:

The character of space-time is a very fundamental issue, so it would be helpful to know whether or not it is the same in a quantum gravity theory as a classical GR theory, as basic piece of context.

I think the answer to this is that it can't be, because the whole point of a full quantum gravity theory is that you don't have a definite spacetime structure; you just have amplitudes for various possible spacetime structures. So you can't even formulate the theory the way the massless spin-2 field theory is formulated, as a standard point particle QFT on Minkowski spacetime. The spacetime structure itself has to be captured by quantum degrees of freedom, or has to emerge from some other underlying quantum degrees of freedom (as in loop quantum gravity).

There might still be some intermediate level where the quantum degrees of freedom that might lead to significant uncertainty in the spacetime structure are all quiescent, so you do have a single spacetime structure that can be effectively treated classically, but you still have other quantum degrees of freedom excited (e.g., gravitational waves) that can't be treated classically. But AFAIK the common belief among physicists in the field is that gravity as an interaction at this level is so weak that by the time you reach an energy scale where its quantum degrees of freedom are significant (e.g., where a classical GR analysis of gravitational waves is no longer a useful approximation), you are also at an energy scale where the spacetime structure itself can no longer be treated classically, so there's simply no regime where the massless spin-2 field QFT on Minkowski spacetime is a useful model.

 

[ohwilleke]

I think the fact that the theory was not renormalizable might have made the question seem not useful back in the 1960s and early 1970s when all that research was going on; the current understanding regarding effective field theories was not really in place then.

This is why I referenced a couple of hints suggesting that perhaps the widely accepted conclusion that the QFT of a massless spin-2 graviton is not renormalizable might contain a non-obvious loophole or two (not unlike the way the renormalization itself made what were facially seemingly impossible calculations in QFT possible).

If these ideas were to go anywhere, the massless spin-2 graviton approach to quantum gravity might become much more relevant again and motivate more interest.

the massless spin-2 field theory is formulated, as a standard point particle QFT on Minkowski spacetime.

This is helpful to know and I hadn't been clear on this point.

I also wonder is some of the mathematical barriers to working out a massless spin-2 field theory formulated, as a standard point particle QFT on Minkowski spacetime, might be resolved if one assumed some new category of spacetime, which is not quite a Minkowski spacetime in some material way, but which is similar enough to a Minkowski spacetime that the Standard Model could still operate in it with minimal modifications that would matter in any practical applications. Loop quantum gravity and related theories, which try to quantize space-time might be examples of that.

For example, maybe you need both LQG-like formulation of space-time and a massless spin-0 graviton, to make the math work.

AFAIK the common belief among physicists in the field is that gravity as an interaction at this level is so weak that by the time you reach an energy scale where its quantum degrees of freedom are significant (e.g., where a classical GR analysis of gravitational waves is no longer a useful approximation), you are also at an energy scale where the spacetime structure itself can no longer be treated classically, so there's simply no regime where the massless spin-2 field QFT on Minkowski spacetime is a useful model.

I would agree that this is a common belief. But AFAIK, this hasn't been rigorously established.

 

[javisot]

I'm simply clarifying and emphasizing that the fact that the "classical limit" does not imply that GR and the massless spin-2 graviton (which couples in proportion to mass energy) are identical.

You can apply the same to gravity and acceleration, mass and energy, ADS and CFT, etc, but as Peter says, it doesn't seem relevant to mention it. (being equivalent and being identical, is not identical)

For a theory A to correspond to a theory B means that all the predictions and results of theory A have their "analogue" in theory B. It may also happen that, although A and B are clearly different theories, they construct exactly the same predictions and results (not analogue).

 

[PeterDonis]

a couple of hints suggesting that perhaps the widely accepted conclusion that the QFT of a massless spin-2 graviton is not renormalizable might contain a non-obvious loophole or two

I'm not sure the non-obvious loopholes help much with the massless spin-2 QFT if it's viewed as a "graviton" theory, because from what I can see, they're non-perturbative, meaning that they invalidate the "particle" picture that the term "graviton" is based on anyway. If anything, they suggest to me that the whole idea of viewing gravity as an "interaction" like those of the Standard Model doesn't really work. (Indeed, similar observations could be made about QCD, which also appears to have significant non-perturbative effects that electroweak theory does not have; one's whole view of bound states like hadrons has to change compared with how, say, one views electrons in atoms or something like positronium.)

 

[mitchell porter]

On the topic of quantizing general relativity (as opposed to other possible theories of gravity), I strongly strongly recommend the papers of John Donoghue, who seems to be the world expert on the subject. Donoghue focuses on the "effective field theory" perspective, which is all about quantum GR in the regime where there aren't problems, and it's just a matter of calculating minuscule quantum corrections to the classical predictions. (I thought he had a paper on the quantum analysis of the three classic tests of general relativity, but maybe that was someone else.)

The EFT perspective is explicitly a pragmatic one which does not concern itself with the ultimate underlying physics. Donoghue has nonetheless written a few papers on that; he seems to favor "quadratic gravity", but perhaps because of its simplicity (it is the simplest extension of general relativity that is renormalizable), rather than out of conviction.

I also find the recent papers of Richard Woodard interesting (he is mentioned by @ohwilleke in #10), as a counterpoint to Donoghue. When it comes to the topic of quantum GR, for me Donoghue is the voice of wise experience, and Woodard is the gadfly who might be right about something. Although I thereby set them up as opposites, that's still within the common context of quantum GR, as opposed to the endless other theoretical directions that are out there (LQG, MOND, string theory...).

While I think of it, those interested in how people thought about quantum gravity between the creation of the standard model and the rise of string theory, you could try Abdus Salam 1974 and Christopher Isham 1985. Salam shows how they hoped to reconstruct the geometric phenomena of general relativity from gravitons, and Isham gives a broader review from first principles.

In #10, @ohwilleke says that the "double copy" construction of gravitational calculations from two gauge-theory calculations multiplied together, is a reason to suppose that GR might be renormalizable after all, since a gauge theory like QCD is. I was ready to say that that can't be logically valid, but I was wrong... The main technical argument for the non-renormalizability of GR is Goroff & Sagnotti 1986, which shows that GR up to two graviton loops is non-renormalizable. For supergravity, I think the same argument kicks in at three loops. But what has been discovered (by Zvi Bern et al) is that there are unexpected cancellations among the Feynman diagrams which actually make supergravity renormalizable to much higher loop orders, and these cancellations are due to the double copy relations. If those arguments can somehow be extended to "N=0 supergravity", i.e. supergravity with zero supersymmetries, i.e. GR, then maybe something happens at higher loops which cancels the Goroff-Sagnotti counterterm. I wouldn't bet on it, but as far as I know, it remains open as a possibility.

On the other hand, in #12, @ohwilleke says that in a theory of gravitons, gravitational energy would be localized (unlike GR) and the details of gravitational self-interaction would be different. This I think is wrong, though I haven't yet dug through my gurus of quantum GR to find an argument.

 

[kodama]

In #10, @ohwilleke says that the "double copy" construction of gravitational calculations from two gauge-theory calculations multiplied together, is a reason to suppose that GR might be renormalizable after all, since a gauge theory like QCD is. I was ready to say that that can't be logically valid, but I was wrong...

is there any hypothesis that 4d GR is holographic duality with "double copy" QCD

 

[ohwilleke]

I wouldn't bet on it, but as far as I know, it remains open as a possibility.

You are exactly where I am on that then. I'm not saying that it is necessarily true, because it isn't entirely clear how far you can go with a "double copy" approach. But, so far as I know, the possibility hasn't been ruled out.

Essentially, if that is true, then there is some sort of non-obvious hidden structure within the graviton propagator that through cancellations leaves fewer possible amplitudes and/or paths than a crude, brute force approach to calculating it would suggest.

While I wouldn't bet on it, however, I think I would give it better odds than you do.

GR doesn't have mathematical hang ups apart from black hole/Big Bang type singularities (and it could be the there is some non-obvious deep connection between those singularities and the superficial appearance that a massless spin-2 graviton theory is not renormalizable). And, if a massless spin-2 graviton theory is equivalent to GR in the classical limit, one would think that the problems that are making the quantum gravity approach non-renormalizable can't be all that pathological.

Also, assuming for sake of argument that gravity is really fundamentally quantum and not classical, Nature manages to come up with "analog" solutions vast numbers of times every second without a glitch all over the Universe. So, we basically have proof that there is some way to solve this problem staring us in the face. And, surprisingly often, simply having absolute confidence that there is a solution to a mathematical problem helps you to actually find that solution.

Maybe this is one of those problems where there is a lot of "quantum magic" involved in the math, i.e. it is one of those problems where a quantum computer is intrinsically vastly superior to a conventional one, and that while the problem may be theoretically possible to solve with ordinary computing but as a practical matter virtually impossible, it may be quite tractable with quantum computing.

On the other hand, in #12, @ohwilleke says that in a theory of gravitons . . . the details of gravitational self-interaction would be different. This I think is wrong, though I haven't yet dug through my gurus of quantum GR to find an argument.

Just to be clear, I didn't say that the end result of the details of gravitational self-interaction would be different, at least in the classical limit (I don't know one way or another, but assuming that a massless spin-2 graviton is identical to GR in the classical limit, presumably there must be no difference).

What I said was that the way gravitational self-interaction presents itself in the analysis and calculations is very different, even if it is equivalent and gets you to the same place in the end.

In a massless spin-2 graviton theory, gravitational self-interactions present on an equal footing with other sources of gravity. The gravitons are just one more element to insert into Feynman diagrams. The fact that graviton-graviton interactions even exist is facially obvious by construction.

In GR, in contrast, gravitational self-interactions manifest through the LHS of Einstein's field equations, while other sources of gravity manifest on the RHS. You have to understand a lot about what is hiding behind the tensor notion in Einstein's field equations and have a pretty deep understanding of them to even realize that there are self-interactions of the gravitational field when it is presented that way.

It could very well be the case that they are exactly equivalent (at least in the classical limit). But the way that they are described is very different.

By analogy, one might compare it to doing mechanics the way you do in first year physics, to doing mechanics with Lagrangians for a system. It's equivalent, but its a very different way of laying out the mathematics and thinking about the same problems.

 

[ohwilleke]

I'm not sure the non-obvious loopholes help much with the massless spin-2 QFT if it's viewed as a "graviton" theory, because from what I can see, they're non-perturbative, meaning that they invalidate the "particle" picture that the term "graviton" is based on anyway. If anything, they suggest to me that the whole idea of viewing gravity as an "interaction" like those of the Standard Model doesn't really work. (Indeed, similar observations could be made about QCD, which also appears to have significant non-perturbative effects that electroweak theory does not have; one's whole view of bound states like hadrons has to change compared with how, say, one views electrons in atoms or something like positronium.)

Certainly, it is true that non-perturbative effects matter in QCD, and in particular, in low energy QCD.

I wouldn't be at all surprised if the key to quantum gravity likewise involves really getting a handle on non-perturbative effects there.
R. P. Woodard and B. Yesilyurt (2024) (from #10) is certainly making that argument.

And Deur, likewise, strenuously makes the case that what we are missing, which is giving rise to the appearance of dark matter and dark energy phenomena, are non-perturbative gravitational effects. And, I'm inclined to find him credible on that point, because his primary specialty is QCD and in particular, the transition from the the non-perturbative to the perturbative regimes in QCD. These kinds of effects in a QFT and this kind of math is something he is very familiar with in a regime where we routinely calculate with it and routinely produce results that are confirmed by experiments with it.

In contrast, for people who come to gravitational physics from the classical GR direction, non-perturbative physics is pretty much like speaking in a second language. It is out of their comfort zone to a greater degree, and their intuition for it does not come as naturally. Dealing with it requires them to set aside their usual, well-used tool boxes and trade them out for a different box of tools that a lot of them haven't really fully broken in.

So, I have a fair amount of hope that injecting more non-perturbative methods into the study and development of quantum gravity, which is an area where scientists have gotten their toes wet without giving these approaches and tools a leading role and making them a primary focus, leaves a lot of unexplored theoretical territory where there might be room for a break though.

 

[PeterDonis]

And Deur, likewise, strenuously makes the case that what we are missing, which is giving rise to the appearance of dark matter and dark energy phenomena, are non-perturbative gravitational effects.

Of course we've discussed Deur's papers in several previous PF threads. The part I still struggle with in his approach is that, as the article you linked to notes, nothing about the effects he proposes is quantum in nature or relies on quantum aspects of gravity; all of them should be present in classical GR. And so far, he apparently hasn't convinced the classical GR community that they are. But the work continues, and we'll see what happens.

 

[ohwilleke]

Of course we've discussed Deur's papers in several previous PF threads. The part I still struggle with in his approach is that, as the article you linked to notes, nothing about the effects he proposes is quantum in nature or relies on quantum aspects of gravity; all of them should be present in classical GR. And so far, he apparently hasn't convinced the classical GR community that they are. But the work continues, and we'll see what happens.

The effect that he proposed is not inherently quantum in character (although it is much more intuitive from a quantum perspective), but it is non-perturbative, from both a quantum and a classical perspective.

 

[PeterDonis]

it is non-perturbative, from both a quantum and a classical perspective.

Yes, agreed. Classical non-perturbative effects, in themselves, are nothing new in GR; black hole solutions are examples. But whether the specific non-perturbative effects Deur describes are there in classical GR, still appears to be an open question as far as the GR community at large is concerned.

 

[kodama]

Yes, agreed. Classical non-perturbative effects, in themselves, are nothing new in GR; black hole solutions are examples. But whether the specific non-perturbative effects Deur describes are there in classical GR, still appears to be an open question as far as the GR community at large is concerned.

do you know of any GR community experts who agree with the specific non-perturbative effects Deur describes are there in classical GR?

shouldn't numerical computer GR verify Deur?

 

[ohwilleke]

Yes, agreed. Classical non-perturbative effects, in themselves, are nothing new in GR; black hole solutions are examples. But whether the specific non-perturbative effects Deur describes are there in classical GR, still appears to be an open question as far as the GR community at large is concerned.

Agreed.

 

[ohwilleke]

do you know of any GR community experts who agree with the specific non-perturbative effects Deur describes are there in classical GR?

shouldn't numerical computer GR verify Deur?

The only serious review of Deur's approach was by a group of physicists who used analytical perturbative classical GR methods to see if they came to the same conclusion, which they did not.

Deur wrote a response to that article pointing out that their perturbative methods assumed away the non-perturbative effects which he claimed.

Deur has used numerical methods, but no other researchers have done so in an attempt to replicate his conclusions.

 

[kodama]

The only serious review of Deur's approach was by a group of physicists who used analytical perturbative classical GR methods to see if they came to the same conclusion, which they did not.

Deur wrote a response to that article pointing out that their perturbative methods assumed away the non-perturbative effects which he claimed.

Deur has used numerical methods, but no other researchers have done so in an attempt to replicate his conclusions.

is there any reason why physicists with a specialty in GR haven't been found Deur non-perturbative effects convincing ie Deur effects aren't in Gravitation written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler

 

[ohwilleke]

is there any reason why physicists with a specialty in GR haven't been found Deur non-perturbative effects convincing ie Deur effects aren't in Gravitation written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler

In part, because that textbook dismisses the possibility in passing, without much analysis to back it up, and doesn't emphasize non-perturbative methods of that kind, more generally. GR trained physicists have some limited familiarity with non-perturbative methods and non-abelian gauge fields, but aren't immersed in it in the same way that someone whose primary work is in QCD is.

Gravitation by C.W. Misner, K.S. thorne and J.A. Wheller (1973), explains in Section 20.4, there are several arguments in favor of the proposition that the energy of a gravitational field cannot be localized and hence cannot be considered in the same way that all other mass-energy is considered in the energy-momentum tensor of general relativity.

This widely held textbook assumption that gravitational energy cannot be localized may be the best explanation for why it has taken so long to seriously explore approaches to incorporate gravitational force self-interaction in phenomenological analysis, because the self-interaction effects that Deur argues can be deduced from a graviton model of gravity can only work when gravitational energy is localized, with quanta, or as classical fields or as classical curvature self-interactions.

But, as A.I. Nikishov of the P.N. Lebedev Physical Institute in Moscow states in an updated July 23, 2013 version of an October 13, 2003 preprint (arXiv:gr-qc/0310072), these arguments "do not seem convincing enough." For example, Feynman's lectures on gravitation assumed that gravity was mediated by a graviton that could be localized with a self-interaction coupling strength equal to the graviton's energy, just as the graviton would with any other particle. String theory and supergravity theories, generically make the same assumptions.

Nikishov also made the same analysis as Deur in his paper "Problems in field theoretical approach to gravitation" dated February 4, 2008 in its latest preprint version arXiv:gr-qc/04100999 originally submitted October 20, 2004, when he states in the first sentence of his abstract that:

We consider gravitational self interaction in the lowest approximation and assume that graviton interacts with gravitational energy-momentum tensor in the same way as it interacts with particles.

Deur and Nikishov are not the only investigators to note the potential problems with the anomalous ways that conventional General Relativity treats gravitational self-interactions, and they are not alone in this respect. Carl Brannen has also pursued some similar ideas.

As another example, consider this statement by A.L. Koshkarov from the University of Petrozavodsk, Russia in his November 4, 2004 preprint (arXiv:gr-qc/0411073) in the introduction to his paper entitled "On General Relativity extension."

But in what way, the fact that gravitation is nonabelian does get on with widely spread and prevailing view the gravity source is energy-momentum and only energy-moment? And how about nonabelian self-interaction? Of course, here we touch very tender spots about exclusiveness of gravity as physical field, the energy problem, etc. . . .All the facts point out the General Relaivity is not quite conventional nonabelian theory.

Koshkarov then goes on to look at what one would need to do in order to formulate gravity as a conventional nonabelian theory like conventional Yang-Mills theory.

Alexander Balakin, Diego Pavon, Dominik J. Schwarz, and Winfried Zimdahl, in their paper "Curvature force and dark energy" published at New.J.Phys.5:85 (2003), preprint at arXiv:astro-ph0302150 similarly noted that "curvature self-interaction of the cosmic gas is shown to mimic a cosmological constant or other forms of dark energy."

Balakin, et al., reach their conclusions using the classical geometric expression of general relativity, rather than a quantum gravity analysis, suggesting that the overlooked self-interaction effects do not depend upon whether one's formulation of gravity is a classical or a quantum one, but the implication once again, is that a failure to adequately account for the self-interaction of gravitational energy with itself may account for all or most dark sector phenomena.

As noted above, there is a rich academic literature expressing dissatisfaction with the precise way that General Relativity was formulated by Einstein on the grounds that it lacks one or another subtle aspects of rigor or theoretical consistency, or makes a subtle assumption that is unnecessary, or needs to be tweaked to formulate it in a way that formulates gravity in a quantum manner.

See also R. P. Woodard and B. Yesilyurt, "The Other ADM" arXiv:2410.05213 (October 7, 2024), mentioned above.

 

[PeterDonis]

that textbook dismisses the possibility in passing

If you're talking about localization of gravitational energy, MTW does no such thing. It quite correctly points out that, in standard classical GR, which is what the textbook is about, gravitational energy indeed cannot be localized: there is no tensor quantity that corresponds to it. You yourself gave the reason why in post #19: "gravity" is on the LHS of the Einstein Field Equation; "energy" is on the RHS. "Gravitational self-interaction" in classical GR simply isn't the kind of thing someone coming from a QFT background would expect; in that context it has to be understood differently.

Of course MTW was published in 1973 and there has been a lot of theoretical work done since then on what kind of model at the next level down GR might be an approximation to, and whether in that model there might indeed be a way for gravitational energy to be localized. But it's hardly fair to criticize MTW for not taking into account work that has been done in the more than 50 years since it was published.

 

[kodama]

If you're talking about localization of gravitational energy, MTW does no such thing. It quite correctly points out that, in standard classical GR, which is what the textbook is about, gravitational energy indeed cannot be localized: there is no tensor quantity that corresponds to it. You yourself gave the reason why in post #19: "gravity" is on the LHS of the Einstein Field Equation; "energy" is on the RHS. "Gravitational self-interaction" in classical GR simply isn't the kind of thing someone coming from a QFT background would expect; in that context it has to be understood differently.

Of course MTW was published in 1973 and there has been a lot of theoretical work done since then on what kind of model at the next level down GR might be an approximation to, and whether in that model there might indeed be a way for gravitational energy to be localized. But it's hardly fair to criticize MTW for not taking into account work that has been done in the more than 50 years since it was published.

so what do you think of the plausibility of Deur "Gravitational self-interaction" in classical GR could explain the missing mass in galaxies without dark matter via non-perturbative effects

 

[PeterDonis]

so what do you think of the plausibility of Deur "Gravitational self-interaction" in classical GR could explain the missing mass in galaxies without dark matter via non-perturbative effects

I don't have enough of an intuition to hazard an opinion. There are no known exact solutions for the primary case of interest (a disk-like matter distribution), and nobody else has tried to check Deur's numerical simulations, and I'm certainly not in a position to do that on my own.

 

[ohwilleke]

it's hardly fair to criticize MTW for not taking into account work that has been done in the more than 50 years since it was published.

Part of the problem is that MTW is still being used as a standard textbook (probably the leading one in its subject), with almost no substantive updates through later editions.

There are lots of disciplines in which the best selling textbooks have been around for that long, but in other disciplines (e.g. economics and law) there have been a dozen or more significant substantive new edition updates since then.

In contrast, MTW has added only a brief updated introduction and maybe some slightly improved printing and paper quality in later printings. AFAIK, it hasn't even gone back and made a comprehensive purge of errata in the original edition (which certainly must exist in one of the largest textbooks for sale in university bookstores these days, which is chock full of highly technical content). No one would even try to cram all of that material into a single volume today.

While GR has not been the most quickly developing field in that time period, the field hasn't been entirely stagnant in that time period. MTW was written before the PC existed, before the Internet, before arXiv, and before space telescopes existed. M, T, and W did their math with slide rules and drew their diagrams by hand with straight edges and curve drawing tools that today's physicists wouldn't recognize at a yard sale. None of them could type, so it was either written long hand, or dictated. They were already esteemed full professors when my late father, who died in his 80s, was awarded his PhD in engineering from Stanford in 1970. It predates the fully elaborated Standard Model of Particle Physics. MTW was written so long ago that it is almost as old now as Einstein's original papers discovering GR were when it was written. Some or all of them had met Einstein himself in person in a professional capacity, even if they weren't strictly his professional contemporaries. There are whole sub-disciplines of relevant math, like chaos theory and the mathematical fruits of string theory, that are relevant to gravitation but didn't exist when it was written.

This contributes to a generation of new astrophysicists who are leaving graduate school unnecessarily behind the cutting edge of new research in the field. We really deserve a new industry standard GR textbook.

 

[kodama]

Are Deur results published in a peer reviewed journal?

 

[PeterDonis]

MTW is still being used as a standard textbook

Is it? It's commonly given as an advanced reference, but I'm not sure it's commonly being used to teach courses in GR.

 

[ohwilleke]

Are Deur results published in a peer reviewed journal?

Yes.

I maintain an annotated bibliography which includes both his published and unpublished papers related to astrophysics and gravity.

Overall he has 230 publications on arXiv, most of which are published QCD papers, and many of which are papers in which he is simply one member of a large HEP collaboration that is publishing its results.

The published astrophysics/gravity papers include:

A. Deur, “Implications of Graviton-Graviton Interaction to Dark Matter” (May 6, 2009) (published at 676 Phys. Lett. B 21 (2009))​

​

Alexandre Deur, "A relation between the dark mass of elliptical galaxies and their shape" arXiv:1304.6932 (2013) (published in MNRAS (2014) doi: 10.1093/mnras/stt2293)​

​

A. Deur, "An explanation for dark matter and dark energy consistent with the Standard Model of particle physics and General Relativity" arXiv:1709.02481 (September 7, 2017 published October 22, 2019) (published in Eur. Phys. J.C.) doi10.1140/epjc/s10052-019-7393-0​

​

A. Deur, “Self-interacting scalar fields at high temperature” (June 15, 2017) (published at Eur. Phys. J. C77 (2017) no.6, 412) (despite the somewhat oblique title, this does address the relevant topic)​

​

Alexandre Deur, "Relativistic corrections to the rotation curves of disk galaxies" (April 10, 2020) (lated updated February 8, 2021 in version accepted for publication in Eur. Phys. Jour. C)​

​

Alexandre Deur, "Effect of gravitational field self-interaction on large structure formation" arXiv: 2018:04649 (July 9, 2021) (Accepted for publication in Phys. Lett. B) DOI: 10.1016/j.physletb.2021.136510​

​

David Winters, Alexandre Deur, Xiaochao Zheng, "New Analysis of Dark Matter in Elliptical Galaxies" arXiv:2207.02945 (July 6, 2022) (published at 518 (2) MNRAS 2845-2852 (2023))​

​

B. Guiot, A. Borqus, A. Deur, K. Werner, "Graviballs and Dark Matter" (June 3, 2020 revised September 3, 2020)(a different hypothesis than his main work). A follow up paper from February 9, 2022 is here​

​

Corey Sargent, William Jackson Clark, Alexandre Deur, Balsa Terzic, "Hubble tension and gravitational self-interaction" Physica Scripta (June 25, 2024)​

​

Given the time that elapses before uploading a preprint and getting an article accepted for publication, this is about as up to date as it is possible to be. His most recent peer reviewed publication of any kind was in February of 2025 (a QCD related chapter in an Encyclopedia of Particle Physics).

He is cited in some papers as well, including:

Valentina Cesare, "Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND" arXiv:2301.07115 (January 17, 2023) (at page 23) (accepted for publication)​

​

Pierfrancesco Di Cintio "Dissipationless collapse and the dynamical mass-ellipticity relation of elliptical galaxies in Newtonian gravity and MOND" arXiv:2310.12114 (October 18, 2023)(accepted for publication)​

The main paper criticizing his result (which is unpublished) is:

W. E. V. Barker, M. P. Hobson and A. N. Lasenby, "Does gravitational confinement sustain flat galactic rotation curves without dark matter?" arXiv:2303.11094 (March 20, 2023)​

He responded with a (currently unpublished) comment in:

Alexandre Deur, "Comment on "Does gravitational confinement sustain flat galactic rotation curves without dark matter?'' arXiv:2306.00992 (May 13, 2023)​

​

​

 

[ohwilleke]

Is it? It's commonly given as an advanced reference, but I'm not sure it's commonly being used to teach courses in GR.

I don't know where to find good statistics, but according to Google AI it is in the top two in response to the query: "most widely used general relativity textbooks"

I'd love to see more authoritative sources as I don't particularly trust AI for accuracy.

 

[weirdoguy]

most widely used general relativity textbooks

Well, that is different from "most used for teaching"

 

[jacobbry]

I have problems understanding gravitons. I would understand them in the context of Newtonian gravitation. The Newtonian gravitational field is a force field and the gravitational interaction takes directly place between specific masses. It would therefore make sense to assume the existence of mediators for the interaction in this context.

The Einsteinian gravitational field, however, is not a force field. As I understand it, the field seems to be spacetime itself. In general relativity, gravitation is a geometric phenomenon and each mass just follows the curvature of spacetime, without direct interaction with other specific masses. I find it difficult to see why mediators would be needed in this picture. It even seems that gravitons would invalidate GR – not as an abstract mathematical model, but as a model of the physical reality. Is the reality of gravitation curved spacetime, or is it an exchange of particles? I don’t see how it can be both.

1. No Einstein’s gravitational field is not space time but rather warps space time.
2. In general relativity masses follow the curvature of space time as you have stated however that is only mostly true as in the physical world all masses actually have a infinitesimally small effect on space time such that it can be ignored in the study and mathematics of general relitivity with the exception of masses with extreme gravitational forces such as black holes that can warp space time as in Einsteins gravitational field