Are gravitons necessary?

[KevinMcHugh]

If gravity is not a force, but rather curvature of spacetime, are gravitons necessary to couple with gravitational field?

 

[KevinMcHugh]

If gravity is not a force, but rather curvature of spacetime, are gravitons necessary to couple with gravitational field?

Never-ending. Just did a search, and got my a swer

 

[PeterDonis]

Just did a search, and got my a swer

What did you find?

 

[Ibix]

Gravitons do not appear in classical gravity, just as photons do not appear in classical electromagnetism. Force carrier particles appear in quantum theories (the photon appears in the quantised version of electromagnetism), and gravitons do appear in at least some attempts at quantum gravity. I don't think they model gravity as spacetime curvature, though.

 

[PeterDonis]

at least some attempts at quantum gravity. I don't think they model gravity as spacetime curvature, though.

The quantum field theory of a massless spin-2 field was developed in the 1960s and early 1970s by Feynman, Deser, and others. "Graviton" is the particle associated with that field, just as "photon" is the particle associated with the massless spin-1 field in quantum electrodynamics. Classical GR is then viewed as the classical limit of the massless spin-2 field QFT, and spacetime curvature is then just an emergent property of that QFT at the classical level.

The main issue with that QFT, as it was viewed when it was developed, was that it was not renormalizable. However, the current view is that non-renormalizability is not a fundamental issue for a QFT as long as it is just an effective theory, valid only up to a certain energy scale, at which new physics emerges. The massless spin-2 field theory, viewed as an effective theory, is simply what we would expect to get if we quantize classical GR along the same lines as QED is what we get if we quantize classical electrodynamics.

The question then is whether there is any regime in which the massless spin-2 field theory is actually useful, i.e., where quantum gravitational effects are happening that it can predict but classical GR doesn't, but the energy scale is still low enough that other new physics does not emerge that invalidates the massless spin-2 field theory itself. It might well turn out that that is not the case: for example, suppose no significant quantum gravitational effects appear at all until the Planck scale, but the Planck scale is also where new physics appears that invalidates the massless spin-2 QFT. In that case the massless spin-2 QFT would basically never get used at all, since classical GR would be sufficient below the Planck scale and new physics beyond the massless spin-2 QFT would be required at and above the Planck scale.

 

[haushofer]

What makes the notion of gravitons a bit weird is that they're defined w.r.t. a fixed background spacetime which must be a solution to Einstein's field equations. The theory thus becomes "background dependent". Mathematically this is a no brainer because perturbation theory is always w.r.t. some vacuum, but the Einstein equations themselves are background independent.

 

[Ibix]

What makes the notion of gravitons a bit weird is that they're defined w.r.t. a fixed background spacetime which must be a solution to Einstein's field equations. The theory thus becomes "background dependent". Mathematically this is a no brainer because perturbation theory is always w.r.t. some vacuum, but the Einstein equations themselves are background independent.

So, paraphrasing and extending to see if I understand, we like GR because it describes the dynamics of spacetime and, although there's apparently arbitrary stuff in there (why 4d? Why locally Lorentz?), it feels like a step towards understanding those questions compared to our pre-relativistic models. Switching to a graviton theory might be seen as a step back from that because it "un-unifies" gravity and spacetime, and leaves us with at least as many questions as we started with. Hence there's an impetus to look for theories that aren't plain vanilla (or plane vanilla?) quantisation of a classical field theory, things like LQG and String Theory.

 

[PeterDonis]

Switching to a graviton theory might be seen as a step back from that because it "un-unifies" gravity and spacetime

More precisely, it splits "gravity" into two pieces, the part that produces the background spacetime geometry, and the "graviton" part that is treated as a perturbation around that background spacetime.

 

[Ken G]

However, the current view is that non-renormalizability is not a fundamental issue for a QFT as long as it is just an effective theory, valid only up to a certain energy scale, at which new physics emerges.

I've never understood why anyone would view any physics theory as something different from an effective theory, if we define it that way. Surely we can't believe that just because a theory works in all domains where it has been tested, it should therefore work in all other domains (which sounds like the requirement to not be an "effective theory" if we define it that way), as that has simply never been true in the entire history of our business, as far as I can see. But I think what you probably mean is that an effective theory is one that allows us to know where it will break down, which you may have implied by saying a "certain" energy scale, whereas a "real" theory is one that doesn't allow us to know that. If so, real theories are only superior to effective ones if they are known to apply over a broader range, whereas effective theories are always superior if we have never tested the place where they break down (because in that case they always tell us more than a real theory does, because we know when they won't work, whereas there's no reason but sheer optimism to think the real theory will work over a wider range).

The question then is whether there is any regime in which the massless spin-2 field theory is actually useful, i.e., where quantum gravitational effects are happening that it can predict but classical GR doesn't, but the energy scale is still low enough that other new physics does not emerge that invalidates the massless spin-2 field theory itself.

This is a very interesting take on the issue, because it's not one I've ever seen before. The usual reason given to quantize gravity is simply that gravity "should be" quantized, to make it fit better with everything else, but not necessarily to produce any new or different predictions. Indeed, I've never even heard anyone suggest the observation of a single graviton, and LIGO is certainly not set up to do so. So I think it would be fairer to say that at present, no one really has any practical reason to expect to need quantization of gravity, yet there is a big effort to do it anyway, just because it should be done. Wouldn't you say that's the state of things? (Maybe there are some early universe issues that it could help with, but that always sounded pretty speculative to me, given that we don't even understand dark matter or dark energy, it seems premature to start understanding the unification of gravity, rather it was always a kind of aesthetic value in being able to unify things therefore having a theory with fewer separate parts but no different predictions that we can test.)

But I agree that your picture is much more like the way science really works, we come up with theories to explain things we observe that we can't already explain, not because we like theories with certain properties that "seem" like they should be there. But of course there have been times when the two approaches diverged for awhile only to be brought back together later, as happened with general relativity. Einstein got pretty far thinking about what "should be", but we must remember he also built a static cosmology and thought entanglement had to be wrong.

It might well turn out that that is not the case: for example, suppose no significant quantum gravitational effects appear at all until the Planck scale, but the Planck scale is also where new physics appears that invalidates the massless spin-2 QFT. In that case the massless spin-2 QFT would basically never get used at all, since classical GR would be sufficient below the Planck scale and new physics beyond the massless spin-2 QFT would be required at and above the Planck scale.

And yet I've never heard any suggestion that anyone thinks something interesting will happen with GR before you get to the Planck scale that we would need a graviton theory to explain. (That may be my lack of knowledge, I'm all ears.) On the surface, the Planck scale is just the scale that emerges from the physical constants of QM and GR, so it is just a scale and not a limit, creating no problems and no reason to expect anything to break down until you look at the QM of the particles, not the GR of the fields. You only get a sense that GR should break down at that scale when you either try to unify it with QM, or try to understand how particles will act. So ironically, there isn't even any reason to think GR by itself (i.e., in a universe without QM) would require new physics at the Planck scale unless you already think it needs to be unified with QM, i.e., needs to be quantized itself, or if you want to understand how it interacts with particles (which of course you do).

The situation strikes me as analogous to how Planck originally thought about his own constant, which he regarded as a quantum of action in the oscillators that couple to the electromagnetic field, not a quantization of the electromagnetic field itself. In other words, he derived the blackbody spectrum without the concept of a photon, it played no role at all in his theory and really didn't gain impetus until Einstein's photoelectric effect. It could have been the same with gravity, where its interactions with particles would need to obey the quantum mechanics of those particles, but gravity itself would not need to be quantized until there was some observation of the nature of the photoelectric effect, i.e., an observation of something that requires the graviton to understand, like you are saying. The idea that there has to be a breakdown at the Planck scale then comes from the particles, not the gravitational field itself, so there still is no need to quantize the gravitational field, you already know it's not going to correctly interact with particles at the Planck scale whether it's quantized or not.

In short, it has never been suggested to me that the reason we need to quantize gravity is so that it will work all the way up to the Planck scale, since we know neither that the unquantized version would fail before that, nor that the quantized version would succeed up to that. It was always just purely because of the desire to unify gravity with QM, to make it look like a quantum theory, something that Planck himself never thought he needed to do because he didn't start with the idea that he should. It turned out to be needed for the electromagnetic field, but I've never seen any evidence it is needed for the gravitational field, but I'm not an expert.

 

[Ken G]

More precisely, it splits "gravity" into two pieces, the part that produces the background spacetime geometry, and the "graviton" part that is treated as a perturbation around that background spacetime.

And that really sounds like the ultimate irony. The main impetus to quantize the gravitational field is to unify it with other fields that need to be quantized, resulting in a cleaner theoretical description of all things. Except that now you have split your gravity into a part that makes the background, and a part that dances across the background. That does not sound like a net unification at all, as @Ibix was alluding to.

 

[PeterDonis]

I think what you probably mean is that an effective theory is one that allows us to know where it will break down

With our current theories, we do have at least a good idea where we expect them to break down, yes. Proponents of a "theory of everything" believe that sooner or later we will discover a theory that doesn't break down in any regime, but even if we had one, I'm not sure we could ever know for sure that it was one, since there will always be regimes we don't have any actual data from.

 

[PeterDonis]

The main impetus to quantize the gravitational field is to unify it with other fields that need to be quantized, resulting in a cleaner theoretical description of all things. Except that now you have split your gravity into a part that makes the background, and a part that dances across the background. That does not sound like a net unification at all, as @Ibix was alluding to.

It's definitely a step back from the idea that we can have everything emerge from the theory. But of course any quantum field theory built on a background spacetime will have that problem, since the background spacetime can't emerge from the theory since it's built into it from the start. The only way to avoid that is to find some other way to build the theory that doesn't include spacetime at all at the fundamental level, and have spacetime itself emerge, along with everything else we observe. Loop quantum gravity at least appear to be aiming at that. I'm not sure string theory actually is since you still have a kind of spacetime geometry built into it.

 

[strangerep]

What makes the notion of gravitons a bit weird is that they're defined w.r.t. a fixed background spacetime which must be a solution to Einstein's field equations. The theory thus becomes "background dependent". Mathematically this is a no brainer because perturbation theory is always w.r.t. some vacuum, but the Einstein equations themselves are background independent.

The local structure at any spacetime point is Minkowskian. The trouble arises from the fact that a Hilbert space at that spacetime point, spanned by a set of orthonormal field modes, is unitarily inequivalent to the Hilbert space at an infinitesimally nearby spacetime point. (Birrell & Davies explain how one must change one's c/a operators via a Bogoliubov transformation.) If we try to encompass this infinity of local Hilbert spaces, we must deal a much larger nonseparable Hilbert space (uncountable basis), but the maths for working with nonseparable Hilbert spaces is still nowhere near as well developed as that for Hilbert spaces.
E.g., (afaik), there is no translation-invariant Lebesgue measure over such an inconveniently infinite-dimensional space.

But,... hmm,... I just noticed this "recent"(2020) paper by John Earman. Abstract follows:

In Mathematical Foundations of Quantum Mechanics (1932) von Neumann made separability of Hilbert space an axiom. Subsequent work in mathematics (some of it by von Neumann himself) investigated non-separable Hilbert spaces, and mathematical physicists have sometimes made use of them. This note discusses some of the problems that arise in trying to treat quantum systems with non-separable spaces. Some of the problems are “merely technical” but others point to interesting foundations issues for quantum theory, both in its abstract mathematical form and its applications to physical systems. Nothing new or original is attempted here. Rather this note aims to bring into focus some issues that have for too long remained on the edge of consciousness for philosophers of physics.

I'll try to read it in the not-too-distant future.

 

[Ken G]

It's definitely a step back from the idea that we can have everything emerge from the theory. But of course any quantum field theory built on a background spacetime will have that problem, since the background spacetime can't emerge from the theory since it's built into it from the start. The only way to avoid that is to find some other way to build the theory that doesn't include spacetime at all at the fundamental level, and have spacetime itself emerge, along with everything else we observe. Loop quantum gravity at least appear to be aiming at that. I'm not sure string theory actually is since you still have a kind of spacetime geometry built into it.

Let's just say that "theories of everything" have a pretty dismal history in our business, so it seems to border on illogical to expect one of those. Unification is a key goal of physics, but any time you push your understanding farther it tends to open up new frontiers, so you kind of unify what is behind you as you press forward into new mysteries. To think you have unified everything would seem to require that you are only looking backward.

 

[Ken G]

It's definitely a step back from the idea that we can have everything emerge from the theory. But of course any quantum field theory built on a background spacetime will have that problem, since the background spacetime can't emerge from the theory since it's built into it from the start. The only way to avoid that is to find some other way to build the theory that doesn't include spacetime at all at the fundamental level, and have spacetime itself emerge, along with everything else we observe. Loop quantum gravity at least appear to be aiming at that. I'm not sure string theory actually is since you still have a kind of spacetime geometry built into it.

Yeah, I think that's very much the hope of loop quantum gravity. Of course I have no idea if it will succeed, but if it does, I think it will still only be a "theory of everything" in the backward looking sense.

 

[Ken G]

E.g., (afaik), there is no translation-invariant Lebesgue measure over such an inconveniently infinite-dimensional space.

This could be an example of the problem with "theories of everything": those darn "issues at the edge of consciousness for philosophers of physics." Issues that I translate into, "the more you know, the more you know you don't know."

 

[Nik_2213]

Like monopoles, gravitons would be nice to find...
( Do gravitational wave detectors sense the graviton equivalent of ELF EM ?? )

IIRC, 'Teleparallel Gravity' --Albeit as several incomplete and currently contradictory flavours of hypothesis-- suggests that EM radiation = photons are space-time twisted one way, and gravitons are kin to photons, but twist space-time another way. As yet, no apparent way to falsify, never mind implement, so 'due care', please ?

 

[Meir Achuz]

Much ado about nothing, since there is no successful theory of quantum gravity.

 

[Nik_2213]

"... there is no successful theory of quantum gravity."
Yet.
One may emerge from the 'String Theory' zoo, or 'Teleparallel Gravity' flavours may converge to a workable version, or a 21st Century Einstein / Hawking / Ramanujan equivalent may come along and surprise us with something utterly unexpected...
Sadly, unlikely to happen in my remaining life-time...