Is the Graviton Fundamental in Quantum Gravity Theories?

[Coin]

From the Not Even Wrong thread on Garrett Lisi's E8 theory:

Does the spin 2 graviton (still) exist in the theory?

Loll recently put the business about gravitons succinctly:

The failure of the perturbative approach to quantum gravity in terms of linear fluctuations around a fixed background metric implies that the fundamental dynamical degrees of freedom of quantum gravity at the Planck scale are definitely not gravitons.

That is (from http://arxiv.org/abs/0711.0273 ) if a theory is fundamental, it should not have gravitons.

One should be able to set up certain fixed situations in which a graviton can be derived as an approximation. But the graviton should not exist in the theory as a fundamental descriptor. If it does exist, then the theory would not be fundamental–according to what Renate Loll says.

I would therefore be surprised if it turned out that the E8 theory being developed by Garrett Lisi (and possibly others lately) should turn out harbor the graviton as a fundamental component.

I had some questions in response to this; Woit complained (quite correctly) that my post didn't have anything to do with E8 or Woit's blog and requested the discussion not continue there. So I'm posting it here instead. My response to Marcus is:

So while I personally find the no graviton approach attractive on several levels, it kind of seems like rejecting the graviton should be considered a dramatic step to take. Not bad-- just dramatic, so it should maybe be done carefully. Do there already exist any other theories of quantum gravity, besides Loll’s, which eschew the graviton or take the “graviton as approximation” approach you describe? Which ones?

Does LQG, for example, have a graviton? Looking I am finding references to a “graviton propagator” in LQG but it is not immediately obvious whether that’s the same thing.

------

Aside from this I find Loll’s argument against the graviton in the paper Marcus links somewhat unconclusive by itself. “Well, we’ve been trying to get useful answers out of this construct for decades and haven’t succeeded, so it’s a good bet we’re doing something wrong” sounds like good strategy to me, but Loll doesn’t seem to actually be putting forth an argument about reality there, only an argument about “how to proceed”. I don’t see any reason that just because we can’t describe the graviton perturbatively, that would mean it doesn’t exist– since, as far as I understand, perturbation theory is supposed to just be an approximation anyway. (And this is of course assuming that perturbatively modeling the graviton is actually impossible, and not just too hard for anyone to manage right now!) Am I missing something about Loll’s argument?

 

[marcus]

Do there already exist any other theories of quantum gravity, besides Loll’s, which eschew the graviton or take the “graviton as approximation” approach you describe? Which ones?

Well all the various approaches that get called LQG---which is quite a bunch. In the GRAVITON PROPAGATOR papers, the graviton that Rovelli gets is in a special approximation that he forces on the theory, forcing it to approximate flat Minkowski space, JUST FOR THE PURPOSE of showing that the theory can act like one expects in that approximation. It is part of showing that the theory has the correct low-energy low-curvature limit.

The graviton is a mathematical object that arises in approaches called PERTURBATIVE where the metric g is the sum of a fixed metric g' and a small ripple disturbance or perturbation h.
So g = g' + h
and the fixed metric is usually the flat (zero gravity, zero matter) solution to Einstein equations called Minkowski. Then there is a series expansion. The perturbative approach does not work where the field is strong, dynamic, lots of curvature---then it cannot be expressed as a static field with a small disturbance added to it. So then gravitons do not arise in the mathematics.

I have to go, back later

Aside from this I find Loll’s argument against the graviton in the paper Marcus links somewhat unconclusive by itself. “Well, we’ve been trying to get useful answers out of this construct for decades and haven’t succeeded, so it’s a good bet we’re doing something wrong” sounds like good strategy to me, but Loll doesn’t seem to actually be putting forth an argument about reality there, only an argument about “how to proceed”. I don’t see any reason that just because we can’t describe the graviton perturbatively, that would mean it doesn’t exist– since, as far as I understand, perturbation theory is supposed to just be an approximation anyway. (And this is of course assuming that perturbatively modeling the graviton is actually impossible, and not just too hard for anyone to manage right now!) Am I missing something about Loll’s argument?

You may have missed the point. Loll's paper is not about the non-existence of gravitons. that is generally taken for granted in the (non-string) QG community and has been as far back as I have looked. The reason I quoted her was she expressed it succinctly and a side comment in her introduction. I like her writing style.

You wouldn't pretend that gravitons are real and use them to describe the early universe or the actual collapse of a star to form black hole because those situations don't have an artificial fixed flat background. Graviton is just an effective mathematical construct that is convenient in a limited field theory context, not something that anybody in the community thinks real, as far as I know, or has ever.

I read Loll's paper as a proud report of progress in her Triangulations approach. It does not revolve around the graviton issue at all!--that is just a side comment which she delivers crisply.

If interested in QG, I would advise forgetting about gravitons for the moment and reading the introduction section of Loll's paper carefully. It is about the emergence of quantum spacetime from fundamental microscopic dynamical degrees of freedom----the emergence not of one single classical spacetime but a whole slew of them: a pathintegral full of spacetimes. Exploring observables like volume correlation, and dimensionality. I think it is interesting. Don't read it unless you do too. If you like it, it can be a taste of what non-string QG is about.

There are others one could sample or start with instead, but you've already downloaded Loll's latest paper, so that's one way to go.

 

[Angryphysicist]

So while I personally find the no graviton approach attractive on several levels, it kind of seems like rejecting the graviton should be considered a dramatic step to take. Not bad-- just dramatic, so it should maybe be done carefully. Do there already exist any other theories of quantum gravity, besides Loll’s, which eschew the graviton or take the “graviton as approximation” approach you describe? Which ones?

I'm (obviously) not Marcus, but I feel compelled to intervene here because I firmly disbelieve in the graviton.

Have you looked up group field theoretic quantum gravity? It begins with one of its premises being there are no gravitons.

It was previously discussed on this forum as a matter of fact.

One of the compelling arguments against perturbative approaches that Thiemann gives in his recent book Modern Canonical Quantum General Relativity (seriously Thiemann, commission is in order for how much I'm plugging your book!):

Roughly the [perturbative quantum gravity approach] is to write the dynamical metric tensor as $$g = \eta + h$$ where $$\eta$$ is the Minkowski metric and h is the deviation of g from it (the graviton) and then to expand the Lagrangian as an infinite power series in h. One arrives at a formal, infinite series with finite radius of convergence which becomes meaningless if the fluctuations are large. Although the naive power counting argument implies that general relativity is so defined is a non-renormalisable theory, it was hoped that due to cancellations of divergences the perturbation theory could actually be finite. However, this hope was unjustified was shown in [38,39] where calculations demonstrated the appearance of divergences at the two-loop level, which suggests that at every order of perturbation theory one must introduce new coupling constants which the classical theory did not know about and one loses predictability.

--emphasis added

From pages 7-8 Modern Canonical Quantum General Relativity by Thomas Thiemann (2007).

The two citations he cites are (from the bibliography):

[38] N. Marcus and A. Sagnotti. The ultraviolet behavior of N=4 Yang-Mills and the power counting of extended superspace. Nucl. Phys. B256 (1985) 77.
[39] M. H. Goroff and A. Sagnotti. Quantum Gravity at Two Loops. Phys. Rev. B160 (1985) 81.

 

[marcus]

I'm (obviously) not Marcus, but I feel compelled to intervene here because I firmly disbelieve in the graviton...

One of the compelling arguments against perturbative approaches that Thiemann gives in his recent book Modern Canonical Quantum General Relativity (seriously Thiemann, commission is in order for how much I'm plugging your book!):

Thanks Angry, you put it like a physicist. I was just saying words.

Over at Woit's blog, AGeek put the matter well:

# AGeek Says:
November 16th, 2007 at 3:50 am

Coin, Renate Loll is a she (her name should be a clue). And assuming that “graviton” means what it’s normally taken to mean, a perturbative free state propagating on some background a la DeWitt, then to say that gravity can not be described perturbatively is to say that gravitons do not exist.

And it has been known for several decades that gravity can not be described perturbatively because (in perturbative context) it is not renormalizable.

 

[Coin]

Hi Marcus and AngryPhysicist, you both seem to be basically saying the same thing, which is that the graviton is actually just an artifact of the perturbative approach to quantum gravity and therefore if you can't perturbatively describe the graviton then it DOESN'T exist. AGeek at NEW responded with the same thing:

Coin, Renate Loll is a she (her name should be a clue).

Oops...

And assuming that “graviton” means what it’s normally taken to mean, a perturbative free state propagating on some background a la DeWitt, then to say that gravity can not be described perturbatively is to say that gravitons do not exist.

So what youall are saying does seem to make sense, I think, although I guess I probably ought to read up on some of this stuff more :) but, in the meantime, there is one thing I am suddenly very confused about.

My (very vague) understanding is that string theory's claim to be a theory of quantum gravity is based around the presence in the string spectrum of a spin 2 massless boson; we for some reason that I don't quite understand get to assume that the spin 2 massless bosons are all gravitons, and therefore since string theory contains gravitons it is a theory of quantum gravity. But if the graviton is something which does not describe all situations in quantum gravity-- as you all say, it can't be used in a nonperturbative theory (as I understand things string theory is currently used as a perturbative theory, but I have seen discussion implying there was at least one time hope of formulating a nonperturbative version), or when the fluctuations in the background metrics would become "large"-- if this is the case then how can string theory be a theory of quantum gravity, if its notion of quantum gravity is based on gravitons? Am I missing something here? Or does String Theory have some way of handling the large-curvature/large-fluctuation cases, besides the literal usage of spin 2 massless bosons?

 

[Sauron]

Gravitons? Uh?

Well, I´ll do a question for stringy people here. What is the S-dual of the graviton mode of a fundamental string?

I thnk that the answer could be interesting to understand what string theory has to say about gravity.

 

[jimgraber]

Disbelieving the graviton?

If you disbelieve the graviton, do you disbelieve in gravitational waves? Or do you believe in gravitational waves and believe that gravitational waves ignore Planck's constant?

If you believe in gravitational waves and Planck's constant, you are nearly forced into believing in the graviton. Of course, Nobel prize winner Willis Lamb famously disbelieved in the photon.

However, my understanding is that graviton disbelievers are a very small minority, even among the LQG crowd. Correct me if I'm wrong.

Instead, I think that some (many?) of them believe the graviton is not elementary, but built up from loops, ribbons, triangulations, (strings), or something else.

I would be very interested to read a short summary of the position of each of the major groups on the graviton. TIA to anyone who can provide it.

Best to all.
Jim Graber

 

[friend]

If you disbelieve the graviton, do you disbelieve in gravitational waves? Or do you believe in gravitational waves and believe that gravitational waves ignore Planck's constant?

I have to wonder if such small amplitude gravity waves can even be detectable. Wouldn't the measuring device have to be larger than the wave itself. And don't small perturbations from flat spacetime mean that those gravity waves would be very long and thus very difficult to detect?

 

[Micha]

Maybe it is obvious, but I already asked myself, how the expansion of the whole universe fits into the spin 2 particle picture of gravity. I guess, the simple answer is, it doesn't.

 

[Angryphysicist]

If you disbelieve the graviton, do you disbelieve in gravitational waves? Or do you believe in gravitational waves and believe that gravitational waves ignore Planck's constant?

If you believe in gravitational waves and Planck's constant, you are nearly forced into believing in the graviton. Of course, Nobel prize winner Willis Lamb famously disbelieved in the photon.

Personally I think this is relatively narrow position (no offense)..."it's either gravitons or else you don't adequately believe in Planck's constant and gravitational waves" is too much of a false dilemma in my opinion.

What about the geon concept proposed by Wheeler? This is based on the principle of gravitational waves, and quantization presents itself rather readily...all the while, we don't really "need" the graviton.

Or, as I mentioned earlier I believe, the group field theoretic quantization of gravity? There is Planck's constant involved there and it doesn't contradict gravitational waves.

Gravity is really a different sort of force since we're dealing with spacetime directly rather than with some force that can be viewed as happening within spacetime. That is where quantum theory sort of...runs into trouble.

If life were as easy as gravitons, then we'd have had a quantum theory of gravity way back in the 1930s. Fortunately life is interesting, so it's been over 70 years of active research and still we don't have a clue. It's not that we've failed, we've merely succeeded at finding ways that don't work.

(And by the by, for those that are wondering why I answered four minutes after Marcus, I originally began before him but got distracted by the mail )

 

[jimgraber]

Hi, Angryphysicist, from a Happy former math student,
I have several responses, (not necessarily answers).

Response Number 1:
Of course, it’s logically possible to believe in the photon and not the graviton, and some physicists have done so, and some still do. Just before the discovery (invention?), of string theory, when many people were despairing of the possibility of a mathematically consistent quantum theory of gravity, this was a more popular idea. But I think it has always been a minority position. I would like your view, and also Marcus’ view on which modern authors uphold this position.

You seem to suggest Oriti (group field theory quantum gravity) and Marcus quotes Loll.

However, the quote that Marcus posted merely states that the graviton is not fundamental, not that it doesn’t exist. We used to think the proton was fundamental, now we believe in quarks. But people who believe in quarks mostly don’t believe that the proton doesn’t exist, only that it is not fundamental. The same can be true for gravitons.

I have scanned some of Oriti’s recent papers on the ArXiv. I didn’t spot any references to gravitons, but there were tons of references to Feynman diagrams and the Feynman propagator for gravitation. The Feynman propagator for gravitation, (actually technically the exchange particle), is the graviton. What makes you think Oriti does not believe in gravitons?

Of course you can believe in virtual gravitons without believing in real gravitons, but that seems to me to be a rather contorted worldview.


Response Number 2
This response is based on the argument that a graviton is necessarily defined as a perturbation on a linear background, and that reality is at least nonlinear, if not background free, thus discrediting the idea of the graviton. Even accepting all the hypotheses in the above argument, some of which are at least arguable if not dubious, it remains true that linearity of spacetime is a very good approximation. Even if the graviton does not exist, it is an excellent approximation. This goes back to “ancient” work by Feynman, Weinberg, Boulware, Deser and others.

Following this idea, the only places I know in the “real world” where linearity of spacetime is not a good approximation are at the big bang and at the formation/evaporation of a small black hole. In these environments nonlinear spacetime effects can be large. Do you think an evaporating black hole emits Hawking radiation including photons, but not gravitons? (I should probably post that as a separate question over at quantum physics.)

Enough for now. I may post a third response later.

Best to all.
Jim Graber

 

[Haelfix]

The graviton is really just a simple consequence of using the Einstein Hilbert action and the rules of quantization. So it exists in so far as those things are physical, and whatever theory you output should in principle reduce to those dynamics in the suitable limits.

By exist of course, we mean in the same way that say a photon or W boson 'exists' (whatever that means). Keep in mind the description of these thigns change as you improve the perturbation series. For instance the form factors of a photon interaction can and does receive nonperturbative corrections in QED.

Likewise gravitons receive nonperturbative corrections, and much of the whold business of quantum gravity is trying to figure out what that is. No one is deluded into thinking local weak field limits are the whole story, and indeed they are most assuredly not.

But yea, it doesn't make much sense to *not* believe in a graviton, and still believe in general relativity and quantum mechanics. They're sort of the same by definition.

 

[Angryphysicist]

Of course, it’s logically possible to believe in the photon and not the graviton, and some physicists have done so, and some still do. Just before the discovery (invention?), of string theory, when many people were despairing of the possibility of a mathematically consistent quantum theory of gravity, this was a more popular idea. But I think it has always been a minority position. I would like your view, and also Marcus’ view on which modern authors uphold this position.

Just a historical background, String theory was originally invented to solve the problem of Strong force. It turned out to be wrong, and they re-applied it to other problems (the foundation of particle physics as a theory of everything, for example).

String theory was one of the approaches that was a consistent perturbative approach, but it wasn't the "only" consistent approach as you suggest.

Other non-perturbative approaches are consistent.

You seem to suggest Oriti (group field theory quantum gravity) and Marcus quotes Loll.

Marcus gives an argument from Loll, but I cite Oriti's work on group field theoretic quantizations of gravity as one concrete example of a theory of quantum gravity sans graviton.

However, the quote that Marcus posted merely states that the graviton is not fundamental, not that it doesn’t exist.

There are some serious theoretical problems with the graviton; there is no conclusive "proof" that it exists or it doesn't.

But as scientists, we're not looking for proofs. We seek evidence.

We used to think the proton was fundamental, now we believe in quarks.

Um...I think that the proton is not fundamental, as we now believe it's made out of quarks. As for the photon being made out of quarks, this is news to me.

But people who believe in quarks mostly don’t believe that the proton doesn’t exist, only that it is not fundamental. The same can be true for gravitons.

Perhaps, if the graviton is massive and fermionic?

I have scanned some of Oriti’s recent papers on the ArXiv. I didn’t spot any references to gravitons, but there were tons of references to Feynman diagrams and the Feynman propagator for gravitation. The Feynman propagator for gravitation, (actually technically the exchange particle), is the graviton. What makes you think Oriti does not believe in gravitons?

Page 24 from his Loops07 Talk.

Response Number 2
This response is based on the argument that a graviton is necessarily defined as a perturbation on a linear background, and that reality is at least nonlinear, if not background free, thus discrediting the idea of the graviton. Even accepting all the hypotheses in the above argument, some of which are at least arguable if not dubious, it remains true that linearity of spacetime is a very good approximation. Even if the graviton does not exist, it is an excellent approximation. This goes back to “ancient” work by Feynman, Weinberg, Boulware, Deser and others.

Yes it is an excellent approximation in a weak gravitational field.

As I quoted Thiemann pointing out, when we break the metric in two $$g = \eta + h$$ with $$g$$ being the metric, $$\eta$$ being the Minkowski metric, and $$h$$ being the deviation from the minkowski metric, we can expand the Lagrangian with $$h$$ terms.

This works when the deviation is within the radius of convergence. Outside of the radius of convergence...like in a black hole, it is utterly useless!

And places like in a black hole, or the big bang, where the deviation is outside the radius of convergence, the model is completely useless.

So the only places that we don't know about classically, we can't know about quantum mechanically! That's not good!

Do you think an evaporating black hole emits Hawking radiation including photons, but not gravitons? (I should probably post that as a separate question over at quantum physics.)

Well, Hawking radiation takes the form of gamma radiation. Unless gamma radiation changes radically due to the existence of gravitons, I don't believe that Hawking radiation includes gravitons.

 

[marcus]

Even if the graviton does not exist, it is an excellent approximation.

An excellent approximation in linear (weak field as Haelfix says) cases, which is most everywhere. I agree of course.

I just think that it misleads people to give them the idea that gravitons exist like real things whizzing around and that is how you should understand how gravity works. They then imagine that is how it works inside the event horizon of a black hole...

If someone naively believes gravitons are really how gravity works, not just an extremely useful approx when appropriately applied, then they can apply the idea inapproapriately, as I've seen happen.

I'd say the graviton exists as a useful analytical tool not as one of God's creatures, and leave it at that.

so I agree with Loll, but I don't see anything wrong with what you and Haelfix say if it is properly understood

Do you think an evaporating black hole emits Hawking radiation including photons, but not gravitons? (I should probably post that as a separate question over at quantum physics.)

Jim, thanks for the careful response! I think the point is that outside the event horizon both graviton and photon are useful mathematical tools and I am happy to think with them (to the best of my ability). But inside the event horizon I do not know how to correctly apply the graviton concept to understand gravity. At some point, out of deference to your expertise, I have to take your word about it. I am hardly an authority. I just think gravitons only exist where it is mathematically valid to apply them
...

Haelfix, thanks for your carefully worded statement. Properly understood, I think your position actually harmonizes with mine and is articulated in a highly knowledgeable way.

The graviton is really just a simple consequence of using the Einstein Hilbert action and the rules of quantization. So it exists in so far as those things are physical, and whatever theory you output should in principle reduce to those dynamics in the suitable limits.

By exist of course, we mean in the same way that say a photon or W boson 'exists' (whatever that means). Keep in mind the description of these things change as you improve the perturbation series. For instance the form factors of a photon interaction can and does receive nonperturbative corrections in QED.

Likewise gravitons receive nonperturbative corrections, and much of the whold business of quantum gravity is trying to figure out what that is. No one is deluded into thinking local weak field limits are the whole story, and indeed they are most assuredly not.
...

This is very informative and reinforces for me that the graviton is a mathematical convention which changes description as needed according to the circumstances in which it is serving as an approximate analytical tool.

I would be happy to believe that none of our fellow PF posters is deluded into thinking that local weak field limits are the whole story. I want them to NOT be deluded and that is why I quoted Loll.

I disagree with the spirit of your final remark

But yea, it doesn't make much sense to *not* believe in a graviton, and still believe in general relativity and quantum mechanics. They're sort of the same by definition

I would draw the opposite conclusion from what you just said. But for me GR and QM are not carved in stone. They are still alive and changing: QM is getting extended to cover spacetime dynamics and GR is getting quantized. Maybe I should imagine them as fixed and finalized and then I could accept the spirit of your final remark there.

 

[marcus]

Ooops, sorry Angry. I didn't see you were already responding. You are much better qualified to engage in this discussion. Hope your cold is better. I will lay off here and let you prevail.

 

[Haelfix]

Theres really no great conceptual difference between the various gauge bosons, take the W boson vs the Graviton. The different quantum numbers, spin and mass will distinguish how they behave, but theoretically the jist is identical. Read they're simply quantum point particles that mediate exchanges and appear mathematically in perturbation series.

These things also live in weak field approximations if you generalize to curved spacetimes. But there too there are ambiguities in description at the global level, which only nonperturbative methods can fully solve. Yet, surely no one disbelieves in the W, since we see them in accelerators.

Now, if quantum mechanics suddenly stops working near the Planck scale, or if general relativity is wrong near the Planck scale then all bets are off. The graviton may not 'exist' (in the sense that the W 'exists') after all.

 

[Coin]

However, the quote that Marcus posted merely states that the graviton is not fundamental, not that it doesn’t exist. We used to think the proton was fundamental, now we believe in quarks. But people who believe in quarks mostly don’t believe that the proton doesn’t exist, only that it is not fundamental. The same can be true for gravitons.

Hi,

So I ask above how it is that, if gravitons cannot represent gravity under some circumstances, that String Theory can still be a theory of quantum gravity when it does its gravity by gravitons.

Is that the explanation, what you say here? I mean, is the idea that the graviton can't be fundamental, but that's okay because the graviton isn't fundamental in string theory, the string is fundamental? Or is something else at work here?

 

[jimgraber]

Hi all,
Real life intervened and I have not had time to continue this conversation.


First of all for Coin:
I believe you have come to the correct logical conclusion:
Someone who disbelieved in the graviton, or
who believed that it was only an aproximation,
would be very likely to conclude that string theory
is an incomplete or unsatisfactory or only approximate explanation of gravitation.

And indeed most LQG folks seem to think string theory is unsatisfactory,
Usually because it is background dependent, in their view.
(There has been much controversy over this,
and other people know much more about it than I do,
so I’ll stop here.)

Second for Angry,
Thanks for the reference to page 24 of Oriti’s talk.
I admit he’s pretty down on the graviton.

Here is what he says:

""
A QFT for Quantum Gravity?
Immediate questions:
A QFT on which spacetime?
a QFT of gravitons on some background doesn’t work
QG should explain origin and properties of spacetime itself (geometry
and topology?)
background independence!
it can be only be a QFT on some auxiliary or internal space (local
symmetry group is natural choice)

a QFT of what? what are the fundamental quanta?
gravitons do not work
quanta of space itself! fundamental excitations of space around the
vacuum (nothing)
""


To repeat what I said last post,
There is a big difference in thinking that the graviton is not fundamental,
and thinking it does not exist.
Now what about “gravitons do not work”?

Not quite the same, but let’s count it as one for the
Don’t believe in gravitons camp”

On the other hand here are a few titles suggesting that
some LQG folks do believe in gravitons or something similar.

Towards the graviton from spinfoams: higher order corrections in the 3d toy model
Etera R. Livine, Simone Speziale, Joshua L. Willis gr-qc/0605123 (2006) [Preprint]

Group Integral Techniques for the Spinfoam Graviton Propagator
Etera R. Livine, Simone Speziale gr-qc/0608131 (2006) [Preprint]

Graviton propagator from background-independent quantum gravity
Carlo Rovelli gr-qc/0508124 (August 2005)

Towards the graviton from spinfoams: the 3d toy model
Simone Speziale J. High Energy Phys. 2006 (2006) [Article]

Finally, I want to ask:

What do you believe if you don’t believe in the graviton?

Two possible answers:

Local moves on graphs (e.g. Fotini Markopoulou)

An unquantized perfect fluid like gravitational field
(or electromagnetic field?)

I’ll post more about these two later, if I get a chance.

Best to all,
Bye for now.
Jim Graber

 

[Angryphysicist]

Marcus:

Ooops, sorry Angry. I didn't see you were already responding. You are much better qualified to engage in this discussion. Hope your cold is better. I will lay off here and let you prevail.

Haha we need to coordinate better is all!

Don't hesitate to give your two cents, I (more than likely) see things far differently than you do so you may have something to add that I overlooked.

And my cold is getting better, thanks for your concern

jimgraber: best of luck to you wading through all of this...

To repeat what I said last post,
There is a big difference in thinking that the graviton is not fundamental,
and thinking it does not exist.
Now what about “gravitons do not work”?

I tend to keep things simple, and cut out what is unnecessary. It's occam's razor.

Gravitons don't work, and we're going to perform excitations of spacetime directly? Then...why would we want to use gravitons? It's rather circular reasoning. If there were empirical evidence of gravitons, perhaps you'd have something; but we don't, so you don't either.

I think the point has been pressed enough that there are serious theoretical problems with the graviton (works as a weak field approximation but not all weak field approximations are good approximations; model becomes totally useless when the fluctuations of spacetime are beyond the radius of convergence for the weak field; perhaps most pressing it tells us nothing new about what we already know, and it tells us nothing about what we don't know, e.g. internals of black holes or the big bang, it's beyond the radius of convergence for the weak field approximation; etc.). I honestly don't see a point rehashing these points again and again. So perhaps we should discuss the "necessity" of the existence of gravitons and the evidence for them.

Until there is a legitimate argument for the existence of gravitons, we don't need to accept their existence. It's unnecessary to do so, by Occam's razor.

But, no offense, you appear to be arguing the exact opposite...which is a fallacy, shifting the burden of proof. Like a religious fellow's argument that "God" exists because you can't prove "His" nonexistence!

I'm still rather confused about your previous remark about electrons not being fundamental and being made out of quarks. This is news to me!

But if the graviton were not fundamental, were to exist, then doesn't it logically follow that it would be made out of components that we should be able to detect? Why can't we detect the existence of a graviton then? Perhaps more pressingly why should a graviton not be fundamental if it exists?

On the other hand here are a few titles suggesting that
some LQG folks do believe in gravitons or something similar.

I'll be sure to give them all medals.

It's of marginal interest to me that these people believe in gravitons, graviolis, gravitinos, or the flying spaghetti monster.

I reiterate my point I previously made: is there any evidence of gravitons? "Give me direct evidence or be quiet!" Isn't that the motto of science? (If not, science has changed a lot since...yesterday...)

There is evidence of gravitational waves, great, and the argument typically goes "Well, applying standard quantization techniques, you get the graviton."

But the standard quantization techniques are dubious when applied to gravitational waves, as I previously stated. Quantization techniques deal with waves or fields in spacetime...now what happens when the field is spacetime?!

The graviton doesn't make any sense anymore. I suppose if you really wanted to you could argue that a graviton "is" spacetime...but this makes no intuitive sense (spacetime is "exchanged" by particles attracting each other via gravitational force in a Feynman diagram? Could I create a "spacetime" ray-gun that attracts stuff to me then?).

Personally, I think that quantum theory needs to be revisited. It appears to be an approximation to some underlying theory. Just my two cents...

What do you believe if you don’t believe in the graviton?

Two possible answers:

Local moves on graphs (e.g. Fotini Markopoulou)

An unquantized perfect fluid like gravitational field
(or electromagnetic field?)

I know I say this a lot, but how narrow! Only these two options? There are no others?

I personally believe that there is no graviton, true; I believe that spacetime comes in quantized "chunks" that are generated by the presence of energy/matter. Somewhat a direct quantization of general relativity guided by Einstein's views of his own theory.

I reiterate that we can't naively apply quantization techniques to general relativity, it's not as simple as that. If it were, then it would have been quantized in the 1930s by people like Bronstein, and we'd be saying "Ah very interesting ... graviton ... blah blah blah ...".

This sort of necessitates a reconsideration of quantum theory, or general relativity. One or the other...or both!

I've made my choice with quantum theory first, maybe general relativity needs to be modified too later on because of this. I don't honestly know, hopefully we'll find out in due time.

But the equivalence principle really allows us to have gravity expressed as the geometry of spacetime; and it's empirically, well, not correct, but it's yet to be falsified.

So even if you change general relativity (somehow), you would run into the same exact problem. It seems a priori that quantum theory should be the prime candidate for inspection.

 

[turbo]

Let's look at the observational evidence so see if theory can approximate what we see. We have theory that tells us that mass is conferred to matter by its interaction with the Higgs field, and that matter's gravitational attraction to other matter is mediated through its interaction with a gravitational field. Is there a problem with this view? I see one. Fields can be polarized/densified/rarified, and they can evolve over time and with location. Everywhere and everywhen we look in our Universe, gravitational behaviors appear to be consistent. If this is to be explained, we must posit that the Higgs field and the gravitational field are exquisitely congruent over all space and time, and this is a coincidence that is unexplained. The observations of gravitational behavior can be most reasonably explained by the explanation that mass, gravitational effects, and inertial effects arise from matter's interaction with a single field. No separate Higgs field and gravitational field, and therefore no mediating particles for these fields. The Higgs boson and the graviton are ruled out by observation unless someone can explain the extraordinary congruence of the the fields that require these mediating particles.

 

[Haelfix]

Angry, arguing against the existence of gravitons makes zero sense if you accept the consistency of quantum mechanics, general relativity and gravitational waves. Like I said, its like disbelieving any gauge boson just b/c they live in weak field approximations, the only difference being that the latter are at experimentally accessable energy ranges.

Unless you stick your accelerator right on top of singularity of the big bang, weak fields is where we do experiments. Now, if you insist on sticking your accelerator right there (or any place with massive curvature), you will have identically the same problems with the W, the photon, the Z and the Graviton.

In fact there is probably no such thing really as a 'particle' in general once you are in curved spacetimes, as they become observer dependant quantities. Thats part of the properties of the Unruh effect, where you will have thermal properties of the vacuum that become apparent depending on your frame of motion.

But all this is known, so when we talk about the 'existence' of gravitons its implied that we are living in its domain of validity.

 

[marcus]

In fact there is probably no such thing really as a 'particle' in general once you are in curved spacetimes, as they become observer dependant quantities. ...

But all this is known, so when we talk about the 'existence' of gravitons its implied that we are living in its domain of validity.

I agree Haelfix. Moreover you have expressed this very clearly. I live in curved spacetime and therefore NOT in its domain of validity, except as a useful approximation. So, in accordance with your logic I should not talk about the 'existence' of gravitons. And I do not. I find your statement of implication correct. (A => B and therefore not-B implies not-A.)

BTW Rovelli has an nicely written informative article about this http://arxiv.org/abs/gr-qc/0409054 It points out how different observers will see different numbers of particles and that the formal presence or absence of a particle depends on a lot of what are basically boundary conditions. To the extent that the thing exists, its existence is contingent. Or as you say, observer-dependent.

The trouble is, I think, that LAY people do not realize this.

You say when WE talk about the 'existence' of gravitons we do so, in effect, with the proper degree of mental reservation and sophistication. But it seems to me that this WE leaves out many of the interested lay people who come with questions about gravity.

BTW how does all this affect the original quote from Renate Loll that Coin started the thread with? Here it is:

The failure of the perturbative approach to quantum gravity in terms of linear fluctuations around a fixed background metric implies that the fundamental dynamical degrees of freedom of quantum gravity at the Planck scale are definitely not gravitons.

Have we now come to any further understanding of this statement, or to some clearer agreement/disagreement regarding it?

 

[Angryphysicist]

Angry, arguing against the existence of gravitons makes zero sense if you accept the consistency of quantum mechanics, general relativity and gravitational waves.

I thought I made it perfectly clear that I don't believe that quantum mechanics is consistent with general relativity and needs to be modified in order to quantize general relativity.

Like I said, its like disbelieving any gauge boson just b/c they live in weak field approximations, the only difference being that the latter are at experimentally accessable energy ranges.

But the weak field approximation doesn't always work when quantizing a system.

For example, if you look this up in Abhay Ashtekar's Quantum Mechanics of Geometry (gr-qc/9901023) for more detail which is where this example comes from, consider the Harmonic oscillator Hamiltonian $$H=p^2 + \omega^2q^2$$ and treat the potential as $$V = \omega^2q^2$$ as an interaction Hamiltonian perturbing the free Hamiltonian $$H_0 = p^2$$ at least for low frequencies $$\omega$$. The exact spectrum of $$H$$ is discrete while that of $$H_0$$ is continuous.

One may ask "So what?" Well, so this: one is never going to see (for any "coupling constant" $$\omega > 0$$) the discreteness of the spectrum of the unperturbed Hamiltonian by doing any perturbation theory, and so one completely misses the correct physics.

Or in short: just because you're using perturbation theory doesn't mean you're doing the right thing.

But all this is known, so when we talk about the 'existence' of gravitons its implied that we are living in its domain of validity.

Yes, now how about using gravitons to explain the interior of black holes? The Big Bang singularity?

It's not that we're within the radius of convergence that's the problem, it's that what we don't know lies beyond the radius of convergence.

The graviton may work within the radius of convergence, and it may prove to be accurate there, but it doesn't really tell us anything new about the problems we have.

 

[jimgraber]

Marcus wrote:
“
I agree Haelfix. Moreover you have expressed this very clearly. I live in curved spacetime and therefore NOT in its domain of validity, except as a useful approximation. So, in accordance with your logic I should not talk about the 'existence' of gravitons. And I do not. I find your statement of implication correct. (A => B and therefore not-B implies not-A.) …”

The point is, all quantum particles are in the same boat as far as a consistent theoretical nonperturbative interactive explanation in curved spacetime.
There ain’t nonesuch. (See the last paragraph of this recent review by Bob Wald for confirmation. Gr-qc/0608018 )

Therefore, to be consistent, you should not talk of the existence of photons, electrons, or protons anymore than gravitons.

Now experimental evidence is another story, but theoretically, the photon and the electron are in as much trouble in curved spacetime as the graviton.
That is why the above argument cuts very little ice with me.
Jim Graber

 

[jimgraber]

Let me try to make another very general point:
If you get rid of the graviton, you must find something else to do the work of the graviton.
You can go back to the old, not yet disproven, idea that gravity is not quantum, or cannot be quantized,
But some people would say that’s admitting defeat.

In string theory the closed string does the work of the graviton and is identified with it.

In some LQG approaches the graviton propagator is constructed from spin foams or something similar. For examples, see the papers in my second post in this thread.
In this case, the graviton is not fundamental but it exists.

In some LQG approaches, such aqs the recent Bilson-Thompson one, the graviton, indeed all of gravity is openly acknowledged as an unsolved problem. My impression is that many others regard it as a partially solved problem.

Maybe some time, I’ll try to say a little more about approaches with quantized matter, but unquantised fields, or unquantised forces. This seems to me to be what Angry has in mind, and it reminds me a lot of the old Willis Lamb approach.
Someone once described it to me this way:

A tornado or a hurricane will knock down individual trees in a forest, but is the wind quantized? Not on the scale of the trees, at least.

Question for everyone:
What does the work of the graviton in your favorite theory?

That’s all for now.
Good night.
Jim Graber

 

[marcus]

Marcus wrote:
“
I agree Haelfix. Moreover you have expressed this very clearly. I live in curved spacetime and therefore NOT in its domain of validity, except as a useful approximation. So, in accordance with your logic I should not talk about the 'existence' of gravitons. And I do not. I find your statement of implication correct. (A => B and therefore not-B implies not-A.) …”

The point is, all quantum particles are in the same boat as far as a consistent theoretical nonperturbative interactive explanation in curved spacetime.
There ain’t nonesuch. (See the last paragraph of this recent review by Bob Wald for confirmation. Gr-qc/0608018 )

Therefore, to be consistent, you should not talk of the existence of photons, electrons, or protons anymore than gravitons.

Of course I talk and think in terms of particles which can be detected, and do so all the time
You are carrying things to extremes. I say these things can exist AS A USEFUL APPROXIMATION and the practicality has to do with the fact that there are instruments like photon counters!

Whenever particles have a practical existence, it is consistent, by my lights to talk of them as existing.

Come on Jim, let's not get bogged down in a semantic discussion of the meaning of "existence"

I choose to speak of photons and electrons as existing because it is useful and practical to do so. The thing has some operational meaning.
And I choose NOT to speak of gravitons because practically speaking they do not exist. Nor do they seem to play a fundamental role in describing spacetime geometry or gravity.

Jim, let's get back to the original statement by Renate Loll. Do you question what she says?

 

[zankaon]

graviton

Isn't the graviton concept just a weak gravitational field description? So how is it descriptive for an extreme pseudo-Riemannian spacetime environment of near to BH horizon, and/or extremes of deformation of manifold i.e. for copious gravity waves?

 

[marcus]

Isn't the graviton concept just a weak gravitational field description? So how is it descriptive for an extreme pseudo-Riemannian spacetime environment of near to BH horizon, and/or extremes of deformation of manifold i.e. for copious gravity waves?

I think you are right, zankaon. Thanks for making this point! It is not descriptive.

In modern quantum gravity the graviton has no important role. So when someone asks "if you don't have a graviton, what does the work of the graviton?" then the answer is nothing because it does essentially no work.

One could imagine that gravitons are important in LQG because there are a few articles that have the word graviton in the TITLE, but it is like supposing that chickens are important to bricklaying just because a skilled bricklayer can build a 20 foot tall giant chicken out of bricks.

The LQG spinfoam is not a perturbative theory, and it has no idea of flatspace, so it is only with considerable skill that one can sedate it and force it to lie flat long enough to calculate terms of the graviton propagator from it. There are no gravitons in Rovelli's gravitonpropagator paper. The great thing is that he and co-workers can extract the appearance---the RESEMBLANCE of a perturbative theory.

One of the coauthors of the LQG spinfoam graviton papers sometimes posts here at PF. I will ask him, next time I see him, if it is fair to say that deriving the resemblance of a graviton (or a term in the propagator series) was like building a chicken out of bricks.

 

[jimgraber]

Marcus,

Slightly more of what Loll wrote:

“
The
failure of the perturbative approach to quantum gravity in terms of linear fluctuations around
a fixed background metric implies that the fundamental dynamical degrees of freedom of
quantum gravity at the Planck scale are definitely not gravitons. At this stage, we do
not yet know what they are. Neither do we have the luxury of hints from experiment or
observation of what they might be, …”

I think that tells the story.
I mostly agree with the last two sentences I have quoted.
The first part, about the failure of gravitons,
My attitude is somewhat skeptical.
In order to say perturbative gravitons have failed,
You are in effect saying two major theories are failures:
First, the older Feynman-Weinberg-Boulware-Deser work,
And second, string theory.
That’s a pretty strong statement.
As a rival to the above two perturbative graviton type theories,
there are lots of speculative approaches, many grouped as Loop Quantum Gravity (LQG). You know a lot more about these than I do.
But my impression is that the only real success
Is the black hole evaporation calculations
Of the older Ashtekar Rovelli Smolin line.

Can you point to any other successful predictions or explanations?

I would like to repeat my question:
If you don’t have a graviton, what replaces it?

As far as I can tell, Loll and her coworkers are nowhere near answering that question for their approach, but I could be wrong.
If so, please correct me.

Off to work now.
Jim Graber

 

[Haelfix]

If we had a galaxy wide accelerator that could probe Planck scale energies (well about 2-3 orders of magnitude just below it). Everyone's first guess for computing observable quantities in the lab (cross sections, etc) would simply be to compute graviton loop diagrams and so forth as an effective field theory.

Far and away the most studied and to this day active area of research in this sort of context are supergravity models. People who work on those models (at whatever energy scale) probably outnumber string theorists 2-1. They are a major enterprise and source of citations in phenomenology. Anyway, regardless if that's right or not, its pretty much expected that you will measure something akin to graviton loop diagrams around there.

Now, having said that, its also almost guarenteed that its not the end of the story. Something else will happen right around the Planck scale (either string theory or some as yet to be discovered other theory of QG). As you up the energy scales further into the transplanckian regime, the whole notion of measuring cross sections ceases to make sense, and you just produce larger and larger black holes (described by classical general relativity). QG is really a window of about 4-5 orders of magnitude where something else has to replace effective field theory and then general relativity.

Also, local observables like cross sections and so forth are probably not the end of the story either (nor is it really clear in principle what you are exactly measuring in the first place). They need not for instance explain the full breadth of what we are interested in (like exactly what does the universe do right around the big bang). They go a long way of course, but still not quite clear even nonperturbatively (say if we could sum the path integral analytically)

 

[friend]

Marcus,

Slightly more of what Loll wrote:

“
The
failure of the perturbative approach to quantum gravity in terms of linear fluctuations around
a fixed background metric implies that the fundamental dynamical degrees of freedom of
quantum gravity at the Planck scale are definitely not gravitons. At this stage, we do
not yet know what they are. Neither do we have the luxury of hints from experiment or
observation of what they might be, …”

So if gravitons are particles associated with weak gravitational fields, then at what level of gravitational curvature do gravitons cease to be relevant? What do they turn into and at what level of gravitation? Are they supposed to decay at some level of gravity - into what? I would think that the impossibility of something slowly disappearing proves they don't exist to begin with, right?

 

[jimgraber]

Hi Friend,
you wrote:
"
So if gravitons are particles associated with weak gravitational fields, then at what level of gravitational curvature do gravitons cease to be relevant? What do they turn into and at what level of gravitation? Are they supposed to decay at some level of gravity - into what? I would think that the impossibility of something slowly disappearing proves they don't exist to begin with, right?"

Think more and more gravitons as the curvature gets stronger, not less and less.
Also think interactions with other kinds of particles (real and virtual) as well as gravitons.

The "failures" only happen down near the Planck scale if they happen at all.
The theoretical failures, which string theory claims to cure, come in the form of uncontrollable or "nonrenormalizable" infinities in the calculations as you go to higher orders.
So take the word "failure" with a big grain of salt. The vast majority of physicists still believe that the zero mass spin two graviton is our best current understanding of gravitation. (I include string theorists in this group. Their graviton is a massless spin two closed string.) Second place goes to good old fashioned unquantized general relativity. Even some of the most developed Loop Quantum Gravity approaches contain gravitons or near equivalents. Only a very small percent of physicists investigate theories with no graviton, or no equivalent. I could be wrong, but I do not know of any well worked out approach that makes significantly different predictions from the graviton theory. However, some people are making valiant attempts along these lines. Some day they may succeed. But I'm not holding my breath.
Best.
Jim Graber

 

[notknowing]

I posted a message already on a more recent tread about the graviton (see 12-06-2007: Could the quanta of gravity be something other than spin 2 particles) but it seems more appropriate to post it here.
I'm also convinced that gravitons do not exist and it is easy to prove by a simple thought experiment:

Describing gravitation by means of virtual particles quickly leads to a contradiction:
Let us suppose indeed that they exist. Even if they are supposed to be (rest)massless spin 2 particles, they should contribute to the total energy of the system, just like the virtual (massless) photons of the electromagnetic field somehow contribute to the mass of the system. The nonlinear character of the Einstein equations also seems to indicate that the "gravitational field" itself gravitates (I know this is strictly not correct, I use this only to guide the intuition). So, if the gravitons themselves are subject to the gravitational field, one should have virtual gravitions exchanging between these gravitons and other gravitons or other masses - AND - you can not stop this process: you just have to keep on adding gravitons to include all the reactions. So, you get an infinite number of gravitons per unit volume resulting in an infinite energy density and the whole of space would be just a massive "block" of gravitons. A ridiculous situation. This proofs that gravitons can not exist.

So, if gravitons do not exist, what then? Well, one can describe gravity as an induced force resulting from all other forces in nature. This was originally proposed by Sakharov. In this case, one does not need gravitons. I have also been publishing a paper about this in 1992 (see http://home.online.no/~avannieu/darkmatter/ first paper)

Rudi Van Nieuwenhove

 

[friend]

Think more and more gravitons as the curvature gets stronger, not less and less.
Also think interactions with other kinds of particles (real and virtual) as well as gravitons.

The "failures" only happen down near the Planck scale if they happen at all. ...

The vast majority of physicists still believe that the zero mass spin two graviton is our best current understanding of gravitation. (I include string theorists in this group. ...

Only a very small percent of physicists investigate theories with no graviton, or no equivalent. I could be wrong, but I do not know of any well worked out approach that makes significantly different predictions from the graviton theory. However, some people are making valiant attempts along these lines. Some day they may succeed. But I'm not holding my breath.

From a previous thread I wrote:

In "QFT in curved spacetime", Robert Wald states that in highly curved or fast changing gravitational field there is no particle interpretation of QFT; it's all just fields. So strictly speaking, in high curvature or fast changing gravitational fields, there are no particles at all - not even gravitons.

Describing gravitation by means of virtual particles quickly leads to a contradiction:
Let us suppose indeed that they exist. Even if they are supposed to be (rest)massless spin 2 particles, they should contribute to the total energy of the system, just like the virtual (massless) photons of the electromagnetic field somehow contribute to the mass of the system. The nonlinear character of the Einstein equations also seems to indicate that the "gravitational field" itself gravitates (I know this is strictly not correct, I use this only to guide the intuition). So, if the gravitons themselves are subject to the gravitational field, one should have virtual gravitions exchanging between these gravitons and other gravitons or other masses - AND - you can not stop this process: you just have to keep on adding gravitons to include all the reactions. So, you get an infinite number of gravitons per unit volume resulting in an infinite energy density and the whole of space would be just a massive "block" of gravitons. A ridiculous situation. This proofs that gravitons can not exist.

There are iterative processes that don't necessarily result in infinity. Self-gravitation may be one of those. In my opinion, it might even be possible that self-gravitation may result in the gravitational effects of dark matter, who knows?

 

[jimgraber]

Disclosure: The giant graviton industry is not paying me a huge bribe to write this post. (Drats!)

I think there are five main categories of alternatives seriously studied or used at the present time:

1. Do not quantize gravity. Keep it continuous.

2. The “old fashioned” spin 2 point particle graviton approach. You can modify this slightly by giving the graviton an extremely tiny rest mass.

3. The “new-fangled” string theory closed string graviton, which is also a spin 2 zero rest mass object.

4. Mixing a spin 2 zero rest mass graviton with a little bit of something else. (The classic thing is a tiny bit of one or more scalar i.e. spin 0 fields, but a little bit of a massive spin 2 graviton has also been looked at. String theory can also generate lots of scalar fields, often called moduli. The new TeVeS theory, related to MOND, also mixes in some vector, or spin 1, contribution.) Scalar-tensor gravity is a big industry, once in eclipse, but now revived by the string theory connection, and also by attempts to work on the dark energy and the dark matter.

5. Replacing gravitons with elementary moves OF or ON some lattice (Dynamic triangulation, spin foam, or what have you. If you want to get fancy, make your lattice out of ribbons rather than lines.) In this case the graviton is not fundamental, but something that acts like a zero rest mass spin two graviton can usually be constructed from these elementary lattice moves. (Otherwise, the theory is likely to predict wrong answers.)

To me, there is very little difference between a fundamental graviton and one that is composite or derived. Of course, if these lattices help build a unified theory, or do some other useful work, more power to them. But that’s different from saying the graviton does not exist, or there is no graviton.

Also, as far as I know, there is no fully worked out version of anything in class 5 that does not have a graviton equivalent. Please correct me if I’m wrong.

Now about quantum theory in curved spacetime. Despite what you might think from the name, it falls in class 1.

I quote the closing lines of Bob Wald’s recent review:

arXiv:gr-qc/0608018v1 3 Aug 2006
The History and Present Status of Quantum Field
Theory in Curved Spacetime
Robert M. Wald


“All of the above results have
been obtained without any appeal to a notion of “vacuum” or “particles”.
These and other results of the past decade have demonstrated that quantum field
theory in curved spacetime has a mathematical structure that is comparable in depth to
such theories as classical general relativity. In particular, it is highly nontrivial that quan-
tum field theory in curved spacetime appears to be mathematically consistent. Although
quantum field theory in curved spacetime cannot be a fundamental description of nature
since gravity itself is treated classically, it seems hard to believe that it is not capturing
some fundamental properties of nature.
The above results suffice to define interacting quantum field theory in curved spacetime
at a perturbative level. However, it remains very much an open issue as to how to provide
a non-perturbative formulation of interacting quantum field theory in curved spacetime.
It is my hope that significant progress will be made on this issue in the coming years.”

It is very true that particles are not appealed to in this theory, but gravity is not quantized.
This also means photons and electrons are not appealed to. There is a very old way of thinking and speaking which says in effect that “photons and electrons do not exist, they are just knots in the electromagnetic field”. You can obviously do the same with gravitons, if you wish. To me it is not clear that anything is gained by this way of thinking or talking, but YMMV.

As I wrote earlier, the way to cut to the chase is to ask yourself, “Do you believe Planck’s constant is relevant for the other forces, but not for gravity?” For me, the answer is “No” and that rules out all approaches in category 1.

Finally, I give below a reference for the work, initiated by Freeman Dyson, but completed by Rothman and Boughn, that shows how difficult it is to detect a single graviton, as opposed to a wave composed of “billions and billions” of gravitons.


arXiv:gr-qc/0601043 [ps, pdf, other]
Title: Can Gravitons Be Detected?
Authors: Tony Rothman, Stephen Boughn
Comments: This version as appeared in Foundations of Physics
Journal-ref: Found.Phys. 36 (2006) 1801-1825
Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph)

Best to all
Jim Graber