What is the rationale behind gravitons?

[Finbar]

Ok so as i see it the facts are that you can use QFT as an effective field and recover classical GR. This means you can use QFT to account for the bending of light. Here i refer to the papers of Donoghue et al already cited by humanino.

The question then remains. Can we interpret these results as graviton exchange? I think yes we can but we probably have to widen our ideas about what a "particle" really is. In particular we can't really stick with the idea that a graviton is a particle that "moves in space" because space and time are only defined in relation to the graviton. On the other hand its clear that the gravitational field once quantized can a)only transfer momentum in discrete packets and b) that information cannot travel faster than light. This must be true if you combine GR with QM. Given a) and b) its natural to want to interpret any given theory of QG based just on the principles of GR and QM as a "particle theory". But because of the nature of gravity the particle interpretation breaks down in the case of QG.

I think though that if we accept that quanta of the gravitational field are probably a reality but that these do not conform to our normal QM idea of a particle then it would perhaps be better to say that a graviton is a "quanta of the gravitational field" rather than a "particle".


Further more i would like to add that gauge fields e.g. photons also have geometrical interpretation. When we quantize them the geometrical interpretation doesn't go away but the interpretation of particles is then valid

 

[Eelco]

I don't get how one can diminish so easy the results and success of Yang-Mills theories as to put it as a horrible reason to follow its procedures...
as bending of light is an effect of atraction as any other gravitational effect, then you should make the same redundant questions you did for graviton also for photons and W and Z's in electoweak theory, and gluons for strong force, that is, how they make possible attraction and repulsion possible? then you'll get the virtual particles concept.

Do the other force carriers interact with oneanother? Not that I've ever heard of, but I could be wrong there. Is there such a thing as a gluon-photon interaction? If not, how does a graviton-photon interaction fit into the picture?

Remarking (again) that gravitational lensing would be as good as usual gravitational atraction of matter the way things are seen now with GR, so your question could be as well, how gravitons can describe gravitational atraction? Then you'll see that gravitational waves would lead to suspect that there can be an associated particle as in QM and there could be virtual gravitons.

I saw a mention to graviton propagator and deflection of light by mean of interchange of gravitons in Zill's "QFT in a Nutshell". (If you stop putting things in that arrogant mood then won't appear that you are attacking anyone.)

It seems i have to put more effort into deciphering your writing, than you put into writing it down. I am trying to be precise as to what I am asking, and if you can not give a precise and directed response, please do not respond at all.

I am aware of my 'arrogance'; I think being blunt is funny, but feel free to disagree. If you do not like my writing style, please do yourself the favor of not responding.

 

[Eelco]

Eelco: Your problem with gravitons (or whatever the answer is) arises in the original post:

You are unintentionally creating a straw man of gravitons here.

Any deeper answer to the question "what is gravity" than general relativity had better explain why spacetime is curved. Spacetime is not flat, and AFAIK, a graviton solution will not say that it is.

Are you implying that general relativity does not predict curved spacetime? I am confused.

Indeed, spacetime does not appear to be flat.

Curvature of spacetime directly leads to 'gravity' for all waves propagating through said space. If a graviton solution will not say that it is flat, ie, is just another way to formulate the evolution of metric, then would you say momentum is transferred by the absorption of the particle, or that it is a curvature effect?

Sure. I should have been more explicit. I will be so here. Saying that physicists should stop with a general relativistic explanation of gravity is aesthetically displeasing. For one thing, there are those nasty singular solutions. For another, it is in essence saying that there is no reason to continue with theoretical physics. We have the standard model and general relativity. Done! All you theoretical physicists can go back to school and learn a new trade.

Singular solutions can be dealt with in other ways, such as CDT.

Im not saying there are no open questions, but it seems a lot as if you are saying QG is a make-work project for physicists. I was hoping for a honest intellectual error, but maybe I am too much of an optimist :).

 

[atyy]

Ehm, no. When i talk of geometry, i talk of metric. Gravity can be explained purely in terms of a hyperbolic evolution of metric. No gravitons needed.

Exactly. No gravity waves needed.

 

[humanino]

I do not see anyone suggesting that gravitons interact with photons.

Photon do interact with gravitons. Not that gravitons carry electric charge, but photons carry energy-momentum, which is what the graviton couple to.

Please try to keep in perspective the difference between a real and a virtual graviton. It is unclear whether we can ever detect a single (real) graviton. Real graviton would be quantum of a gravitational wave, which essentially we can picture as propagating over a given metric. Virtual graviton on the other hand allow us to compute the amplitude for scattering in a gravitational potential order by order, that works fine in a non-relativistic limit, and we can compute the metric from that. Virtual "particles" are not constrained to stay inside a light-cone, a single virtual graviton exchange has a non-zero amplitude to violate all sorts of things including causality, but everything is restored when including the other terms, especially the interference between the first order and the lowest one (without any exchange) restores things together when neglecting higher order contributions.

Anyway, if you are confident you trust your QFT, I strongly suggest reading Feynman's lecture on gravitation. You may find there a wonderful discussion for how you can derive Einstein's GR from massless spin-2 exchange.

 

[Eelco]

Ok so as i see it the facts are that you can use QFT as an effective field and recover classical GR. This means you can use QFT to account for the bending of light. Here i refer to the papers of Donoghue et al already cited by humanino.

The question then remains. Can we interpret these results as graviton exchange? I think yes we can but we probably have to widen our ideas about what a "particle" really is. In particular we can't really stick with the idea that a graviton is a particle that "moves in space" because space and time are only defined in relation to the graviton. On the other hand its clear that the gravitational field once quantized can a)only transfer momentum in discrete packets and b) that information cannot travel faster than light. This must be true if you combine GR with QM. Given a) and b) its natural to want to interpret any given theory of QG based just on the principles of GR and QM as a "particle theory". But because of the nature of gravity the particle interpretation breaks down in the case of QG.

I think though that if we accept that quanta of the gravitational field are probably a reality but that these do not conform to our normal QM idea of a particle then it would perhaps be better to say that a graviton is a "quanta of the gravitational field" rather than a "particle".


Further more i would like to add that gauge fields e.g. photons also have geometrical interpretation. When we quantize them the geometrical interpretation doesn't go away but the interpretation of particles is then valid

Thank you, this seems like an honest and informed attempt at an answer to my question.

I know other fields also have a geometrical interpretation, but gravity is the only force which has an interpretation in terms of an evolution of metric, right?

A deformation of metric leads to gravity effects. Forces can similarly be transferred by particles. They may be but different interpretations of the same thing: I am cool with that, but one of these interpretations directly explains the appearent interaction with other force carriers (ie, light), whereas i completely miss the analogy of this effect in the other interpretation. Can i draw a feynman diagram where a photon absorbs a graviton, and thus alters its momentum/direction?

But essentially you are saying: a normal wave-particle interpretation is not applicable to gravitons. That would be a disappointment. How is that to be justified from a unification perspective? Has anyone ever simulated anything using gravitons, the way we have with photons or regge calculus? Do gravitons pass this basic sanity test?

 

[Eelco]

Exactly. No gravity waves needed.

Hyperbolic equations admit propagating wave solutions. That this actually happens, has fairly strong experimental backing. That is true regardless of any quantization tricks you wish to apply to it.

 

[humanino]

I know other fields also have a geometrical interpretation, but gravity is the only force which has an interpretation in terms of an evolution of metric, right?

Alain Connes has derived the standard model as a geometrical gravity theory (Einstein-like) over a non-commutative space.

 

[Eelco]

Photon do interact with gravitons. Not that gravitons carry electric charge, but photons carry energy-momentum, which is what the graviton couple to.

Thank you, that makes sense.

Are gravitons unique in this regard? Or are these similarly (weak) interactions between other force-carriers?

Please try to keep in perspective the difference between a real and a virtual graviton. It is unclear whether we can ever detect a single (real) graviton. Real graviton would be quantum of a gravitational wave, which essentially we can picture as propagating over a given metric. Virtual graviton on the other hand allow us to compute the amplitude for scattering in a gravitational potential order by order, that works fine in a non-relativistic limit, and we can compute the metric from that. Virtual "particles" are not constrained to stay inside a light-cone, a single virtual graviton exchange has a non-zero amplitude to violate all sorts of things including causality, but everything is restored when including the other terms, especially the interference between the first order and the lowest one (without any exchange) restores things together when neglecting higher order contributions.

I am not sure how this is relevant, but that could be me.

Anyway, if you are confident you trust your QFT, I strongly suggest reading Feynman's lecture on gravitation. You may find there a wonderful discussion for how you can derive Einstein's GR from massless spin-2 exchange.

Thanks, i will do that!

 

[Finbar]

I understand QFT to some degree, and i have no objections to it. I am just not sure why it should apply to gravity.

I noticed they calculate metrics. That had me confused, perhaps you can elaborate. All gravity can be explained in terms of curvature encoded in such a metric. If these gravitons in effect carry the metric, ie, if there presence deforms spacetime, then there is not any reason for them to be absorbed in the same way a photon is, to transfer its momentum, right? Because then youd be double-counting gravity. Are they absorbed without any effect, or not absorbed at all?

Your thinking is all confused here. If we're talking about QG(loops, strings, QFT) there isn't just "a metric" that describes gravity there is a quantum superposition of all metrics. But we can't even measure the metric directly we can only see its effects on matter. The matter we look at will be in some momentum state if we measure this state and then allow it to interact with a gravitational field then it will either change its state or remain in the same state. If it changes we can interpret this as it absorbing or emitting a graviton. remember these are virtual gravitons though so really we are just imagining that there is an exchange of a real graviton(this is the same in QED). Measuring a real graviton would amount to measuring the quanta of a gravitational wave(or in QED measuring light).

 

[Eelco]

Alain Connes has derived the standard model as a geometrical gravity theory (Einstein-like) over a non-commutative space.

I believe Garrett Lisi is doing the same thing, right?

It is over my head, unfortunately. Evolving a metric over a manifold or evolving a function over a given manifold with metric seem like conceptually very different things to me, and i am not sure how you can unify those things without loss of information, or why youd want to.

 

[Eelco]

Your thinking is all confused here. If we're talking about QG(loops, strings, QFT) there isn't just "a metric" that describes gravity there is a quantum superposition of all metrics. But we can't even measure the metric directly we can only see its effects on matter. The matter we look at will be in some momentum state if we measure this state and then allow it to interact with a gravitational field then it will either change its state or remain in the same state. If it changes we can interpret this as it absorbing or emitting a graviton. remember these are virtual gravitons though so really we are just imagining that there is an exchange of a real graviton(this is the same in QED). Measuring a real graviton would amount to measuring the quanta of a gravitational wave(or in QED measuring light).

I may be confused, but you are not telling me anything new here.

A (quantized) wave will 'change direction' as judged by some observer when it propagates over a curved metric, while locally, it is doing nothing but following a geodesic.

Now you might explain attraction in terms of discrete exchange between 'particles' too, but why then bother with the metric? We don't say an electron excerts a force by an electric field AND photon exchange, right? They are complimentary ways of looking at the same thing. If you seek to explain gravity in terms of momentum transfer by particle, then shouldn't you be able to do that without even mentioning a metric?

 

[atyy]

Ehm, no. When i talk of geometry, i talk of metric. Gravity can be explained purely in terms of a hyperbolic evolution of metric. No gravitons needed.

Hyperbolic equations admit propagating wave solutions. That this actually happens, has fairly strong experimental backing. That is true regardless of any quantization tricks you wish to apply to it.

Spacetime metric or spatial metric?

 

[Haelfix]

There's a lot of fog in this thread. You cannot invoke GR to falsify Graviton mechanics. Simply enough, there is no prediction of General relativity, that isn't also a prediction of graviton mechanics, at least for any conceivable experiment. That includes gravitational lensing!

Up to tiny corrections of order hbar, the field equations are identical, the kinematics and dynamics are identical, the geometry is identical..

To falsify quantum gravity, you would need to run precision experiments on black holes, or places where the energy density gets enormous. There, and only there, will you ever be able to see a difference between the classical theory and the quantum one.

 

[Eelco]

Spacetime metric or spatial metric?

When did the topic of this discussion change from 'please explain gravitons to eelco' to 'please explain GR to atyy'?

If you have any questions regarding how the curvature of spacetime can explain the effects we associate with gravity, there is nothing i could explain more clearly than mister Regge did.

 

[Eelco]

There's a lot of fog in this thread. You cannot invoke GR to falsify Graviton mechanics. Simply enough, there is no prediction of General relativity, that isn't also a prediction of graviton mechanics, at least for any conceivable experiment. That includes gravitational lensing!

Up to tiny corrections of order hbar, the field equations are identical, the kinematics and dynamics are identical, the geometry is identical..

To falsify quantum gravity, you would need to run precision experiments on black holes, or places where the energy density gets enormous. There, and only there, will you ever be able to see a difference between the classical theory and the quantum one.

Yeah, i realize this equivalence is claimed. I wondered how this claim can possibly be realized. So far, it seems to depend strongly on whom responds, and I am not 100% sure anyone has yet completely understood my question. Most people have not, but that's probably me.

Recapping: my original post clearly asked:

How is something like gravitational lensing explained in a flat spacetime with gravitons? Are there force-carrier-to-force-carrier interactions in such a model?

It took me three pages of tangential nonsense to get an answer to that, being a plain old yes. I didnt know that, and yes i see how that opens up a possiblity for gravitons approaching GR in the non-quantum limit.

Is the graviton as proposed unique in that regard, or is this possible between all force carriers? That would be news to me as well.

That said, I think gravitons create more problems than they solve. Do they solve any problems aside from black-hole singularities? And if they are your preferred solution to this problem, why?

 

[Finbar]

I understand QFT to some degree, and i have no objections to it. I am just not sure why it should apply to gravity.

I noticed they calculate metrics. That had me confused, perhaps you can elaborate. All gravity can be explained in terms of curvature encoded in such a metric. If these gravitons in effect carry the metric, ie, if there presence deforms spacetime, then there is not any reason for them to be absorbed in the same way a photon is, to transfer its momentum, right? Because then youd be double-counting gravity. Are they absorbed without any effect, or not absorbed at all?

I may be confused, but you are not telling me anything new here.

A (quantized) wave will 'change direction' as judged by some observer when it propagates over a curved metric, while locally, it is doing nothing but following a geodesic.

Now you might explain attraction in terms of discrete exchange between 'particles' too, but why then bother with the metric? We don't say an electron excerts a force by an electric field AND photon exchange, right? They are complimentary ways of looking at the same thing. If you seek to explain gravity in terms of momentum transfer by particle, then shouldn't you be able to do that without even mentioning a metric?

No its the same in QED and in gravity. I have the electromagnetic field and I sum over the superposition states of it. When the EM field interacts with a charged particle it exchanges quanta of momentum. These we interpret as photon exchange. There is an EM field(metric) at a point in space regardless of there being a charged particle(matter/energy) present at that point. One does not describe QED in terms of particles without mentioning EM field.

I think you should really ask yourself if you understand QED in terms of fields and particles.

 

[Haelfix]

Is the graviton unique as a force carrier for gravity, at least at low energies? Emphatically yes! Proving this, unfortunately would require a bit of a lecture b/c you could imagine several ways around it (say more than one massless spin 2 particle, or say a composite particle). Why that isn't allowed is technical. You could imagine some allowed modifications, but then they would also modify GR as well.

For your question regarding gravitational lensing, see Weinberg's GR book for a treatment (he rederives all of GR with tensor fields -aka spin 2 perturbations).

Is it useful? Well that depends what you mean by useful. In the classical regime, it is essentially the difference between using gravitational waves vs the geometric formulation. And in fact, the former can more easily solve some questions than the latter, and viceversa. For instance the behaviour of binary pulsars, or colliding black holes is far easier to deal with in the linearized formulation. So yes, its useful!

For the quantum behaviour, keep in mind modern developments like inflation crucially rely on this technology.

 

[Eelco]

No its the same in QED and in gravity. I have the electromagnetic field and I sum over the superposition states of it. When the EM field interacts with a charged particle it exchanges quanta of momentum. These we interpret as photon exchange. There is an EM field(metric) at a point in space regardless of there being a charged particle(matter/energy) present at that point. One does not describe QED in terms of particles without mentioning EM field.

I think you should really ask yourself if you understand QED in terms of fields and particles.

My understanding of QED in terms of fields is most certainly limited.

By 'metric' i mean some mathematical object specifying a notion of distance.

How you could describe an EM field purely with a metric, by a deformation of spacetime, is completely beyond me. My naive understanding is that any field quantity lives on a manifold, having some (dynamic) metric. Any photonic or matter fields will influence the underlying metric by the presence of their energy, but the metric and the various fields are otherwise independent quantities, in my understanding.

When you say 'metric', do you mean that in some more abstract mathematical way (ie, the metric of some functional), or in a physical way: that which influences measurements of distance?

Either this is a confusion over terminology, or i really do not get QFT at all.

 

[Eelco]

Is the graviton unique as a force carrier for gravity, at least at low energies? Emphatically yes! Proving this, unfortunately would require a bit of a lecture b/c you could imagine several ways around it (say more than one massless spin 2 particle, or say a composite particle). Why that isn't allowed is technical.

For your question regarding gravitational lensing, see Weinberg's GR book for a treatment (he rederives all of GR with tensor fields -aka spin 2 perturbations).

Rederives with tensor fields? You lost me again: as far as i know, GR was originally formulated as a metric tensor field.

Is it useful? Well that depends what you mean by useful. In the classical regime, it is essentially the difference between using gravitational waves vs the geometric formulation. And in fact, the former can more easily solve some questions than the latter, and viceversa. For instance the behaviour of binary pulsars, or colliding black holes is far easier to deal with in the linearized formulation. So yes, its useful!

Again, we have a problem of terminology. The geometric formulation is to me the formulation of Einstein and Regge. Gravitational waves are implied by it, they are a geometric phenomena under any interpretation of these terms i can think of. What exactly are you talking about?

I can calculate colliding black holes using regge calculus just fine, no linearizations needed. I wasnt inquiring into practical matters: I know what real analysis has going for it in that regard, in the 21th century: nothing. My question concerns theoretical insight. What theoretical problems do gravitons solve?

For the quantum behaviour, keep in mind modern developments like inflation crucially rely on this technology.

Inflation theories are far too speculative to count as a justification of anything, in my opinion. Who knows what inflation theory will be fashionable next year?

 

[Haelfix]

Incidentally, you might wonder? Couldn't gravity as a force, remain classical to all orders? Why do we need to quantize it in the first place?

The problem is we know the other 3 forces are in fact quantum, and lo and behold they show up in the stress energy tensor. So perhaps we could just treat Einsteins equation classically and replace this object with say, its expectation value <Tuv> (which now must live in a hilbert state of spaces and so forth).

But you immediately run into an obstruction. Solving for the metric and then using that to find an operator for the time evolution of states yields a catastrophe. The time evolution operator in question is nonlinear!

We don't know how to make sense of quantum mechanics with nonlinear modifications, all such theories that have ever been constructed have been failures. Evidently, we have to go about finding a sensible theory in a different way (insert your list of favorite quantum gravity proposals)

 

[Haelfix]

"Rederives with tensor fields? You lost me again: as far as i know, GR was originally formulated as a metric tensor field."

I'll say it in another terminology: Weinberg rederives all of GR in the weak field approximation or with mostly algebraic methods. He constructs the theory by symmetry arguments and the principle of equivalance, rather than positing geometric structure. The two formulations are mathematically isomorphic.

http://en.wikipedia.org/wiki/Linearized_gravity

"I can calculate colliding black holes using regge calculus just fine, no linearizations needed. "

You can, but you don't have too. It depends what you find easier to calculate with.

 

[Eelco]

But you immediately run into an obstruction. Solving for the metric and then using that to find an operator for the time evolution of states yields a catastrophe. The time evolution operator in question is nonlinear!

In my humble opinion, that is an artifact of real analysis.

Evolving a Schrodinger equation over a metric/geometry produced by regge calculus, or some form of discrete differential geometry, works just fine, no complications at all. It is nonlinear as viewed through the wrong lens, but any equation can be made nonlinear by squaring it.

I really do have the feeling that most of the developments in modern physics are driven more by limitations of, and confusion over real analysis, than by any physical considerations.

 

[Finbar]

My understanding of QED in terms of fields is most certainly limited.

By 'metric' i mean some mathematical object specifying a notion of distance.

How you could describe an EM field purely with a metric, by a deformation of spacetime, is completely beyond me. My naive understanding is that any field quantity lives on a manifold, having some (dynamic) metric. Any photonic or matter fields will influence the underlying metric by the presence of their energy, but the metric and the various fields are otherwise independent quantities, in my understanding.

When you say 'metric', do you mean that in some more abstract mathematical way (ie, the metric of some functional), or in a physical way: that which influences measurements of distance?

Either this is a confusion over terminology, or i really do not get QFT at all.

Sorry i confused you. I was saying that the metric was analgous to the EM field. Not that you could describe EM in terms of a metric. Actually to be acurate the metric tensor g_ab(x) is analgous to the potential A_a(x). Where a and b spacetime indices and take values 0,1,2 and 3 and by x i mean a point in spacetime. So these are both essentially fields. But when i do QTF i have to consider superpostion states such that there isn't just one metric or one potential. if i have some matter in the gravity case or a charge in the QED case then they may gain or lose momentum due to an interaction with the quantum superposition state of the metric or potential. Because momentum is conserved this must be an exchange of momentum.

 

[Eelco]

Sorry i confused you. I was saying that the metric was analgous to the EM field. Not that you could describe EM in terms of a metric. Actually to be acurate the metric tensor g_ab(x) is analgous to the potential A_a(x). Where a and b spacetime indices and take values 0,1,2 and 3 and by x i mean a point in spacetime. So these are both essentially fields. But when i do QTF i have to consider superpostion states such that there isn't just one metric or one potential. if i have some matter in the gravity case or a charge in the QED case then they may gain or lose momentum due to an interaction with the quantum superposition state of the metric or potential. Because momentum is conserved this must be an exchange of momentum.

That sounds suspect to me.

How can you say the metric is analogous to other fields? Other fields are crucially dependent on the metric for their evolution. It defines the space in which the other quantities live.

To regard the metric as 'just another tensor field' seems conceptually borked to me. Even if such a unification pans out mathematically, have you physically done anything but confuse yourself?

 

[atyy]

That sounds suspect to me.

How can you say the metric is analogous to other fields? Other fields are crucially dependent on the metric for their evolution. It defines the space in which the other quantities live.

To regard the metric as 'just another tensor field' seems conceptually borked to me. Even if such a unification pans out mathematically, have you physically done anything but confuse yourself?

As a matter of fact, the metric needs the other fields to exist physically. The pure vacuum solutions of GR are undetectable - one always needs a test particle or test photon to see it. Test particles are contrary to the diffeomorphism invariance of GR.

 

[Finbar]

That sounds suspect to me.

How can you say the metric is analogous to other fields? Other fields are crucially dependent on the metric for their evolution. It defines the space in which the other quantities live.

To regard the metric as 'just another tensor field' seems conceptually borked to me. Even if such a unification pans out mathematically, have you physically done anything but confuse yourself?

Other fields are dependent on the metric but the metric is also dependent on the other fields so it works both ways. This is true of classical field theory ie general relativity aswell. There's no confusion here. The metric tensor is a field because it is a function of spacetime g_ab(x) and it depends on the other fields via the einstein field equations.

 

[Eelco]

As a matter of fact, the metric needs the other fields to exist physically. The pure vacuum solutions of GR are undetectable - one always needs a test particle or test photon to see it. Test particles are contrary to the diffeomorphism invariance of GR.

Yes, i realize the former. The latter statement makes no sense to me.

 

[atyy]

Yes, i realize the former. The latter statement makes no sense to me.

A test particle propagates on a fixed background.

 

[Eelco]

Other fields are dependent on the metric but the metric is also dependent on the other fields so it works both ways.

Yes, i realize that, but these dependencies seem conceptually very different to me. Since when are a source term and a metric interchangable concepts?

This is true of classical field theory ie general relativity aswell. There's no confusion here. The metric tensor is a field because it is a function of spacetime g_ab(x) and it depends on the other fields via the einstein field equations.

Yeah, but they are mathematically and physically different dependencies. Space is space and matter is matter.

If gravitons seek to dissolve the distinction between space and matter, that's an ambitious goal, and I am surprised i havnt seen it stated like that: ill believe it works when somone does a simulation involving gravitons, that doesn't depend on arguments such as 'yeah it reduces to the einstein field equations because of this general abstract nonsense, so actually, we are solving that instead. The linearized variant, yeah.'