What is the rationale behind gravitons?

[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.'

 

[Eelco]

A test particle propagates on a fixed background.

I understand such is customary in real analysis, yeah. That is a limitation of the mathematical tools you are using. Why does everyone insist on confusing that with something physical?

 

[Finbar]

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


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.'

No your still confused. The metric tensor isn't spacetime. Its a function of spacetime. The metric has a value at each point in spacetime. The same goes for the EM potential. These are fields. What exists as absoloute concepts are the fields. We can make a general coordinate transform and change the spacetime coordinates so spacetime isn't an absolte concept.

Look both the EM field(U1 gauge field) and the gravitational field have geometic interpretations. In fact gravity is a gauge theory aswell. Yes gravity is a theory of the metric and therefore defines lengths and yes this leads to many conceptual and mathematical problems. But despite this you have to agree that the gravitational field created by a body A will transfer momentum to a body B. Momentum is consvered and according to general pricplies of QM comes in discrete packets. Therefore we can interprete the exchange of this momentum as a "particle". Buts its just an interpretation. Nobody starts off with the idea of a gravition and produces a quantum theory of gravity. It's just a useful concept when dealing with QM where quantities such as momentum do not take continuous values and when also using relativity when means that momentum must travel between two points in spacetime ie there is some notion of propagation.

 

[Eelco]

No your still confused. The metric tensor isn't spacetime. Its a function of spacetime. The metric has a value at each point in spacetime. The same goes for the EM potential. These are fields. What exists as absoloute concepts are the fields. We can make a general coordinate transform and change the spacetime coordinates so spacetime isn't an absolte concept.

You are arguing over real analysis, not over physics. In Regge calculus, id definitely say the metric is spacetime.

Look both the EM field(U1 gauge field) and the gravitational field have geometic interpretations. In fact gravity is a gauge theory aswell. Yes gravity is a theory of the metric and therefore defines lengths and yes this leads to many conceptual and mathematical problems. But despite this you have to agree that the gravitational field created by a body A will transfer momentum to a body B. Momentum is consvered and according to general pricplies of QM comes in discrete packets. Therefore we can interprete the exchange of this momentum as a "particle". Buts its just an interpretation. Nobody starts off with the idea of a gravition and produces a quantum theory of gravity. It's just a useful concept when dealing with QM where quantities such as momentum do not take continuous values and when also using relativity when means that momentum must travel between two points in spacetime ie there is some notion of propagation.

I agree, a non-gravitonic spacetime seems hard to reconcile with discrete energy quanta.

That said: why should i care about conservation laws in anything but a time averaged sense, when wavefunction collapse does not either?

 

[Finbar]

You are arguing over real analysis, not over physics. In Regge calculus, id definitely say the metric is spacetime.


I agree, a non-gravitonic spacetime seems hard to reconcile with discrete energy quanta.

That said: why should i care about conservation laws in anything but a time averaged sense, when wavefunction collapse does not either?

What is real analysis? the metric tensor g_ab defines a length ds^2 = dx^a dx^b g_ab(x). So it defined a infintessimal length ds in spacetime. Saying "the metric is spacetime" is totally meaningless.

Energy conservation is always obeyed in physics. Its just a common misconception that QM or the uncertainty principle does't conform to it.

 

[atyy]

Isn't Regge calc the motivation behind CDT?

CDT may be a computational version of either Asymptotic safety or Horava-Lifschitz - both of which have gravitons.

 

[Haelfix]

Regge calculus is about the earliest form of spacetime discretization that I am aware off that was also solutions of the field equations of GR. So yes, it is a precursor to dynamic triangulations, random triangulations, and so forth. Its heavily used in numerical approximations for hard problems in GR (the aforementioned black hole collisions for instance).

Later people tried to get it to work as a quantum gravity or quantum cosmology programs (not to be confused with the original intent). Like most such work, before CDT arrived, the problem was that all the various primordial simplexes would have a tendency to crumble up in numerical simulations and the classical flat limit was never achieved.

 

[Eelco]

What is real analysis? the metric tensor g_ab defines a length ds^2 = dx^a dx^b g_ab(x). So it defined a infintessimal length ds in spacetime. Saying "the metric is spacetime" is totally meaningless.

Real analysis is most of mathematics, including the calculus of real variables you are talking about here.

Even if you implicitly assume a flat spacetime, you are assuming a metric. When you propose a function of three variables, you are implicltly assuming a metric. There is no spacetime without a metric.

Energy conservation is always obeyed in physics. Its just a common misconception that QM or the uncertainty principle does't conform to it.

Dunno, there are published papers on the subject.

My understanding: The expectation value of energy is conserved. Then your wavefunction collapses, at some arbitrary point, without further particle exchange. Does that state it collapses to not affects its energy?

 

[Eelco]

Regge calc does not have gravitons.

The QG variants thereof might; depending on your interpretation. I don't mind thinking of space in terms of superpositions, and if youd want to call that gravitons, fine. My problem is with propagating the defining property of spacetime, over spacetime. How do you cut that knot? What do you start with? A flat spacetime is no less arbitrary than any other, and the only reason you are picking it, is because otherwise the real analysis gets too complicated.

 

[tom.stoer]

How do you formulate energy conservation in gravity theories?
- there is a locally conserverd energy momentum tensor in GR - fine
- if you enlarge your theoretical framework and introduce torsion, this conservation law vanishes
- I do not see how you can define a globally conserved energy (as a volume integral transforming as the zeroth component of a four vector)
- I do not see how you can define energy in QG theories (LQG, CDT, ...)

So we should restrict ourselves to talk about local symmetries; energy conservation may be a concept that works only in certain scenarios with appropriate symmetries, asymptotic conditions etc.

(is there an expert in this forum who can talk about quasi-local mass and things like that?)

 

[fleem]

Can someone explain the rationale behind gravitons to me?

My background is computational physics, and as such i may be biased towards physics that is actually computable, such as LQG and regge calc. I have some clue what this is all about, but i have some questions:Is there any reason (beyond aestetics which i disagree with anyway) to favor a particle over a geometric explanation? Any sort of empirical matter gravitons may help explain?

We know that energy stored in a gravitational system can be converted to energy stored in other kinds of systems. all those other kinds of systems require that energy be quantized. If energy in a gravitational system were not quantized, then how could it smoothly flow into another type of system which accepted energy in packets? So this is why gravitational energy must be quantized.

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? I have a hard time imagining how youd explain bending of light with gravitons. It seems likea pressing question to me, but no one else seems to care, as far as i can tell.

SR and GR, space-time, continuums, manifolds, dimensions, and Newtonian mechanics are descriptions of the large-scale behavior of many individual machines (particle interactions). You are right, there is no reasonable merging with the behavior of individual particle interactions for any of those large-scale theories. Scientists continue to erroneously presume theories developed solely to describe the average behavior of many simple machines will also be the founding theories in describing the behavior of each of those machines. There is no reason to believe that.