Gravitrons and General Relaivity

[josephwouk]

General Relativity shows that gravity is the curvature of space-time reacting to mass, energy and pressure rather than an attractive force. This separates it from the other 3 forces which are attractive/repulsive interactions between matter.

Why then, is it presumed that gravity should be quantized? Why should interaction between mass and space-time have to follow the same pattern as interactions between mass and mass?

 

[tom.stoer]

Good question. We discuss this quite frequently in the "beyond the SM forum".

It is clear that our world is currently described by "general relativity + standard model". We know that GR has its intrinsic problems like singularities where the theory breakes down; we know that the SM has intrinsic problems, too, namely diverent terms especially due to to the short-distance behaviour which is not fully understood. We know that when combining both a semiclassical approximation wher the SM is quantized but GR stays classical becomes inconsistent (and is not able to solve the problems mentioned before). And last but not least we we know that the combination of both theories is even worse as we suspect that the quantization methods we know from the SM break down when naively applied to GR.

So most people think that a) GR has to be quantized as well, but b) that the required methodes differ from the methods well-known from the SM.

Many people think that the trivial way to quantize gravity using gravitons as small fluctuations on top of a smooth manifold is the wrong turn - and indeed this naive method has failed for decades. There are indications that it can be made consistent in one theory of supergravity and string theory, but in even in tstring theory there are indications that the quantization of small fluctuations on top of a smooth and somehow fixed spacetime w/o backreaction from quantization to its structure is wrong.

Looking at standard QFT there is one step that shows where most of the problems come from: looking at a commutation relation between field operators one assumes that one knows the spatial or timelike distance between these two operators and that one can calcuate the commutator. But in quantum gravity one cannot be sure that one knows this distance as it is not an input using classical spacetime, but that it has to be a dynamical output of the theory.

Therefore most people think that the quantization methods have to be changed (and e.g. string theory and loop quantum gravity do exactly this) in order to arrive at a viable theory. In this theory the notion of gravitons need not be fundamental; they may emerge as a special approximation in a certain regime, but will no longer play a fundamental role.

If you look at the lengthy discussion regarding virtual particles here in this forum you may find out that even in standard QFT there is a kind of confusion between "quantization" and "approximation" like perturbation theory. Virtual particles, perturbation theory, ... became so familiar and successful (and prominent in popular examples) that sometimes it's hard to distiguish between quantization as the fundamental program and these approximations. One must not confuse them.

So my summary is that quantization of gravity is required in order to harmonize gravity with the SM (or QFT in general) and to cure internal inconsistencies, but that this quantization will look different from what we are used to in ordinary QFT.

There are some intersting approaches like string theory, loop quantum gravity, but there are even more radical approaches like causal sets. It's hard to give you a hint where you should start reading. Perhaps the quantum gravity article at wikipedia is an interesting starting point.

 

[josephwouk]

Thank you for your response.

I still don't understand how a force particle can have the effect of curving space-time. Just what is it that the gravitron is supposedly interacting with?

 

[physeven]

you have to understand the hypothesized particle first: the graviton must have a spin of 2 and be massless.

to answer your question: Just what is it that the gravitron is supposedly interacting with?

the graviton, as aforementioned, is a massless particle with a spin of 2. therefore it cannot be distinguished if it does interact at all, because since the source of gravitation is a stress tensor, it would interact in the same way with the stress tensor as a gravitational field does.

i hope that answers your question.

 

[josephwouk]

It probably would, but for my ignorance.

I don't understand why having a spin of 2 and no mass would make a gravitron behave the same as a gravitational field.

I also fail to see how anything would happen at all if there were "no interaction."

Space-time is the manifold and mass/energy are the tensors. What purpose other than matching the other SM forces does the gravitron serve? Can't we live without it?

 

[tom.stoer]

I still don't understand how a force particle can have the effect of curving space-time.

This is exactly the problem with "gravitons as exciations on top of spacetime". Fixing a spacetime and putting gravitons on top is WRONG, b/c these gravitons cannot curve this fixed spacetime. You identified the main problem of the whole approach.

 

[Alanine]

But my friend then tom.stoer had already stated in post #2 that in beyond SM the notio of SM being semi-classical(and quantized) and GR being classical(involving continuous varibles/inputs) is untenable thus graviton .But I agree that this concept of graviton is obscure even that that of virtual particles

 

[tom.stoer]

But ... tom.stoer had already stated in post #2 that ... SM ... being quantized and GR being classical ... is untenable thus graviton .But I agree that this concept of graviton is obscure ...

This was a misunderstanding. I said that gravity must be quantized, but that does not mean that this quantization is based on something we would call a graviton. In string theory and in LQG one can derive something like a graviton, but it is never used as a fundamental building block of the theory. So let's try something like

... SM ... being quantized and GR being classical ... is untenable thus quantum gravity.

 

[josephwouk]

Thanks for your replies.

Given the whole problem with even the concept of a graviton, why is it given the credence that it is?

I mean, after "photon", graviton is the most well known force particle. Much more than say, gluon.

It seems to me that it is misleading at best to presume the existence of the graviton under these circumstances, yet every discussion of the standard model always includes them.

 

[josephwouk]

I said that gravity must be quantized

I don't understand why it has to be quantized. Is there no other way space-time could curve in reaction to mass/energy?

This sounds weird, but I put it forward as a simple possible other approach...

Since according to relativity everything is moving through space-time at the speed of light, could the curvature be the result of being dragged after the passing matter? Like a leaf being dragged after a passing truck...

This is a classical approach. We don't know enough yet about the properties of space-time to dismiss it out of hand, do we?

 

[tom.stoer]

... after "photon", graviton is the most well known force particle. Much more than say, gluon.

... yet every discussion of the standard model always includes them.

Certainly not! Gluons, W- and Z-bosons are prominent "force-carrying particles" which have been (indirectly) detected decades ago, including their properties like spin, mass, etc. and which serve as useful and well-understood concepts in QFT.

Given the whole problem with even the concept of a graviton, why is it given the credence that it is?

The graviton is a concept that is useful in certain special situations, e.g. when small perturbations of a smooth manifold are indeed reasonable. In these limiting cases one can do reasonable calculations based on "quantum gravity constructed from gravitons" and therefore one expects that even in approaches like string theory (there it becomes rather explicit) and LQG (here it is much more difficult) there are quasi-classical and/or perturbative regimes where something like gravitons will emerge and will describe physics rather well.

So the whole confusion starts when one blindly identifies "quantum gravity" with a "quantum field theory constructed from gravitons".

I think that all experts in these fields understand perfectly well that this identification is misleading, but that they are not able to avoid this confuson when talking to non-experts, selling popular books and trying to fund their research projects. Therefore it's more a confusion when talking about quantum gravity than a confusion within quantum gravity itself.

 

[A. Neumaier]

I don't understand why having a spin of 2 and no mass would make a graviton behave the same as a gravitational field.

Do you understand why having a spin of 1 and no mass makes a photon behave the same as an electromagnetic field?

- If you do, you can probably write down a first approximation to what it could mean in case of the graviton. This would others give a better perspective for what they should contribute to help you.

- If not, you'd first make yourself well-acquainted with the simpler (and well-understood) situation rather than trying your wits on things that are much more difficult.

First steps first.

 

[A. Neumaier]

Many people think that the trivial way to quantize gravity using gravitons as small fluctuations on top of a smooth manifold is the wrong turn - and indeed this naive method has failed for decades.

Many others don't share this view. The paper
D.F. Litim
Fixed Points of Quantum Gravity and the Renormalisation Group
http://arxiv.org/pdf/0810.3675
says on p.2: ''. It remains an interesting and open challenge to prove, or falsify, that a consistent quantum theory of gravity cannot be accommodated for within the otherwise very successful framework of local quantum field theories.'' The paper
J. Gomis and S. Weinberg,
Are Nonrenormalizable Gauge Theories Renormalizable?
http://arxiv.org/pdf/hep-th/9510087.
removed the old complaints about the defects of canonical gravity, and indeed, one can treat covariant quantum gravity just one treats nonrenormalizable effective field theories, and fares well with it.See, for example,
C.P. Burgess,
Quantum Gravity in Everyday Life:
General Relativity as an Effective Field Theory
Living Reviews in Relativity 7 (2004), 5
http://www.livingreviews.org/lrr-2004-5
for 1-loop corrections, and
Donoghue, J.F., and Torma, T.,
Power counting of loop diagrams in general relativity,
Phys. Rev. D, 54, 4963-4972,
http://arxiv.org/abs/hep-th/9602121
for higher-loop behavior.

Section 4.1 of the paper by Burgess discussed recent computational
studies showing that covariant quantum gravity regarded as an effective
field theory predicts quantitative leading quantum corrections to the
Schwarzschild, Kerr-Newman, and Reisner-Nordstroem metrics.
Only a few new parameters arise at each loop order, in particular only
one (the coefficient of curvature^2) at one loop.
In particular, at one loop, Newton's constant of gravitation becomes
a running coupling constant with
G(r) = G - 167/30pi G^2/r^2 + ...
in terms of a renormalization length scale r.

Here is a quote from Section 4.1:
''Numerically, the quantum corrections are so miniscule as to be
unobservable within the solar system for the forseeable future.
Clearly the quantum-gravitational correction is numerically extremely
small when evaluated for garden-variety gravitational fields in the
solar system, and would remain so right down to the event horizon even
if the sun were a black hole. At face value it is only for separations
comparable to the Planck length that quantum gravity effects become
important. To the extent that these estimates carry over to quantum
effects right down to the event horizon on curved black hole
geometries (more about this below) this makes quantum corrections
irrelevant for physics outside of the event horizon, unless the
black hole mass is as small as the Planck mass''

My bet is that the canonical approach will win the race!

 

[haushofer]

It probably would, but for my ignorance.

I don't understand why having a spin of 2 and no mass would make a gravitron behave the same as a gravitational field.

Take a look at Tong's String Theory notes, somewhere in the beginning.

Quantizing a massless spin-1 field gives you, naively, "ghosts": states with negative norm. However, gauge invariance comes to the rescue: you need gauge invariance to remove these ghost states.

If you quantize the (linearized!) massless spin-2 particle, you'll see that you need diffeomorphisms in order to remove the ghost states. Quantizing a massless spin-2 particle means obtaining gravitons.

 

[tom.stoer]

But gravitons with spin 2 alone do not solve the problem of fully dynamical spacetime. Perhaps the direction indicated by A. Neumaier is interesting.

 

[A. Neumaier]

I don't understand why having a spin of 2 and no mass would make a gravitron behave the same as a gravitational field.

If you quantize the (linearized!) massless spin-2 particle, you'll see that you need diffeomorphisms in order to remove the ghost states. Quantizing a massless spin-2 particle means obtaining gravitons.

A simpler argument: Gravitation is described by a metric (symmetric 2-tensor field) modulo general covariance, which gives locally, in the tangent Minkowski space of any point, a spin 2 representation of the Poincare group modulo longitudinal directions, which forces mass 0 and helicity 2.

Gravitational waves also have to be (classically) long range, which again requires (after quantization) massless particles. Thus gravitons (although never observed) should be massless spin 2 particles.

 

[A. Neumaier]

But gravitons with spin 2 alone do not solve the problem of fully dynamical spacetime. Perhaps the direction indicated by A. Neumaier is interesting.

Weinberg proves in Phys.Rev. 138 (1965), B988-B1002 that canonical minimal self-coupling of a massles spin 2 field leads classically to Einstein's equations for general relativity.

Quantization leads to a corresponding nonrenormalizable quantum theory. But it is perturbatively renormalizable if you allow (as in effective field theories) for an infinite number of counter terms suppressed by increasingly high powers of the Planck mass.

Today this no longer looks as strange as in the old days where the myth of non-quantizability of gravitation was coined.

Indeed, the predictive power is as large as that of a power series whose coefficients are suppressed by a high power of the Planck mass, where you only know the first few coefficients.

 

[tom.stoer]

I agree that the AS program looks promising, but afaik there is no notion of gravitons; AS is an entirely non-perturbative approach; it's more related to coarse graining than to approaches using Greens function and "particles".

 

[wher456]

Excuse me:
Of what order of perturbation you are talking about?

 

[tom.stoer]

I am talking about no perturbation at all.

QFT is often formulated an "solved" in terms of a perturbation series in the coupling constant. This seems to be inappropriate for GR.

 

[A. Neumaier]

I agree that the AS program looks promising, but afaik there is no notion of gravitons; AS is an entirely non-perturbative approach; it's more related to coarse graining than to approaches using Greens function and "particles".

Asymptotic safety (AS) starts with a bare action containing bare gravitons, and then renormalizes it towards a fixed point of the RG equations.

This most likely preserves the massless spin 2 nature of the graviton, since there must be analogues of the Ward identities that ensure Lorentz gauge invariance, in the same way as Ward identities for QED ensure U(1) gauge invariance and preserve the massless nature of the photon in the renormalization process.

 

[tom.stoer]

Now you are talking about a spin-2 graviton field which need not have a spin-2 particle interpretation, correct? I mean in order to do that one would have to construct a Hilbert space or define asymptotic states for scattering. A Hilbert space is not introduced in AS and asymptotic states / scattering are not discussed.

Is it clear that a graviton-particle interpretation is valid in all regimes of AS? Or is this restricted to the perturbative regime only? How does it compare to QCD and gluons (where in the IR a gluon as a particle seems to be the wrong concept)?

 

[A. Neumaier]

Now you are talking about a spin-2 graviton field which need not have a spin-2 particle interpretation, correct? I mean in order to do that one would have to construct a Hilbert space or define asymptotic states for scattering. A Hilbert space is not introduced in AS and asymptotic states / scattering are not discussed.

Is it clear that a graviton-particle interpretation is valid in all regimes of AS? Or is this restricted to the perturbative regime only? How does it compare to QCD and gluons (where in the IR a gluon as a particle seems to be the wrong concept)?

I don't understand how a quantum field cannot have a particle interpretation, in the commonly used sense of the word in which quarks are particles. In QFT, fields and particles are kind of synonymous...

It may not have an interpretation as an asymptotic particle (e.g., quarks and gluons don't), but that gravitons are confined would contradict the observed long-range nature of gravitation. Thus they should exist as asymptotic particles.

In any case, perturbation theory for renormalized gravity behave even better than perturbation theory for renormalized QED, unless you study effects directly at the Planck scale. I have no idea what to expect on this scale.