# On gravitons

1. Dec 4, 2004

### orange

Hello everyone!

How does the effects of gravitons work in different media? I know it expands with the speed of light, but since light has different speeds in different media, does gravitons aswell?

2. Dec 5, 2004

### mathman

This is pure speculation. The fact that photons slow down in media is a result of photons interacting with the material. I suspect that gravitons would pass through untouched. However, gravitons have never been detected, so there is no experimental information available.

3. Dec 5, 2004

### silverpig

That's a great question and one I'm gonna ask my GR prof when I see her this week :)

Photons slow down in a medium because of how they interact with the electrons (mostly) in the atoms. The photon group velocity is still c through the medium, but the phase velocity slows down (IIRC) because of effects I don't have the will to type right now. So basically it's the photon's interaction with particles of electric charge that slow down the apparent velocity of light in a medium.

The analog to this in gravity would be the slowing down of gravitational waves through a medium with particles of mass charge. I mean, it should be consistent right? I guess a rigorous explanation would require a quantum theory of gravity.

4. Dec 6, 2004

### Garth

i.e. matter?

Good point, although I cannot imagine gravitational effects being transported at speeds other than c.

On the other hand GR has only been tested in vacuo and so what actually happens in the middle of a lump of matter is anybody's 'guess'.

If you come to QG from the GR side you think of gravity as geometry and a property of space-time, but from the QM side you think of it as the effect of a 'force-particle', the graviton, and therefore it would be open to such interaction as above.

It will be interesting to see who wins.

Garth

5. Dec 6, 2004

### Stingray

I wish people would remember that almost all properties of light are adequately described by classical waves (meaning Maxwell's theory). You can explain the speed of light through a material without ever referencing photons. Similarly, GR does predict a similar effect for gravitational waves travelling through matter. It is incredibly tiny in any imaginable situation, though.

Also, Garth, gravitational waves do travel at speeds other than c even in a vacuum. If the curvature is very high then perturbations actually travel at all speeds less than and equal to c (along all causal curves, to be technical). The more slowly moving components are "scattering" off of the curvature in a sense.

6. Dec 6, 2004

### hellfire

In electromagnetism the fields can propagate as waves due to the existence of the displacement current in Ampere’s law. Different propagation speeds arise due to the dependence of the displacement current on the permittivity of the medium.

In general relativity, in the weak field approximation, one defines a perturbation of a flat metric guv = nuv + huv. This may be splitted as P ~ h00, wi ~ h0i and the term hij.

In electromagnetism one derives the electric and magnetic fields from the scalar and vector potentials. In analogy to this, one can define here a gravitoelectric and a gravitomagnetic field from P and w.

Substituting then into the Einstein equations one obtains a set of equations similar to Maxwell equations. The corresponding Ampere equation does not contain a displacement current. Thus, the gravitoelectric and a gravitomagnetic fields do not obey a common wave equation.

So, taking an analogy to electromagnetism, this ‘source’ of different propagation speeds in different media does not exist in general relativity.

On the other hand, the terms huv do obey a wave equation. In the weak field limit this propagation speed is always c.

Is my understanding correct?

If the weak field limit is not applicable, can we still talk about ‘gravitational waves’ or ‘gravitons’?

Last edited: Dec 6, 2004
7. Dec 6, 2004

### Stingray

Ok, but that's not the most physical way to think about it. On a microscopic level (but still in classical physics), the electromagnetic field interacts with the material it's travelling through. The shaking charged particles give off waves of their own, which are superimposed with the original wave. The sum (usually) appears to travel at less than c. This turns out to be equivalent to saying that the matter changed the permittivity and/or permeability. I think this is worked out in Feynman's lectures. Any advanced E&M book would have it as well.

Yes. This is probably the simplest way to look at it. As the wave travels through matter (at c), it shakes it a little bit. These motions generate their own gravitational waves, which combine with the original in a particular way to make the sum look a bit different than it otherwise would.

You can talk about gravitational waves even in full GR, but it becomes much more difficult, and not as general a concept as one might like. As for gravitons, I don't think anyone agrees on what they would mean beyond the weak field limit.

You are being more restrictive than necessary though. It is still possible for everything to make sense if you linearize the equations on top of a curved background. So you can still talk about everything in a strongly curved spacetime as long the perturbations away from a solution is sufficiently small. In this case, the vacuum also has an "index of refraction" in some sense.

8. Dec 7, 2004

### hellfire

OK thanks, I see. What I wrote does not really make sense. It is relevant for the generation of gravitational waves (the tensor component instead of the vector component of the perturbation), but does not reveal anything about the propagation of gravitational waves in media.

Now, for my understanding: in case of electromagnetism the electric displacement, which enters the right hand side of Ampere's law, gets modified due to the polarization existing in a medium ($$\inline D = E + 4 \pi P$$). This leads to a different propagation speed than in vacuum, where P = 0.

What is then the corresponding quantity (to the polarization) in case of gravitational waves? May be the curvature generated by the energy-momentum tensor of the medium?

9. Dec 7, 2004

### Stingray

I suppose it would be related to the locally induced quadrupole moment, but I don't really remember. I'll try to look it up today.

10. Dec 7, 2004

### marlon

In string theory the difference is made between open and closed strings (like lines connected at one side to a surface and circles on that surface). Particles of the standard model, like photons, are represented by open strings and the graviton is represented by a closed string. In Brane-cosmology it can be proven that only open strings can live on such a brane. This means that photons only live on a brane.

Now in string theory 10 dimensions are used (one option, there are others) of which 9 are space like and one dimension is time. Of that 9 space-dimensions we have our three well know dimensions and in each point of our space-continuum there are 6 other dimensions curled up (a bit like macaroni ). This is an idea from the Kaluza-Klein-theory.So the entity that we call a point is not really a point but a small sphere consisting of 6 dimensions (think of six axises all curled up).

Our three-dimensional world is considered to be such a brane with three visible space dimensions. . Photons can only live on a brane and this is the reason why we observe them in our "universe"...They can never escape to the other six dimensions...

Gravitons on the other hand can live in all 9 dimensions and the only way to observe them in our three dimensions would be via the interactions of gravitons with photons for example. Given the fact that they CAN live in our three dimensions, yet we did not see them, they must interact very weakly with our known "matter". So to answer your question : we don't know the properties you are asking for but they must be very weak.

Biggest problem with observing gravitons is the fact that we need to be able to look at a veeeeeeery small distance scale. This is not possible with our current technology...

regards
marlon

11. Dec 7, 2004

### Stingray

Ok, I was right. You find the dispersion of gravitational waves by writing down an equation for the matter's induced quadrupole moment. There's a model calculation of this in section 2.4.3 of one of Kip Thorne's old review articles: http://elmer.caltech.edu/ph237/week6/g.pdf

12. Dec 8, 2004

### hellfire

In the microscopic description, an electromagnetic wave propagating in a medium can be assumed to excite the atoms in the medium and make them oscilate, inducing a dipole and thus generating additional radiation. The same aplies for gravitational waves (but now with an induced quadrupole) as you have already explained, and as it is explained in this reference. However, my question was about a "macroscopic" description. The macroscopic description is given by the polarization in the medium, or by the electric displacement which enters the Maxwell equations (Ampere's law) and provides directly a solution with propagation speed different from c. I was wondering whether it exists a similar way to proceed in case of gravitational waves.

13. Dec 8, 2004

### Stingray

Since the electric polarization is basically the induced dipole moment per unit volume, I suppose the analogous quantity would be the induced quadrupole per unit volume. As far as I know, this doesn't have a name. I don't think it was ever considered very useful to have separate 'macroscopic' and 'microscopic' wave equations in GR. The distinction in EM seems to me to be more for historical reasons that anything else.

14. Dec 12, 2004

### Creator

Interesting analogy, Hellfire, but I thought the correct equation for electric dispacement was:
D = e0E + P

Did I miss something ?Or are you using a different form?
Creator

15. Dec 12, 2004

### Stingray

SI vs. Gaussian units.

16. Dec 12, 2004

### Creator

Well, that makes me feel rather dumb.
But now that's clear; let me ask you a question. Wasn't this equation derived for the polarization due to a static E field?
Thus the gravitational analog (to that eqn.) would seem to be applicable to a static gravitoelectric field, no? How that is possible would require some interesting speculation. Although I agree with you that the grav. quadrupolar moment should be analogous to electric dipole, such is not possible without a time varying (quadrupolar) gravitational source .
What is the polarization eqn. for time varying E fields?

Creator

Last edited: Dec 12, 2004
17. Dec 12, 2004

### Stingray

I'm pretty sure that the same equation applies to time varying E-fields as well.

18. Dec 12, 2004

### Creator

Really? If that is the case, then how can we arbitrarily decide that the time varying analog should be applicable while the static situation is obviously not? I mean 'obviously not applicable' without some sort of serious modification of our definition of gravitational charge.

If we insist on using the analog in the broadest sense to include both cases, we would possibly need to postulate some heretofore unrecognizeable 'negative' mass/gravitational charge to account for the unobservable polarization in the static situation.

In any case, to satify Hellfire, if the electric polarization eqn. is applicable to dynamic E, then we would first need to recognize that we can define P in terms of E in the usual sense:

P = e0(k-1)E (where k is the ratio of electric field in the vacuum to that in the medium, i.e., k=E0/E)

Thus we satisfy the condition of zero polarization when k is at unity, as should be the case in a vacuum.

Taking liberty with great caution, and provided we don't run amuck with the linearized (Maxwellian) GR equations, we transpose the usual linearized gravitational quantities into the above eqn., i.e., e0---> 1/{4(pi)G} for gravitational permissivity (or capacivity), and E now becomes the gravitational field in vacuum, and k becomes the ratio of gravitational field in the vacuum to gravitational field in the medium.

That would seem to be an acceptable 'linearized' equation for gravitational
'polarization'.
Of course, I haven't done so, but one would need to check the units to see if they are reasonable and correspond to the electric polarization which is given, strictly speaking, in coul/m2.

Creator

P.S. BTW, thanks for the Kip Thorne reference which appears to be an excellent resource.

Last edited: Dec 12, 2004
19. Dec 13, 2004

### Stingray

How is it that the static situation won't work? If gravity is acting on bound matter, a static gravitational field will perturb the equilibrium configuration a little bit, but the system will still be in equilibrium. So we could define an induced quadrupole even in this case.

It isn't very obvious, though, that only the quadrupole matters in the static case. As you say, the absence of "negative charge" here makes things a little more tricky. Anyways, whatever the relevant quantity is, it still seems clear to me that it wouldn't be too hard to define. Just find the difference in field from the perturbed matter versus unperturbed matter.

20. Dec 13, 2004

### Creator

Well, true enough; but I guess I am considering the situation to be unbound matter in a static field, i.e., in free fall.

You make it sound so simple. I'm going to have to tell the guys at LIGO how easy this is going to be. :tongue:
Just kidding; I do understand what you mean, and you are correct; that is the usual (theoretic) preceedure; (however, i still have grave doubts that GW detection is possible using laser interferometry).
Creator

Last edited: Dec 13, 2004