Graviton Effects in Different Media: Investigating the Variations

[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?

I'd appreciate any answers.

 

[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.

 

[silverpig]

That's a great question and one I'm going to 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.

 

[Garth]

The analog to this in gravity would be the slowing down of gravitational waves through a medium with particles of mass charge.

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

 

[Stingray]

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.

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 traveling 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.

 

[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 g_uv = n_uv + h_uv. This may be splitted as P ~ h₀₀, w_i ~ h_0i and the term h_ij.

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 h_uv 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’?

 

[Stingray]

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.

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 traveling 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.

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

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.

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

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.

 

[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?

 

[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.

 

[marlon]

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?

I'd appreciate any answers.

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

 

[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

 

[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.

 

[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.

 

[Creator]

.

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? ?

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

 

[Stingray]

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

SI vs. Gaussian units.

 

[Creator]

SI vs. Gaussian units.

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

 

[Stingray]

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

 

[Creator]

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

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.

 

[Stingray]

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.

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.

 

[Creator]

... If gravity is acting on bound matter, a static gravitational field will perturb the equilibrium configuration a little bit,... So we could define an induced quadrupole even in this case.

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

Just find the difference in field from the perturbed matter versus unperturbed matter.

You make it sound so simple. I'm going to have to tell the guys at LIGO how easy this is going to be.
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

 

[Louis Cypher]

Have you ever thought that there might be no force carrier for gravity, that it may simply be a side effect of somethings mass be it an atom or a planet?

As for string theory it belongs in the realms of philosophy, you'll find very few scientists hold any regard for it whatsoever; it's a trendy throw away theory with no basis in reality; I can't work out how to unify A with B so I come up with C but conveniantly it might never be proven?!? without proof it's not science, it bares more simillarities with religion, blind faith in the exitence of it without any tangible proof?

There are several theories of how gravity works without the graviton one I've seen is the Nyman Theory if you're interested I'll send you some info and an avi to show how it works?

It's interesting, who knows it might even be true...

 

[Garth]

Have you ever thought that there might be no force carrier for gravity,

In GR gravity is seen to be purely an effect of geometry. Gravitation is an inertial force, not a 'real' one, at least not in the 4-dimensional geometric view of the world. As such it needs no graviton and the fundamental 'real' forces may have already been unified in the Grand Unified Theory.

Just a thought.

Garth

 

[Chronos]

If gravity were impeded by matter in the same manner as light, it could be refracted, deflected, etc. with the right combination of materials and geometry. Such effects, at least any that are non-trivial have not been observed in nature: e.g. the moons orbital path does not change when the Earth passes between it and the sun. There may, however, be some minor perturbations [e.g., Allias effect]. The graviton, if it exists, makes neutrinos look as interactive as bowling balls.

 

[Creator]

If gravity were impeded by matter in the same manner as light, it could be refracted, deflected, etc. with the right combination of materials and geometry.

Well, that's interesting you should bring that up -- that was the undisclosed reason I entered this discourse with Stingray and Hellfire; in order to possibly identify some amplification (and/or detection) mechanism for GW absorption/dispersion which in the usual sense is predicted to be miniscule. (see previous Kip Thorne reference).

..Such effects, at least any that are non-trivial have not been observed in nature: e.g. the moons orbital path does not change when the Earth passes between it and the sun.

True, but in your example you are making the assumption that the focal length of any Earth refracton of solar gravity is about 1 lunar distance and that the magnitude of such effect should be sufficient to alter orbital parameters, neither which is probably justified. For example I believe the refractive effect of the sun on a passing (extrasolar) GW has been calculated to have a focal length that extends out to about Jupiter... (see again Thorne). Maybe that's what's sucking in all those asteroids into Earth's orbit. he, he.

Creator

-edited for clarity

 

[Stingray]

If gravity were impeded by matter in the same manner as light, it could be refracted, deflected, etc. with the right combination of materials and geometry. Such effects, at least any that are non-trivial have not been observed in nature: e.g. the moons orbital path does not change when the Earth passes between it and the sun. There may, however, be some minor perturbations [e.g., Allias effect]. The graviton, if it exists, makes neutrinos look as interactive as bowling balls.

The test you propose is extremely weak. GR corrections to Newton's theory are extremely small in the solar system.

Also, your statement about gravitons being even more elusive than neutrinos isn't a very good analogy (although I understand what you're saying). We all feel the force of gravity, so if that is due to to gravitons (whatever they are), then they clearly interact quite strongly in physical situations.

Anyways, you might find this paper interesting:
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1979GReGr..11..105P&db_key=PHY&high=41bfd3b60a19173
Unfortunately, it's not available online, but you can read the abstract.

 

[Louis Cypher]

Yep, you're probably right, looking at the difference between gravity and electromagnetism in terms of strength, gravity seems just too weak; does it have a force carrier? Maybe that's a bit like asking does God have a force carrier?

 

[Louis Cypher]

Gravity and force carriers

Look if gravity had a force carrier and the moon passed in front of the sun, wouldn't this force carrier be blocked somewhat by the moon? the moons force carrier would be stronger than the same area of the sun would it not? G being inversely proportional to distance, and we should see mysterious gravitational fluxes, surely; which is interesting because It has been reported for many years that this is precisely what some people have picked up in regards to pendulum experiments, some seem to speed up erratically, whilst just to add more confusion to what is allready dubious some people have never observed any effect.

Anyway a team of physisists is set to prove or dissprove once and for all any contentions, in the next eclipse in 2005.

Am I the devils advocate?

 

[Creator]

Look if gravity had a force carrier and the moon passed in front of the sun, wouldn't this force carrier be blocked somewhat by the moon? the moons force carrier would be stronger than the same area of the sun would it not? G being inversely proportional to distance, and we should see mysterious gravitational fluxes, surely; which is interesting because It has been reported for many years that this is precisely what some people have picked up in regards to pendulum experiments, some seem to speed up erratically, whilst just to add more confusion to what is allready dubious some people have never observed any effect.

If you are referring to anamolous results (gravitational measurements) during solar eclipses, then yes, there are some unusual reports. The ones I'm somewhat familiar with seem to point to a diffractive effect similar to what Chronos was alluding to, because they report a greater effect in the 1st and 4th contact, as may be expected in the case of refraction. However, without some sort of amplifying mechanism these observations are at odds ( both qualitatively & quantitatively) with the predictions of Gen. Rel.
Here's one in particular done with sensitive gravitometers that may interest you:
http://www.eclipse2006.boun.edu.tr/sss/paper03.pdf

Creator

 

[Louis Cypher]

Indeed it's definitely worth considering if nothing else? Interesting stuff thanks, as an under graduate who'd came to physics in later life, I do find it somewhat shocking, plank's quote! Does the graviton exist, or have we allready unifed the forces, it's a fascinating area, without knowing the math I can't postulate more, but then Einstien got colleagues do the math for him, before he learned the applied stuff: he was allready thinking outside the envelope, then came up with math to explain his theories, I read an article that said, the reason we're so short of physisists is that we place too much emphasis on math, we should learn the theory and then do the math, the fascinating world of physics before the application; I did an OU course, and it did precisely that, it is indeed why I'm so passionate about physics, the theories the interresting stuff, let's leave the maths until we understand what's behind it otherwise we frighten potential students away with the ogre of maths; the greatest physisist of the 20th century was only good at maths, he became excellent at it by stidying implications after the fact surely?

 

[ohwilleke]

Here's one in particular done with sensitive gravitometers that may interest you:
http://www.eclipse2006.boun.edu.tr/sss/paper03.pdf

Facinating study!

 

[godzilla7]

I've seen this one it certainly is puzzling they hope to clear it up in the next solar eclipse, to say once and for all what is happening or to disprove it as experimental error, either way. If it were indeed a positive result, we'd need to question qm laws again to establish what's was going on.