Dispersion relation for light in vaccuum

[gregory_]

Hello, I was wondering if someone more knowledgeable in loop-quantum gravity or string theory could discuss a bit about the following topic for me:

If there is a lower size limit (or length itself is quantized), does this (or can this) mean that there would be a dispersion relation for light in vacuum (for example like the phonon dispersion relation due to the fact that there is a finite lattice spacing)?


If you are knowledgeable in other "beyond the standard model" theories, I would be interested to hear their qualitative predictions as well.

And finally, if any theories do predict a dispersion relation for light in vaccuum, have these been calculated? (if possible, can you please provide references to papers where I could read up on this)

Thank you very much.

 

[hossi]

Hi gregory,

there are about one million works on the topic since 2000 or so. You might want to start with this very nice review

http://xxx.lanl.gov/abs/gr-qc/0501053
The Search for Quantum Gravity Signals
Authors: G. Amelino-Camelia, C. Lämmerzahl, A. Macias, H. Müller



B.

 

[marcus]

...

And finally, if any theories do predict a dispersion relation for light in vacuum, have these been calculated? (if possible, can you please provide references to papers where I could read up on this)

Thank you very much.

Hi gregory, welcome. good bunch of questions.
Please see if this article is useful to you.
http://arxiv.org/abs/hep-th/0501091
Falsifiable predictions from semiclassical quantum gravity
Lee Smolin
9 pages

"Quantum gravity is studied in a semiclassical approximation and it is found that to first order in the Planck length the effect of quantum gravity is to make the low energy effective spacetime metric energy dependent. The diffeomorphism invariance of the semiclassical theory forbids the appearance of a preferred frame of reference, consequently the local symmetry of this energy-dependent effective metric is a non-linear realization of the Lorentz transformations, which renders the Planck energy observer independent. This gives a form of deformed or doubly special relativity (DSR), previously explored with Magueijo, called the rainbow metric. The general argument determines the sign, but not the exact coefficient of the effect. But it applies in all dimensions with and without supersymmetry, and is, at least to leading order, universal for all matter couplings.
A consequence of DSR realized with an energy dependent effective metric is a helicity independent energy dependence in the speed of light to first order in the Planck length. However, thresholds for Tev photons and GZK protons are unchanged from special relativistic predictions. These predictions of quantum gravity are falsifiable by the upcoming AUGER and GLAST experiments."

AUGER is actually in progress and from preliminary results I gather it is working out in agreement with Smolin's predictions.
GLAST has been planned to fly in 2007. But there have been budget cuts and i do not know if GLAST is affected. I hope very much that GLAST (gammary large array space telescope) will fly.

If GLAST flies and it does NOT detect a dispersion in the very high energy gamma arriving from distant gammaray bursts, this will be a black eye for Smolin. LQG does, according to him, predict some dispersion, some energy dependence of the speed.

But it is so slight that it would only be detectable in very high energy and after photons in the burst had been traveling a long time, like a billion years. So this is why GLAST could see it, but other things not see it.

Smolin seems willing to stick his neck out about this dispersion relation.
this is supported by some other LQG papers and maybe his references can give you leads.

Some other LQG people are more cautious and are NOT predicting that GLAST should see dispersion. I know. This frustrating. It is not clear cut, at least not so far.

Jerzy Kowalski-Glikman is a DSR (doubly special relativity) expert and he disagrees with Smolin and says that there should NOT be an energy dependence. Too bad they can't agree, it would make the test better (if GLAST actually does go up)
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Hi hossi!, I did not see til now that you had already responded. If I had seen yours I would not have written mine. Thanks for helping. Since you are actually doing QG research it makes it extra reliable.