Does Loop Quantum Gravity Suggest Photons Can Travel Faster Than Light?

[MathematicalPhysicist]

the next statement was in wikipedia:"LQG predicts that more energetic photons should travel ever so slightly faster than less energetic photons. "
does it imply faster than light speed? (i don't think so because lqg attempts to unite between GR and QM).

here's the link:http://www.wikipedia.org/wiki/Loop_quantum_gravity

 

[marcus]

Originally posted by loop quantum gravity
the next statement was in wikipedia:"LQG predicts that more energetic photons should travel ever so slightly faster than less energetic photons. "
does it imply faster than light speed? (i don't think so because lqg attempts to unite between GR and QM).

here's the link:http://www.wikipedia.org/wiki/Loop_quantum_gravity

This is right. The ongoing experimental tests of LQG and some expected in the near-term future are discussed on pages 18-20
of Smolin's recent review article
http://arxiv.org/hep-th/0303185

This is a very interesting section of the survey called
"The near term experimental situation"

The predicted dispersion is so slight that it can only be tested over cosmological distances using very high energy photons so the most promising method is by observing gamma ray bursts (GRB). Smolin gives these references:

G. Amelino-Camelia, John Ellis, et al "Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
http://arxiv.org/astro-ph/9712103 (published in Nature in 1998)

J. P. Norris et al "GLAST, GRBs, and Quantum Gravity"
http://arxiv.org/astro-ph/9912136

John Ellis et al "Quantum Gravity Analysis of Gamma-Ray Bursts using Wavelets"
http://arxiv.org/astro-ph/0210124

 

[MathematicalPhysicist]

doesnt this dissobey the postulate in relativity that the speed of light is constant?

 

[marcus]

the dispersion relation

This is a fascinating area. It is not unreasonable to expect physics at Planck scale (e.g. very high energies, small distances) to diverge from the everyday and classical. But there is a scarcity of ways to test LQG because the Planck scale is so small and so high-energy.
One cannot just build an accelerator to get things up to Planck energy, it is too high!
But by being clever one can nevertheless find ways to test the theory. And already people are doing that! Here is what Smolin says on page 17,

"It turns out that this has consequences for the question of whether special relativity, and lorentz invariance, is exactly true in nature, or is only an approximation which holds on scales much longer than the Planck scale [28]-[40]. Several recent calculations...yield predictions for modifications to the energy momentum relations for elementary particles. These are of the form,

E² = p² + M² + αE³ + βE⁴

where predictions have been found for the leading coefficients α, which generally depend on spin and helicity [36]-[38]..."

The GRB observations are trying to find a bound on this α parameter.

 

[marcus]

Originally posted by loop quantum gravity
doesnt this dissobey the postulate in relativity that the speed of light is constant?

It certainly does. I would assume that only the low-energy limit is constant. This is true about several basic constant---there is divergence from them at very high energy or at very small scale.
The postulates of special relativity are not sacred and
even in general relativity already one finds that special relativity is just a very good local approximation.

so there are some very tiny divergences which it looks like it will be possible to test maybe even within the next 5 years

 

[marcus]

When I quoted from Smolin just now I left out some units, Planck length l_Pl and Planck area l²_Pl Here is the same thing with these very small quantities inserted,

"It turns out that this has consequences for the question of whether special relativity, and lorentz invariance, is exactly true in nature, or is only an approximation which holds on scales much longer than the Planck scale [28]-[40]. Several recent calculations...yield predictions for modifications to the energy momentum relations for elementary particles. These are of the form,

E² = p² + M² + αl_Pl E³ + β l²_Pl E⁴

where predictions have been found for the leading coefficients α, which generally depend on spin and helicity [36]-[38]..."

I gather that the predicted values of alpha are no larger than order one. So since alpha gets multiplied by Planck length, in the energy momentum relation, and Planck length is around 10^-35 in metric terms, the effect is miniscule. One apparently only expects it to show up in high energy light that has traveled very long distances (to allow for higher energy photons to get slightly ahead of the pack). The situation is reminiscent of back around 1919 when Eddington went and measured the bending of light around the sun during an eclipse. But so far the observations of gamma ray bursts are not sufficiently precise, so we have to wait.

 

[MathematicalPhysicist]

another thing doesn't lqg contradicts itself by predicting a speed greater than the speed of light (because one of it's parts are GR and its postulate that the speed of light is constant)?