- Prospects for constraining quantum gravity dispersion with near term observations
By Giovanni Amelino-Camelia, Lee Smolin
We discuss the prospects for bounding and perhaps even measuring quantum gravity effects on the dispersion of light using the highest energy photons produced in gamma ray bursts measured by the Fermi telescope. These prospects are brigher than might have been expected as in the first 10 months of operation Fermi has reported so far eight events with photons over 100 MeV seen by its Large Area Telescope (LAT). We review features of these events which may bear on Planck scale phenomenology and we discuss the possible implications for the alternative scenarios for in-vacua dispersion coming from breaking or deforming of Poincare invariance. Among these are semi-conservative bounds, which rely on some relatively weak assumptions about the sources, on subluminal and superluminal in-vacuo dispersion. We also propose that it may be possible to look for the arrival of still higher energy photons and neutrinos from GRB's with energies in the range 1014 - 1017 eV. In some cases the quantum gravity dispersion effect would predict these arrivals to be delayed or advanced by days to months from the GRB, giving a clean separation of astrophysical source and spacetime propagation effects.
While the discussed effects on the propagation of photons are extremely tiny and way too feeble to be observable in experiments on Earth, they could add up when the travel is very long distance. In the models the authors consider, the strength of the effect depends on the energy of the photon. The speed of light is then no longer a constant but a function of the energy of the photon. In the low energy limit, photons travel with what we usually call THE speed of light, c .
To first approximation there are two cases: either the high energetic photons are faster than the low energetic ones, or the high energetic photons are slower than the low energetic ones. I would have guessed the majority of people had thought if such a scenario is true then the photons with higher energy should be faster. If only because we are secretly all dreaming of traveling faster than the speed of light. But that's not what the data seems to suggest to me.
These scenarios can be tested with signals from gamma ray bursts, highly energetic flashes of light originating in faraway Galaxies. Their spectrum covers a large range of energies. If one records photons of different energies with an exact timing, one can compare their arrival time. In my previous post we had been discussing the gamma ray burst GRB 080916C (the number encodes the date). In this burst, the high energy photons seem to be arriving with a delay relative to the lower energetic ones. However, the statistics of that one burst isn't very convincing. Yes, there was that one lazy high energy photon with 13 GeV that arrived 16.3 seconds after the onset of the burst. And okay, there were a couple more photons that seemed to be delayed, but then the low energy signal had two peaks rather than one. This might have indicated it was a fairly uncommon burst.
However, Giovanni and Lee sifted through some databases and found a couple more gamma ray bursts that were recorded during the last year that show similar characteristics, if not so pronounced. In all cases, the high energetic photons were delayed. Their paper offers a neat table summarizing these events, but unfortunately no statistical analysis for how significant the patterns are.
In the following sections of the paper they constrain several models with that data, most notably those who break and those who only deform Lorentz Invariance. In the first case, the universe has a preferred frame relative to which the energy of the photons is defined. In the second case there is no such preferred frame . They further distinguish between the case where high energetic photons are faster (superluminal) and those in which they are slower (subluminal), and extract bounds on the quantum gravity scale for both cases. It is somewhat unintuitive to extract bounds also on the superluminal case when there is a trend in the data for higher energetic photons to arrive later, but it could be an astrophysical effect that is hiding superluminal propagation. The bounds on the superluminal case however are weaker.
There is quite a lot of astrophysics involved in the emission of these photons and the most conservative explanation for the delay is certainly that the photons were emitted with delay. While Giovianni and Lee's analysis offers useful first estimates, what would be needed is a procedure that allows to cleanly separate astrophysical source effects from effects during propagation. To do so, one had to extract the dependence of the signal on the distance to the source.
In the final section of the paper, Giovanni and Lee suggest to obtain further experimental data by looking for photons of even higher energies (that could be delayed up to months) or neutrinos that are emitted from the same source. In both cases, I wonder whether it is feasible to obtain any sensible statistic within the lifetime of the average physicist.
Altogether it is a very useful paper that summarizes the status. It leaves one wanting though for a more thorough data analysis.
 Not to be confused with theories with a varying speed of light which usually means a variation with time, not with energy.
 I wrote a paper showing the second case doesn't make sense if you have an energy dependent speed of ligh. You can wind yourself out of my proof by making your theory even weirder.