Two weeks ago, an

arXiv preprint came out with a new analysis of the highest energetic gamma ray bursts (GRBs) observed with the Fermi telescope. This paper put forward a bound on an energy-dependent speed of light that is an improvement of 3 orders of magnitude over existing bounds. This rules out a class of models for Planck-scale effects. If you know the background, just scroll down to "News" to read what's new. If you need a summary of why this is interesting and links to earlier discussions, you'll find that in the "Avant-propos".

**Avant-propos**Deviations from Lorentz-invariance are the best studied case of physics at

the Planck scale. Such deviations can have two different expressions: Either an explicit breaking of Lorentz-invariance that introduces a preferred restframe, or a so-called deformation that changes Lorentz-transformations at high energies without introducing a preferred restframe.

Such new effects are parameterized by a mass scale that, if it is a quantum gravitational effect, one would expect to be close by the Planck-mass. Extensions of the standard model that explicitly break Lorentz-invariance are very strongly constrained already, to 9 orders of magnitude above the Planck mass. Such constraints are derived by looking for effects on particle physics that are a consequence of higher order operators in the standard model.

Deformations of special relativity (DSR) evade that type of constraints, basically because there is no agreed upon effective limit from which one could actually read off higher order operators and calculate such effects. It is also difficult, if not impossible, to make sense of DSR in position space without ruining locality and these models have so-far unresolved issues with multi-particle states. So, as you can guess, there's some controversy among the theorists about whether DSR is a viable model for quantum gravitational effects. (

See also this earlier post.) But that's arguments from theory, so let's have a look at the data.

Some models of DSR feature an energy-dependent speed of light. That means that photons travel with different speeds depending on their energy. This effect is very small. In the best case, it scales with the photon's energy over the Planck mass which, even for photons in the GeV range, is a a factor 10

^{-19}. But the total time difference between photons of different energies can add up if the photons travel over a long distance. Thus the idea is to look at photons with high energies coming to us from far away, such as those emitted from GRBs. It turns out that in this case, with distances of some Gpc and energies at some GeV, an energy-dependent speed of light can become observable.

There's two things one should add here. First, not all cases of DSR do actually have an energy-dependent speed of light. Second, not in all cases does it scale the same way. That is, the above discussed case is the most optimistic one when it comes to phenomenology, the one with the most striking effect. For that reason, it's also the case that has been talked about the most.

There had previously been claims from analysis of GRB data that the scale at which the effect becomes important had been constrained up to about 100 times the Planck mass. This would have been a strong indication that the effect, if it is a quantum gravitational effect, is not there at all, ruling out a large class of DSR models. However,

we discussed here why that claim was on shaky ground, and

indeed it didn't make it through peer review. The presently best limit from GRBs is just about at the Planck scale.

**News**Now, three researchers from

Michigan Technological University, have put forward a new analysis that has appeared on the arxiv:

Limiting properties of light and the universe with high energy photons from Fermi-detected Gamma Ray Bursts

By Robert J. Nemiroff, Justin Holmes, Ryan Connolly

arXiv:1109.5191 [astro-ph.CO]

Previous analysis had studied the difference in arrival times between the low and high energetic photons. In the new study, the authors have exclusively looked at the high energetic photons, noting that the average

*difference* in energies between photons in the GeV range is about the same as that between photons in the GeV and the MeV range, and for the delay it's only the difference that matters. Looking at the GeV range has the added benefit that there is basically no background.

For their analysis, they have selected a subsample of the total of 600 or so GRBs that Fermi has detected so far. From all these events, they have looked only at those who have numerous photons in the GeV range to begin with. In the end they consider only 4 GRBs (080916C, 090510A, 090902B, and 090926A). From the paper, it does not really become clear how these were selected, as

this paper reports at least 19 events with statistically significant contributions in the GeV range. One of the authors of the paper, Robert Nemiroff, explained upon my inquiry that they selected the 4 GRBs with the best high energy data, numerous particles that have been identified as photons with high confidence.

The authors then use a new kind of statistical analysis to extract information from the spectrum, even though we know little to nothing about the emission spectrum of the GRBs. For their analysis, they study exclusively the timing of the high energetic photons' arrival. Just by looking at the Figure 2 from their paper you can see that on occasion two or three photons of different energies arrive almost simultaneously (up to some measurement uncertainty). They study two methods of extracting a bunch from the data and then quantify its reliability by testing it against a Monte Carlo simulation. If one assumes a uniform distribution and just sprinkles photons in the time interval of the burst, a bunch is very unlikely to happen by coincidence. Thus, one concludes with some certainty that this 'bunching' of photons must have been present already at the source and was maintained during propagation. An energy-dependent dispersion would tend to wash out such correlations as it would increase the time difference between photons with different energies. Then, from the total time of the bunch of photons and its variability in energy, one can derive constraints on the dispersion that this bunch can have undergone.

Clearly, what one would actually want to do is a Monte Carlo analysis with and without the dispersion and see which one fits the data better. Yet, one cannot do that because one doesn't know the emission spectrum of the burst. Instead, the procedure the authors use just aims at extracting a likely time variability. In that way, they can then identify in particular one very short substructure in GRB 090510A that in addition also has a large spread in energy. From this (large energy difference but small time difference) they then extract a bound on the dispersion and, assuming a first order effect, a bound on the scale of possible quantum gravitational effects that is larger than 3060 times the Planck scale. If this result holds up, this is an improvement by 3 orders of magnitude over earlier bounds!

**Comments**The central question is however what is the confidence level for this statement. The bunching they have looked at in each GRB is a 3Ïƒ effect, i.e. it would appear coincidentally only in one out of 370 cases that they generated per Monte Carlo trials: "Statistically significant bunchiness was declared when the detected counts... occurred in less than one in 370 equivalent Monte Carlo trials." Yet they are extracting their strong bound from one dataset (GRB) of a (not randomly chosen) subsample of all recorded data. But the probability to expect such a short bunch just by pure coincidence in one out of 20 cases is higher than the probability to find it coincidentally in just one. Don't misunderstand me, it might very well be that the short-timed bunch in GRB 090510A has a probability of less than one in 370 to appear just coincidentally in the data we have so far, I just don't see how that follows from the analysis that is in the paper.

To see my problem, consider that (and I am not saying this has anything to do with reality) the GRB had a completely uniform emission in some time window and then suddenly stops. The only two parameters are the time window and the total number of photons detected. In the low energy range, we detect a lot of photons and the probability that the variation we see happened just by chance even though the emission was uniform is basically zero. In the high energy range we detect sometimes a handful, sometimes 20 or so photons. If you assume a uniform emission, the photons we measure will simply by coincidence sometimes come in a bunch if you measure enough GRBs, dispersion or not. That is, the significance of one bunch in one GRB depends on the total size of the sample, which is not the same significance that the authors have referred to. (You might want to correlate the spectrum at high energies with the better statistic at low energies, but that is not what has been done in this study.)

The significance that is referred to in the paper is how well their method extracts a bunch from the high energy spectrum. The significance I am asking for is a different one, namely what is the confidence by which a detected bunch does actually tell us something about the spectrum of the burst.

**Summary**The new paper suggests an interesting new method to extract information about the time variability of the GRB in the GeV range by estimating the probability that the observed bunched arrivals of photons might have occurred just by chance even though there is dispersion. That allows to bound a possible Planck scale effect very tightly. Since I have written some papers arguing from theoretical grounds that there should be no Planck scale effect in the GRB spectra, I would be pleased to see an observational confirmation of my argument. Unfortunately, the statistical relevance of this new claim is not entirely clear to me. The relevance that is referred to in the paper I am not sure how to translate into the relevance of the bound. Robert Nemiroff has shown infinite patience to explain the reasoning to me, but I still don't understand it. Let's see what the published version of the paper says.