Having said that, you can of course hypothesize Planck scale effects that do not respect Special Relativity and then go out to find constraints, because maybe quantum gravity does indeed violate Special Relativity? There is a whole paper industry behind this since violations of Special Relativity tend to result in large and measurable consequences, in contrast to other quantum gravity effects, which are tiny. A lot of experiments have been conducted already looking for deviations from Special Relativity. And one after the other they have come back confirming Special Relativity, and General Relativity in extension. Or, as the press has it: “Einstein was right.”Since there are so many tests already, it has become increasingly hard to still believe in Planck scale effects that violate Special Relativity. But players gonna play and haters gonna hate, and so some clever physicists have come up with models that supposedly lead to Einstein-defeating Planck scale effects which could be potentially observable, be indicators for quantum gravity, and are still compatible with existing observations. A hallmark of these deviations from Special Relativity is that the propagation of light through space-time becomes dependent on the wavelength of the light, an effect which is called “vacuum dispersion”.
There are two different ways this vacuum dispersion of light can work. One is that light of shorter wavelength travels faster than that of longer wavelength, or the other way round. This is a systematic dispersion. The other way is that the dispersion is stochastic, so that the light sometimes travels faster, sometimes slower, but on the average it moves still with the good, old, boring speed of light.
The first of these cases, the systematic one, has been constrained to high precision already, and no Planck scale effects have been seen. This has been discussed since a decade or so, and I think (hope!) that by now it’s pretty much off the table. You can always of course come up with some fancy reason for why you didn’t see anything, but this is arguably unsexy. The second case of stochastic dispersion is harder to come by because on the average you do get back Special Relativity.
I already mentioned in September last year that Jonathan Granot gave a talk at the 2014 conference on “Experimental Search for Quantum Gravity” where he told us he and collaborators had been working on constraining the stochastic case. I tentatively inquired if they saw any deviations from no effect and got a head shake, but was told to keep my mouth shut until the paper is out. To make a long story short, the paper has appeared now, and they don’t see any evidence for Planck scale effects whatsoever:
A Planck-scale limit on spacetime fuzziness and stochastic Lorentz invariance violationWhat they did for this analysis is to take a particularly pretty gamma ray burst, GRB090510. The photons from gamma ray bursts like this travel over a very long distances (some Gpc), during which the deviations from the expected travel time add up. The gamma ray spectrum can also extend to quite high energies (about 30 GeV for this one) which is helpful because the dispersion effect is supposed to become stronger with high energy.
Vlasios Vasileiou, Jonathan Granot, Tsvi Piran, Giovanni Amelino-Camelia
What the authors do then is basically to compare the lower energy part of the spectrum with the higher energy part and see if they have a noticeable difference in the dispersion, which would tend to wash out structures. The answer is, no, there’s no difference. This in turn can be used to constrain the scale at which effects can set in, and they get a constraint a little higher than the Planck scale (1.6 times) at high confidence (99%).
It’s a neat paper, well done, and I hope this will put the case to rest.
Am I surprised by the finding? No. Not only because I knew the result since September, but also because the underlying models that give rise to such effects are theoretically unsatisfactory, at least for what I am concerned. This is particularly apparent for the systematic case. In the systematic case the models are either long ruled out already because they break Lorentz-invariance, or they result in non-local effects which are also ruled out already. Or, if you want to avoid both they are simply theoretically inconsistent. I showed this in a paper some years ago. I also mentioned in that paper that the argument I presented does not apply for the stochastic case. However, I added this because I simply wasn’t in the mood to spend more time on this than I already had. I am pretty sure you could use the argument I made also to kill the stochastic case on similar reasoning. So that’s why I’m not surprised. It is of course always good to have experimental confirmation.
While I am at it, let me clear out a common confusion with these types of tests. The models that are being constrained here do not rely on space-time discreteness, or “graininess” as the media likes to put it. It might be that some discrete models give rise to the effects considered here, but I don’t know of any. There are discrete models of space-time of course (Causal Sets, Causal Dynamical Triangulation, LQG, and some other emergent things), but there is no indication that any of these leads to an effect like the stochastic energy-dependent dispersion. If you want to constrain space-time discreteness, you should look for defects in the discrete structure instead.
And because my writer friends always complain the fault isn’t theirs but the fault is that of the physicists who express themselves sloppily, I agree, at least in this case. If you look at the paper, it’s full with foam, and it totally makes the reader believe that the foam is a technically well-defined thing. It’s not. Every time you read the word “space-time foam” make that “Planck scale effect” and suddenly you’ll realize that all it means is a particular parameterization of deviations from Special Relativity that, depending on taste, is more or less well-motivated. Or, as my prof liked to say, a paramterization of ignorance.
In summary: No foam. I’m not surprised. I hope we can now forget deformations of Special Relativity.