Micha said:
It is always said, that string theory makes no testable predictions.
At least there are some qualitative predictions like supersymmetry and extra dimensions.
One prediction of loop quantum gravity is a violation of Lorentz invariance.
Are there other predictions of loop quantum gravity?
I wouldn't count the quantization of space and area, because a direct test seems forever impossible.
It's a good question to be asking, Micha. As I think you know I am an observer on the sidelines---I can't speak for the researchers in the various nonstring QG (like Loop, like spinfoam, like causal triangulations...) I just do the best I can to report overview and trends.
Almost all the nonstring QG embodies 3 spatial dimensions. Several approaches would be badly refuted if experimentalists were to find extra spatial dimensions.
More specifically Causal Triangulations QG (Loll et al) predicts 4D spacetime at macro scale going continuously down to around 2D at micro scale. So dimensionality declines with scale. It would be badly refuted if evidence showed up of extra dimensions of the sort string theorists imagine.
So there is clearly falsifiability in as much as many presumed LHC experts have written about the possibility of LHC to find evidence of extra dimensions (I do not think it at all likely but they talk about it as a possibility.)
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There is no LQG prediction as far as I know of breaking Lorentz invariance---it does not predict violation in the sense of the existence of a preferred frame. As you probably know there is a prediction in some versions of a modified Lorentz invariance in which both the speed c and an energy like the Planck energy appear the same to all observers. (sometimes called DSR for doubly special relativity.) There are different versions of DSR, and also an energy-dependent metric conjecture (the socalled rainbow metric).
Certain versions of LQG apparently
differ as to what they predict in the way of energy-dependent metric, or energy-dependent speed of photons. I have seen predictions differing as to SIGN of the energy-dependent effect. The situation is confused. Anything along these lines will necessarily rule out SOME of the versions. At least it will narrow down the field.
The Fermi Gammaray Space Telescope (formerly called GLAST) has started to report data. It is sensitive enough to detect an energy-dependent advance or delay in arrival time of the expected size. Either way it goes will be helpful.
But there is no
overall prediction about this derived from LQG as a whole. there is no one single modification of Lorentz invariance that all the approaches predict!
So one cannot say that testing for energy-dependent arrival times by the Fermi satellite will be a global test of LQG as a whole. It will just help them narrow down what to work on.
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So Micha, I don't see very much in the way of unique hard predictions. Some ongoing observations, as by the gammaray telescopes, and conceivably LHC, will be helpful. But there is no blanket commitment to a falsifiable prediction. As far as I can see.
In his recent talk at Geneva, Rovelli stressed that the goal at present is to find at least one consistent theory--constructing a quantum field theory NOT on a pre-ordered space, and having the correct behavior in the limit. It is a hard job and they are still working on that--just find one theory that works. When there are two or more, then will be the time to test, so as to rule out one or the other. for them now, getting GR in the limit is the big test.
(that is how I measure the progress they have made in the past two years)