The LIGO paper https://dcc.ligo.org/LIGO-P150914/public puts limits on the dispersion of gravitational waves, which can be interpreted as an upper limit of 10^-22 eV on the mass of the graviton. We all know that low-amplitude gravitational waves are supposed to propagate at c according to the Einsten field equations, although proving this is a bit of work and not entirely transparent. Clearly if gravitational waves have some fixed velocity, it has to be c, because there is no other invariant velocity. I guess if the graviton had a mass, there would have to be some other unitful constants in the field equations besides G and c, since you can't build anything with units of mass out of G and c. But is there any simple way of looking at the field equations and seeing that they predict no dispersion for gravitational waves? By "simple" I mean something simpler than linearizing them and showing that the solutions propagate at c. There was a time about 10 years ago when Lee Smolin was pushing the idea that LQG predicted dispersion of light, and he claimed that there were prospects for testing and confirming that prediction soon. Turns out that he was wrong on theoretical grounds. I wonder if this limit on dispersion of gravitational waves puts any constraints on LQG or any other theories of quantum gravity.