Jerzy K-G is, as far as I know, one of the world's top experts on DSR (doubly special rel). He is scheduled to give a talk on DSR this month which I expect will be available online video. The planned date is 22 September. http://pirsa.org/10090070 "Doubly" just means that a second physical quantity (a length or energy) is invariant and appears the same to all observers---in the same way that in ordinary SR the speed c appears the same to all observers. For several years (especially 2005-2007) it was thought by some people that A. Some type of DSR would turn out to be a flat limit of LQG, in 4D. This was shown to happen in 3D (Freidel Livine 2005) so it was natural to guess it might be true in 4D. Jerzy K-G was one of the main people trying to extend the 3d result during 2005-2007. B. DSR would involve observable dispersion--the dependence of speed on photon energy. In that case the standard speed c would be the speed of the low-energy photons we experience as ordinary light, but very high energy gamma would differ very slightly, perhaps travel slightly slower. DSR remains interesting. The first idea ("A", connection with LQG) turned out to be difficult to prove in 4D and for a while people stopped trying. But it is always possible that some obstacle that stood in the way has been overcome. Jerzy K-G may report something new on this! The second idea ("B", dispersion) is controversial. There are actually versions of DSR which do not involve dispersion---and involve a curved momentum space. This has never been clear to me, although I recall seeing it discussed in a paper of K-G as far back as 2002-2003. So there are issues surrounding DSR that are both interesting and in need of clarification. My hope is that the 22 September talk by Jerzy K-G will clear up the picture. ============== It's possible that people will eventually be able to prove rigorously that the current version(s) of 4D LQG have some type of DSR as a flat limit. Back in 2007 this did not seem possible and those working on it appeared to give up, but they may get back to it and make a breakthrough. (There are intuitive reasons one would expect this.) It's also always possible that this type of DSR would exhibit first-order dispersion! and that this would then serve to falsify whatever form of LQG had it as flat limit! Or it might turn out that the type of DSR in question did not have dispersion. The questions are not resolved. Have to go out for a few hours. Back later.