Btw.. I have a question. It is said that "the discrete nature of space causes higher-energy gamma rays to travel slightly faster than lower-energy ones". Why is that? I saw this claimed in 2004. How did Rovelli banish the problem? I read the following in Smolin article in Scientific American in January of 2004 (I know it's old news but I can't understand the above paper):
"RADIATION from distant cosmic explosions called gamma-ray bursts might provide a way to test whether the theory of loop quantum gravity is correct. Gamma-ray bursts occur billions of light-years away and emit a huge amount of gamma rays within a short span. According to loop quantum gravity, each photon occupies a region of lines at each instant as it moves through the spin network that is space (in reality a very large number of lines, not just the five depicted here). The discrete nature of space causes higher-energy gamma rays to travel slightly faster than lower-energy ones. The difference is tiny, but its effect steadily accumulates during the rays’ billion-year voyage. If a burst’s gamma rays arrive at Earth at slightly different times according to their energy, that would be evidence for loop quantum gravity. The GLAST satellite, which is scheduled to be launched in 2006, will have the required sensitivity for this experiment."
Again, what is the reason for the statement "The discrete nature of space causes higher-energy gamma rays to travel slightly faster than lower-energy ones" and how did Rovelli make the problem go away??