The article is a well written discussion of this recent topic viewtopic.php?f=74&t=8534
The most important take away of Ethan's article is this:
The best working hypothesis then is that there is no granular structure to space time in a quantum gravity. It's much more likely that quantum gravity retains Lorentz invariance. If it doesn't show up at the Planck energy let alone 2000 times higher it's a bad bed.What's fascinating about this result is that it sets a limit on the energy scale at which Lorentz invariance violation is allowed to take place. Based on the latest HAWC results, we can conclude that there are no violations of this symmetry up to an energy scale of 2.2 × 10^31 eV: nearly 2,000 times the Planck energy scale.
I'm wondering how this affects noncummutative geometry approaches like Alain Connes's work.... There is a little wiggle room there... I can see how it could go either way.
