My impression was that only misinformed people argue that LQG discreteness is in conflict with Lorentz invariance. This was resolved a long time ago, i thought. Does anyone disagree? Want to talk about it? Explain something to me that I am missing? http://arxiv.org/abs/gr-qc/0205108 Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction Carlo Rovelli, Simone Speziale 12 pages, 3 figures (Submitted on 25 May 2002) "A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further Lorentz contracted. We show that this is not the case within loop quantum gravity. In loop quantum gravity the minimal length (more precisely, minimal area) does not appear as a fixed property of geometry, but rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted observer can see the same observable spectrum, with the same minimal area. What changes continuously in the boost transformation is not the value of the minimal length: it is the probability distribution of seeing one or the other of the discrete eigenvalues of the area. We discuss several difficulties associated with boosts and area measurement in quantum gravity. We compute the transformation of the area operator under a local boost, propose an explicit expression for the generator of local boosts and give the conditions under which its action is unitary." Discreteness in LQG is a serious issue. For various reasons I've always thought of it as a bit of a liability for the theory. FOR ONE THING THE LOOP COMMUNITY IS ALMOST ALL WORKING ON things like spinfoam, groupfieldtheory, simplicial (e.g. Loll CDT), renorm'ble quantum metric (e.g. Reuter) and these are THINGS WHICH DON'T HAVE MINIMAL LENGTH. It is a strange anomaly to have a community called Loop and have almost nobody working in canonical LQG proper, and to have canonical Loop the only approach with e.g. an area operator with discrete spectrum. It makes it seem as if the community connects to discreteness in geometrical measurement only by its historical accident name. That is bad enough but it is worse when we get people who don't know what they are talking come in and say that LQG can't possibly be right BECAUSE discrete spectrum of a geometric observable breaks LORENTZ. It simply does not. That is just something badmouth people say who don't know any better.