It is an interesting issue. Right at the end of the seminal paper of Livine (Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity) that selfAdjoint recently referred to as "Projected..." at the end of the Conclusions and Outlooks section, he says: "Finally, using an explicitly covariant formalism opens the door to the systematic study of space-time related issues such as transformations of areas under Lorentz boosts, as studied in LQG." this shows that Livine thinks the issues raised by Rovelli and Speziale in reference  are important ones, so I looked at their paper, which is 12 pages and dated May 2002: "Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction." So in this thread I'm talking about a 12-page paper ("Reconcile...") and a 15-page paper ("Projected...") http://arxiv.org/gr-qc/0205108 http://arxiv.org/gr-qc/0207084 Naively stated the concern is that, since quantum gravity has a minimal length (or area), it must be incompatible with local coordinate change to a boosted observer who would see lengths contracted. This may have encouraged the illusion that loop gravity is doomed to fail. It may seem self-evident to some people that any theory with a minimum length cant be right because it cant survive boosts. So this connection to controversy makes the issue extra piquant. But it is kind of interesting anyway, apart from that. How is a surface (whose area is to be observed) determined in a diffeo-invariant theory? You have to have some matter---the area is a physical desktop, say. And then how about the spectrum of the operator which corresponds to observing that desktop's area? How does the spectrum change, if at all, under boosts? Notice that the area can change without the spectrum of the operator changing---at least no a priori reason it couldn't AFAIK. Anyway it's interesting. So I want to look at these two papers, one of which is by way of being a reply to the other: Livine "Projected..." responds in a certain sense to Rovelli/Speziale "Reconcile..."