Kathy Copic wrote a nice article about the exciting rumors of superluminal neutrinos observed by the OPERA Collaboration. See her article in QD here.
Apparently an important theoretical impetus for the OPERA measurements comes from a 2008 paper by John Ellis, Nicholas Harries, Anselmo Meregaglis, Andre Rubbi and Alexander S. Sakharov, Probes of Lorentz Violation in Neutrino Propagation. The authors point out that neutrinos are special among the elementary particles, not simply because their masses are extremely small and the interact via the weak force only, but also because they are candidates for violating relativity at the quantum level. Photons, electrons and protons are known to obey special relativity (think of the LEP and SLD electron machines, or the Tevatron and LHC proton colliders). Neutrinos, however, oscillate due their mass and the fact that neutrinos are electrically neutral, and this makes the key difference. In their scenario, the violation of special relativity would be greater when the neutrino energy is greater.
As Kathy pointed out, the timing ability of the experiment and the time structure of the neutrino beam is crucial for the measurement, and the Ellis et al. paper discusses the important points as well as outlining a possible analysis. This might turn out to be a prototype for the actual OPERA analysis we expect to hear at the CERN seminar on 23-Sept. Key ideas are to use the time structure of the beam and the spread in energy and to look at the edges of the distribution of event times. See, for example, this figure which represents the standard model expectation and an example of evidence for neutrinos which come 100 ns too early:
(Keep in mind that the rumors say that the OPERA results show an offset of 60 ns.)
Variations of this analysis are discussed including changes to the time structure of the beam, which could greatly boost the sensitivity of the OPERA experiment. I do not know whether these changes were implemented (I would assume not).
As to quantum gravity, that lies well beyond what I can explain. As Jonathan Asaadi says, let’s see now what OPERA shows at the seminar!