As many people have now heard, the OPERA collaboration is reporting a very surprising observation. The OPERA experiment is part of CERN, and is an experiment meant to study neutrino flavor oscillations. The idea is, the proton beam at CERN creates a beam of neutrinos. Since neutrinos hardly interact with normal matter, they move in a straight line right through the earth, and pass through the experimental station in Gran Sasso, Italy, where some small fraction of them are then detected. There are (according to the Standard Model) three flavors of neutrinos, the electron neutrino, muon neutrino, and tau neutrino. It has been determined experimentally that those flavors are not exact "mass eigenstates". That means that if you start off with a tau neutrino of particular energy, for example, and let it propagate for a while, it will change into a muon neutrino with some probability that oscillates in time. Anyway, OPERA wanted to study this phenomenon, and in doing so, they measured the time it takes neutrinos to go from their production point at CERN to the detector in Gran Sasso, using precisely synchronized special clocks. They also used differential GPS to measure the distance between the production point and the detector to within 20 cm. Dividing the distance by the time, they found much to their surprise that the neutrinos appear to traverse the distance about 60 ns faster than would be expected if they traveled at the speed of light in vacuum.
So, what could be going on here? There are a few possibilities. First, they could have the distance measurement wrong. This seems unlikely, given the use of differential GPS and the sensitivity (they could clearly see the change in the distance due to a 2009 earthquake, as shown in Fig. 7 of the paper). Second, they could have a problem in their synchronization of the clocks. That seems more likely to me, given that the procedure is comparatively complicated. Third, there is some other weird systematic at work that they haven't found. Fourth, neutrinos are actually tachyons. That would be all kinds of awesome, but given how challenging it would be to reconcile that with special relativity and causality, I'm not holding my breath.