The King Prawn started a conversation about this earlier, but it attracted only six comments and didn't make it to the Main Feed, so let me try again. Here is my idiosyncratic take on the CERN announcement that results from CERN's OPERA experiment provide evidence that neutrinos propagate faster than the speed of light.
Since the 1990s there have been tantalising hints that the mass of the neutrino might beimaginary based upon studies of the endpoint of the energy spectrum of the decay of tritium. Here is the 1998 paper which first caused my ears to perk up about this.
Now, if the mass of a particle is imaginary, Einstein's equations predict that it is a “tachyon”—a particle which always travels faster than light and cannot travel slower, just as a real mass particle cannot ever reach or exceed the speed of light. There is nothing in this which implies “Einstein was wrong”, just that at the time he wrote down his equations in 1905 nobody imagined there would be particles with imaginary mass. If neutrinos have a very small imaginary mass, then it's perfectly consistent with special relativity that they travel slightly faster than light.
That said, I think it will be quite a while before this result is generally accepted. For the results to mean anything at all, you have to assume that they've accurately measured the location of the source and target of the neutrinos to better than 60 feet (as light travels about one foot per nanosecond) over a distance of around 500 miles, with both the source and target underground. A very small surveying error could null out the reported effect.
The press release from CERN and the preprint describing the work were both very cautious and simply presented the results as (paraphrasing) “Here's what we've seen, and we invite others to look over our shoulders and see if we've made a mistake and other labs to see if they can reproduce the results in their own experiments”. This is precisely what they should have said, and any blowing of this out of proportion is due to the media, not the experimenters or the labs for whom they work.
If this is confirmed (which will probably take years, as experiments in the U.S. and Japan will have to be reconfigured to make similar measurements), the consequences will behuge, at least from a theoretical standpoint. If the neutrino is a tachyon, it means you can (in principle) build a “tachyonic antitelephone” which allows sending signals into one's own past light cone and thus potentially violate causality. For example, imagine sending a signal from a sensor which has detected a superluminal neutrino via another neutrino beam to the source which, if detected, causes the source to cancel sending the original neutrino. This signal, in the reference frame of the source, will arrive before the original neutrino was sent and cause it not to be sent. Then where did the neutrino which started the whole process originate?