Last (?) Edit: The "problem" is solved: it was mainly a problem in the timing chain, due to a badly screwed optical fibre. A high level description of the problem is given here and a more detailed explanation of the investigation is here.
List of possible systematic biases
I thought it might be a good idea to list the possible systematic biases which could lead xkcd's character to win his bet. As many physicists (including, I guess, many people from the OPERA collaboration), I think it will end like the Pioneer anomaly. Of course, the current list only contains biases which are unlikely, but less unlikely than a causality violation.
Location errors and clocks drifts
The arXiv paper studied them, and seem to exclude it. The distance seems to be known within 20 cm and the synchronisation seems to be within 15 ns (6.9 statistical and 7.4 systematic). If this would however end up to be the explanation, it would be quite boring.
Update: Rumors seems to tell that the boring explanation is the good one.
Not the same neutrinos detected
The neutrinos are emitted on a 10.5 µs window, 175 times longer than the observed effect. It might be possible that the neutrino emitted early are not exactly the same as the one emitted late. Neutrino oscillation might, for example, then make early neutrino more detectable by the distant detector.
However, the detectors were built to measure the oscillation, so I guess that the OPERA collaboration thought about it, and rejected it for whatever reason. I suppose an explanation along these lines would mean interesting new particle physics.
Update: This possibility excluded by a new experiment with 3 ns pulses.
Errors in the statistical timing analysis
The timing itself is based on a quite elaborate statistical analysis. Furthermore, the pulses are quite long (10 μs), so an error in this analysis could easily be of the good order of magnitude.
Update: This possibility excluded by a new experiment with 3 ns pulses.
Before I answer, a couple caveats:
- As Adam said, the universe isn't going to start behaving any differently because we discovered something.
- Right now it seems much more likely (even by admission of the experimenters) that it's just a mistake somewhere in the analysis, not an actual case of superluminal motion.
Anyway: if the discovery turns out to be real, the effect on theoretical physics will be huge, basically because it has the potential to invalidate special relativity shows that special relativity is incomplete. That would have a "ripple effect" through the last century of progress in theoretical physics: almost every branch of theoretical physics for the past 70+ years uses relativity in one way or another, and many of the predictions that have emerged from those theories would have to be reexamined. (There are many other predictions based on relativity that we have directly tested, and those will continue to be perfectly valid regardless of what happens.)
To be specific, one of the key predictions that emerges out of the special theory of relativity is that "ordinary" (real-mass) particles cannot reach or exceed the speed of light. This is not just an arbitrary rule like a speed limit on a highway, either. Relativity is fundamentally based on a mathematical model of how objects move, the Lorentz group. Basically, when you go from sitting still to moving, your viewpoint on the universe changes in a way specified by a Lorentz transformation, or "boost," which basically entails mixing time and space a little bit. (Time dilation and length contraction, if you're familiar with them) We have verified to high precision that this is actually true, i.e. that the observed consequences of changing your velocity do match what the Lorentz boost predicts. However, there is no Lorentz boost that takes an object from moving slower than light to moving faster than light. If we were to discover a particle moving faster than light, we have a type of motion that can't be described by a Lorentz boosts, which means we have to start looking for something else (other than relativity) to describe it.
Now, having said that, there are a few (more) caveats. First, even if the detection is real, we have to ask ourselves whether we've really found a real-mass particle. The alternative is that we might have a particle with an imaginary mass, a true tachyon, which is consistent with relativity. Tachyons are theoretically inconvenient, though (well, that's putting it mildly). The main objection is that if we can interact with tachyons, we could use them to send messages back in time: if a tachyon travels between point A and point B, it's not well-defined whether it started from point A and went to point B or it started from B and went to point A. The two situations can be transformed into each other by a Lorentz boost, which means that depending on how you're moving, you could see one or the other. (That's not the case for normal motion.) This idea has been investigated in the past, but I'm not sure whether anything useful came of it, and I have my doubts that this is the case, anyway.
If we haven't found a tachyon, then perhaps we just have to accept that relativity is incomplete. This is called "Lorentz violation" in the lingo. People have done some research on Lorentz-violating theories, but it's always been sort of a fringe topic; the main intention has been to show that it leads to inconsistencies, thereby "proving" that the universe has to be Lorentz-invariant. If we have discovered superluminal motion, though, people will start looking much more closely at those theories, which means there's going to be a lot of work for theoretical physicists in the years to come.
Best Answer
Yes a few people wrote papers looking a tachyonic/superlumminal in the 1990s after experiments measuring the mass squared of a neutrino from tritium decay. Tritium decays with a fixed total energy into a neutrino an electron and helium-3, by the measuring the maximum energy of the electron and subtracting, you get the minimum energy of a neutrino and thus its mass. It turned out the neutrino actually seemed to have negative squared mass, (tachyonic), but this was totally within the error bars,e.g. m_{nu}^{2}=-0.67+/- 2.53 {eV}^{2}, at the Troitsk experiment. The error bar is much bigger than the data point, so it was pretty much ignored. But a number of papers where written, and several other experiment also showed negative squared mass data points.
Neutrinos have also been looked at for tachyonic behaviour because of the chiral nature. Since there only left handed neutrino, and right handed anti-neutrino (that a known so far, experiment might find sterile revered version of the known ones). This means that when the vacuum creates a neutrino anti-neutrino pair, back to back emission so opposite momentum, that the total has a spin 1. For any non-chiral particles the spin could be zero, meaning that the vacuum would decay, if the particle could exist with negative energy. But the chiral nature of the neutrino means this can't happen, and the vacuum is safe even with tachyonic neutrinos.
The small tachyonic masses (can I say measured, that would be wrong, clearly any random measurement around zero, would find a negative number half the time), however don't match the -(120 MeV) squared needed to fit the OPERA result using tachyonic neutrino, nor can it be the result of oscillating to a much more negative massed sterile state with such a large imaginary mass, since the faster than light measurement was for all the recorded particles.