Superluminal neutrinos 
I was quite surprised to read this all over the news today:

Elusive, nearly massive subatomic particles called neutrinos appear to travel just faster than light, a team of physicists in Europe reports. If so, the observation would wreck Einstein's theory of special relativity, which demands that nothing can travel faster than light.

—source
Apparently a CERN/Gran Sasso team measured a faster-than-light speed for neutrinos.


*

*Is this even remotely possible?

*If so, would it be a real violation of Lorentz invariance or an "almost, but not quite" effect?


The paper is on arXiv; a webcast is/was planned here.
News conference video here
 A: Suppose this is real, that the neutrinos arrive very slightly faster than light would through the vacuum. Wouldn't that point to there being a slightly higher c which actually limits speeds, and some slight slow-down for light from this maximum due to interactions of the electromagnetic field with other particles, including virtual particles?
After all, you can move an electron faster than a photon in glass, and we don't call it the end of relativity, we call it Cherenkov radiation.
So the definition of refractive index might need adjusting, but effectively the vacuum has a non-zero refractive index, or rather the vacuum is not entirely empty. Which we know. 
It makes sense that a neutrino is not subject to the same interactions, given its famed reluctance to interact with anything. Perhaps it is just an indication that the particles in a vacuum are more likely to be electromagnetic-interacting than weak-interacting.
Or am I labouring under a false premise? Is the speed of light in a vacuum already adjusted for virtual particle interactions?
A: 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.
A: You have a few longer answers which were already updated, but here is a concise statement of the situation in mid-2014:


*

*An independent measurement by the ICARUS collaboration, also using neutrinos traveling from CERN to Gran Sasso but using independent detector and timing hardware, found detection times "compatible with the simultaneous arrival of all events with equal speed, the one of light."

*In an edited press release (and probably in the peer-reviewed literature as well), all four of the neutrino experiments at Gran Sasso report results consistent with relativity.

*The mumblings that begin a few months after the initial report, that a loose cable caused a timing chain error, have been accepted by the experimenters.  Frédéric Grosshans links to a nice discussion by Matt Strassler
which includes this image:

You can clearly see that the timing offset was introduced in mid-2008 and not corrected until the end of 2011.
It's important to remember the scale of the problem here.  In vacuum, the speed of light is one foot per nanosecond.  In copper/poly coaxial cable it's slower, about six inches per nanosecond, and in optical  fiber it's comparable.  A bad cable connector can take a beautiful digital logic signal and reflect part of it back to the emitter, in a time-dependent way, turning the received signal into an analog mess with a complicated shape.  And a cable can go bad if somebody hits it the wrong way with their butt while they are working in the electronics room.
(I actually had something similar happen to me on an experiment: I had an analog signal splitter "upstairs" that sent a signal echo back to my detectors "downstairs", and a runty little echoed pulse came back upstairs after about a microsecond and got processed like another event.  I wound up spending several thousand dollars on signal terminators to swallow the echo downstairs.  It was an unusual configuration and needed unusual termination hardware and I must have answered the question "but couldn't you just" a hundred times.)
Gran Sasso is an underground facility for low-background experiments — the detectors can't see GPS satellites directly, because there's a mountain in the way, and their access to the surface is via a tunnel whose main purpose is to carry traffic for a major Italian motorway.  I'm quite impressed that they had ~100 ns timing resolution between the two laboratories; the "discovery" came about because they were trying to do ten times better than that.
As an experimentalist I don't begrudge the OPERA guys their error at all.  I'm sure they spent an entire year shitting pineapples because they couldn't identify the problem.  When they finally did release their result, they had the courage to report it at face value.  The community was properly incredulous and the wide interest prompted a large number of other checks they could make.  Independent measurements were performed.  An explanation was found.  Science at its best.
A: There are strong reasons for disbelieving this result.
[This paragraph is disproved  by the Nov. 17 result.] It uses an experimental design that was never intended for this purpose, and that is inherently poorly suited to it; the beam pulses were 10,000 ns wide, and the shift they claim to have measured is only 60 ns. This means that the shift can only be detected statistically, and it makes the result extremely vulnerable to unanticipated systematic errors, e.g., correlations between the time of emission of the neutrinos and their energy (which strongly affects the efficiency of detection) or the direction of emission. They did another run at the end of October, with beam pulses 1-2 ns wide. That's the correct design if you want to measure the speed of the neutrinos reliably. They should have simply waited until after they had those data before announcing their results. (In fact, five senior members of the collaboration did not put their names on the paper.) I have a bet running with a colleage, for a six-pack of Fat Tire, that the new run will show that the original result was bogus. The result may be announced as soon as November or December. [The result was announced Nov. 17, and I lost my six-pack.]
Another reason to disbelieve it is that there are strong and fairly model-independent reasons to believe that it cannot be correct. A superluminal neutrino beam would have lost a lot of its energy via radiation, but a measurement by another detector shows that this was not the case: http://arxiv.org/abs/1110.3763 Superluminal motion for neutrinos would also cause superluminal motion for electrons, which is contrary to observation  http://arxiv.org/abs/1109.5682 , and it would also have caused a suppression of pion decay, so that the beam could never have been produced in the first place http://arxiv.org/abs/1109.6630 . All of this holds regardless of the details of the model. E.g., it holds both for tachyonic neutrinos without a preferred frame and for models in which neutrinos are not tachyonic and there is a preferred frame.
Yet another reason for disbelief is that the velocity of propagation of neutrinos has been measured to much higher precision by other techniques, so if you want to believe the OPERA result, you have to posit a very strange energy-dependence of the velocity.
A: •Is this even remotely possible?
Well yes, of course it's possible in the same way that it's possible that invisible neutrino fairies are messing around with the neutrinos underground and hence causing havoc with the mental health of physicists around the world. It's just... unlikely, very unlikely, just as the 4-sigma evidence for new CP violation in like-sign dimuons was possible, only to fall flat on its face when ATLAS and CMS failed to see the same thing. But, it's still possible! Even so, let's focus on what's more likely: There are no neutrino fairies, and the conflict between data and special relativity lies with >> 6-sigma likelyhood of it being an error with the experiment.
•If so, would it be a real violation of Lorentz invariance or an "almost, but not quite" effect?
It would be one hell of a kick-up-Einsten's-backside violation of Lorentz invariance. All particles show the same speed limit as light, yet neutrinos with a rest mass greater than light possess a larger speed limit?
A: 
  
*
  
*Is this even remotely possible?
  

Well... "possible," yes, but kind of like how tunneling through a brick wall is "possible": while you can't definitively prove it impossible, you'd feel pretty safe saying "this will never happen." Relativity is really well-tested, and it's really hard to conceive of a way that neutrinos could travel faster than light without it having other consequences that we would have discovered by now. That being said, I don't know the field inside-out and I'm sure some theorist has come up with some wacky idea that allows it. I asked another question that might come up with something.

  
*
  
*If so, would it be a real violation of Lorentz invariance or an "almost, but not quite" effect?
  

If the results from OPERA are accurate, this effect would be a full-blown real Lorentz violation, not just an apparent effect like Cerenkov radiation or astronomical superluminal motion. That's why everyone is so excited about it. (Unless the neutrinos are tachyons; in that case, I guess Lorentz invariance is technically still intact, but the observation of a tachyon would be equally big news.)
The setup of CERN and OPERA is conceptually very simple, basically just two observers located a known distance apart with synchronized clocks. It's a direct measurement of average velocity. There's no complicated theoretical analysis that needs to be done to determine whether the speed of light was exceeded. Either they are wrong about either the distance (mismeasurement, or there is a spacetime "rift" within the Earth :-P) or the time (clock synchronization error or drift), or they have actually discovered superluminal neutrinos.
A: According to Dr. Phil Plait, there's a rumour that it's been a faulty connection. In summary: nothing is wrong with the calculation, the theoretical assumptions, rotation of the Earth, etc... A hardware problem caused the 60 ns time gap.
It's still gossip, so take this with abundance of caution, but here's what he had to say:


According to sources familiar with the experiment, the 60 nanoseconds discrepancy appears to come from a bad connection between a fiber optic cable that connects to the GPS receiver used to correct the timing of the neutrinos’ flight and an electronic card in a computer. After tightening the connection and then measuring the time it takes data to travel the length of the fiber, researchers found that the data arrive 60 nanoseconds earlier than assumed. Since this time is subtracted from the overall time of flight, it appears to explain the early arrival of the neutrinos. New data, however, will be needed to confirm this hypothesis.


—source
A: UPDATE 2011-10-15
This phenomena may have been explained. The crux of the problem had to do with differing reference frames - the distance traveled according to the satellites which measured the time was different from the distance traveled according to us on earth. If you're going to measure speed (distance / time), you have to get the distance and time both from the same reference frame. We were getting distance from our reference frame and time from the (very fast) satellite's reference time.
This article explains it in a very accessible way:

To understand how relativity altered the neutrino experiment, it helps to pretend that we're hanging out on one of those GPS satellites, watching the Earth go by underneath you. Remember, from the reference frame of someone on the satellite, we're not moving, but the Earth is. As the neutrino experiment goes by, we start timing one of the neutrinos as it exits the source in Switzerland. Meanwhile, the detector in Italy is moving just as fast as the rest of the Earth, and from our perspective it's moving towards the source. This means that the neutrino will have a slightly shorter distance to travel than it would if the experiment were stationary. We stop timing the neutrino when it arrives in Italy, and calculate that it moves at a speed that's comfortably below the speed of light.
"That makes sense," we say, and send the start time and the stop time down to our colleagues on Earth, who take one look at our numbers and freak out. "That doesn't make sense," they say. "There's no way that a neutrino could have covered the distance we're measuring down here in the time you measured up there without going faster than light!"
And they're totally, 100% correct, because the distance that the neutrinos had to travel in their reference frame is longer than the distance that the neutrinos had to travel in our reference frame, because in our reference frame, the detector was moving towards the source. In other words, the GPS clock is bang on the nose, but since the clock is in a different reference frame, you have to compensate for relativity if you're going to use it to make highly accurate measurements.

The original paper publishing these findings is here: Times of Flight between a Source and a Detector observed from a GPS satelite.

Original Post
Sources: [1] (Associated Press), [2] (Guardian.co.uk), [3] (Original Publication - Cornell University)

Scientists around the world reacted with cautious shock on Friday to results from an Italian laboratory that seemed to show that certain subatomic particles can travel faster than light.
The journey would take a beam of light around 2.4 milliseconds to complete, but after running the Opera experiment for three years and timing the arrival of 15,000 neutrinos, the scientists have calculated that the particles arrived at Gran Sasso 60 billionths of a second earlier, with an error margin of plus or minus 10 billionths of a second. The speed of light in a vacuum is 299,792,458 metres per second, so the neutrinos were apparently travelling at 299,798,454 metres per second.

Ignoring the boilerplate media hype about the possibilities of time travel and alternate dimensions - I'm looking for academic sources that might suggest how this could be true, or alternatively, how this discrepancy could be accounted for.

I read the published article, Measurement of the neutrino velocity with the OPERA detector in the CNGS beam, with their findings. It looks like they took an insane amount of care with their measurement of distance and time.
One of the most common skepticism of people who no nothing about the experiment is stuff like:

You might worry about[...] have they correctly accounted for the time delay of actually reading out the signals? Whatever you are using as a timing signal, that has to travel down the cables to your computer and when you are talking about nanoseconds, you have to know exactly how quickly the current travels, and it is not instantaneous. [2]

This experiment doesn't use that sort of 'stopwatch' timing mechanism though. There is no 'T=0', and no single firing of neutrinos. What is detected is watermark patterns in the steady stream of particles. The streams at the input and output are time stamped using the same satellites and any position along each stream has a precise time associated with it. By identifying identical patterns at input and output streams, they can identify how long it took particles to travel between the points. [1]

As for distance, they use GPS readings to get the east, north, and altitude position along the path travelled to great precision. So much so that they even detect slow earth crust migration and millimetres of changes in distance between source and destination when something like an earthquake occurs. When your particles are travelling on the scale (730534.61 ± 0.20) metres, this is more than enough precision:

It's going to take a lot more than grassroots skepticism to think of what could have caused this discrepancy. I've seen suggestions such as the gravity of the Earth being different along the path of the neutrinos, which warps space/time unevenly. The neutrino might not actually be travelling as far as they think if space/time is contracted at one or more points along the path where gravity varies.
Anyway, I'll be interested in seeing how it pans out. Like most scientists, my guess is an unaccounted for systematic error (because they definitely have statistical significance and precision on their side) that has yet to be pointed out, but it probably won't take too long with all the theoretical physicists that will be pouring through this experiment.
A: May be the case that this problem has to do with the «one-way» light speed and the referential that is used. 
Afaik the only known measures of the c are done in a «two-way» version (mean value in a closed path). 
When a photon is released in space it starts its journey at c speed independently of the source and of the receiver. The CMB referential clearly is the only referential to «observe» the light as isotropic. As the Earth moves we observe a dipole, and in different directions we measure different wavelengths for the same physical object (photon).

This paper (Cosmological Principle and Relativity - Part I) analyses the anisotropy of light speed for a moving observer.   
Fig.3 and eq. 18, pag 14 
The one-way light speed is : $c_{A}^{r}=\frac{c_{0}}{1+V/c_{0}\cdot\cos\phi_{A}}$  
Using $c_0=299792.458$ Km/s is two-way light speed, $V\;$  is the speed of the lab in relation to the CMB: $V=V_{SS}+V_E$=369$\pm$30 km/s  (data from here)
  gives the max value of $\frac{\left|c_{V\pm\delta V}-c_{V}\right|}{c_{V}}\cdot10^{5}$=10.2.
All experimental measures of |v-c|/c are within this limit.  
Anyway Einstein is correct.  
I suspect that the syncronization used in the GPS is in the same as in the above paper and not as Einstein did.
In the pic  Sat A must be synchronized with C at the same time thru the shortest red path and thru the longest blue path. At the same time B is in sync with C thru other paths with different lengths. IMO this is only possible if they are synchronised as in the above paper (instant observer) and not in the Einstein way that only considers one path  between the observer and any other point (Synchronisation around the circumference of a rotating disk gives a non vanishing time difference that depends on the direction used). 
Anyway Einstein is correct, and the neutrinos are not superluminal.
A careless reading of the paper might make you think that it is contrary to Einstein, but it is not.
A: Did anybody catch this?

Speedy neutrino result may be due to instrument glitch

http://www.newscientist.com/blogs/shortsharpscience/2012/02/speedy-neutrino-result-may-be.html

Loose Cable Explains Faulty 'Faster-than-light' Neutrino Result 

http://www.space.com/14654-error-faster-light-neutrinos.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+spaceheadlines+%28SPACE.com+Headline+Feed%29
A: I do not agree with the superluminal neutrinos news for very simple reasons. The difference they found with respect to the speed of light is very small, so some errors in the calulations must have been made. Neutrino is not faster than light.
The Special Theory of Relativity (STR) of Einstein, through the principle of the speed limit, makes the magnetic force come from the electric one and the magnetic force is an electric force, as physicists know; an easy demonstration of that can be found in chapter 3 of my file at the following link (also English inside):
http://www.fisicamente.net/FISICA_2/UNIFICAZIONE_GRAVITA_ELETTROMAGNETISMO.pdf
If you get rid of the speed limit principle, the magnetic field cannot exist anymore.
Moreover, as c=1/square root of(epsilon x µ), if you change c with a c'>c, then you have to accept a µ'<µ, so you have to accept different intensities of magnetic fields from a given electric current, so you have to get rid of the electromagnetism, but it's describing so well the currents, the fields, the real world etc. Therefore, there's a mistake in the computation of the speed of neutrinos, in the calculations on the run lenght, in the interaction time calculations, during the generation and also the detection of those evanescent particles!
(another interesting file, also related to this subject):
http://www.mednat.org/new_scienza/strani_legami_numerici_universo.pdf
A: There was a very reliable report of finding a monopole in 1980s by Caberera(?). There was no other explanation of the glitch in the arrangement of the SQUID, but a capture of one monopole. That never repeated. Never confirmed. Never rejected as being a fake effect. I believe this question needs a couple of years more investigation. A question of physics should be repeatedly be confirmed before a postulate or an inference can be derived. Even after that derivation a sensitive experiment should be perceived to break it through further. 
A: I will bet all my beans into the idea that they didn't estimate the spacetime curvature inside the earth well and over the beam trajectory, and what they actually discovered is a great way to measure space-time inside the Earth.
EDIT it seems this effect is settled to be a missing correction due to sattelite-speed terms: http://arxiv.org/abs/1110.2685. Until i hear or read any counter-claims to that paper, i'll consider this to be a settled matter
A: This is not a true answer... none is knowing the explanation, so far.
However, I will post this "consideration" anyway...
Now, November 21, 2011, with 3ns pulses, the new value for the "missing time" is 62.1ns +/-3.7 (only 20 events).
My answer is only a "would-be" consideration that, if read by the experimenters, could give them some "debug" clues. 
First of all my assumptions:
it is unlikely that the neutrinos go superluminal or SR is not holding true anymore


*

*it is unlikely that the distance is measured incorreclty

*it is unlikely that the GPS setup/usage is incorrect

*it is also unlikely that the light speed has been measured incorreclty so far. 
Then two hypotesis:


*

*the "missing time" is 62.5ns (compatible with 62.1 +/-3.7ns)

*the electronics involved in the time measurement has some clock domain running at 16MHz.
Of course the conclusion would be to investigate if there is one circuit running on one clock pulse less than expected by design / testing.
