Some, like Cohen and Glashow (http://arxiv.org/abs/1109.6562), only look at the average velocity and then explain to us why the neutrinos could not possibly travel that fast. That is a little silly, because we already know for many years, namely from supernova data, that neutrinos do not travel that fast over long distances. Sure, Glashow is Glashow, so to some this must be a “beautiful refutation of the OPERA result”, even if it ignores that precisely the OPERA results indicate neutrinos may not have had a constant velocity at all. As I will point out below, C&G should have thought deeper about the 10 nanoseconds of uncertainty in the data and not be hung up on the 60 nanoseconds early arrival time. (UPDATE: the newest data from OPERA further strengthen the discussion here. They are afflicted by a 25 ns "jitter" which is clearly separated from the 10 ns statistical error, which is explained in the new article "OPERA Confirms Faster Than Light Neutrinos And Indicates Ultra Superluminal Small Initial Jumps".)
We know already why the neutrinos could go faster and what new experiments this suggests, why it does not imply time travel or violates causality, and why it is somewhat expected for neutrinos. Now let us focus on what kind of superluminal velocity is indicated.
There are three reasons for expecting extremely high superluminal velocities over short distances. This can be argued looking at three aspects, namely
1) the totality of all neutrino experiments,
2) the expectation from modern emergent relativity, and
3) the small 10 nano second statistical deviation in the OPERA data.
1) Totality of all Neutrino Experiments
The MINOS experiment a few years back already found evidence that neutrinos might move faster than the speed of light c, namely at 1.000051 (+/- 0.000029) c. Supernova1987A in the Large Magellanic Cloud 168 thousand light-years away indicated at most a tiny increase over the speed of light. 23 neutrinos were seen over 13 seconds arriving 3 hours earlier than the light. In fact, this time difference is mostly due to the neutrinos carrying most of the nova’s energy (in a type II supernova) through the outer layers of the star while much visible light emerges only after the shock wave from the stellar core collapse reaches the surface of the star. OPERA is reported to indicate a velocity of only one part in 100000 above the speed of light.
Looking at all these experiments, the superluminal speed is going down along with the total distance over which the neutrinos have traveled. This indicates that they just traveled a short distance x faster than light, after which they slowed down and traveled further with a velocity just under the speed of light. The longer they travel afterward, the less the initial short distance x of initial superluminal propagation is noticeable as an increase of the average velocity v. The average v equals total travel time divided by the large total distance D, so it seems as if there is only a small increase over light speed.
2) Expectation from Emergent Relativity
I discussed at great length [see links above and the archive paper http://lanl.arxiv.org/abs/0912.3069] about so called emergent relativity. Einstein relativity has been confirmed to emerge naturally in several condensed state systems (graphene, super fluid helium, crystals’ dislocations). Relativity is an unsurprising symmetry in condensed states of matter. Particle physics (standard model, Higgs condensate, string theory) and gravity (Einstein-ether) look very much like as if they are emergent from an underlying, more fundamental condensate. Now you may hold the opinion that an Einstein-ether is complete nonsense, but even if such is ‘merely a similarity in the mathematical description’, you already agree with everything claimed here!
The limit velocity inside a condensate is the internally valid “light velocity c*”. If you look at the limit velocity in super fluid helium for example, it is the Landau limit that was first estimated to be 58 meters per second (the last measurement I looked at gives 46 m/s for 4HeII). Above this velocity, superfluidity breaks down and heat is dissipated, meaning that sound is generated. Sound travels with a velocity V* much faster than the Landau limit, namely several hundred meters per second or more, depending on pressure. Thus, a high V*= 10 c* is to be expected.
If we look at the limit velocity of fluid helium droplets outside of a superfluid helium bath, it is of course our light velocity c. This means that for this system, the limit velocity inside of it is about c* = 50 meters per second, while velocities outside can go up to V* = 299792458 meters per second, a factor of 10000000 higher!
Thus, if this (namely condensed state physics emergent gravity) is any indication at all; if our universe is describable as a condensed state, you should expect superluminal phenomena with V = 10 c. If for example our universe has some sort of effective outside like extra dimensions (as string theory indeed claims), you should not be entirely surprised if superluminal phenomena with amazing velocities V = 10000000 c are possible! By the way: Such could be involved in the Cosmic ray paradox where protons appear with energies far above the Greisen-Zatsepin-Kuzmin Limit.
3) The 10 Nanosecond Uncertainty in the OPERA Data
The third indication of that the phenomenon indicated by OPERA is one that has many times the speed of light (but only for about 20 meters around the neutrino creation) comes straight from the data.
Assuming, as is standard, that neutrinos usually travel at just under the speed of light c, and having T denote the 60 nanoseconds early arrival measured at OPERA, the initial distance over which superluminal propagation with velocity V could have occurred is simply
x = c * T / [ 1 - (c/V) ]
At high superluminal velocity V above 10 c, the approximation x = c * T suffices.
V = 10 c results in x = 20 meters; V = 10000000 c gives x = 18 meters. Note that the two meters of difference here is close to the uncertainty in the data, which is Del T = 10 nanoseconds and thus also corresponds to about three meters. So, depending on the detailed assumptions about the perhaps involved mechanisms, it may be that if for example neutrinos were to splash around with a wide variety of velocities around 1000 c, some maybe 10000 c, some only 100 c, which is obviously a huge difference, x would be, surprise surprise, the same 18 meters!
This is different at low superluminal velocities: V = 1.2 c gives x = 108 meters, while V = 1.1 c gives already almost 200 meters, almost double the distance. Any smaller V leads to rapidly larger results for x. In other words, if you assume any distribution of velocities around a small average V, the standard distribution around x should be very large, namely hundreds of meters, kilometers, ... .
However, the error in the data is only 10 nanoseconds. At an assumed small average V = 1.2 c for example, if the uncertainty were only due to statistical noise, 10 ns will translate into a standard deviation of merely Del x = 18 meters. Do not get confused by the coincidence of having the same value of 18 m; focus instead on that these 18 meters of uncertainty Del x are much smaller than the difference between 108 meters and 200 meters! The crux is that adding even a small variation of V would spread out the data much more than observed.
At the small superluminal velocities that Cohen and Glashow for example assume, a ridiculously small variation around V is implied. So, basically they "proved" that the OPERA result is a systematic error afflicting a sub-luminal speed by assuming that it is a systematic error afflicting a sub-luminal speed. If you do not assume what you want to prove right from the start, if you take it as the statistical error of a superluminal velocity like the OPERA team's data analysis tells us, the result is radically different.
Thus, depending again on many other assumptions about the details of what is actually going on of course, the relatively small statistical error in the data hints at a very high velocity V around or far above 10 c over a small distance x, consistent with the previous two considerations. This is all more clearly perhaps explained with taking the 25 ns "jitter" of the new OPERA data into account here.