For the context, the notion of superluminal neutrinos have been floating around for at least a couple of decades, ever since the tritium decay experiments, but they are mostly pushed by a few Polish physicists, like Jacek Ciborowski, with little interest from elsewhere.
This issue is rather interesting from the Bayesian point of view: the priors for superluminal neutrinos are so low, the evidence for them, even when taken all at once, like in the paper you cite, is still not compelling enough to assign high credence to the model. And the aftermath of the OPERA experiment analysis shows that the experimental data can deceive us in rather unexpected ways, even if collected with extreme diligence.
Now, if there was a clear replicable way to show that neutrino travel superluminally, the situation would change. As it currently stands, Ehrlich is rather biased, having written several pro-FTL neutrino papers on the issue, including one withdrawn from arXiv after the issues with OPERA came to light, and so his writings do not increase the credence of the FTL side much.
This is not to say that neutrino hold no mysteries: just the fact that they are always left-handed is one, and the suggested seasaw mechanism predicts a very massive but yet unobserved partner of the very light observed neutrino. FTL neutrinos, on the other hand, would not need a heavy partner. Too bad they would require a major revision of several well-tested theories.
This issue is rather interesting from the Bayesian point of view: the priors for superluminal neutrinos are so low, the evidence for them, even when taken all at once, like in the paper you cite, is still not compelling enough to assign high credence to the model.
Basically agreement here although I think that some degree of disagreement may show up when one unpacks "high credence." It would seem to me that the evidence is sufficient enough to merit detailed investigation, especially because many of the obvious things to do are experiments which will provide other interesting data. At minimum, this is another reason for careful attention to the neutrino distribution the next time there's a supernova as close as SN 1987A.
As it currently stands, Ehrlich is rather biased, having written several pro-FTL neutrino papers on the issue, including one withdrawn from arXiv after the issues with OPERA came to light, and so his writings do not increase the credence of the FTL side much.
I'm not sure I agree with this. In this context, most of the paper's analysis is pretty straightforward so I don't think his biases are that relevant to evaluating it. I'd still put a higher probability on some sort of systematic error going on here than on FTL neutrinos (by a wide margin), but that's for essentially the same reasons you mentioned (the hypothesis having a verylow prior) together with the empirical problems like SN 1987A.
with an apparent square of the mass being close to -0.11 electron-volts.
It's square electron-volts, since you're measuring square of mass.
The problem for FTL neutrinos is that if the neutrinos were even a tiny bit faster than the speed of light they should have arrived much much earlier.
Wouldn't the same logic say that if they were even a tiny bit slower than the speed of light they should have arrived much later? It gives an upper bound on the magnitude of the mass. It's the same upper bound regardless of if the mass is real or imaginary.
Second, there's reason to believe that tachyons if they existed would emit Cherenkov-like radiation.
How could they emit light? They have no electric charge.
Followup: Looking at this more, you are correct about the upper v. lower bound, and given the high energy levels in the paper, one expects it to be so close to the speed of light (whether the mass is real or imaginary) that the SN 1987A data isn't relevant.
It's square electron-volts, since you're measuring square of mass.
Thanks. Corrected.
Wouldn't the same logic say that if they were even a tiny bit slower than the speed of light they should have arrived much later? It gives an upper bound on the magnitude of the mass. It's the same upper bound regardless of if the mass is real or imaginary.
I'm not sure completely. My impression is that there's a lack of symmetry here but it isn't clear to me where it arises.
Second, there's reason to believe that tachyons if they existed would emit Cherenkov-like radiation.
How could they emit light? They have no electric charge.
Hence the term "Cherenkov-like". The Glashow paper shows a mechanism where something very similar to Cherenkov radition occurs with tachyons even without electric charge.
Relevant predictions on PredictionBook http://predictionbook.com/predictions/54627 and http://predictionbook.com/predictions/54628.
I think you'll have trouble finding people who will take the other side on that if the odds are even.
That the electron neutrino has imaginary mass or that it actually is a tachyon in the classical sense of going faster than the speed of light? Strictly speaking, this is evidence more for 1 and not 2. If I can get either or both one side then I'll take 99 to 1.
In 2012, a large amount of attention was given to the OPERA experiment's apparent sighting of faster than light neutrinos. This turned out to be erroneous due to a faulty cable, and similar experiments confirmed the same results. However, while this was occurring, a distinct point was made: some attempts to determine the mass of the electron neutrino(one of the three known neutrino types) found that the square of the mass was apparently negative, which would be consistent with an imaginary mass and thus electron neutrinos would be tachyons. While little attention was paid to at the time, a new paper by Robert Ehrlich looks again at this approach. Ehrlich points out that six different experimental results seem to yield an imaginary mass for the electron neutrino, and what is more, all the results are in close agreement, with an apparent square of the mass being close to -0.11 electron-volts squared.
There are at least two major difficulties with Ehrlich's suggestion, both of which were also issues for OPERA aside from any philosophical or metaconcerns like desire to preserve causality. First, it is difficult to reconcile with Ehrlich's suggestion is one of the same data points that apparently tripped up OPERA, that is the neutrinos from SN 1987A neutrinos. In the SN 1987A supernova (the first observed in 1987 hence the name), the supernova was close enough that we were actually able to detect the neutrinos from it. The neutrinos arrived about three hours before the light from the supernova. But that's not evidence for faster than light neutrinos, since one actually expects this to happen. In the standard way of viewing things, the neutrinos move very very close to the speed of light, but during a core-collapse supernova like SN 1987A, the neutrinos are produced in the core at the beginning of the process. They then flee the star without interacting with the matter, whereas the light produced in the core is slowed down by all the matter in the way, so the neutrinos get a few hours head start.
The problem for FTL neutrinos is that if the neutrions were even a tiny bit faster than the speed of light they should have arrived much much earlier. This is strong evidence against FTL neutrinos. In the paper in question, Ehrlich mentions SN 1987A in the context of testing his hypothesis in an alternate way using a supernova and the exact distribution of the neutrinos from one but doesn't discuss anywhere I can see the more basic issue of the neutrinos arriving at close to the same time as the light. It is conceivable that electron neutrinos are the only neutrinos which are tachyons, and if this is the case, then it seems like neutrino oscillation (the tendency for neutrinos to change types spontaneously) could account for part of what is going on here, but having only some types of neutrinos be tachyons would possibly lead to other problems.
Second, there's reason to believe that tachyons if they existed would emit Cherenkov-like radiation. Andrew Cohen and Sheldon Glashow wrote a paper showing that this would be a major issue in the context of OPERA. Ehrlich seems to claim in the new paper that this shouldn't be an issue in the context he is working in, but does not provide any reasoning. Hopefully someone who is more of an expert can comment on what is going on there.
This seems like potentially stronger evidence for tachyonic neutrinos than the OPERA experiment since this is the same result from a variety of different experiments all giving very close to the same results.