In a paper appearing today on arXiv, Wie et al. have used the close coincidence of the time of arrival of gamma rays from GRBs and the detection of single 3-30 TeV neutrinos at the IceCube observatory, to say that the velocity difference between neutrinos and photons is no bigger than $$ | v-c | < 2.5\times 10^{-18} c.$$
Leaving aside whether these are genuine coincidences, this means the Lorentz factor of these neutrinos is $\gamma >4.4\times 10^{8}$, and for a neutrino energy of 3 Tev, means that the neutrino rest mass energy is $< 6.8$ keV.
The authors do not calculate this mass and do not comment on the neutrino rest mass. My question is surely we already know (from cosmological considerations) that the rest mass of neutrinos is (much) less than 6.8 keV so is this result in any way noteworthy, or am I missing a bigger picture?
Answer
Let's turn it around and ask a different question. Is there another direct measurement of the neutrino speed that sets such a tight limit? (Admittedly, the directness is contingent on the coincidence representing both a common source and negligible delay between the gammas and the nus at the source, but just taking that as a given arguendo.)
It might be significant in that sense even if the mass limit set is rather uninteresting.
And indeed, the authors write in the summary
We showed that significant improvements can be obtained on limits on the neutrino velocity, the violation of Lorentz invariance, and the accuracy of the EEP, by using the observed time delays between the neutrinos and photons.
They also discuss some other limits that are set by the measurement (I think they are taking the conditions above as a given here, though I haven't read in enough detail to be sure).
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