Here’s a link to an old web page which credibly addresses the tachyonic neutrino hypothesis:
It goes back a way (1992), but gives the gist of some of the real (i.e., experimental) physics issues involved in dealing with neutrinos. Cramer has written other columns e.g., on whether there is a consistent theory of tachyons. Don’t agree with everything he writes. E.g., he thinks the neutrino is “probably not” a tachyon, but how do you come up with such a probability other than from experiment? Tritium beta decay experiments from the 90’s were at least 96.5% in the negative mass squared regime, and later experiments were appearing to boost this number even closer to 100% when people stopped calculating it. Also, he didn’t mention the Mont Blanc neutrinos (flavour not known) that were received 4.7 hours earlier than the Kamiokande II and IMB neutrinos pulses (the Kamiokande burst consisted entirely of electron neutrinos). The Mont Blanc signal has been labelled a “highly improbable spurious burst”, but the only reason given for this is that its existence doesn’t fit the most plausible model of supernova core collapse. If the Mont Blanc signal consisted of tachyonic muon neutrinos, then they could have beaten the electron neutrinos & a back-of-the-envelope calc. shows the tachyonic mass parameter to be around 1 keV, which is well within experimental bounds of m^2 measurements given by other experiments. Also, this would be independent of the supernova model since it involves a different assumption about the dynamics of the neutrino. OK, there’s a lot more to it than that, since one needs a valid quantum field theory (QFT) of tachyons, but that’s what I’ve been cogitating on since 1998 & I think there is one which is so far working. At least from what I’ve seen, I’m pretty doubtful that a direct, rigorous proof of nonexistence of every kind of tachyonic QFT will ever be found.