Now that the superluminal neutrino fiasco is winding down, I'm interested in seeing if I can consolidate what I know about tachyons. One of the things I learned from following the OPERA debacle is that you can have tachyons without Lorentz violation, or you can have FTL particles (still called tachyons?) with Lorentz violation. I guess it's been known for a really long time that tachyons can't be charged. This paper http://arxiv.org/abs/1109.5682 by Giudice, Sibiryakov, and Strumia talks about Lorentz-violating Lagrangians for neutrinos, and says that they would cause the superluminality to extend to electrons and muons, since they couple to neutrinos through the weak interaction. The Cohen-Glashow model, http://arxiv.org/abs/1109.6562 , also says you'd get Cherenkov-like radiation from superluminal particles coupling to the weak force. This paper also seems to assume Lorentz violation. Do these results extend to tachyonic particles in models without Lorentz violation? In other words, is there some kind of general theorem that says that tachyons not only can't be charged, but can't participate in weak interactions without running into these other problems? What happens with tachyons that couple to the strong force? Are these also ruled out because they would make protons superluminal via the Giudice mechanism? Re gravity, I guess the equivalence principle requires that tachyons, if they exist, *do* interact gravitationally. Baez has this nice discussion of tachyons: http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html He claims that the tachyonic telephone can't exist, based on the behavior of the Klein-Gordon equation. This confuses me, because when the error in the OPERA result hadn't been found yet, plenty of theorists were running around building theories in which tachyonic neutrinos were propagating information faster than c from CERN to Gran Sasso. How did they avoid the constraint referred to by Baez?