U. D. Jentschura, B. J. Wundt
Consider a gedanken experiment in which a massive left-handed neutrino, traveling on an autobahn at a speed of v=0.999c is overtaken by a tuned-up Cagiva V-Raptor 1000 traveling at a speed of 0.999999c. The biker, looking back, would see a right-handed neutrino. Unless one invokes exotic mechanisms like a sterile neutrino, this "autobahn paradox" implies that a massive subluminal (tardyonic) neutrino necessarily has to be a Majorana particle, i.e, equal to its own antiparticle. In turn, this would require us to assign the same lepton number to charged leptons and antileptons, essentially voiding the concept of lepton number. By contrast, an infinitesimally superluminal (tachyonic) neutrino is not equal to its own antiparticle and allows us to assign proper lepton number, just as if the neutrino were a Weyl particle. Furthermore, if Lorentz symmetry holds, then an infinitesimally tachyonic neutrino remains superluminal upon Lorentz transformation, which implies that it is impossible to overtake it in a gedanken experiment. Consistently, right-handed neutrino and left-handed antineutrino states have recently been shown to acquire negative norm under the assumption of an ever-so-slightly tachyonic neutrino, and it would thus not be necessary to invoke a seesaw mechanism. An infinitesimally superluminal neutrino does not necessarily violate causality, as has been discussed in the literature. This paper is devoted to an illustrative discussion of related questions. Under certain conditions, an infinitesimally superluminal neutrino could appear to solve at least as many problems as it raises.
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http://arxiv.org/abs/1206.6342
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