Since the original tachyon paper, Recami and Mignani, Recami, and later Cohen and Glashow and other theorists have suggested various ways to accommodate particles, including the adoption of nonstandard dispersion relations, which can avoid imaginary rest masses, but at the price (in the Cohen-Glashow case) of making the value of a particle’s rest mass dependent on the choice of reference frame. However, in these cases, there is no superluminal motion of particles or information with the possibility of a violation of causality, making them outside the scope of this review. A nice overview of these and other allowed types of superluminal motion can be found in Recami. Thus, Recami and others have considered localized X-shaped solutions to Maxwell’s equations, quantum tunneling through two successive barriers, and the apparent separation speed of quasars. There are, of course, cases of allowed superluminal motion. Moreover, tachyons have the weird property as Figure 1 shows of speeding up as they lose energy, and approaching infinite speed as E approaches zero. In this scheme, becomes a two-way infinite energy barrier, an upper limit to normal ( ) particles and a lower limit to hypothetical tachyons, thus allowing all matter to be divided into three classes with being positive, negative, or zero. Sudarshan and colleagues noted that if a particle was allowed to have a rest mass that was imaginary, or, one could use the usual formula to compute its real total energy, as long as the particle was never allowed to have For those concerned about the meaning of an imaginary rest mass, reminds us that only energy and momentum, by virtue of their direct observability and conservation in interactions, must be real and that the hypothetical imaginary rest mass particles offend only the traditional way of thinking.
Hypothetical faster-than-light particles, now known as tachyons, were first suggested in 1962 by Bilaniuk, Deshpande, and Sudarshan as a way to extend special relativity to the realm. The KATRIN experiment should serve as the unambiguous test of the model and its tachyonic mass state. Furthermore, this dark matter model is supported by several datasets: rays from the galactic center, and the Kamiokande-II neutrino data on the day of SN 1987A. Published empirical evidence for the model is summarized, including an interpretation of the mysterious Mont Blanc neutrino burst from SN 1987A as being due to tachyonic neutrinos having This possibility requires an 8 MeV antineutrino line from SN 1987A, which a new dark matter model has been found to support. A review is given of hypothetical faster-than-light tachyons and the development of the author’s model of the neutrino mass states, which includes one tachyonic mass state doublet.