Abstract
The tachyon problem is considered on the basis of the kinematics of the extended hyperbolic space of relativistic momenta, including a two-sheet hyperboloid of momenta of subluminal particles, a cone of massless particles propagating at the speed of light, and a one-sheet hyperboloid of momenta of superluminal particles. The concept of mutually polar four-dimensional momenta is introduced. It is shown that the four-momentum corresponding to infinite velocity is polar to the rest frame on the upper part of a two-sheet hyperboloid . The Lorentz transformation is found that translates an arbitrary four-momentum of a tachyon into a four-momentum which time component is zero (tachyon’s proper frame of reference). The kinematics of the decay of a tachyon into a particle and its antiparticle (neutrino-antineutrino) in an arbitrary frame of reference and in the tachyon’s proper frame is considered. A test for detecting such a process is proposed.
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Kurochkin, Y.A., Shaikovskaya, N.D. Superluminal Particle Motion from the Hyperbolic Momentum Space Point of View. Phys. Part. Nuclei Lett. 19, 638–641 (2022). https://doi.org/10.1134/S1547477122060140
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DOI: https://doi.org/10.1134/S1547477122060140