# Theoretical particle limiting velocity from the bicubic equation: Neutrino example

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Pursuing the theoretical formulation of particle limiting velocities, here directly from the special relativistic kinematics, in which all physical quantities are in the overall mathematical consistency with each other, one treats formally the velocity of light c as yet to be deduced particle limiting velocity, and derives the bicubic equation for the particle limiting velocity in the arbitrary reference frame. Of the three solutions for squares of the limiting velocities, denoted as c 1 2 , c 2 2 , and c 3 2 , here in the practical case of high energy region, E >> mc 2, at least one, c 3 2 has a chance to be equal to c 2, exhibiting the Lorentz invariance (LI), which was imprinted from the LI relativistic mass-shell condition. Here, c 2 2 is negative and as such unphysical. Solution c 1 2 is Lorentz violating (LV) and potentially much larger than c 2 and, as such, unlikely to be observed. So its LV is irrelevant. With these exact solutions one can treat physical limiting velocities, for any particle, electron, neutrino, photon, etc. As to the neutrino, for the sake of simplicity, one assumes that the distance travelled is such that it does not change significantly its flavor. That agrees well with the so called ν Standard Model (νSM) in which the usual Dirac neutrino mass appears due to the presence of the right-handed neutrino field. Although here one will not go into the details of the νSM, the effect of the Dirac neutrino mass will be equated with the averaged mass-state neutrino masses around the fixed Dirac neutrino flavor. The OPERA 17 GeV muon neutrino velocity experiments are discussed through the limiting velocity c 3 because the deduced neutrino mνc 2 of 0.076 eV, being negligible, makes c 1 >> c, and, even if physical, presently unobservable. Furthermore, because in OPERA experiments, m ν c 2 << E ν, one finds out that c 3 = c(1 + Δ) c because Δ is negligible (it varies from O(−10−6) to O(10−6)). This practically implies the LI of the neutrino energy‐ momentum dispersion relation.
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Document Type: Research Article

Affiliations: JZS Phys-Tech, Vienna, Virginia 22182, USA

Publication date: September 16, 2014

• Physics Essays has been established as an international journal dedicated to theoretical and experimental aspects of fundamental problems in Physics and, generally, to the advancement of basic knowledge of Physics. The Journal's mandate is to publish rigorous and methodological examinations of past, current, and advanced concepts, methods and results in physics research. Physics Essays dedicates itself to the publication of stimulating exploratory, and original papers in a variety of physics disciplines, such as spectroscopy, quantum mechanics, particle physics, electromagnetic theory, astrophysics, space physics, mathematical methods in physics, plasma physics, philosophical aspects of physics, chemical physics, and relativity.
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