Abstract
From recently established bicubic equation, three particle limiting velocities are derived, primary, c1,obscure, c2 and normal, c3,that in principle may belong to a single particle. The values of limiting velocities are governed by the congruent particle parameter, z = 3\sqrt3mv2=2E, with m; v and E being, respectively, particle mass, velocity and energy, generally satisfying 1 &lt;= z &lt;= 1, and here just 0 &lt;= z &lt;= 1.<br />While c3 is practically the same in value as v, c1 and c2 can depart from v as z changes from 1 to 0, since c1, c2 and c3; are, in forms, explicitly different from each other, which offers the chance to look at possible new forms of matter, such as dark matter. For instance, one finds that c3 could be slightly different from c, the velocity of light, for the 2010 Crab Nebula Flare PeV electron energy region and for the OPERA 17 GeV muon neutrino velocity experiments, while at the same time, although not measurable in these experiments, calculated c1 and jc2j, are numerically about 105 times larger than c3.<br />There is a belief that an exemplary particle of small velocity, v = 10-3c ,and small energy, E = 1eV , but as yet of not known mass, should belong to the dark matter class. Once knowing z the value of the mass is fixed with 3\sqrt3m(z)v2 = 2Ez ,and its maximum value m(1) is at z = 1, m(1) = 2E=(v23\sqrt3):This mass value defines the test particle, with which one calulates primary, obscure and normal particle rest energies at z = 1: Snce at z = 1 theory predicts c21(1) = (3=2) v2;c22<br />(1) = 3v2; c23 (1) = (3=2) v2, the rest energies are m(1) c21(1) = m(1) c23(1) = 0:58eV and m(1)(c22(1))= 1:15eV. The primary and normal particles, with positive kinetic energies self-creation process increase their energies from 0:58eV to desired1eV: The obscure particle, with negative kinetic energy self-annihilation process decreases its energy of 1:15eV to desired 1eV. This makes the obscure (imaginary c2) particle as a good candidate for a dark matter particle,since as it is believed that a trapped dark matter particle with self-annihilation properties helps keeping the equilibrium between capture and annihilation rates in the sun.
Highlights
The three solutions of the recently established particle limiting velocity bicubic equation (Soln, 2014, 2015) sets a particle into three possible categories: a primary particle with primary limiting velocity c1, an obscure particle with the obscure imaginary limiting velocity c2 and a normal particle with the normal limiting velocity c3
The values of limiting velocities are governed by the congruent particle parameter, z = 3 3mv2/2E, with m, v and E being, respectively, particle mass, velocity and energy, generally satisfying −1 ≤ z ≤ 1, and here just 0 ≤ z ≤ 1
One finds that c3 could be slightly different from c, the velocity of light, for the 2010 Crab Nebula Flare PeV electron energy region and for the OPERA 17 GeV muon neutrino velocity experiments, while at the same time, not measurable in these experiments, calculated c1 and |c2|, are numerically about 105 times larger than c3
Summary
The three solutions of the recently established particle limiting velocity bicubic equation (Soln, 2014, 2015) sets a particle into three possible categories: a primary particle with primary limiting velocity c1, an obscure particle with the obscure imaginary limiting velocity c2 and a normal particle with the normal limiting velocity c3. This, with squares of limiting velocities at (z = 1,yi)eld the primary, obscure and normal particle rest energies as, m(1)c21 (1) = m(1) (3/2) v2 = 0.58eV, m(1) −c22 (1) = m(1)3v,2 = 1.15eV, m(1)c23 (1) = m(1) (3/2) v2 = 0.58eV .The self-creation energy processes of primary and normal particle changes 0.58eV to 1eV in energy, while the self-annihilation energy process of obscure particle decreases.1.15eV to 1eV in energy.This fact makes it a good dark matter particle since in Adrian-Martnez et al (2016) a particle with such a property helps keeping the equilibrium between capture and annihilation rate in the sun, for example At these low energy the absolute values of c1, c2 and c3 are all bellow c, the velocity of light. Associated with three limited velocity forms, c1, c2 and c3, here, w√ithin the inverse trigonometric function formalism, three identities for the dimensionless congruent variable z = 3 3mv2/2E, are presented With their help, three particle energy expressions with Lorentz-like factors, are derived associated with the primary, c1, obscure, c2 and normal, c3, limiting particle velocity forms.
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