Theoretical particle limiting velocity from the bicubic equation: Neutrino example

Šoln, Josip

doi:10.4006/0836-1398-27.3.448

Cited by 4 publications

(13 citation statements)

References 8 publications

(23 reference statements)

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“…As shown in references ( 'Soln, 2014'Soln, , 2015'Soln, , 2016'Soln, , 2017'Soln, , 2018, for the sake of completeness, the best thing is to start with the bicubic equation for the particle limiting velocity,generically denoted with c,…”

Section: Energies and Momenta Expressions With Positive And Negative mentioning

confidence: 99%

“…Here, the hypothesis that the flavor neutrino ν(α) may be described either by positive m +ν (α) or negative m −ν (α) neutrino mass is tested on the case of the OPERA muon neutrino ,ν(µ), velocity experiment (Adam et al, 2013). For our purposes, we continue with data from Adam et al (2013) as prepared and appearing in 'Soln (2014'Soln ( , 2016, with addition of a negative neutrino mass. In order to find m −ν (µ) one needs to have m +ν (µ).…”

Section: Energies and Momenta Expressions With Positive And Negative mentioning

confidence: 99%

“…The bicubic equation limiting particle velocity formalism ('Soln, 2014('Soln, , 2015('Soln, , 2016('Soln, , 2017 evolved to the point that it was straightforward to indicate the possibility of a negative particle mass ('Soln, 2018) as discussed by Gaal (2017) and experimentally observed by Khamehchi et al (2017) in their "Negative mass hydrodynamics in a spin-orbit-coupled Bose-Einstein condensate".…”

Section: Introductionmentioning

confidence: 99%

“…Finally, one can address the question as to the limiting velocity of the muon neutrino υ(µ) from the OPERA measurement (Adam et al, 2013) and analyses in 'Soln (2014'Soln ( ,2016 here denoted as c 3 (m ν (µ). Then with presumed positive and negative neutrino masses m +ν (µ) ≽ 0 and m −ν (µ) ≼ 0 the values of c 2 3 (m +ν (µ)) and c 2 3 ( m −ν (µ)) should be the same.…”

Section: Introductionmentioning

confidence: 99%

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Similarities and differences between positive and negative particle masses in the bicubic equation limiting particle velocity formalism: positive or negative muon neutrino mass?

Šoln¹

2018

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Here, rather detailed numerical comparisons of energies and momenta for$\ $\ positive $m_{+}=m\succ 0$ \ and negative \ $m_{-}=-m\prec 0$ \ \particle masses with $m_{+}^{2}=m_{-}^{2}=$ $m^{2}$ , within the bicubic equation limiting particle velocity formalism with three particle limiting velocities $c_{1},$ $c_{2}$\ and $c_{3}$, are done. Already these limiting velocities, on a global scale, can differentiate positive, $m_{+}$ and negative \ $m_{-}$ particle masses. While $c_{1}(m_{+})$, $c_{2}(m_{+})$ and $c_{3}(m_{+})$ are real, imaginary and real, corresponding, respectively, to primary, obscure and normal particles; $c_{1}(m_{-})$, $c_{2}(m_{-})$ and $% c_{3}(m_{-})$ are respectively imaginary, real and real, now representing respectively, obscure, primary and normal particles. In fact, from limiting velocity solutions, one identifies: $c_{1}^{2}(m_{+})=$ $% c_{2}^{2}(m_{-}),c_{1}^{2}(m_{-})=c_{2}^{2}(m_{+})$, $c_{3}^{2}(m_{-})=$ $% c_{3}^{2}(m_{+})$.\ \ The unified particle mass-shell like forms with particle energies and momenta are readily expressible for $m_{+}=m\succ 0$ and $m_{-}=-m\prec 0$ masses with respective limiting velocities, separating $c_{3}(m_{+})$ from $c_{3}(m_{-})$ as well as $c_{1}(m_{+})$ from $% c_{1}(m_{-})$ and $c_{2}(m_{+})$ from $c_{2}(m_{-}).$ We assume that flavor neutrinos, which, while in process do not change flavor, belong to normal limiting velocity $c_{3}$ class. Then the muon neutrino from OPERA velocity measurement should maintain the same velocity squares $v^{2}$ and $c_{3}^{2}$ when one changes the positive neutrino mass $% m_{+\nu }\left( \mu \right) \succ 0$ into the negative neutrino mass $% m_{-\nu }\left( \mu \right) \prec 0$ , since theoretically $% c_{3}^{2}(m_{+\nu }(\mu ))=c_{3}^{2}(m_{-\nu }(\mu ))$. For OPERA measurements this is verified perturbatively by simultaneously evaluating squares of normal limiting velocities with $m_{+\nu }(\mu )$ and $m_{-\nu }(\mu )$ masses, yielding the same result $c_{3}^{2}(m_{+\nu }(\mu )=c_{3}^{2}(m_{-\nu }(\mu )\simeq v_{\nu }^{2}\left( \mu \right) \simeq c^{2} $.

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Section: Energies and Momenta Expressions With Positive And Negative mentioning

confidence: 99%

Section: Energies and Momenta Expressions With Positive And Negative mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Similarities and differences between positive and negative particle masses in the bicubic equation limiting particle velocity formalism: positive or negative muon neutrino mass?

Šoln¹

2018

APR

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“…The particle limiting velocity solutions of primary c 1 , obscure c 2 and normal c 3 (Soln, 2014(Soln, , 2015(Soln, , 2016), repeated bellow with (2.0, 1, 2, 3), cathegorize particles respectively into the primary, obscure and normal particles with the help of dimensionless congruent particle parameter…”

Section: Introductionmentioning

confidence: 99%

Connecting dark matter particles with the primary, obscure and normal particles through implicit causality

Šoln¹

2017

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The primary, obscure and normal particles with respective limiting velocities c 1 , c 2 and c 3 ,solutions from bicubic equation, offer comfortable venues to tackle the newly emergent dark matter particles. Particular emphasis is given to particles with velocities of O(10 −3 c) ( with c the velocity of light) and whose energies are from 1eV to over 100GeV for which the congruent parameter z = 3 √ 3mv 2 /2E assumes values of 10 −6 and 10 −7 . At z = 10 −6 with mc 2 = 100GeV one can have E = 260GeV or with E = 1eV one can have mc 2 = 0.38eV; while at z = 10 −7 with mc 2 = 100GeV one can have E = 2.6T eV or with E = 1eV one can have mc 2 = 0.038eV. The small values of the congruent parameter z allow the limiting velocities c 1 , c 2 and c 3 as well as the resulting energy expressions be written down perturbatevly in terms of the congruent parameter z.It is shown that for mc 2 = 100GeV particle in the Milky Way Dark Matter Velocity Profile (Laha, 2016), the derived limiting velocities of primary, obscure and normal particles as dark matter particles are: c 1 = 1, 7c (z = 10 −7 ), 1.34c, 2.15c (z = 10 −6 ); c 2 = ±i1, 7c (z = 10 −7 ), ±i1.34c, ±i2.15c (z = 10 −6 ), and c 3 = v (z = 10 −7 , 10 −6 ). Perturbatively, for a very small common primary and obscure particle velocity v compared to the absolute values of their limiting velocities, one shows that the obscure particle acquires (−mv 2 ) intrinsic negative energy with respect to the primary particle,with m being their common mass.

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Complex Limiting Velocity Expressions as Likely Characteristics of Dark Matter Particles

Šoln¹

2020

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Many astrophysical and cosmological observations suggest that the matter in the universe is mostly of the dark matter type whose behavior goes beyond the Standard Model description. Hence it is justifiable to take a drastically different approach to the dark matter particles which is here done through the bicubic equation of limiting particle velocity formalism. The bicubic equation discriminant $D$ in this undertaking satisfy $D\succeq 0 $ determined by the congruent parameter $z$ satisfying $z^{2}\succeq 1$, where formally $z(m)=3\sqrt{3}mv^{2}/2E$, \ with $m$, $v$, and $E$ being respectively, particle mass, velocity and energy. Also nonlinearly related to the the particle congruent parameter $z$ is the particle congruent angle $% \alpha $ . These two dimensionless\ parameters $z$ \ and $\alpha $ simplify expressions in the bicubic equation limiting particle velocity formalism when evaluating the three particle limiting velocities, $c_{1},$ $c_{2}$\ and $c_{3},$ (primary, obscure and normal) in terms of the ordinary particle velocity, $v$. Corresponding to these limiting velocities \ one then deduces, with equal values, dark matter particle energies $E\left(c_{1}\right) $, $E\left( c_{2}\right) $ and $E\left( c_{3}\right) $. The exemplary values of the congruent parameters are in these regions, $1\preceq z\prec 3\sqrt{3}$ $/2$ and $\pi /2\succeq \alpha \succeq \pi /3$ . Already within these ranges of congruent parameters, the bicubic formalism yields for squares of particle limiting velocities that $c_{1}^{2}$ and $c_{2}^{2}$ are complex conjugate to each other, $c_{1}^{2\ast }=c_{2}^{2}$ ,and that $% c_{3\text{ }}^{2}$is real. The imaginary portions of $c_{1}^{2}$ and $% c_{2}^{2}$ do not change the realities of numerically equal to each other dark matter energies $E\left( c_{i}\right) ,i=1,2,3.$ In fact, real $E\left(c_{1,2}\right) $ energies can be equally evaluated with $c_{1,2}^{2}$ or $% \func{Re}$ $c_{1,2}^{2}$ or even with $\func{Im}c_{1,2}^{2}$ so that in new notation, $E\left( _{1,2}^{2}\right) =E\left( \func{Re}c_{1,2}^{2}\right) =E\left( \func{Im}c_{1,2}^{2}\right) $ $=E\left( c_{3}^{2}\right) $ all with the same real values. However, in these notations, the real particle momenta are $\overrightarrow{p}\left( (\func{Re}c_{1,2}^{2}\right) $ and $\\overrightarrow{p}\left( (c_{3}^{2}\right) $, defined with respective energies and, while in similar forms , numerically are different from each other.

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Theoretical particle limiting velocity from the bicubic equation: Neutrino example

Cited by 4 publications

References 8 publications

Similarities and differences between positive and negative particle masses in the bicubic equation limiting particle velocity formalism: positive or negative muon neutrino mass?

Similarities and differences between positive and negative particle masses in the bicubic equation limiting particle velocity formalism: positive or negative muon neutrino mass?

Connecting dark matter particles with the primary, obscure and normal particles through implicit causality

Complex Limiting Velocity Expressions as Likely Characteristics of Dark Matter Particles

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