scholarly journals Positive and Negative Particle Masses in the Bicubic Equation Limiting Particle Velocity Formalism

2018 ◽  
Vol 10 (1) ◽  
pp. 14
Author(s):  
Josip Soln
Keyword(s):  
Particle Velocity ◽  
Primary Particle ◽  
Point Of View ◽  
Particle Mass ◽  
Spin Orbit ◽  
Positive Mass ◽  
Negative Mass ◽  
Negative Particle ◽  
Normal Particle ◽  
Limiting Velocity

The interest in the negative particle mass here got encouraged by the Rachel Gaal July 2017 APS article (Gaal, 2017)describing Khamehchi et al. (2007) observation of an effective negative mass in a spin-orbit coupled Bose-Einsteincondensate. Hence, since in the bicubic equation limiting particle velocity formalism (Soln, 2014, 2015, 2016, 2017)positive m+ = m ≻ 0 and negative m− = −m ≺ 0 masses with m2+ = m2− = m2 are equally acceptable, then from a purelytheoretical point of view, the evaluation of particle limiting velocities for both m+ and a m− masses should be done.Starting with the original solutions for particle limiting velocities c1; c2 and c3, given basically for a positive particlemass m+ (Soln, 2014, 2015, 2016, 2017), now also are done for a negative particle mass m− This is done consistent withthe bicubic equation mathematics, by solving for c1; c2 and c3 not only form+ but also for m−. Hence, in addition tohaving the limiting velocities of positive mass m+ primary, obscure and normal particles, now one has also the limitingvelocities of negative mass m− primary, obscure and normal particles, however, numerically equal to limiting velocities,respectively of m+ masses obscure, primary and normal particles, forming the m+ and m− masses of equal limiting velocityvalue doublets : c1(m−) = c2(m+), c2(m−) = c1(m+) , c3(m−) = c3(m+). Now, one would like to know as to which particlewith a negative mass m− = −m ≺ 0, obtained from the positive mass m+ = m ≻ 0 with the substitution m −  −m, canhave a real limiting velocity? It turns out that it is the obscure particle limiting velocity c2(m+) that changes from theimaginary value, c22(m+) ≺ 0, into the real limiting velocity value c22(m−) ≻ 0 when the change m+ −  m− is made and,at the same time, retaining the same energy. Similar procedure applied to the original primary particle limiting velocitystarting with c21(m+) ≻ 0 , keeping the total energy the same,with the change m −  −m one ends up with c21(m−) ≺ 0 that is, imaginary c1. The procedure of changing m+ −  m− in normal particle limiting velocity causes no change, it remains the same realc3. Because m2 (= m2+ = m2−), E2 and v2 remain the same , these mass regenerations, m+ −  m− and m− −  m+ could in principle also occur spontaneously.

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

2018 ◽  
Vol 10 (5) ◽  
pp. 40
Author(s):  
Josip Soln
Keyword(s):  
Neutrino Mass ◽  
Particle Velocity ◽  
Velocity Measurement ◽  
Mass Shell ◽  
Global Scale ◽  
Muon Neutrino ◽  
Negative Particle ◽  
Negative Muon ◽  
Similarities And Differences ◽  
Limiting Velocity

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} $.

scholarly journals Formation of Particle Real Energy in the Bicubic Equation Limiting Particle Velocity Formalism with Possible Applications to Light Dark Matter

2019 ◽  
Vol 11 (2) ◽  
pp. 92
Author(s):  
Josip Soln
Keyword(s):  
Dark Matter ◽  
Particle Velocity ◽  
Dark Matter Particle ◽  
Particle Energy ◽  
Physical Parameters ◽  
The Real ◽  
Complex Particle ◽  
Particle Parameters ◽  
Real Value ◽  
Limiting Velocity

The complex particle energy, appearing in this article, with the suggestive choices of physical parameters,is transformed simply into the real particle energy. Then with the bicubic equation limiting particle velocity formalism, one evaluates the three particle limiting velocities, $c_{1},$ $c_{2}$\ and $% c_{3},$ (primary, obscure and normal) in terms of the ordinary particle velocity, $v$, and derived positive $m_{+}=m\succ 0$ \ and negative \ $% m_{-}=-m\prec 0$ \ \ particle masses with $m_{+}^{2}=m_{-}^{2}=$ $m^{2}$. In general, the important quantity in solving this bicubic equation is the real square value $\ z^{2}(m)$ of the congruent parameter, $z(m)$, that connects real or complex value of particle energy, $E,$ and the real or complex value of particle velocity squared, $v^{2}$, $2Ez(m)=3\sqrt{3}mv^{2}$% . With real $z^{2}(m)$ one determines the real value of discriminant, $D,$ of the bicubic equation, and they together influence the connection between $% E$ and $v^{2}.$ Hence, when $z^{2}\prec 1$ and \ $D\prec 0$ one has simply that $E\gg mv^{2}$. However,with $D\succeq 0$ and $z^{2}\succeq 1$ , both $E$ and $v^{2}$ may become complex simultaneously through connecting relation $% E=3\sqrt{3}mv^{2}/2z(m)$, with their real values satisfying \ Re $E\succcurlyeq m\left( \func{Re}v^{2}\right) $, keeping, however $z^{2}$ the same and real. In this article, this new situation with $D\succeq 0$ is discussed in detail.by looking as how to adjust the particle\ parameters to have $\func{Im% }E=0$ with implication that automatically also Im$v^{2}=0.$.In fact, after having adjusted the particle\ parameters successfully this way, one simply writes Re$E=E$ and Re$v^{2}=v^{2}$. \ \ This way one arrives at that the limiting velocities satisfy $c_{1}=c_{2}$\ $\#$ $c_{3}$, which shows the degeneracy of $c_{1}$ and $c_{2}$ as the same numerical limiting velocity for two particles. This degeneracy $c_{1}$ =$c_{2}$ is simply due to the absence of $\func{Im}E$. It would start disappearing with just an infinitesimal $\func{Im}E$. Now,while $c_{1}=c_{2}$ is real, $c_{3}$ is imaginary and all of them associated with the same particle energy, $E$. With these velocity values the congruent parameter becomes quantized as $% z(m_{\pm })=3\sqrt{3}m_{\pm }v^{2}/2E=\pm 1$ which, with the bicubic discriminant $D=0$ value, implies the quantization also of the particle mass, $m,$ into $m_{\pm }=\pm m$ values . The numerically equal energies,from $E=\func{Re}E$ can be expressed as $\ \ \ \ \ \ \ \ \ \ \ $$E(c_{1,2}($ $m_{\pm }))=E(c_{3}(m_{\pm }))$ either directly in terms of $% c_{1}(m_{\pm })=c_{2}(m_{\pm })$ and $c_{3}(m_{\pm })$ or also indirectly in terms of particle velocity, $v$, as well as in the Lorentzian fixed forms with $v^{2}\#$ $c_{1}^{2},$ $c_{2}^{2}$\ or $c_{3}^{2}$ assuring different from zero mass, $m$ $\#$ $0$. At the end, with here developed formalism, one calculates for a light sterile neutrino dark matter particle, the energies associated with $m_{\pm} $ masses and $c_{1,2}$and $c_{3}$ limiting velocities.

NUMERICAL STUDY OF THE INTERACTION BETWEEN POSITIVE AND NEGATIVE MASS OBJECTS IN GENERAL RELATIVITY

2012 ◽  
Vol 21 (07) ◽  
pp. 1250061 ◽  
Author(s):  
ZHOUJIAN CAO
Keyword(s):  
Boundary Condition ◽  
General Relativity ◽  
Numerical Study ◽  
Naked Singularity ◽  
Newtonian Limit ◽  
Computational Domain ◽  
Positive Mass ◽  
Negative Mass ◽  
Mass Particle ◽  
Causal Property

Based on Baumgarte–Shapiro–Shibata–Nakamura formalism and moving puncture method, we demonstrate the first numerical evolutions of the interaction between positive and negative mass objects. Using the causal property of general relativity, we set our computational domain around the positive mass black hole while excluding the region around the naked singularity introduced by the negative mass object. Besides the usual Sommerfeld numerical boundary condition, an approximate boundary condition is proposed for this nonasymptotically-flat computational domain. Careful checks show that either boundary condition introduces smaller error than the numerical truncation errors. This is consistent with the causal property of general relativity. Except for the numerical truncation error and round-off error, our method gives an exact solution to the full Einstein's equation for a portion of spacetime with two objects whose masses have opposite signs. So our method opens the door for numerical explorations with negative mass objects. Based on this method, we investigate the Newtonian limit of spacetime with two objects whose masses have opposite sign. Our result implies that this spacetime does have a Newtonian limit which corresponds to a negative mass particle chasing a positive mass particle. This result sheds some light on an interesting debate about the Newtonian limit of a spacetime with positive and negative point masses.

scholarly journals Mass Balance of Four Cirque Glaciers in the Torngat Mountains of Northern Labrador, Canada

1986 ◽  
Vol 32 (111) ◽  
pp. 208-218
Author(s):  
Robert J. Rogerson
Keyword(s):  
Mass Balance ◽  
Temporal Pattern ◽  
Climatic Conditions ◽  
Spatial Variations ◽  
Equilibrium Line ◽  
Positive Mass ◽  
Negative Mass ◽  
Equilibrium Line Altitude ◽  
Ice Surface ◽  
Debris Cover

AbstractThe net mass balance of four small cirque glaciers (0.7–1.4 km2) in the Torngat Mountains of northern Labrador was measured for 1981–84, allowing three complete mass-balance years to be calculated. The two largest glaciers experienced positive mass-balance conditions in 1982 while all the glaciers were negative in 1983. The temporal pattern relates directly to general climatic conditions, in particular winter snowfall. Spatial variations of mass balance on the glaciers are the result of several factors including altitude, extent of supraglacial debris cover, slope, proximity to side and backwalls of the enclosing cirque, and the height of the backwall above the ice surface. Abraham Glacier, the smallest studied and with consistently the largest negative mass balance (–1.28 m in 1983), re-advanced an average of 1.2 m each year between 1981 and 1984. Mean equilibrium-line altitude (ELA) for the four glaciers is 1050 m, varying substantially from one glacier to another (+240 to –140 m) and from year to year (+60 to –30 m).

scholarly journals Negative-Mass Hydrodynamics in a Spin-Orbit–coupled Bose-Einstein Condensate

2017 ◽  
Vol 118 (15) ◽  
Author(s):  
M. A. Khamehchi ◽  
Khalid Hossain ◽  
M. E. Mossman ◽  
Yongping Zhang ◽  
Th. Busch ◽  
...  
Keyword(s):  
Einstein Condensate ◽  
Spin Orbit ◽  
Negative Mass ◽  
Bose Einstein Condensate ◽  
Bose Einstein

scholarly journals Technical Note: The single particle soot photometer fails to detect PALAS soot nanoparticles

2012 ◽  
Vol 5 (4) ◽  
pp. 4905-4925 ◽  
Author(s):  
M. Gysel ◽  
M. Laborde ◽  
J. C. Corbin ◽  
A. A. Mensah ◽  
A. Keller ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Single Particle ◽  
Primary Particle ◽  
Particle Morphology ◽  
Counting Efficiency ◽  
Particle Mass ◽  
Effective Density ◽  
Soot Particles ◽  
Primary Particles ◽  
Small Primary

Abstract. The single particle soot photometer (SP2) uses laser-induced incandescence (LII) for the measurement of atmospheric black carbon (BC) particles. The BC mass concentration is obtained by combining quantitative detection of BC mass in single particles with a counting efficiency of 100% above its lower detection limit (LDL). It is commonly accepted that a particle must contain at least several tenths of femtograms BC in order to be detected by the SP2. Here we show the unexpected result that BC particles from a PALAS spark discharge soot generator remain undetected by the SP2, even if their BC mass, as independently determined with an aerosol particle mass analyser (APM), is clearly above the typical LDL of the SP2. Comparison of counting efficiency and effective density data of PALAS soot with flame generated soot (combustion aerosol standard burner, CAST), fullerene soot and carbon black particles (Cabot Regal 400R) reveals that particle morphology can affect the SP2's LDL. PALAS soot particles are fractal-like agglomerates of very small primary particles with a low fractal dimension, resulting in a very low effective density. Such loosely-packed particles behave like "the sum of individual primary particles" in the SP2's laser. Accordingly, the PALAS soot particles remain undetected as the SP2's laser intensity is insufficient to heat the primary particles to vaporisation because of their small size (primary particle diameter ~5–10 nm). It is not surprising that particle morphology can have an effect on the SP2's LDL, however, such a dramatic effect as reported here for PALAS soot was not expected. In conclusion, the SP2's LDL at a certain laser power depends on total BC mass per particle for compact particles with sufficiently high effective density. However, for fractal-like agglomerates of very small primary particles and low fractal dimension, the BC mass per primary particle determines the limit of detection, independent of the total particle mass. Consequently, care has to be taken when using the SP2 in applications dealing with loosely-packed particles that have very small primary particles as building blocks.

The effect of the negative particle velocity in a soliton gas within Korteweg–de Vries-type equations

2017 ◽  
Vol 72 (5) ◽  
pp. 441-448 ◽  
Author(s):  
E. G. Shurgalina ◽  
E. N. Pelinovsky ◽  
K. A. Gorshkov
Keyword(s):  
Particle Velocity ◽  
Negative Particle ◽  
De Vries
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