arXiv subjects

A. I. Arbab

Publications and source records attributed to A. I. Arbab.

At least 19 recordsLinked to original sources

arXiv2022

Electrodynamics with quaternionic mass

New electrodynamics with quaternionic mass is found to yields interesting results. The quaternionic mass involves longitudinal as well as transverse (vector) masses. Because of these two masses, an application of a magnetic field in a system induces electric charge and current densities in the system. Frank Wilczek axion electrodynamics is derived from this new electrodynamics bearing a quantum signature. A new version of Maxwell-Proca equations that are invariant under the gauge transformations is derived from the new electrodynamics. New electric and magnetic fields that are different from the standard formalism are proposed to describe massive electrodynamics. Axion electrodynamics are shown to be equivalent to Proca electrodynamics. The energy and momentum conservation equations are not influenced by the quaternionic mass.

physics.gen-ph↗

arXiv2022

Quantum mechanics with quaternionic mass

Quantum mechanics with quaternionic mass is considered. The momentum eigen-value equation with quaternionic mass yields the Klein-Gordon equation with a mass consisting of longitudinal and traverse masses. The scalar field total mass is found to be a sum of these masses. This field appears to be connected with two subfields conserving linear momentum. It is found that a particle with real mass satisfies the quantum Telegraph equation, whereas that one with quaternionic mass satisfies the Klein-Gordon equation. A quantum force acting on the particle is found to be proportional to its velocity. When the particle field is coupled to an electromagnetic field, an additional term in the particle's energy appears reflecting the interaction of the particle's angular momentum with the magnetic field.

physics.gen-ph↗

arXiv2020

Do we need to modify Maxwell's equations?

Maxwell's equations are modified to incorporate a scalar field to account for the London's superconductivity. Assuming the electromagnetic field is described by the Klein-Gordon equation, London's equations of superconductivity are then derived, which are invariant under a new set of transformations. The invariance of the modified Maxwell's equations under these transformations requires the electromagnetic field and the scalar field to be scale-invariant. Relying on these transformations, a quantized Josephson-like current is derived. This current gives rise to a residual magnetic field. The spatial and temporal variations of the scalar field are linked to the electric polarization such that the polarization vector is curl-less.

physics.gen-ph↗

arXiv2020

Coupling of a biquaternionic Dirac field to a bosonic field

We extend the biquaternionic Dirac equation to include interactions with a background bosonic field. The obtained biquaternionic Dirac equation yields Maxwell-like equations that hold for both a matter field and an electromagnetic field. The resulting equations are generalizations of the equations of Wilczek fields.

physics.gen-ph↗

arXiv2018

Bohmian quantum mechanics revisited

By expressing the Schrödinger wave function in the form $ψ=Re^{iS/\hbar}$, where $R$ and $S$ are real functions, we have shown that the expectation value of $S$ is conserved. The amplitude of the wave ($R$) is found to satisfy the Schrödinger equation while the phase ($S$) is related to the energy conservation. Besides the quantum potential that depends on $R$, \emph{viz.}, $V_Q=-\frac{\hbar^2}{2m}\frac{\nabla^2R}{R}$\,, we have obtained a phase potential $V_S=-\frac{S\nabla^2S}{m}$ that depends on the phase $S$ derivative. The phase force is a dissipative force. The quantum potential may be attributed to the interaction between the two subfields $S$ and $R$ comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass $mc^2$ with an internal frequency of $2mc^2/\hbar$, satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz $R$ satisfies the Klein-Gordon equation, then $S$ must satisfies the wave equation. Conversely, if $R$ satisfies the wave equation, then $S$ yields the Einstein relativistic energy momentum equation.

quant-ph↗

arXiv2018

Dual quantum mechanics and its electromagnetic analog

An eigenvalue equation representing symmetric (dual) quantum equation is introduced. The particle is described by two scalar wavefunctions, and two vector wavefunctions. The eigenfunction is found to satisfy the quantum Telegraph equation keeping the form of the particle fixed but decaying its amplitude. An analogy with Maxwellian equations is presented. Massive electromagnetic field will satisfy a quantum Telegraph equation instead of a pure wave equation. This equation resembles the motion of the electromagnetic field in a conducting medium. With a particular setting of the scalar and vector wavefunctions, the dual quantum equations are found to yield the quantized Maxwell's equations. The total energy of the particle is related to the phase velocity ($v_p$) of the wave representing it by $E=p\,|v_p|$\,, where $p$ is the matter wave momentum. A particular solution which describes the process under which the particle undergoes a creation and annihilation is derived. The force acting on the moving particle is expressed in a dual Lorentz-like form. If the particle moves like a fluid, a dissipative (drag) quantum force will arise.

physics.gen-ph↗

arXiv2018

Massive electrodynamics for London's superconductivity and Josephson effect

Massive electrodynamics for London's superconductivity and Josephson effect are derived. The propagation of massive boson inside a medium yields electric phenomena that are reflected in the Josephson effect. Critical force, magnetic field and temperature are found to be related to the critical current of the junction. The mass of the boson depends only on the critical current of the junction. The electromagnetic interaction between the Cooper pairs in the two sides of the superconductor in the josephson junction is mediated by a massive boson. The propagation of the electromagnetic waves mediated by the massive bosons gives rise to the electric properties of the Josephson junction. Of these properties are a quantized resistance of Hall type corresponding to a non-quantized magnetic flux, and a quantized capacitance. A non zero magnetic flux encompassing a magnetic charge is found to arise despite the fact that it is not a priori assumed.

physics.gen-ph↗

arXiv2018

Field theoretic model for the Josephson effect

The Josephson effect is found to stem from the quantum behavior of massive photons existing in a superconducting medium. Accordingly, the Josephson coupling energy is found to be equal to the rest mass energy of these photons. The Josephson effect is described by propagation of massive photon field following the universal quantum equation instead of being due to quantum tunnelling. The mass of the photon is found to be dependent on the electric properties of the junction. A characteristic (critical) quantized capacitance of the junction is found to be inversely related to the critical current. The quantum (kinetic) inductance induced in the junction is found to be equal to $L_q=μ_0λ_J$\,, where $λ_J$ is the Josephson penetration depth, and $μ_0$ is the free space permeability.

physics.gen-ph↗

arXiv2017

On Abraham-Lorentz force, Unruh and Hawking radiations

Assuming the radiation emitted by an accelerating charge follows the Unruh radiation, we obtained the characteristics of the de Broglie wave associated with the accelerating charge. The de Broglie wavelength of the accelerating charged particle is found to be inversely proportional to the temperature of the emitted radiation. Merging the Abraham-Lorentz and Unruh formulae shows that the particle de Broglie wavelength is found to vary inversely with its acceleration. It is found to have the same structure as that of the Wien's displacement law relating the maximum wavelength of the Black Body radiation to its temperature. A maximum acceleration that a charged particle can attain is derived that sets a limit to the the maximum electric field. The Abraham-Lorentz force for a black hole radiation is found to be proportional to its evaporation rate. The final mass of the black hole left-over is found to be $\sqrt{\frac{α\hbar c}{24 πG} }$, where $G$ is the gravitational constant, $c$ the speed of light, $h=2π\hbar$ is the Planck constant, and $α$ is the fine structure constant. The minimum entropy and spin of the black hole emitting Hawking radiation are, respectively, found to be $(α/6) k_B$ and $(α/6)\hbar$. The presently observed universal acceleration is a manifestation of the Unruh black body temperature of $10^{-29}K$. This agrees with the black body radiation temperature ($T$) relating $TR=const.$ prevailing since the time of the big bang, where $R$ is the universe radius.

physics.gen-ph↗

arXiv2017

On relativistic harmonic oscillator

A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic quantum harmonic oscillator. This quaternionic equation also yields the Klein-Gordon wave equation with a covariant (space-time dependent) mass. This mass is quantized and is given by $m_{*n}^2=m_ω^2\left(n_r^2-1-β\,\left(n+1\right)\right)\,,$ where $m_ω=\frac{\hbarω}{c^2}\,,$ $β=\frac{2mc^2}{\hbar\,ω}\, $, $n$, is the oscillator index, and $n_r$ is the refractive index in which the oscillator travels. The harmonic oscillator in 3+1 dimensions is found to have a total energy of $E_{*n}=(n+1)\,\hbar\,ω$, where $ω$ is the oscillator frequency. A Lorentz invariant solution for the oscillator is also obtained. The time coordinate is found to contribute a term $-\frac{1}{2}\,\hbar\,ω$ to the total energy. The squared interval of a massive oscillator (wave) depends on the medium in which it travels. Massless oscillators have null light cone. The interval of a quantum oscillator is found to be determined by the equation, $c^2t^2-r^2=λ^2_c(1-n_r^2)$, where $λ_c$ is the Compton wavelength. The space-time inside a medium appears to be curved for a massive wave (field) propagating in it.

physics.gen-ph↗

arXiv2017

Thermo-electromagnetic transport

Maxwell's equations incorporating thermoelectric and thermomagnetic effects are studied. Energy transport involving electric field only flows along the velocity direction and a direction perpendicular to it. Magnetic energy transport associated with magnetic field only is found to flow along the velocity direction and a direction normal to it. The temperature is transmitted like an electromagnetic wave traveling at the speed of light. Thermoelectric and thermomagnetic polarizations are induced in the medium that are directly proportional to the temperature. An electronic transport due to temperature variations only and without electric or magnetic field is found to be accessible. Electric and magnetic fields due to temperature gradient are shown to arise provided the photon is massive.

physics.gen-ph↗

arXiv2017

Maxwellian quantum mechanics

Expanding the ordinary Dirac's equation in quaternionic form yields Maxwell-like field equations. As in the Maxwell's formulation, the particle fields are represented by a scalar, $ψ_0$ and a vector $\vecψ$. The analogy with Maxwell's equations requires that the inertial fields are $\vec{E}_D=c^2\vecα\times\vecψ$, and $\vec{B}_D=\vecα\,ψ_0+cβ\,\vecψ$ and that $ψ_0=-cβ\,\vecα\cdot\vecψ$, where $β$, $\vecα$ and $c$ are the Dirac matrices and the speed of light, respectively. An alternative solution suggests that magnetic monopole-like behavior accompanies Dirac's field. In this formulation, a field-like representation of Dirac's particle is derived. It is shown that when the vector field of the particle, $\vecψ$, is normal to the vector $\vecα$, Dirac's field represents a medium with maximal conductivity. The energy flux (Poynting vector) of the Dirac's fields is found to flow in opposite direction to the particle's motion. A system of equivalently symmetrized Maxwell's equations is introduced. A longitudinal (scalar) wave traveling at speed of light is found to accompany magnetic charges flow. This wave is not affected by presence of electric charges and currents. The Lorentz boost transformations of the matter fields are equivalent to $c\vecψ\,' =c\vecψ\pmβ\vecα\,ψ_0\,,ψ_0\,'=ψ_0\mp cβ\vecα\cdot\vecψ\,.$

physics.gen-ph↗

arXiv2014

The consequences of complex Lorentz force and violation of Lorenz gauge condition

The complex Lorentz force is introduced and extended to include magnetic scalar. This scalar is found to be associated with a prevailing magnetic field permeating the whole space. It also introduce an extra force in Lorentz complex force. The magnetic scalar is associated with the vacuum energy. The Proca-Maxwell's massive electrodynamics is derived from the extend current-density transformations. Proca-Maxwell's theory is found to be invariant under the extended gauge transformations (current-charge density). The Lorenz gauge condition is shown to express the photon charge conservation. Any violation of Lorenz gauge (photon charge) or electronic charge conservation would lead to spin zero scalar particles. This is manifested in superconductivity. The total charge comprising the electron and photon is always conserved. Owing to superconductivity, the photon charge is related to electron charge by $e_p=\sqrt{\frac{m_p}{m_e}}\,\,e$. Photons inside superconductors are shown to be massive. It is shown that Maxwell's equations expressed in complex form are more convenient to study duality transformations.

physics.gen-ph↗

arXiv2013

The planetary spin and rotation period: A modern approach

Using a new approach, we have obtained a formula for calculating the rotation period and radius of planets. In the ordinary gravitomagnetism the gravitational spin ($S$) orbit ($L$) coupling, $\vec{L}\cdot\vec{S}\propto L^2$, while our model predicts that $\vec{L}\cdot\vec{S}\propto \frac{m}{M}\,L^2$, where $M$ and $m$ are the central and orbiting masses, respectively. Hence, planets during their evolution exchange $L$ and $S$ until they reach a final stability at which $MS\propto mL$, or $S\propto \frac{m^2}{v}$, where $v$ is the orbital velocity of the planet. Rotational properties of our planetary system and exoplanets are in agreement with our predictions. The radius ($R$) and rotational period ($D$) of tidally locked planet at a distance $a$ from its star, are related by, $D^2\propto \sqrt{\frac{M}{m^3}}\,\,R^3$ and that $R\propto \sqrt{\frac{m}{M}}\,\, a$.$a$ from its star, are related by, $D^2\propto \sqrt{\frac{M}{m^3}} R^3$ and that $R\propto \sqrt{\frac{m}{M}} a$.

physics.gen-ph↗

arXiv2012

A novel model for the fractional quantum Hall effect

A novel model of complex quantum harmonic oscillator is found to account for the observed Fractional quantum Hall effect (FQHE). The sequences of the observed FQHE conductivity and charge are explained. The two sequences are found to express a quantity and its complex conjugated partner. The oscillator is found to have two degenerates states, $ψ_n$, with angular momenta $\pm \,n\,\hbar$\,, where $h = 2π\hbar $ is the Planck's constant, and $n$ is the principal quantum number of the oscillator. The filling factor, $i$, that Klitzing has found for the integer quantum Hall effect (IQHE) is $i=n+1$. Analytical expressions for longitudinal resistance and Hall's voltage are obtained. The width of the plateau between two states is found to be $ΔB=\frac{1}{n(n+1)}\,\frac{n_sh}{e}\,,$ where $n_s$ is the electron number density.

quant-ph↗

arXiv2012

The emergent longitudinal wave from space and time derivatives transformations

We have shown that a longitudinal wave emerges as a result of general transformations similar to gauge transformations of electrodynamics. The time derivative and the gradient of the gauge function and their alike yield the longitudinal wave. The de Broglie wave associated with the particle motion is a longitudinal one. This wave accompanied the motion of all massive objects. It has a zero magnetic field (or vorticity). The invariance of Dirac equation under these transformations makes the electron to behave as a massless particle while having a mass.

quant-ph↗

arXiv2012

The generalized Newton's law of gravitation versus the general theory of relativity

Einstein general theory of relativity (GTR) accounted well for the precession of the perihelion of planets and binary pulsars. While the ordinary Newton law of gravitation failed, a generalized version yields similar results. We have shown here that these effects can be accounted for as due to the existence of gravitomagnetism only, and not necessarily due to the curvature of space time. Or alternatively, gravitomagnetism is equivalent to a curved space-time. The precession of the perihelion of planets and binary pulsars may be interpreted as due to the spin of the orbiting planet ($m$) about the Sun ($M$)\,. The spin ($S$) of planets is found to be related to their orbital angular momentum ($L$) by a simple formula, \emph{viz}., $S\propto \,\frac{m}{M}L$\,.

physics.gen-ph↗

arXiv2004

On the Electromagnetism of Gravitational System and the Four Dimensional Constants (c, h, k, G)

We presented a model for unification of electricity and gravity. We have found a consistent description of all physical quantities pertaining to the system. We have provided limiting values for all physical values. These values are neither zero nor infinity. Our universe is described at all times by the four dimensional constants $c, \hbar, k, G$ only. The remnant of vacuum remains at all epochs with different values. The present cosmological puzzles are justified as due to the consequences of cosmic quantization developed in this work.

gr-qc↗