arXiv subjects

Arbab I. Arbab

Publications and source records attributed to Arbab I. Arbab.

At least 19 recordsLinked to original sources

arXiv2018

The quaternionic commutator bracket and its implications

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, \emph{viz.} $\widetildeψ=(\frac{i}{c}\,ψ_0\,,\vecψ)$, represents a state of a particle with orbital angular momentum, $L=3\,\hbar$, resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector $\vecψ$, points along the direction of $\vec{L}$. When a charged particle is placed in an electromagnetic fields the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov-Bohm and Aharonov-Casher effects.

physics.gen-ph↗

arXiv2011

The unified quantum wave equation

The quaterionic formulation of quantum mechanics yields the unified quantum wave equation (UQWEs). From these equations, Dirac, Klein - Gordon and Schrodinger equations can be derived. While the UQWEs represent a matter wave (de Broglie), the Maxwell equations represent a transverse wave (field). Owing to UQWEs, the spin-0 and spin-1/2 particle are described by a wavepacket consisting of waves traveling to the left and to the right with speed of light. UQWEs show that spin-0 and spin-1/2 are in continuous states of creation and annihilation that are compatible with Heisenberg uncertainty relation. The creation - annihilation process is a result of the time translation property of the particle wavefunction. These are $E'=E-im_0c^2$ and $E'=E\pm m_0c^2$, for Klein-Gordon' and Dirac' particles, respectively. It is found that $\frac{\hbar}{m_0c^2}$ is the period of the creation -annihilation process.

physics.gen-ph↗

arXiv2010

A New Formulation of Quantum Mechanics

A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and Schrodinger probability density while keeping the Klein -Gordon and Schrodinger current unaltered. We have found time and space transformations under which Dirac's equation is invariant. The invariance of Maxwell's equations under these transformations shows that the electric and magnetic fields of a moving charged particle are perpendicular to the velocity of the propagating particle. This formulation agrees with the quaternionic formulation recently developed by Arbab.

physics.gen-ph↗

arXiv2010

On the electric and magnetic properties of conductors

Application of the generalized continuity equation reveals that the drift current in conductors is equivalent to a negative diffusion current. A phenomenological model of conductivity is developed using the generalized continuity equations. Consequently, a limiting conductivity is obtained that amounts to $1.09\times \,10^9\,Ω^{-1}m^{-1}$. A magnetomotive force (current) is hypothesized to exist, which is exhibited when a voltage changes with time. Magnetic charges and currents are found to be related to displacement current.

physics.gen-ph↗

arXiv2010

Derivation of Dirac, Klein-Gordon, Schrodinger, Diffusion and quantum heat transport equations from a universal quantum wave equation

A universal quantum wave equation that yields Dirac, Klein-Gordon, Schrodinger and quantum heat equations is derived. These equations are related by complex transformation of space, time and mass. The new symmetry exhibited by these equations is investigated. The universal quantum equation yields Dirac equation in two ways: firstly by replacing the particle my $m_0$ by $im_0$, and secondly by changing space and time coordinates by $it$ and $i\vec{r}$, respectively.

physics.gen-ph↗

arXiv2010

A mass-extended 't Hooft-Nobbenhuis complex transformations and their consequences

We have extended the 't Hooft-Nobbenhuis complex transformations to include mass. Under these new transformations, Schrodinger, Dirac, Klein-Gordon and Einstein general relativity equations are invariant. The non invariance of the cosmological constant in Einstein field equations dictates it to vanish thus solving the longstanding cosmological constant problem.

physics.gen-ph↗

arXiv2010

A quaternionic unification of electromagnetism and hydrodynamics

We have derived energy conservation equations from the quaternionic Newton's law that is compatible with Lorentz transformation. This Newton's law yields directly the Euler equation and other equations governing the fluid motion. With this formalism, the pressure contributes positively to the dynamics of the system in the same way mass does. Hydrodynamic equations are derived from Maxwell's equations by adopting an electromagnetohydrodynamics (EMH) analogy. In this analogy the hydroelectric field is related to the local acceleration of the fluid and the Lorentz gauge is related to the incompressible fluid condition. An analogous Lorentz gauge in hydrodynamics is proposed. We have shown that the vorticity of the fluid is developed whenever the particle local acceleration of the fluid deviates from the velocity direction. We have also shown that Lorentz force in electromagnetism corresponds to Euler force in fluids. Moreover, we have obtained Gauss's, Faraday's and Ampere's -like laws in Hydrodynamics.

physics.gen-ph↗

arXiv2010

Post-Galilean transformations of space and time derivatives and their consequences

Using post-Galilean space and time derivatives transformations and quantum mechanics, we have found a new particle-wave equation besides the Klein-Gordon equation describing a spinless scalar particle. This new equation can also be obtained from Dirac's equation if $β=γ(1\pm\frac{v}{c})$. Biot-Savart law and additional continuity equations are obtained as a consequence of the invariance of Dirac's equation and Maxwell's equations under these transformations.

physics.gen-ph↗

arXiv2010

On the generalized continuity equation

A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz invariant. The transport properties of electrons are found to be governed by Schrodinger-like equation and not by the diffusion equation.

physics.gen-ph↗

arXiv2010

The Quaternionic Quantum Mechanics

A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form $\frac{1}{c^2}\frac{\partial^2ψ_0}{\partial t^2} - \nabla^2ψ_0+2(\frac{m_0}{\hbar})\frac{\partialψ_0}{\partial t}+(\frac{m_0c}{\hbar})^2ψ_0=0$. This reduces to the massless Klein-Gordon equation, if we replace $\frac{\partial}{\partial t}\to\frac{\partial}{\partial t}+\frac{m_0c^2}{\hbar}$. For a plane wave solution the angular frequency is complex and is given by $\vecω_\pm=i\frac{m_0c^2}{\hbar}\pm c\vec{k} $, where $\vec{k}$ is the propagation constant vector. This equation is in agreement with the Einstein energy-momentum formula. The spin of the particle is obtained from the interaction of the particle with the photon field.

physics.gen-ph↗

arXiv2010

A New Formulation of Electrodynamics

A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $ϕ$ and the Lorentz gauge connecting them. With the same formalism, the continuity equation is written in terms of these new differential commutator brackets. Keywords: Mathematical formulation, Maxwell's equations

physics.gen-ph↗

arXiv2007

Viscous Dark Energy Models with Variable G and Lambda

We consider a cosmological model with bulk viscosity ($η$) and variable cosmological $(Λ\propto ρ^{-α}, α=\rm const.$) and gravitational ($G$) constants. The model exhibits many interesting cosmological features. Inflation proceeds du to the presence of bulk viscosity and dark energy without requiring the equation of state $p=-ρ$. During the inflationary era the energy density ($ρ$) does not remain constant, as in the de-Sitter type. Moreover, the cosmological and gravitational constants increase exponentially with time, whereas the energy density and viscosity decrease exponentially with time. The rate of mass creation during inflation is found to be very huge suggesting that all matter in the universe was created during inflation.

hep-th↗

arXiv2007

Phantom Energy with Variable G and Lambda

We have investigated a cosmological model of a phantom energy with a variable cosmological constant ($Λ$) depending on the energy density ($ρ$) as $Λ\propto ρ^{-α}$, $α=\rm const.$ and a variable gravitational constant ($G$). The model requires $α<0$ and a negative gravitational constant. A negative gravitational constant may forbid \emph{black holes} to form a particle horizon in a background of phantom energy. This implies that black holes are naked, and consequently the \emph{Cosmic Censorship} theorem is violated. The cosmological constant evolves with time as, $Λ\propto t^{-2}$. For $ω>-1$ and $α<-1$ the cosmological constant, $Λ<0$, $G>0$ and $ρ$ decrease with cosmic expansion. For ordinary matter (or dark matter), i.e., $ω>-1$ we have $-1<α<0$ and $β>0$ so that $G>0$ increases with time and $ρ$ decreases with time. Cosmic acceleration with dust particles is granted provided $-{2/3}<α<0$ and $Λ>0$.

hep-th↗

arXiv2007

Cosmological Models in the Generalized Einstein Action

We have studied the evolution of the Universe in the generalized Einstein action of the form $R+βR^2$, where $R$ is the scalar curvature and $β=\rm const.$. We have found exact cosmological solutions that predict the present cosmic acceleration. These models also allow an inflationary de-Sitter era occurring in the early Universe. The cosmological constant ($Λ$) is found to decay with the Hubble constant ($H$) as, $Λ\propto H^4$. In this scenario the cosmological constant varies quadratically with the energy density ($ρ$), i.e., $Λ\propto ρ^2$. Such a variation is found to describe a two-component cosmic fluid in the Universe. One of the component accelerated the Universe in the early era, and the other in the present era. The scale factor of the Universe varies as $a\sim t^{n}$, $n=1/2$ in the radiation era. The cosmological constant vanishes when $n=4/3$ and $n=1/2$. We have found that the inclusion of the term $R^2$ mimics a cosmic matter that could substitute the ordinary matter.

hep-th↗

arXiv2007

The length of day in the past

We have found an empirical law for the variation of the length of the Earth's day with geologic time employing Wells's data. We attribute the lengthening of the Earth's day to the present cosmic expansion of the Universe. The prediction of law has been found to be in agreement with the astronomical and geological data. The day increases at a present rate of 0.002 sec/century. The length of the day is found to be 6 hours when the Earth formed. We have also found a new limit for the value of the Hubble constant and the age of the Universe.

physics.gen-ph↗

arXiv2007

An Alternative Model for the Tidal Evolution of the Earth-Moon-Sun System

We have found that the expansion of the universe has immense consequences on our local systems. We present a model based on cosmic expansion that fits well with observation. The close approach problem inflicting tidal theory is averted in this model. We have shown that the astronomical and geological changes of our local systems are of the order of Hubble constant.

astro-ph↗

arXiv2007

On the Planetary acceleration and the Rotation of the Earth

We have developed a model for the Earth rotation that gives a good account (data) of the Earth astronomical parameters. These data can be compared with the ones obtained using space-base telescopes. The expansion of the universe has an impact on the rotation of planets, and in particular, the Earth. The expansion of the universe causes an acceleration that is exhibited by all planets.

astro-ph↗

arXiv2004

The Equivalence between Different Dark (Matter) Energy Scenarios

We have shown that the phenomenological models with a cosmological constant of the type $Λ=β(\frac{\ddot R}{R})$ and $Λ=3αH^2$, where $R$ is the scale factor of the universe and $H$ is the Hubble constant, are equivalent to a quintessence model with a scalar ($ϕ$) potential of the form $V\propto ϕ^{-n}, n$ = constant. The equation of state of the cosmic fluid is described by these parameters ($α, β, n$) only. The equation of state of the cosmic fluid (dark energy) can be determined by any of these parameters. The actual amount of dark energy will define the equation of state of the cosmic fluid. All of the three forms can give rise to cosmic acceleration depending the amount of dark energy in the universe.

astro-ph↗