arXiv subjects

Viktor Ariel

Publications and source records attributed to Viktor Ariel.

7 recordsLinked to original sources

arXiv2021

Quaternion Space-Time and Matter

In this work, we use the concept of quaternion time and demonstrate that it can be applied for description of four-dimensional space-time intervals. We demonstrate that the quaternion time interval together with the finite speed of light propagation allow for a simple intuitive understanding of the time interval measurement during arbitrary relative motion between a signal source and observer. We derive a quaternion form of Lorentz time dilation and show that the norm corresponds to the traditional expression of the Lorentz transformation and represents the measured value of time intervals, making the new theory inseparable from the theory of measurement. We determine that the space-time interval in the observer reference frame is given by a conjugate quaternion expression, which is essential for proper definition of the quaternion derivatives in the observer reference frame. Then, we apply quaternion differentiation to an arbitrary potential, which leads to generalized Lorentz force. The second quaternion derivative of the potential leads to expressions similar to generalized Maxwell equations. Finally, we apply the resulting formalism to electromagnetic and gravitational interactions and show that the new expressions are similar to the traditional expressions, with the exception of additional terms, related to scalar fields, that need further study and experimental verification. Therefore, the new mathematical approach based on Hamilton's quaternions may serve as a useful foundation of the unified theory of space-time and matter.

physics.gen-ph↗

arXiv2018

The Real Quaternion Relativity

In this work, we use real quaternions and the basic concept of the final speed of light in an attempt to enhance the standard description of special relativity. First, we demonstrate that it is possible to introduce a quaternion time domain where a coordinate point is described by a quaternion time. We show that the time measurement is a function of the observer location, even for stationary frames of reference. We introduce a moving observer, which leads to the traditional Lorentz relation for the time interval. We show that the present approach can be used in stationary, moving, or rotating frames of reference, unlike the traditional special relativity, which applies only to the inertial moving frames. Then, we use the quaternion formulation of space-time and mass-energy equivalence to extend the quaternion relativity to space, mass, and energy. We demonstrate that the transition between the particle and observer reference frames is equivalent to space inversion and can be described mathematically by quaternion conjugation. On the other hand, physical measurements are described by the quaternion norm and consequently are independent of the conjugation, which seems to be the quaternion formulation of the relativity principle.

physics.gen-ph↗

arXiv2017

Quaternion Time, Mass, and Particle Velocity

In this work, we propose using real quaternions for the definition of the time interval resulting in an alternative formulation of the relativistic space-time. We proceed with the quaternion definition of the particle mass that we derive using the mass-energy equivalence. This results in the quaternion mass dispersion relation, which is equivalent to the relativistic energy-momentum dispersion, however, with a positive quadratic norm of the resulting quaternion space. Then, we define the quaternion particle velocity, which can be applied to relativistic particles and electrons in non-parabolic solid-state materials. We show that the relativistic Lorentz expressions apply only to the absolute values of the time, mass and velocity while the physical 4-vector quantities are described by real quaternions. Finally, we introduce the quaternion electromagnetic potential and demonstrate that it has an effect on the particle mass and velocity. In particular, we show a direct connection between the electrostatic potential and the particle rest mass. We compare the present model to experimental measurements of the electron velocity in InSb where we demonstrate quasi-relativistic electron velocity saturation at high electric fields. Therefore, it appears that physical quantities can be expressed by real quaternions while their measured observables and relativistic Lorentz transformations correspond to the quaternion absolute values. It seems that the quaternion approach presented here can be used as a basis for an alternative mathematical description of particle physics.

physics.gen-ph↗

arXiv2012

Energy Band Model Based on Effective Mass

In this work, we demonstrate an alternative method of deriving an isotropic energy band model using a one-dimensional definition of the effective mass and experimentally observed dependence of mass on energy. We extend the effective mass definition to anti-particles and particles with zero rest mass. We assume an often observed linear dependence of mass on energy and derive a generalized non-parabolic energy-momentum relation. The resulting non-parabolicity leads to velocity saturation at high particle energies. We apply the energy band model to free relativistic particles and carriers in solid state materials and obtain commonly used dispersion relations and experimentally confirmed effective masses. We apply the model to zero rest mass particles in graphene and propose using the effective mass for photons. Therefore, it appears that the new energy band model based on the effective mass can be applied to relativistic particles and carriers in solid state materials.

physics.gen-ph↗

arXiv2012

Anisotropic Effective Mass

In this work, we derive a three-dimensional effective mass that is suitable for treatment of electrons in anisotropic semiconductors. We show that it is possible to define a scalar anisotropic three-dimensional mass that reduces to a one-dimensional definition for isotropic materials. We extend the effective mass definition and apply it to electrons in non-parabolic semiconductors and demonstrate that the effective mass is generally dependent on particle energy. Finally, we show that the proposed definition of the effective mass is compatible with the experimentally measured cyclotron mass in isotropic materials while leading to a more accurate result in anisotropic semiconductors.

cond-mat.other↗

arXiv2012

Electron Effective Mass in Graphene

The particle effective mass in graphene is a challenging concept because the commonly used theoretical expression is mathematically divergent. In this paper, we use basic principles to present a simple theoretical expression for the effective mass that is suitable for both parabolic and non-parabolic isotropic materials. We demonstrate that this definition is consistent with the definition of the cyclotron effective mass, which is one of the common methods for effective mass measurement in solid state materials. We apply the proposed theoretical definition to graphene and demonstrate linear dependence of the effective mass on momentum, as confirmed by experimental cyclotron resonance measurements. Therefore, the proposed definition of the effective mass can be used for non-parabolic materials such as graphene.

physics.gen-ph↗

arXiv2012

Effective Mass and Energy-Mass Relationship

The particle effective mass is often a challenging concept in solid state physics due to the many different definitions of the effective mass that are routinely used. Also, the most commonly used theoretical definition of the effective mass was derived from the assumption of a parabolic energy-momentum relationship, E(p), and therefore should not be applied to non-parabolic materials. In this paper, we use wave-particle duality to derive a definition of the effective mass and the energy-mass approximation suitable for non-parabolic materials. The new energy-mass relationship can be considered a generalization of Einstein's E=mc^2 suitable for arbitrary E(p) and therefore applicable to solid state materials and devices. We show that the resulting definition of the effective mass seems suitable for non-paraboic solid state materials such as HgCdTe, GaAs, and graphene.

physics.gen-ph↗