Related papers: Some coordinate transformations relevant to refrac…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
The paper aims to apply the complex-sedenions to explore the field equations of four fundamental interactions, which are relevant to the classical mechanics and quantum mechanics, in the curved spaces. J. C. Maxwell was the first to utilize…
The magneto-optic effects and electro-optic effects are the essential optic effects, although their theoretical explanations are not unified in the classical electromagnetic theory. Describing with the algebra of octonions, the…
The paper discusses some scalar invariants in the gravitational field and electromagnetic field by means of the characteristics of the quaternions. When we emphasize some definitions of quaternion physical quantities, the speed of light,…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
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…
The paper aims to apply the trigintaduonion spaces to explore the physical properties of four interactions simultaneously, including the electromagnetic fields, gravitational fields, weak nuclear fields, and strong nuclear fields. J. C.…
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
The effects of physical interactions are usually incorporated into the quantum theory by including the corresponding terms in the Hamiltonian. Here we consider the effects of including the gravitational potential energy of massive particles…
Light propagating in opposite directions around the same loop in general shows a relative phase shift when recombined. This phenomenon is known as the Sagnac effect after Georges Sagnac who, in 1913, demonstrated with an interferometer on a…
The interpretations of octonion wave equations in eight dimensional space-time have been discussed. We have made an attempt to discuss the octonion field equation as the equation of motion for particles carrying simultaneously electric and…
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex,…
The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that…
Recently, a number of experimental observations on the superluminal group velocities of pulses propagating in dispersive media have led to reconsidering electromagnetism theory in an unconventional framework. To consider faster-than-light…
The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics.…
Magnetoelectric coupling in multiferroic materials opens new routes to control the propagation of light. The new effects arise due to dynamic magnetoelectric susceptibility that cross-couples the electric and magnetic fields of light and…
The fact that electromagnetic effects propagate at the speed of light suggests how the Lorenz-gauge scalar and vector potentials of a uniformly moving point charge must be modified when the charge was initially at rest and then set suddenly…
The Laplace's equations for the scalar and vector potentials describing electric or magnetic fields in cylindrical coordinates with translational invariance along azimuthal coordinate are considered. The series of special functions which,…
It is a matter of common knowledge that the field of gravitation influences the propagation of light, but the question to which extent electromagnetic fields do something similar is not completely answered. The birefringence caused by…
A new theory of a (flat) spacetime gravitational interaction is presented. This theory follows almost effortlessly from a new Lagrangian formulation of Maxwell's theory for photons and electrons (and positrons) whose associated Euler…