Related papers: Urusovskii's geometry, algebrodynamics and univers…
Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution---the exact seven parameter solution of Pleba\'nski--Demia\'nski (PD)---to demonstrate these analogies for…
We review the recent experimental evidence on arbitrary values of the speed of light within physical media (interior dynamical problems); we recall that classical (operator) theories with speeds of light different than that in vacuum are…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead…
We derive the analogues of the Dirac and Pauli equations from a spatially fourth-order Klein--Gordon equation with a universal length scale. Starting from a singularly perturbed variant of Maxwell's equations, we deduce a 32-dimensional…
We discuss the recent proposal of implementing Doubly Special Relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give…
A pedagogical description of a simple ungeometrical approach to General Relativity is given, which follows the pattern of well understood field theories, such as electrodynamics. This leads quickly to most of the important weak field…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…
We propose in this paper a new approach to the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering a natural geometric definition of a…
In 1900, Macfarlane proposed a hyperbolic variation on Hamilton's quaternions that closely resembles Minkowski spacetime. Viewing this in a modern context, we expand upon Macfarlane's idea and develop a model for real hyperbolic 3-space in…
More then forty years ago R.I. Pimenov introduced a new geometry -- semi-Riemannian one -- as a set of geometrical objects consistent with a fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to which the physically…
We present a mathematical model for a physical theory that is compatible with Einstein's Special Relativity Theory. Our model consists of three pseudo-complex dimensions, representing three real dimensions of space, dual to what could be…
A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…
A reference frame on a set $M$ is given by a 3-dimensional euclidean space $E$, a function from $M$ to $E$, a 1-dimensional affine space $A$ and a function from $M$ to $A$. The definition allows an intuitive and coordinate-free formulation…
A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski…
Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…
This is an article contributed to the Brill Festschrift, in honor of the 60th birthday of Prof. D.R. Brill, which will appear in the Vol.2 of the Proceedings of the International Symposia on Directions in General Relativity. In this article…
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three…