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In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory…
The shortening of bodies in the direction of motion, Lorentz contraction, follows from the solution of Maxwell's equations. Moving light clocks will tick slower than those at rest because the speed of light does not depend on a source of…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
Explicit models for the restricted conformal group of the Einstein static universe of dimension greater than two and for its universal covering group are constructed. Based on these models, as an application we determine all oriented and…
Some facts of the theory of the Lorentz group are specified for looking at the problems of light polarization optics in the frames of vector Stokes-Mueller and spinor Jones formalism. In view of great differences between properties of…
While internal space-time symmetries of relativistic particles are dictated by the little groups of the Poincar\'e group, it is possible to construct representations of the little group for massive particles starting from harmonic…
We show that the kinematics underlying Poincare's elongated ellipse, immediately deduced from Lorentz Transformation (LT), is not the same as Einstein's kinematics. The two main differences are : On one hand the relationship of Lorentz…
The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers…
By confusing the radiance of a single mode light beam, constant in a transparent medium, with the irradiance which decreases away from the source, Menzel purports to show that coherent interactions of light with the diluted media of…
The problem of covariance of physical quantities has not been solved fundamentally in the theory of relativity, which has caused a lot of confusion in the community; a typical example is the Gordon metric tensor, which was developed almost…
Sagnac effect has been studied in terms of Gyroscopic system in both Lorentz frame as well as flat Einstein frame. The Einstein equivalence principle has been used to determine the phase shift due to pseudo force in the transformation from…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
We show that the Lorentz transformations for the space-time coordinates of the same event are a direct consequence of the principle of relativity and of Einstein's distant clocks synchronization procedure. In our approach, imposing the…
A Lorenz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac's formalism of…
The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection of basic building blocks. In application domains where such techniques are deployed, we frequently encounter…
Many different mathematical languages have been invented to describe the ideas of Einstein's special relativity. One of the most powerful languages is the Minkowski space-time algebra of D. Hestenes. We discuss the ideas of special…
Kant and Hegel are among the philosophers who are guiding the way in which we reason these days. It is thus of interest to see how physical theories have been developed along the line of Kant and Hegel. Einstein became interested in how…
We present a pedagogical approach to the Lorentz group. We start by introducing a compact notation to express the elements of the fundamental representation of the rotations group.Lorentz coordinate transformations are derived in a novel…
Einstein's program of the unified field theory transformed nowadays to the TOE requiring new primordial elements and relations between them. Definitely, they must be elements of the quantum nature. One of most fundamental quantum elements…