Related papers: Novel, first-principles approach to deriving Elect…
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…
In this paper we develop a framework allowing a natural extension of the Lorentz transformations. To begin, we show that by expanding conventional four-dimensional spacetime to eight-dimensions that a natural generalization is indeed…
In this article, matrix and vector formalisms for Lorentz transformations in time ($t$) and two space dimensions ($x$ and $y$) are developed and discussed. Lorentz transformations conserve the squared interval $t^2 - x^2 - y^2$. Examples of…
In the first part of this paper we review the fundamental difference between the usual transformations of the three-dimensional (3D) vectors of the electric field $\mathbf{E}$, the magnetic field $\mathbf{B}$, the polarization $\mathbf{P}$,…
We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration [1] to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic…
A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes…
We present an elementary, symmetry-first derivation of the Lorentz transformation together with a methodological clarification of the linearity step. Starting from the Principle of Relativity, supplemented by spacetime homogeneity,…
We show that the electromagnetic field tensor and the Lorentz Force are both a natural consequence of the geometric structure of Minkowskian space, being related to infinitesimal boosts and rotations in spacetime. The longstanding issue…
The theoretical framework of electromagnetism played a foundational role in Einstein's development of special relativity. To support conceptual understanding, we present a fully special relativistic computer simulation that visualizes…
Boost-rotation symmetric spacetimes are exceptional as they are the only exact asymptotically flat solutions to the Einstein equations describing spatially bounded sources ("point-like" particles, black holes) undergoing non-trivial motion…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. Tey are reviewed in the work presented. It is drawing the attention on the following aspects. EM-field has in general case quaternion…
This paper revisits the geometric foundations of electromagnetic theory, by studying Faraday's concept of field lines. We introduce "covariant electromagnetic field lines," a novel construct that extends traditional field line concepts to a…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
We investigate the asymptotic structure of electromagnetism in Minkowski space in even and odd spacetime dimensions $\geq 4$. We focus on $d>4$ since the case $d=4$ has been studied previously at length. We first consider spatial infinity…
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
In this paper it is proved by using the Clifford algebra formalism that the standard transformations (ST) of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not the Lorentz transformations (LT) of…
For a relativistic charged particle moving in a constant electromagnetic field, its velocity 4-vector has been well studied. However, despite the fact that both the electromagnetic field and the equations of motion are purely real, the…
We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the…
We introduce the concept of emergent electric field. This is distinguished from the fundamental one in that the emergent electric field directly appears in observations through the Lorentz force, while the latter enters the phase space as…
We show that the transformation of relativistic velocities derived without using the Lorentz-Einstein transformation for the space-time coordinates of the same event and the fact that we can define the proper value of length, time interval,…