Related papers: Lorentz transformation in Maxwell equations for sl…
It is traditionally believed that the Lorentz transformations (LT) and Einstein's theorem of velocity addition (ETVA), underlying special relativity, cannot be obtained from non-relativistic (classical) mechanics. In the present paper it is…
To consider a medium carrying light and electromagnetic waves is impossible, when this medium shall have properties according to the principle of constant speed of light, that is, isotropy of speed of light in every system of reference.…
Maxwell's equations and the Lorentz force density are expressed using an alternative simultaneity gauge. As a result, they describe electrodynamics for an observer travelling with a constant velocity through an isotropic medium. If desired,…
The Lorentz transformation is derived without assuming the existence of Maxwell's equations, or that the speed of light is a constant, or even that light exists. This leads us logically to sonsider the existence of a primal field called…
We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a…
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
On the basis of all commutation relations of the k-deformed phase space incorporating the k-Minkowski space-time, we have derived in this paper an extended first approximation of both Maxwell's equations and Lorentz force in doubly (or…
After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is…
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…
We prove the pointwise decay of solutions to three linear equations: (i) the transport equation in phase space generalizing the classical Vlasov equation, (ii) the linear Schrodinger equation, (iii) the Airy (linear KdV) equation. The usual…
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 curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
We analyze the transformation properties of Faraday law in an empty space and its relationship with Maxwell equations. In our analysis we express the Faraday law via the four-potential of electromagnetic field and the field of…
In this paper Maxwell equations are used to analyze the propagation of oscillating electric and magnetic fields from a moving electric dipole source. The results show that both the magnetic field and electric fields generated propagate…
In this extended note a critical discussion of an extension of the Lorentz transformations for velocities faster than the speed of light given recently by Hill and Cox is provided. The presented approach reveals the connection between…
In the usual Clifford algebra formulation of electrodynamics the Faraday bivector field F is decomposed into the observer dependent sum of a relative vector E and a relative bivector e_5 B by making a space-time split, which depends on the…
After a short Historical bibliographical note, in the Starting points attention will be focused on some postulates common to classical mechanics and special relativity. Starting from these premises, in the sections The deduction of the form…
We prove almost sharp decay estimates for the small data solutions and their derivatives of the Vlasov-Maxwell system in dimension $n \geq 4$. The smallness assumption concerns only certains weighted $L^1$ or $L^2$ norms of the initial…
The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the…
Einstein utilized Lorentz invariance from Maxwell's equations to modify mechanical laws and establish the special theory of relativity. Similarly, we may have a different theory if there exists another covariance of Maxwell's equations. In…