Derivation of the Lorentz Transformation from the Maxwell Equations

Abstract

The Special Theory of Relativity had been established nearly one century ago to conciliate some seemingly contradictory concepts and experimental results such as the Ether, universal time, contraction of dimensions of moving bodies, absolute motion of the Earth, speed of the light, etc. Hence the fundamental revolutionary formulas of the Theory, i.e., the Lorentz Formulas, had been derived first by Einstein by dwelling on a postulate which stipulated the constancy of the speed of the light. To this end he had first postulated that every reference system has a time proper to itself and then redefined the notions of simultaneity, synchronous clocks, time interval, the length of a rod in a system at rest, the length in a moving system, etc. A second postulate of Einstein, which stated that every physical theory is invariant under the Lorentz transformation, enabled him to claim that the Theory of Electromagnetism is correct but the Newtonian Mechanics has to be re-established. Since then the Theory was almost always presented in this way by both Einstein and others except only a few. The aim of this paper is to show that the Lorentz formulas can be derived from the Maxwell equations if one pstulates that the total electric charge of an isolated body does not change if it is in motion. To this end one dwells only on the permanence principle of functional equations, which is not a physical but purely mathematical concept. Thus, from one side the Special Relativity becomes a natural issue (or a part) of the Maxwell Theory and, from the other side, the derivation of the transformation rules pertinent to the electromagnetic field becomes straightforward and easy.

The Relativistic Proper-Velocity Transformation Group

“…According to a recent result of M. Idemen in [4], the Lorentz transformation group is inherent in Maxwell equations. Hence we finally remark that the discovery of the proper Lorentz transformation may pave the way to uncover the proper time Maxwell equations.…”

“…According to M. Idemen [4] the Lorentz transformation group is inherent in Maxwell equations. Hence, it is hoped that by employing techniques that Idemen developed in [4], our proper time, proper velocity Lorentz transformation group (32) can pave the way to uncover the proper time Maxwell equations. These, in turn, can reveal the electromagnetic field generated by a moving source in terms of the invariant proper time of the source.…”

“…Idemen has recently shown in [4] that the Lorentz transformation group of Einstein's special theory of relativity is inherent in Maxwell equations. One may therefore hope that the translation of the Lorentz group from its standard representation by means of coordinate time and coordinate velocities to a new representation by means of proper time and proper velocities will pave the way for the translation of Maxwell equations from their standard coordinate time representation to their proper time representation.…”

Electromagnetostatic Charges and Fields in a Rotating Conducting Sphere

“…Consider an isolated conducting body of revolution that rotates with constant angular velocity ω ω ω = ωu z around its axis of revolution. Under steady-state conditions, in the inertial rest frame Σ I of the axis (the lab frame), according to Minkowski's electrodynamics of moving media ( [22][23][24][25], cf also [26][27][28]), for the system considered Maxwell's equations reduce to…”

Analysis of Output Power Delay in Coaxial Vircator

“…The beam passes through the anode, and is injected into the area on the other side of the anode. When the beam current is higher than the space-charge-limited current of this area, a virtual cathode is formed at certain position that reflects a certain part of the electron beam [7]. The position of the virtual cathode and the ratio of beam reflection depend very much on the electron energy.…”