Derivation of Lorentz Field Dependent Transformation using Lorentz Electromagnetic Force Equation

Abstract

Lorentz transformation is one of the cornerstone of special relativity. It is concerned only with inertial frames within the framework of special relativity, but doing nothing for non-inertial frames. Attempts were made to account for this effect by using space-time language, without any link with electromagnetic theory. The aim of this work is to cure this defect. The research methodology is based on the mathematical analytical framework of electromagnetic Lorentz force. Then the result obtained is compared with previous studies and observations. The Lorentz electromagnetic expression for the force, beside Maxwell relation between electric and magnetic field intensity are used to find Lorentz force in terms of velocity and electric field intensity. This relation of magnetic and electric field intensity was found by using two approaches, in one of them the relation between the curl of electric intensity with the time variation of the magnetic one was used, in the second approach the relation between curl of magnetic intensity with the displacement current was used also. The velocity in accelerated frame and curved space-time is incorporated in this expression to make Lorentz sensitive to field’s potentials. The field potential was incorporated first by replacing the acceleration with the potential in Newton’s equations of motion, then replacing the average velocity with final velocity and potential. In another approach, the expression for the interval was also used to relate the average velocity to the final velocity and potential. A third approach used the interval in a curved space to incorporate the potential through space-time Lorentz transformation. Fortunately, this transformations reduces to that of SR in the absence of fields, thus share with it all its success and compatibility with observations. It also conforms with generalized special relativity, thus shares with it also all its successes. More importantly it link electromagnetic theory with generalized Lorentz transformations.