Invariance of Electric and Magnetic Fields in Relativistic Electrodynamics

Abstract

<title>Abstract</title> <p>The classical four-dimensional spacetime coordinate approach of special relativity is known to yield the electric (or magnetic) field components in one reference frame as mixture of both electric and magnetic field components in another reference frame. In this work we show that adding two extra time coordinates to four dimensional spacetime coordinates of classical theory yields electric (or magnetic) field components in one frame as mixture of only electric (magnetic) field components in another frame. In doing so, we use the conformal invariance condition for the six-dimensional metric and homogeneous Maxwell’s electromagnetic wave equations under the Voigt transformation between two massive inertial frames to derive a set of six dimensional linear spacetime coordinate equations in forward and inverse Lorentz transformations. The three space coordinates yield time contraction (expansion) of volume with three-time coordinates vary linearly with space coordinates for forward (inverse) transformation between two massive frames moving relative to each other. We show that in such massive inertial framework the cartesian components of electric and magnetic fields are Lorentz invariant along three axes between two massive inertial frames. Furthermore, we prove that the components of electric and magnetic fields in one massive inertial frame can be expressed in terms of their components in another massive inertial frame. We further show that Maxwell’s electromagnetic wave equations are Lorentz invariant between two massive inertial frames in vacuum and material medium with and without charge and current.</p>