Relativistic Formulation of Maxwell’s Equations for Free Space

Einstein assumed in his Special Theory of Relativity that Maxwell’s equations, including Faraday’s law and the AmpereMaxwell equation, were invariant in any inertial frame, and that the Lorentz transformation equations must be used when two inertial frames were in relative motion. Starting with a modification of the Ampere-Maxwell equation that allows for two observers of the magnetic field in different inertial frames, I offer an alternative formulation of Maxwell’s wave equations for free space. The modification is based on two equal but different definitions of the speed of light. One definition relates to the particle-like properties of light and the other relates to the wave-like properties of light. The proposed formulation is consistent with the two postulates of the Special Theory of Relativity. The resulting equations, which are invariant in any inertial frame and are based on Euclidean space and Newtonian time, do not require the Lorentz transformations. The resulting equations allow for anisotropy in the electromagnetic waves that leads to an anisotropy in the Poynting vector that is able to act on a particle with a charge and/or a magnetic moment moving through a radiation field. The anisotropy of the Poynting vector results in radiation friction that opposes the movement of the particle and limits the velocity of the particle to the speed of light.