Abstract

In this work, Maxwell-Hertz electrodynamics (MHE), valid for non-uniform motions as they occur in the physical reality and hold for the non-inertial reference frame of our laboratory but at small velocities only, is extended at relativistic velocities.  The new theory, called Hertz's relativistic electrodynamics only, is completely independent and built-up in a completely different way as regards Einstein's special relativity (ESR).  HRE, a coordinate-free formulation, does not need postulates, but confirms the constancy principle of speed of light in vacuum.  All experiments of first and second order in v²/c² are correctly interpreted.  To this theory a Hertzian kinematics and dynamics are associated.  HRE with its corresponding mechanics from Hertz's special relativity (HSR), as a complementary theory to ESR.  According to the principle of complementary and neglecting the gravitational effects, the Extended Special Relativity (ExSR) is a double faced theory which becomes either ESR when the motion is inertial or HSR when the motion is non-inertial.  The complementarity of both theories assumes that the two descriptions cannot be employed for the same motion, being mutually exclusive.  Consequently, to every statement of one of the ExSR a complementary statement of the other ExSR corresponds.  The completeness of ESR with HSR ensures an extended view over the relativity in our physical world.