A generalisation of classical electrodynamics for the prediction of scalar field effects

Abstract

Within the framework of Classical Electrodynamics (CED) it is common practice to choose freely an arbitrary gauge condition with respect to a gauge transformation of the electromagnetic potentials. The Lorenz gauge condition allows for the derivation of the inhomogeneous potential wave equations (IPWE), but this also means that scalar derivatives of the electromagnetic potentials are considered to be \emph{unphysical}. However, these scalar expressions might have the meaning of a new physical field, $\mathsf S$. If this is the case, then a generalised CED is required such that scalar field effects are predicted and such that experiments can be performed in order to verify or falsify this generalised CED. The IPWE are viewed as a generalised Gauss law and a generalised Ampe\`re law, that also contain derivatives of $\mathsf S$, after reformulating the IPWE in terms of fields. Some recent experiment show positive results that are in qualitative agreement with the presented predictions of scalar field effects, but further quantitative tests are required in order to verify or falsify the presented theory. The importance of Nikola Tesla's pioneering research, with respect to the predicted effects, cannot be overstated.