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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 unphysical. However, these scalar expressions might have the meaning of a new physical field, 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 S, after reformulating the IPWE in terms of fields. V.
The introduction of gauge conditions in CED implies that scalar derivatives of the electromagnetic potentials are non-physical. This negative hypothesis cannot be tested, and it should be reversed into the testable and positive hypothesis of measurable scalar field effects, such as longitudinal electric vacuum waves, longitudinal electrodynamic forces, and energy conversions by means of static charge and a scalar field. If these effects cannot be detected in general, then finally a physical justification for gauge conditions has been obtained. However, there are indications that positive results have been achieved. Further quantitative tests are needed in order to obtain scientific proof for the existence of a physical scalar field S, as defined in this paper. A positive quantitative verification will have enormous consequences for the science of physics. The qualifications ”unphysical” scalar photons and ”unphysical” longitudinal photons are incorrect, since these qualifications require experimental proof and the usual arguments that seem to prove them are circular. This neglect of Galileo Galilei’s philosophy of physics by the physics community, with respect to gauge conditions, had serious consequences for one of the most brilliant minds in history, Nikola Tesla. There are urgent reasons to review Tesla’s scientific legacy, such as the need for new forms of energy and new energy technologies.