Title: Longitudinal electric field: from Maxwell equation to non-locality in time and space,
Abstract: In this paper we use the classical electrodynamics to show that the Lorenz
gauge can be incompatible with some particular solutions of the d Alembert
equations for electromagnetic potentials. In its turn, the d Alembert equations
for the elec- tromagnetic potentials is the result of application of the Lorenz
gauge to general equations for the potentials. The last ones is the
straightforward consequence of Maxwell equations. Since the d Alembert
equations and the electromagnetic poten- tials are necessary for quantum
electrodynamics formulation, one should oblige to satisfy these equations also
in classical case. The solution of d Alembert equations, which modifies
longitudinal electric field is found. The requirement of this modifi- cation
follows from the necessity to satisfy the physical condition of impossibility
of instantaneous transferring of interaction in space.