Derivation of Maxwell's equations: The statistical theory of the macroscopic equations

Abstract

The macroscopic Maxwell equations are derived in covariant way from the “atomic field equations”. The latter were themselves obtained previously from the field equations of electron theory for point particles, by means of a covariant multipole expansion. In the statistical derivation an appropriate averaging procedure is used in a so-called “ fluxion space”, i.e., the space spanned by the atomic positions, the atomic multipole moments and the first and higher time derivatives of these variables, on which the fields may depend. Retardation of the fields is also taken into account.