  A close examination of the Maxwell-Lorentz theory of electrodynamics reveals
that polarization and magnetization of material media need not be treated as
local averages over small volumes - volumes that nevertheless contain a large
number of electric and/or magnetic dipoles. Indeed, Maxwell's macroscopic
equations are exact and self-consistent mathematical relations between
electromagnetic fields and their sources, which consist of free charge, free
current, polarization, and magnetization. When necessary, the discrete nature
of the constituents of matter and the granularity of material media can be
handled with the aid of special functions, such as Dirac's delta-function. The
energy of the electromagnetic field and the exchange of this energy with
material media are treated with a single postulate that establishes the
Poynting vector S = ExH as the rate of flow of electromagnetic energy under all
circumstances. Similarly, the linear and angular momentum densities of the
fields are simple functions of the Poynting vector that can be unambiguously
evaluated at all points in space and time, irrespective of the type of material
media, if any, that might reside at various locations. Finally, we examine the
Einstein-Laub force- and torque-density equations, and point out the
consistency of these equations with the preceding postulates, with the
conservation laws, and with the special theory of relativity. The set of
postulates thus obtained constitutes a foundation for the classical theory of
electrodynamics.
