  The derivation of Casimir forces between dielectrics can be simplified by
ignoring absorption, calculating energy changes due to displacements of the
dielectrics, and only then admitting absorption by allowing permittivities to
be complex. As a first step towards a better understanding of this situation we
consider in this paper the model of a dielectric as a collection of
oscillators, each of which is coupled to a reservoir giving rise to damping and
Langevin forces on the oscillators and a noise polarization acting as a source
of a fluctuating electromagnetic (EM) field in the dielectric. The model leads
naturally to expressions for the quantized EM fields that are consistent with
those obtained by different approaches, and also results in a
fluctuation-dissipation relation between the noise polarization and the
imaginary part of the permittivity; comparison with the Rytov
fluctuation-dissipation relation employed in the well-known Lifshitz theory for
the van der Waals (or Casimir) force shows that the Lifshitz theory is actually
a classical stochastic electrodynamical theory. The approximate classical
expression for the energy density in a band of frequencies at which absorption
in a dielectric is negligible is shown to be exact as a spectral thermal
equilibrium expectation value in the quantum-electrodynamical theory. Our main
result is the derivation of an expression for the QED energy density of a
uniform dispersive, absorbing media in thermal equilibrium. The spectral
density of the energy is found to have the same form with or without
absorption. We also show how the fluctuation-dissipation theorem ensures a
detailed balance of energy exchange between the (absorbing) medium, the
reservoir and the EM field in thermal equilibrium.
