  We study the physical content of the electromagnetic vacuum energy of a
random medium made of atomic electric dipoles. First, we evaluate the
contribution of statistical fluctuations to the average total vacuum energy,
which is made out of the integration of the variations of the Lamb shift with
respect to the coupling constant. While the Lamb shift is a function of the
electrical susceptibility only, the vacuum energy is generally not. Second, we
make clear why the effective medium bulk energy does not account for the total
vacuum energy of a molecular dielectric. Consequently, the Lamb shift does not
derive from the effective medium bulk energy except at leading order in the
molecular density. The local field factors provide natural cutoffs for the
spectrum of the total vacuum energy at a wavelength of the order of the
correlation length. Third, we investigate to what extent shifts in the spectrum
of the dielectric constant may be attributed to the binding energy of a
dielectric. In particular, in the continuum approximation we have found a
relation between the electrostatic binding energy and the Lorentz-Lorenz shift.
Nonetheless, we conclude that the knowledge of the spectrum of the refractive
index is insufficient either to quantify the energy of radiative modes or to
estimate the electrostatic binding energy of molecular clusters.
