  In the classical theory of electromagnetism, the permittivity and the
permeability of free space are constants whose magnitudes do not seem to
possess any deeper physical meaning. By replacing the free space of classical
physics with the quantum notion of the vacuum, we speculate that the values of
the aforementioned constants could arise from the polarization and
magnetization of virtual pairs in vacuum. A classical dispersion model with
parameters determined by quantum and particle physics is employed to estimate
their values. We find the correct orders of magnitude. Additionally, our simple
assumptions yield an independent estimate for the number of charged elementary
particles based on the known values of the permittivity and the permeability,
and for the volume of a virtual pair. Such interpretation would provide an
intriguing connection between the celebrated theory of classical
electromagnetism and the quantum theory in the weak field limit.
