  We present an entirely microscopic calculation of the Casimir force $f(d)$
between two metallic plates in the limit of large separation $d$. The models of
metals consist of mobile quantum charges in thermal equilibrium with the photon
field at positive temperature $T$. Fluctuations of all degrees of freedom,
matter and field, are treated according to the principles of quantum
electrodynamics and statistical physics without recourse to approximations or
intermediate assumptions. Our main result is the correctness of the asymptotic
universal formula $ f(d) \sim -\frac{\zeta(3) \kB T}{8\pi d^3}$, $d\to\infty$.
This supports the fact that, in the framework of Lifshitz' theory of
electromagnetic fluctuations, transverse electric modes do not contribute in
this regime. Moreover the microscopic origin of universality is seen to rely on
perfect screening sum rules that hold in great generality for conducting media.
