  The standard expression of the high-temperature Casimir force between perfect
conductors is obtained by imposing macroscopic boundary conditions on the
electromagnetic field at metallic interfaces. This force is twice larger than
that computed in microscopic classical models allowing for charge fluctuations
inside the conductors. We present a direct computation of the force between two
quantum plasma slabs in the framework of non relativistic quantum
electrodynamics including quantum and thermal fluctuations of both matter and
field. In the semi-classical regime, the asymptotic force at large slab
separation is identical to that found in the above purely classical models,
which is therefore the right result. We conclude that when calculating the
Casimir force at non-zero temperature, fluctuations inside the conductors can
not be ignored.
