  We consider the Casimir pressure between two metallic plates and calculate
the four contributions to it determined by the propagating and evanescent waves
and by the transverse magnetic and transverse electric polarizations of the
electromagnetic field. The range of interplate separations is considered where
nearly the whole pressure has its origin in the electromagnetic response of
conduction electrons. In the Casimir physics, this response is described either
by the dissipative Drude model resulting in contradictions with the measurement
data or by the experimentally consistent but dissipationless plasma model. It
is shown that the total transverse magnetic contribution to the Casimir
pressure due to both the propagating and evanescent waves and the transverse
electric contribution due to only the propagating waves, computed by means of
the Drude model, correlate well with the corresponding results obtained using
the plasma model. The conclusion is made that a disagreement between the
theoretical predictions obtained using the Drude model and precision
measurements of the Casimir force is not caused by the account of dissipation
in itself, but arises from an incorrect description of the response of metals
to the low-frequency transverse electric evanescent waves by this model. It is
demonstrated that the Drude model has no supporting experimental evidence in
the range of transverse electric evanescent waves, so that the above conclusion
is consistent with all available information. The alternative test of the Drude
model for the transverse electric evanescent waves suggested in the framework
of classical electrodynamics is discussed.
