  At the physical level of rigour it is shown that there are no substantial
theoretical arguments in favour of using either plasma mode permittivity or
Drude model permittivity in the Lifshitz formula. The decision in this question
rests with the comparison of theoretical calculations with the experiment. In
the course of the study the derivation of the fluctuation-dissipation theorem
is proposed where it is displayed clear at which reasoning stage and in what
way the dissipation is taken into account. In particular it is shown how this
theorem works in the case of the system with reversible dynamics, that is when
dissipation is absent. Thereby it is proved that explicit assertion according
to which this theorem is inapplicable to systems without dissipation is
erroneous. The research is based on making use of the rigorous formalism of
equilibrium two-time Green functions in statistical physics at finite
temperature.
