  The spatially nonlocal response functions are proposed which nearly coincide
with the commonly used local response for electromagnetic fields and
fluctuations on the mass shell, but differ significantly for the off-shell
fluctuating field. It is shown that the fundamental Lifshitz theory using the
suggested response functions comes to an agreement with the measurement data
for the Casimir force without neglecting the dissipation of free electrons. We
demonstrate that reflectances of the on-shell electromagnetic waves calculated
using the nonlocal and commonly employed local responses differ only slightly.
The Kramers-Kronig relations for nonlocal response functions possessing the
first- and second-order poles at zero frequency are derived, i.e., the proposed
response satisfies the principle of causality. An application of these results
to resolution of the Casimir puzzle, which lies in the fact that the Lifshitz
theory is experimentally consistent only with discarded dissipation, is
discussed.
