  The Casimir friction problem for a pair of dielectric particles in relative
motion is analyzed, utilizing a microscopic model in which we start from
statistical mechanics for harmonically oscillating particles at finite
temperature moving nonrelativistically with constant velocity. The use of
statistical mechanics in this context has in our opinion some definite
advantages, in comparison with the more conventional quantum electrodynamic
description of media that involves the use of a refractive index. The
statistical-mechanical description is physical and direct, and the oscillator
model, in spite of its simplicity, is nevertheless able to elucidate the
essentials of the Casimir friction. As is known, there are diverging opinions
about this kind of friction in the literature. Our treatment elaborates upon,
and extends, an earlier theory presented by us back in 1992. There we found a
finite friction force at any finite temperature, whereas at zero temperature
the model led to a zero force. As an additional development in the present
paper we evaluate the energy dissipation making use of an exponential cutoff
truncating the relative motion of the oscillators. For the dissipation we also
establish a general expression that is not limited to the simple oscillator
model.
