  In this paper we show how to compute the shear relaxation time from an
underlying microscopic theory. We prove that the shear relaxation time in
Israel-Stewart-type theories is given by the inverse of the pole of the
corresponding retarded Green's function, which is nearest to the origin in the
complex energy plane. Consequently, the relaxation time in such theories is a
microscopic, and not a macroscopic, i.e., fluid-dynamical time scale.
