  We study the time-dependent tachyon backgrounds of the string collective
field theory using the formalism of the $S$-matrix generating functional. In
the process we clarify the connection between two ways of calculating the
$S$-matrix, the one using the Feynman rule and the other using the classical
solution to the nonlinear equation of motion. We develop the formalism for
general backgrounds and apply it to the gravitational sine-Gordon model in
detail. We reproduce the conformal field theory calculation which was based on
expanding around the static $c=1$ theory. Furthermore, we prove that the tree-
level partition function of this model shows the scaling behavior corresponding
to $c=0$ model in the limit $p \to 0$ of sine-Gordon `momentum' $p$.
