  In this paper we analyze a Rutherford type experiment where light probes are
inelastically scattered by an ensemble of excited closed strings, and use the
corresponding cross section to extract density-density correlators between
different pieces of the target string. We find a wide dynamical range where the
space-time evolution of typical highly excited closed strings is accurately
described as a convolution of brownian motions. Moreover, we show that if we
want to obtain the same cross section by coherently scattering probes off a
classical background, then this background has to be time-dependent and
singular. This provides an example where singularities arise, not as a result
of strong gravitational self-interactions, but as a byproduct of the
decoherence implicit in effectively describing the string degrees of freedom as
a classical background.
