  The scattering matrix was measured for a flat microwave cavity with
classically chaotic dynamics. The system can be perturbed by small changes of
the geometry. We define the "scattering fidelity" in terms of parametric
correlation functions of scattering matrix elements. In chaotic systems and for
weak coupling the scattering fidelity approaches the fidelity of the closed
system. Without free parameters the experimental results agree with random
matrix theory in a wide range of perturbation strengths, reaching from the
perturbative to the Fermi golden rule regime.
