Electrodynamics of the 2D superconductor-insulator transition

Using microwave cavities and a novel cryogenic system we have probed the evolution of the low frequency electrodynamics of thin InO$_x$ films across the nominal 2D field-tuned superconductor insulator quantum phase transition. Such a finite study allows us, at least in principle, to access the true phase coherent ($\hbar \omega > k_B T$) quantum critical behavior. A number of other interesting items are found including evidence for significant finite frequency superfluid density well into the ``insulating" regime of the phase diagram. Various scenarios for frequency dependent scaling are also investigated.