  We investigate the response of a two-dimensional electron gas, in the
fractional quantum Hall regime, to the sudden appearance of a localised charged
probe using the Chern-Simons theory of composite fermions. The dynamic
structure factor of the electron gas is found to have a major influence on the
spectral function of the probe. In particular, there is an orthogonality
catastrophe when the filling factor is an even-denominator filling fraction due
to the compressibility of the state, but there is no catastrophe at
odd-denominator filling factors because these states have a gap to excitations.
The catastrophe is found to be more severe for composite fermions in zero
effective magnetic field than it is for electrons in zero real magnetic field.
Oscillations in the spectral function, arising when the composite fermions are
at integer filling, have a period equal to the composite fermion cyclotron
energy. We propose a tunneling experiment which directly measures the spectral
function from which one could determine the composite fermion effective mass.
