We discuss the emergence of an orthogonality catastrophe in the respon
se of a composite fermion liquid as the filling factor nu approaches 1
/2m, where m = 1.2. 3.... A tunnelling experiment is proposed in which
dramatic changes in the I-V characteristic should be observable as nu
is varied. Explicit I-V characteristics calculated within the so-call
ed modified random phase approximation, are provided for nu = 1/3 -->
1/2.