  A remarkable feature of quantum many-body systems is the orthogonality
catastrophe which describes their extensively growing sensitivity to local
perturbations and plays an important role in condensed matter physics. Here we
show that the dynamics of the orthogonality catastrophe can be fully
characterized by the quantum speed limit and, more specifically, that any
quenched quantum many-body system whose variance in ground state energy scales
with the system size exhibits the orthogonality catastrophe. Our rigorous
findings are demonstrated by two paradigmatic classes of many-body systems --
the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin
model.
