The law of equipartition breaks down when the thermal energy k B T is significantly smaller than the spacing between energy levels. Equipartition no longer holds because it is a poor approximation to assume that the energy levels form a smooth continuum, which is required in the derivations of the equipartition theorem above. Historically, the failures of the classical equipartition theorem to explain specific heats and black-body radiation were critical in showing the need for a new theory of matter and radiation, namely, quantum mechanics and quantum field theory.