It is pointed out that the Ferrell-Glover-Tinkham sum rule relating the 'missing area' in the low frequency conductivity to the penetration depth can be violated in certain superconductors. Its breakdown indicates that the effective mass of the carriers changes in entering the superconducting state, and implies a change in the conductivity at frequencies much higher than the superconducting gap, possibly near infrared or visible. The model of hole superconductivity predicts the existence of this phenomenon.