Using only classical electromagnetic energy conservation laws and causality, we show that the net average power absorbed by any mechanically isolated illuminated medium in steady state must be zero, but that for linear model media it is nonzero. This contradiction implies that all media must behave inelastically. We also show in general that the average power absorbed at an incident frequency, which is equal to the total taken from an incident wave minus that scattered elastically, is also equal to the average power scattered inelastically plus that carried off mechanically, if any. Finally, we infer that while the conventional linear theory cannot predict the spectral distribution of inelastic scattering, it may be applied as always to predict the propagation, absorption, and elastic scattering of weak illumination in passive media.