In his article on the Zero-point Energy: http://www.calphysics.org/zpe.html Bernard Haisch says: That the spectrum of zero-point radiation has a frequency-cubed dependence is of great significance. That is the only kind of spectrum that has the property of being Lorentz invariant. The effect of motion is to Doppler shift detected electromagnetic radiation, but a frequency-cubed spectrum has the property that up- and down-shifting of the radiation is exactly compensated, i.e. there is as much radiation Doppler shifted into a given frequency interval as there is shifted out by uniform motion. Does anyone know a (simple) proof that a frequency-cubed energy spectrum is Lorentz invariant?