Wien's displacement law, expressed as E(T,ν) = ν³F(ν/T), predicts infinite radiation energy due to the divergence of the integral when integrating over all frequencies from 0 to infinity. This conclusion stems from classical statistical physics principles applied by Lord Rayleigh in June 1900, where he derived the function F as a constant. While the derivation is correct within classical physics, it leads to the absurdity of infinite total radiation energy, which is not physically realizable.
PREREQUISITESPhysicists, students of quantum mechanics, and anyone interested in the historical and theoretical aspects of radiation laws and their implications in physics.
... Rayleigh, who apparently found the function F in June 1900. He used a standard result from classical statistical physics (the equality, or “equipartition” of energy among all the degrees of freedom) and applied it to the radiation oscillators. He found F to be a constant. The result is perfectly correct from the standpoint of classical physics but at the same time perfectly absurd because his expression predicts that the total radiation energy (E(T,v)dv is infinite.