17 The Laws of Black Body Radiation just confirm the Transformation of k · T
A cavity in a black body of temperature T jis filled with radiation. Friedrich Hasenöhrl has analyzed the state variables of this radiation (in thermal equilibrium) and the transformation of these state variables due to a velocity v of the cavity relative to an observer. He did this in 1904, that is before Einstein's first publication on STR !
Hasenöhrl used nothing but electrodynamics (cf. Pauli's above mentioned publication , § 49, p.697). Radiation, moved in a box, carries momentum and massi! Kurd von Mosengeil reformulated these results 1906 in terms of STR. Mosengeil died very young in a climbing accident. So Planck told another assistent of his, namely Max von Laue, to give von Mosengeil's dissertation the final touch. The complete results were published in 1907.
In all of these results a factor a · T4 jshows up - the only exception is the entropy term. Now, the konstant a jcontains the Boltzmann value k jto the power of 4, too (cf. Pauli's above mentioned publication, § 49, p.698)! Thus we only have a further path leading to the insight that the product k · T j transforms for a fast moving observer by multiplying with the root. There is no additional hint on which of the state variables, temperature T jor entropy Sj, should be invariant in STR.