Necessary Physical Assumptions Underlying the Derivation of Planck’s Radiation Law

(F. Russell v. Bichowsky. Phys. Rev. 1918, No. 1).

In an address delivered at a meeting of the American Physical Society in Washington in April 1917, Russell v. Bichowsky pointed out that the common opinion according to which the quantization of energy is necessary for the derivation of Planck’s radiation law is not entirely correct. Bichowsky shows that the weakest side of Planck’s theory lies not in the fact that radiation has a quantum character, but in the assumption that Maxwell’s law of the uniform distribution of energy is applicable to black-body radiation.

In Bichowsky’s opinion, the assumptions that 1) Planck’s law

is an experimental fact; 2) radiation is of a quantum character; 3) Maxwell’s law is applicable to radiation—these assumptions are not independent of one another. The validity of any two of them necessarily leads to the third, and consequently by no mathematical transformations can one obtain Planck’s formula without making the assumption of the applicability of Maxwell’s law to radiation.

The source of the contradictions that exist between Planck’s theory and classical mechanics is Maxwell’s law, and only a proper generalization of it will make it possible to avoid these contradictions and to rid oneself of the necessity of assuming that radiation occurs in quanta. As such a generalization Bichowsky indicates Gibbs’s formula for the canonical distribution of energy, a formula which made it possible for S. Ratnowsky, from the smallest number of hypotheses, to arrive at Planck’s formula. Bichowsky reprints the mathematical part of Ratnowsky’s work as a supplement to his own work.

A. Predvoditelev.