D O C . 1 2 9 T H E O R Y O F R A D I A T I O N E Q U I L I B R I U M 1 2 5

129. “On the Quantum Theory of Radiation

Equilibrium”

[Einstein and Ehrenfest 1923]

Received 16 October 1923

Published 8 December 1923

In: Zeitschrift für Physik 19 (1923): 301–306.

In a paper to appear imminently in this journal on the compatibility between

Planck’s radiation formula and the quantum theory of radiation scattering by freely

moving electrons, W. Pauli has postulated an interesting statistical law for the prob-

ability with which elementary scattering events by quanta, as is possible according

to the theory by Compton and Debye, occur in an (isotropic) radiation

field.[1]

This

involves an elementary process of scattering, in which on the one hand a quantum

is transferred from one directional domain dκ and frequency domain dν into anoth-

er directional domain dκ′ and frequency domain dν′, while on the other hand, at the

same time, an electron from a three-dimensional velocity (i.e. momentum) domain

dω is transferred by collision into another domain dω′ differing finitely, such that

during this transfer the conservation laws of momentum and energy are preserved.

For the probability of such “transitions of a determined kind” Pauli hypothetically

proposed the probability law

(1)

Here ρ means the radiation density belonging to ν, the ρ′ the density belonging to

ν′, while A and B denote the quantities dependent on the choice of elementary do-

mains but independent of ρ (ν ). Pauli shows that given the validity of a statistical

law of this form, an electron gas with a Maxwellian velocity distribution stays in

statistical equilibrium with a Planck radiation field of the same temperature.

The apparently paradoxical issue about this equation is the second term in the

parentheses, according to which the number of elementary events of scattering oc-

curring to an electron (quasi at rest) per unit time increases faster than in proportion

to the radiation density, and depends on the radiation density ρ′ of frequency ν′

which the quantum modified by the elementary event manifests. Pauli showed,

however, that upon omission of this term, Wien’s radiation formula would have to

[p. 301]

dW Aρ Bρρ′)dt + ( =