3 1 2 D O C U M E N T 3 0 9 A U G U S T 1 9 2 4

The remarks about associated light quanta cannot shake my objection, because

the assumption of that possibility draws into question Bose’s entire ¢combinatorial²

statistical apparatus. Regarding the associated quanta, the probability of their pres-

ence is neither proportional to the spatial volume nor even to the volume in momen-

tum space; neither is the momentum cell equally large for all quanta of the same

color.

The assumption made so often in the literature about multiple quanta has hither-

to never been able to deliver the radiation law, rather always just to infer the degree

of association from it, that is, from its derivation

(Bothe).[6]

Bose’s combinatorial

apparatus would have to be changed as well in the case of association.

I do not want to close without referring once again to my comment expressed at

the outset.

With my best compliments to you, Professor, I am yours sincerely,

Otto Halpern.

The interchangeability of quanta inside the same cell that are supposed to decide

between Wien’s and Planck’s law, as you, Professor, have put forward, visibly does

not fulfill this purpose, because it legitimately applies both to the “urn statement”

as well as to the “sphere

statement.”[7]

309. To Otto Halpern

[Berlin, after 26 August

1924][1]

Dear Colleague,

You clearly illuminated in your letters a point of essential

significance.[2]

Two

different hypotheses are indeed involved regarding elementary cases of equal prob-

ability.

(1). All distributions of the individual quanta throughout the “cells” are equally

probable (Wien’s law).

(2). All the different models of quantum distributions across the cells are equally

probable (Planck’s law).

Hypothesis (2) does not fit with the hypothesis of an independent distribution of

the individual quanta but rather expresses—in the language of the theory of exist-

ing quanta—a mutual dependence of the latter on one another.