D O C U M E N T 3 0 8 A U G U S T 1 9 2 4 3 1 1

following the core of my objection again. Beforehand, though, I must express my

sincere regret—which should mean more than the usual manner of speech—about

my becoming a burden to you, time and again. Yet this time it’s happening for a

number of reasons. First of all, I hope that this letter will succeed in making the ex-

isting difference of opinion reach settlement along this route by letter.—Further-

more, the fact that a derivation of Planck’s radiation formula with the assumption

of independent light

quanta[1]

has been given also appears to me so fundamentally

important that every effort is appropriate toward elucidating its derivation; and fi-

nally, I would like to express my definite conviction that I am right about the fol-

lowing remarks (with reference to Ehrenfest and

Krutkow[2]

).

It concerns the following problem in probability theory: Given a number of K

spheres and U urns, we seek the most probable distribution of the K spheres over

the U urns. If we count the urns separately, there results altogether

distributions (combinations with repetition of U elements to the Kth class). In de-

termining the probability of a state, all distributions differing in that 2 urns merely

exchange their number of spheres should then be aggregated.

Thus far, all theories concur.[3]

Posing the question this way is meaningless, because it does not make any state-

ment yet about equally probable individual cases. The neglect of this point seems

to me to cause the difference of opinion on both sides. From among the manifold

of all assumptions about equally probable cases, we now draw 2, which we shall

call the urn and sphere statements.

First, the urn statement: Each one of the complexions is equally

probable. This statement corresponds to the Planck interpretation of radiation the-

ory. We illustrate this assumption by the simple example: 2 urns, 2 spheres. Ac-

cording to our above assumption, 2 of the 3 complexions, (2,0;

0,2)[4]

are identical;

their relevant distribution is twice as probable as the one in which there is one

sphere in each urn. I believe Bose also falsely calculates using this formula. His for-

mula for the probability transforms by specialization into those state-

ments.

Second, the sphere statement: Each sphere goes independently of the others with

equal probability into each urn. This corresponds to the distribution of independent

light quanta on resonators (eigenfrequencies, cells). According to this assumption,

the distribution 11 is just as probable as the distribution 20. The complete combi-

natorial formulas, indicated by Krutkow, then lead to Wien’s

formula.[5]

U K 1)! –+ (

K!( U 1)! –

------------------------------

U K 1)! –+ (

K!( U 1)! –

------------------------------

A!

p0!p1!p2!

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