THE PHOTON 405
It was known at that time that one can obtain Planck's expression for p by
introducing the quantum prescription* that the electromagnetic field oscillators
could have only energies nhv. However, both Ornstein and Zernike, and Ehren-
fest found that the same prescription applied to the fluctuation formula gave the
wrong answer. The source of the trouble seemed to lie in Einstein's entropy
additivity assumption (see Eq. 4.21). According to Uhlenbeck (private communi-
cation), these discrepancies were for some years considered to be a serious prob-
lem. In their joint 1925 paper, Born, Heisenberg, and Jordan refer to it as a
fundamental difficulty [Bl]. In that same paper, it was shown, however, that the
new quantum mechanics applied to a set of noninteracting oscillators does give the
Einstein answer. The noncommutativity of coordinates and momenta plays a role
in this derivation. Again, according to Uhlenbeck (private communication), the
elimination of this difficulty was considered one of the early successes of quantum
mechanics. (It is not necessary for our purposes to discuss subsequent improve-
ments on the Heisenberg-Born-Jordan treatment.))**
21 b. Spontaneous and Induced Radiative Transitions
After 1909 Einstein continued brooding about the light-quantum for almost
another two years. As mentioned in Chapter 10, in May 1911 he wrote to Besso,
'I do not ask anymore whether these quanta really exist. Nor do I attempt any
longer to construct them, since I now know that my brain is incapable of fath-
oming the problem this way' [E6]. For the time being, he was ready to give up.
In October 1911 Einstein (now a professor in Prague) gave a report on the quan-
tum theory to the first Solvay Congress [E7], but by this time general relativity
had already become his main concern and would remain so until November 1915.
In 1916, he returned once again to blackbody radiation and made his next
advance. In November 1916 he wrote to Besso, 'A splended light has dawned on
me about the absorption and emission of radiation' [E8]. He had obtained a deep
insight into the meaning of his heuristic principle, and this led him to a new der-
ivation of Planck's radiation law. His reasoning is contained in three papers, two
of which appeared in 1916 [E9, E10], the third one early in 1917 [Ell]. His
method is based on general hypotheses about the interaction between radiation
and matter. No special assumptions are made about intrinsic properties of the
objects which interact with the radiation. These objects 'will be called molecules
in what follows' [E9]. (It is completely inessential to his arguments that these
molecules could be Planck's oscillators!)
Einstein considered a system consisting of a gas of his molecules interacting
with electromagnetic radiation. The entire system is in thermal equilibrium.
"The elementary derivation due to Debye is found in Section 24c.
"The reader interested in these further developments is referred to a paper by Gonzalez and Werge-
land, which also contains additional references to this subject [Gl].