A LOSS OF IDENTITY: THE BIRTH OF QUANTUM STATISTICS 431
form alternative to Eq. 23.13. He counted the number of ways in which Ns indis-
tinguishable particles in the dEs interval can be partitioned over the Z! cells. This
yields
Einstein's Eq. 23.21 rather than Bose's Eq. 23.13 is the one now used in all
textbooks.
- Einstein on the Third Law of Thermodynamics. As was noted at the end
of Section 20c, in 1914 Nernst introduced the hypothesis that the third law of
thermodynamics applies to gases. It was also mentioned that no sensible model of
a gas with that property was available at that time. In 1925 Einstein made his last
contribution to thermodynamics by pointing out that the BE gas does satisfy the
third law. (A Boltzmann gas does not do so, Einstein remarked.) Indeed, since all
particles go into the zero energy state as T — 0, we have in this limit N° = N,
all other A^ = 0. Hence W — 1 and S —• 0 as T — 0. It was as important to
him that a molecular BE gas yield Nernst's law as that a BE photon gas yield
Planck's law. - Einstein and Nonconservation of Photons. After 1917 Einstein ceased to
write scientific articles on questions related to radiation.* The only mention of
radiation in the 1924-5 papers is that 'the statistical method of Herr Bose and
myself is by no means beyond doubt, but seems only a posteriori justified by its
success for the case of radiation' [Ell].
There can be no doubt that he must have noted the nonconservation of photons.
In his language, this is implemented by putting A = 1 in Eq. 23.16. Yet I have
not found any reference to nonconservation, either in his scientific writings or in
the correspondence I have seen. I cannot state with certainty why he chose to be
silent on this and all further issues regarding photons. However, I do believe that
it is a fair guess that Einstein felt he would have nothing fundamental to say about
photons until such time as he could find his own way of dealing with the lack of
causality he had noted in 1917. Such a time never came.
Other physicists had followed Einstein's work on quantum statistics with inter-
est. Lorentz invited him to speak on this subject at the 1927 Solvay congress. Ein-
stein's reply, written in June 1927, may serve as a most appropriate preliminary
to my subsequent discussion of quantum mechanics.
I recall having committed myself to you to give a report on quantum statistics
at the Solvay congress. After much reflection back and forth, I come to the con-
viction that I am not competent [to give] such a report in a way that really'Except for a brief refutation of an objection to his work on needle radiation [E9]. I found a notice
by Einstein in 1930 announcing a new paper on radiation fluctuations [E10]. This paper was never
published, however.(23.21)