EINSTEIN AS A TRANSITIONAL FIGURE: THE BIRTH OF WAVE MECHANICS 437where Z(v) is the number of states per interval dv given in Eq. 23.4. In his paper
submitted on January 8, 1925, Einstein showed that Eq. 24.2 holds equally well
for his quantum gas, as long as one defines v in the latter case by E = hv = p^1 /
2m and uses Eq. 23.15 instead of Eq. 23.4 for the number of states [E2].
When discussing radiation in 1909, Einstein recognized the second term of Eq.
24.1 as the familiar wave term and the first one as the unfamiliar particle term.
When in 1924 he revisited the fluctuation problem for the case of the quantum
gas, he noted a reversal of roles. The first term, at one time unfamiliar for radia-
tion, was now the old fluctuation term for a Poisson distribution of (distinguish-
able) particles. What to do with the second term (which incorporates indistin-
guishability effects of particles) for the gas case? Since this term was associated
with waves in the case of radiation, Einstein was led to 'interpret it in a corre-
sponding way for the gas, by associating with the gas a radiative phenomenon'
[E2]. He added, 'I pursue this interpretation further, since I believe that here we
have to do with more than a mere analogy.'
But what were the waves?
At this point, Einstein turned to de Broglie's thesis [B7], 'a very notable pub-
lication.' He suggested that a de Broglie-type wavefield should be associated with
the gas and pointed out that this assumption enabled him to interpret the second
term in Eq. 24.2. Just as de Broglie had done, he also noted that a molecular
beam should show diffraction phenomena but added that the effect should be
extremely small for manageable apertures. He also remarked that the de Broglie
wavefield had to be a scalar (the polarization factor is 2 for Eq. 23.4, as noted
above, but it is 1 for Eq. 23.15!).
It is another of Einstein's feats that he would be led to state the necessity of the
existence of matter waves from the analysis of fluctuations. One may wonder what
the history of twentieth century physics would have looked like had Einstein
pushed the analogy still further. However, with the achievement of an indepen-
dent argument for the particle-wave duality of matter, the twenty-year period of
highest scientific creativity in Einstein's life, at a level probably never equalled,
came to an end.
Postscript, Summer 1978. In the course of preparing this chapter, I noticed
a recollection by Pauli of a statement made by Einstein during a physics meeting
held in Innsbruck in 1924. According to Pauli, Einstein proposed in the course of
that meeting 'to search for interference and diffraction phenomena with molecular
beams' [PI]. On checking the dates of that meeting, I found them to be September
21-27. This intrigued me. Einstein arrived at the particle-wave duality of matter
via a route that was independent of the one taken by de Broglie. The latter
defended his thesis in November. If Pauli's memory is correct, then Einstein made
his remark about two months prior to that time. Could he have come upon the
wave properties of matter independently of de Broglie? After all, Einstein had
been thinking about the molecular gas since July. The questions arise, When did