436 THE QUANTUM THEORY
published before him) the density of radiation states in terms of particle (photon)
language. That was in October 1923—one month after his enunciation of the
epochal new principle that particle-wave duality should apply not only to radia-
tion but also to matter. 'After long reflection in solitude and meditation, I suddenly
had the idea, during the year 1923, that the discovery made by Einstein in 1905
should be generalized by extending it to all material particles and notably to elec-
trons' [B7].
He made the leap in his September 10, 1923, paper [Bl]: E = hv shall hold
not only for photons but also for electrons, to which he assigns a 'fictitious asso-
ciated wave.' In his September 24 paper [B2], he indicated the direction in which
one 'should seek experimental confirmations of our ideas': a stream of electrons
traversing an aperture whose dimensions are small compared with the wavelength
of the electron waves 'should show diffraction phenomena.'
Other important aspects of de Broglie's work are beyond the scope of this book
(for more details, see, e.g.. [Kl]). The mentioned articles were extended to form
his doctoral thesis [B7], which he defended on November 25, 1924. Einstein
received a copy of this thesis from Langevin, who was one of de Broglie's exam-
iners. A letter to Lorentz (in December) shows that Einstein was impressed and
also that he had found a new application of de Broglie's ideas:
A younger brother of... de Broglie has undertaken a very interesting attempt
to interpret the Bohr-Sommerfeld quantum rules (Paris dissertation 1924). I
believe it is a first feeble ray of light on this worst of our physics enigmas. I,
too, have found something which speaks for his construction. [El]24b. From de Broglie to Einstein
In 1909 and again in 1917, Einstein had drawn major conclusions about radiation
from the study of fluctuations around thermal equilibrium. It goes without saying
that he would again examine fluctations when, in 1924, he turned his attention
to the molecular quantum gas.
In order to appreciate what he did this time, it is helpful to again present the
formula (Eq. 21.5) given earlier for the mean square energy fluctuation of elec-
tromagnetic radiation:
Put Vpdv=n(v)hv and (e^2 ) = A(v)^2 (hv)^2. The term n(v) can be interpreted as
the average number of quanta in the energy interval dv, and A(c)^2 as the mean
square fluctuation of this number. One can now write Eq. 24.1 in the form