70 STATISTICAL PHYSICSif V is small.* Thus he believed that radiation is 'the only kind of physical system
... of which we can suspect that it exhibits an energy fluctuation.'
This subject deserves two comments. First, the conclusion is incorrect. Consider
the radiation to be composed of n modes. Then (E) = aVT^4 = nkT, so that
again £ = 0(n"'). In the classical theory (which, of course, Einstein was using in
1904), fluctuations are therefore not all that different for radiation and for an
ideal gas. Second, the reasoning was most important for Einstein's work in 1905,
since it drew his attention to the volume dependence of thermodynamic quantities,
a dependence which played a crucial role in his formulation of the light-quantum
hypothesis, which appeared in his very next paper.
Nevertheless, in 1904 Einstein had already taken a bold new step (of which he
was aware): he had applied statistical reasonings to radiation.** In 1905 he was
to do this again. In 1909, Eq. 4.13 would again be his starting point, and it would
lead him to the realization of the particle-wave duality of electromagnetic radia-
tion. In 1925, a formula closely related to Eq. 4.13 would make it clear to him
that a similar duality has to exist for matter. These topics will be discussed in
detail in Part VI of this book. For now, two last comments on Eq. 4.13. When
Einstein first derived it, he did not know that Gibbs had done so before him [G2].
And it is his most important and only memorable result prior to 1905.
In May 1905, Einstein was again busy with fluctuations, though in a different
style, when he did his work on Brownian motion, to be discussed in Chapter 5.
The remainder of the present chapter is devoted to a discussion of Einstein's gen-
eral views on statistical physics, in 1905 and in the years following.4d. Einstein and Boltzmann's Principle
I have already stressed that all of Einstein's main contributions to the quantum
theory are statistical in origin. Correspondingly, most of his more important com-
ments on the principles of statistical mechanics are found in his papers on quan-
tum physics. His light-quantum paper of 1905 [E13] is a prime example. Two-
and-a-half of its seventeen pages deal with the photoelectric effect—nine with sta-
tistical and thermodynamic questions. This paper, in which the term Boltzmann's
principle appears in the literature for the first time, contains a critique of Boltz-
mann's statistical method.
During the years 1905 to 1920, Einstein stated_more than once his displeasure
with the handling of probability by others. In 1905 he wrote, 'The word proba-
bility is used in a sense that does not conform to its definition as given in the theory
of probability. In particular, "cases of equal probability" are often hypothetically
defined in instances where the theoretical pictures used are sufficiently definite to
*For £ = 1, F'/3 « 0.4/Tand X^ « 0.3/7. Einstein found this near-coincidence pleasing.
**Rayleigh had done so before him (see Section 19b), but I do not believe that Einstein knew that
in 1904.