56 STATISTICAL PHYSICStributions to statistical physics and kinetic theory as neither more nor less than
extremely ingenious and important applications of principles discovered indepen-
dently by him but initially developed by others. Take, for example, his treatment
of Brownian motion. It bristles with new ideas: particles in suspension behave like
molecules in solution; there is a relation between diffusion and viscosity, the first
fluctuation-dissipation theorem ever noted; the mean square displacement of the
particles can be related to the diffusion coefficient. The final conclusion,* that
Avogadro's number can essentially be determined from observations with an
ordinary microscope, never fails to cause a moment of astonishment even if one
has read the paper before and therefore knows the punch line. After 1905, Ein-
stein would occasionally mention in conversation that 'it is puzzling that Boltz-
mann did not himself draw this most perspicuous consequence [i.e., the explana-
tion of Brownian motion], since Boltzmann had laid the foundations for the whole
subject' [SI]. However, it is hard to imagine the embattled Boltzmann evincing
the serious yet playful spirit with which Einstein handled the problem of molec-
ular reality.
Even more profoundly novel are Einstein's applications of statistical ideas to
quantum physics. In his first paper on this subject, the light-quantum hypothesis
is arrived at by a statistical argument. This work was completed two months
before his paper on Brownian motion. After 1905, Einstein did occasionally return
to classical statistical physics, but in those later years all his main work on statis-
tical problems was in the domain of the quantum theory. In fact, a stronger state-
ment can be made: all of Einstein's principal contributions to the quantum theory
are statistical in origin. They include his work on specific heats, on particle-wave
duality, on the particle nature of the light-quantum, on spontaneous and induced
radiative processes, and on a new derivation of the blackbody radiation formula.
His last encounter with statistics occurred as an aside—as he put it [S2]—late in
1924 and early in 1925, when he was already working hard on unified field the-
ory. The three papers produced at that time brought him to the very threshold of
wave mechanics.
Since Einstein's papers on statistical physics cover so much ground, it may be
helpful to preface a more detailed discussion of their main points with a brief
chronology.
1901-2. Thermodynamics of liquid surfaces [E5] and of electrolysis [E6]. In
these papers, Einstein was looking for experimental support for a hypothesis con-
cerning molecular forces. Making an analogy with gravitation, he conjectured that
the potential between two molecules of species i and j is of the form CjCj$(r), where
the c's are characteristic for the species and 0( r) is a universal function of distance.
In a further analogy with gravitation, he assumed that each c-, is of the form Sca,
where ca is a number characteristic for the ath atom in the molecule of kind i. He
was able to relate the c's to the specific volume and to the surface tension and its
"This reasoning will be discussed in detail in Chapter 5.