68 STATISTICAL PHYSICSdifferent derivation, in that use is made of the canonical ensemble, yet it contains
once again the assumption Hertz had criticized.
It is interesting but not all that surprising that in 1903 and 1904 Einstein, in
his isolation, had missed the point about time reversal. After all, the great Boltz-
mann had done the same thirty years earlier. However, the exchange between
Einstein and Hertz took place in 1910, when Einstein was a professor at Zurich
(and taught the kinetic theory of heat during the summer semester of that year
[S8]). By that time, he had read Boltzmann's work of 1877 (as mentioned earlier),
in which it was stated that the entropy does not always, but rather almost always,
increase. A month before replying to Hertz, he had phrased the second law quite
properly in another paper. * One can only conclude that Einstein did not pay much
attention when he replied to Hertz.
As a postscript to the issue of the second law, it is fitting to recall the first
personal exchange between Einstein and Ehrenfest, which took place in Prague
in February 1912. The Einsteins had come to the train to meet the Ehrenfests.
After the first greetings, 'their conversation turned at once to physics, as they
plunged into a discussion of the ergodic hypothesis' [K6].What was the harvest of Einstein's scientific efforts up to this point? Five
papers. The first two, dealing with his quest for a universal molecular force, are
justly forgotten.** One main ambition of the next three, to establish a dynamic
basis for the thermodynamic laws, did not entirely come to fulfillment either.
Nothing indicates Einstein's flowering in 1905, which begins with his very next
paper. Nothing yet. However, there is one aspect (not yet mentioned) of his brief
1904 paper which does give the first intimations of things to come. In the years
1902 to 1904, Einstein may not have grasped the awesome problems—still a sub-
ject of active research—which have to be coped with in giving the second law a
foundation which stands the tests of requisite mathematical rigor. Yet these early
struggles of his played an important role in his development. They led him to ask,
in 1904, What is the meaning of the Boltzmann constant? How can this constant
be measured? His pursuit of these questions led to lasting contributions to statis-
tical physics and to his most important discovery in quantum theory.
In the opening paragraphs of Einstein's paper of 1904 [E12], reference is made
to Eq. 4.3: 'An expression for the entropy of a system ... which was found by
Boltzmann for ideal gases and assumed by Planck in his theory of radiation... .'
Here, for the first time, Planck appears in Einstein's writings, and we also catch
a first brief glimpse of Einstein's subsequent concern with the quantum theory in
*'The irreversibility of physical phenomena is only apparent ... [a] system probably [my italics]
goes to states of greater probability when it happens to be in a state of relatively small probability'
[E29].
**See Section 4a.