20
Einstein and Specific Heats
The more success the quantum theory has, the sillier it looks.
A. Einstein in 191220a. Specific Heats in the Nineteenth Century
By the end of the first decade of the twentieth century, three major quantum the-
oretical discoveries had been made. They concern the blackbody radiation law, the
light-quantum postulate, and the quantum theory of the specific heat of solids. All
three arose from statistical considerations. There are, however, striking differences
in the time intervals between these theoretical advances and their respective exper-
imental justification. Planck formulated his radiation law in an uncommonly short
time after learning about experiments in the far infrared that complemented ear-
lier results at higher frequencies. It was quite a different story with the light-
quantum. Einstein's hypothesis was many years ahead of its decisive experimental
tests. As we shall see next, the story is quite different again in the case of specific
heats. Einstein's first paper on the subject [El], submitted in November 1906,
contains the qualitatively correct explanation of an anomaly that had been
observed as early as 1840: the low value of the specific heat of diamond at room
temperature. Einstein showed that this can be understood as a quantum effect.
His paper contains one graph, the specific heat of diamond as a function of tem-
perature, reproduced here below, which represents the first published graph in
the history of the quantum theory of the solid state. It also represents one of only
three instances I know of in which Einstein published a graph to compare theory
with experiment (another example will be mentioned in Section 20b).
In order to recognize an anomaly, one needs a theory or a rule or at least a
prejudice. As I just mentioned, peculiarities in specific heats were diagnosed more
than half a century before Einstein explained them. It was also known well before
1906 that specific heats of gases exhibited even more curious properties. In what
way was diamond considered so exceptional? And what about other substances?
For a perspective on Einstein's contributions, it is necessary to sketch the answer
to these questions. I therefore begin with a short account of specific heats in the
nineteenth century.
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