EINSTEIN
AND
STERN ON ZERO-POINT
ENERGY
271
puzzled physicists
since the end of
the
nineteenth
century,
was
the
contribution of
the
rotational motion of molecules
to
the
specific
heat of
gases. Applying
the
quantum
hypothesis
to this
problem
was
therefore
a
natural
step,
but
the
problem
of the
quan-
tization of the rotational motion of
gas
molecules
proved
to be
a
major conceptual
stumbling
block.[5]
By
the end of
1910
Einstein had found
a
method for
determining
the
specific
heat of
a
diatomic molecule
on
the basis of Planck's radiation formula.
"The
matter is
quite simple,"
he wrote to
a
collaborator,
"but of
course
somewhat
problematic."[6]
While Einstein
apparently
hesitated
to
publish
his result,
Nernst
in 1911
postulated
a
simple quantum
formula for the rotational motion of
a
molecule
and
attempted
an
explanation
of the
specific
heat of diatomic
gases
at low
temperatures.[7]
He
also
encouraged
measurements
of
the
specific
heat of
hydrogen,
because
quantum
effects
on
the rotational motion should
in this
case
be
observable
even
at
higher temperatures.
Measurements
were
performed
by
Arnold Eucken
in
Nernst's
laboratory
in
Berlin,[8]
but Eucken's
results,
published
in
1912,
could neither
be
explained
by
Nernst's
simple
formula
nor by
the
equally simple
but
more
consistent
approach
that Einstein had
first
advanced
in 1910
and then
presented
at
the
Solvay Congress
in
1911.[9]
III
When Einstein learned about Eucken's results
in
early
1912,[10]
he
made several
attempts
to
explain
them
theoretically.[11]
He
then abandoned
the
problem during
the
first
intensive
phase
of
his
collaboration with Marcel Grossmann
on
the
theory
of
gravitation
and
only
returned
to it in late
1912.[12]
The result
was
Einstein and Stern
1913
(Doc.
11).
As the
authors
point
out in
the
first
section of their
paper,
a gas
of
rotating
diatomic molecules
is ideal
for
testing
Planck's
assumption
of
a
zero-point
energy,
because for such
a
system
a
zero-point
term
should reveal itself
in
the
specific
heat.
Combining
Einstein's earlier
approach
to
the
quantization
of rotational motion
with Planck's
new
formula,
Einstein
and
Stern found
a
striking agreement
with
Eucken's results
on
hydrogen.
Einstein
may
have discussed
some
of these ideas
with Otto
Stern
already
in
the
summer
of 1912.
Stern,
a
recent graduate
in
chemistry,
had
joined
Einstein
in
Prague
[5]For
historical
discussion,
see,
e.g.,
Kuhn
1978,
pp.
219-220.
[6]"Die Sache
ist
recht
einfach,
aber
natürlich
etwas
problematisch"
(Einstein to
Ludwig
Hopf, 27
December
1910
[Vol. 5,
Doc. 239]).
[7]See
Nernst
1911, §5,
and
Nernst and Lindemann
1911.
[8]See
Eucken
1912.
[9]See
Einstein 1914a
(Vol. 3,
Doc.
26), §4.
[10]See
Arnold Eucken
to Einstein, 23
January
1912
(Vol. 5,
Doc.
340).
[11]See
Einstein
to
Heinrich
Zangger,
27
January
1912
(Vol.
5,
Doc.
344), and
Einstein
to
Heinrich
Zangger,
20
May
1912
(Vol.
5,
Doc.
398).
[12]See
Einstein
to
Paul
Ehrenfest,
20-24 December
1912
(Vol.
5, Doc. 425).