EINSTEIN
AND STERN ON
ZERO-POINT
ENERGY 273
retracted his results. Soon after the
publication
of the
paper,
he wrote
in
a
letter that
the theoretical
untenability
of
its
results had become
apparent
to
him
"with terrible
clarity."[20]
Without
going
into details,
Einstein
explained
in
a
discussion remark
at
the second
Solvay Congress
in
October
1913
that
in
pursuing
the
implications
of their
derivation of Planck's
formula, he
and Stern had encountered
contradictions,
and that
as a
result their
explanation
of
the
temperature dependence
of
the
specific
heat of
hydrogen
had lost
its foundation.[21] He
also criticized the notion of
a
zero-point
energy
from
an
experimental point
of
view,
finding
it
incompatible
in
particular
with
the
phenomenon
of
superconductivity.[22]
From these
as
well
as
from
other
arguments
Einstein concluded that the
zero-point energy
was
"dead
as a
doornail."[23]
Einstein then returned
to
an
approach
that had
occupied
him after
the first
Solvay
Congress.[24]
The calculation of the
mean
energy
of
a
rotating dipole
in
equilibrium
with
a
radiation
field,
in
analogy
to the
calculation for
a
resonator
performed
by
Einstein and
Hopf
in
1911,
had remained
an
open problem.
When Adriaan
Fokker,
a
former student of
Lorentz's,
came
to
Zurich
in
early
November
1913,[25]
this
was
apparently
the
first
problem
on
which
he
collaborated
with Einstein.[26]
Within
a
month
Fokker
came
to
the conclusion that the calculation of
the
mean
energy
of
a
rotating
dipole
in
equilibrium
with
a
radiation
field
governed
by
Planck's
law
could
not account
for Eucken's
measurements.[27]
Only
after
more
than
a
decade
did it turn out
that these
measurements
were
unsuitable
as a
test
of the
theory
of
the
quantization
of rotational
motion,
since
they
were
clouded
by
complexities
later
to be
described
in terms
of the
distinction between ortho-
and
parahydrogen.[28]
The notion of
a
zero-point energy,
however,
survived
its first
unsuccessful
application
to
the
problem
of
specific
heats
by
Einstein and
Stern,
and
eventually
reemerged as a rigorous consequence
of
quantum
mechanics.
[20]"mit
schrecklicher
Deutlichkeit"
(Einstein
to
Ludwig Hopf,
2
November
1913
[Vol. 5,
Doc.
480]). In
summer
semester 1913
Einstein discussed Eucken's results
in
his
course on
the
molecular
theory
of heat
(see
Appendix A).
According
to
the
notes
on
this
course
taken
by
his
student,
Walter
Dällenbach,
Einstein concluded the discussion with
the
remark: "God
only
knows
why
and
according
to
which law"
("Kein
Teufel weiss
warum
und nach welchem
Gesetz").
[21]See
Laue
et
al. 1921
(Doc. 19),
p.
127.
[22]See
Laue
et
al. 1921
(Doc. 19),
p.
124.
[23]"mausetot"
(Einstein
to
Paul
Ehrenfest,
before
7
November
1913
[Vol.
5,
Doc.
481]).
[24]See
Einstein
to
H. A. Lorentz, 23
November
1911
(Vol. 5,
Doc.
313).
[25]Fokker arrived
in
Zurich
on
7
November
1913
(see
Einstein
to
Elsa
Löwenthal, 7
Novem-
ber
1913
[Vol. 5,
Doc.
482]).
[26]See,
also for the
following,
A. D.
Fokker
to H. A. Lorentz,
4 December
1913 (Vol.
5,
Doc.
490).
See
Needell
1980,
pp.
263-268,
for
a
historical
account.
[27]For
the
publication
of Fokker's
results,
see
Fokker
1914.
[28]See
Dennison 1927
and,
for historical
comments,
Fowler and
Guggenheim 1949,
pp.
83-
93,
and Mehra and
Rechenberg 1982,
p.
148.