272
EINSTEIN AND
STERN
ON
ZERO-POINT ENERGY
after
obtaining
his
doctorate
in the
spring
of
1912
and later followed
him to Zurich.[13]
From
a
later recollection
by
Stern
it is
clear that
his
principal
contribution
was
the
derivation, in the
second
part
of
the
joint paper,
of Planck's radiation
law using
the
zero-point
term.[14] According to
Stern's
recollection,
Einstein had
suggested
to
him
that
this
result
might
be
achieved
by
modifying
a
derivation of
the
classical
Rayleigh-
Jeans
law
that Einstein and
Hopf
had
developed
earlier.[15]
Stern
performed
the
cal-
culation but found that
he
needed
a
zero-point
term
of
hv
instead of Planck's
hv/2.
Einstein asked
him to
redo
the
calculation
and
eventually
did it
himself
as
well,
each
time with the
same
result.
Although
the
particular
value for
the
zero-point energy
found
by
Einstein and
Stern
was
not
confirmed
by
Eucken's
measurements,
their
derivation showed that
one
could also obtain Planck's radiation
law
without
the
assumption
of
a discontinuity.
Successful
as
Einstein
and Stern's
explanation
of
the
temperature
dependence
of
the
specific
heat of
hydrogen
seemed
to be,
it
was
marred
by
a
number of
problematic
assumptions.
In
order
to
simplify
their
calculation,
they
assumed that
all molecules
rotate
with
the
same
speed.
What
is
more,
their
very use
of Planck's formula
with
a
zero-point
term
was
questionable,
since the
derivations of
this formula-by
Planck
as
well
as
by
Einstein and
Stern-refer
to resonators
whose
energy
is
independent
of
their
frequency,
and
not
to rotators. It
was
therefore natural that various other
avenues
to the
quantization
of diatomic molecules
were
pursued.
Einstein and Lorentz had
discussed
one
such
approach already
in
1911.[16]
Lorentz
presented
it at the first
Solvay
Congress, arguing
that
the
quantum hypothesis
should
be
applied directly
to
restrict
the
possible energy
values,
and
hence
the
possible frequencies
of
a single
rotator.
Einstein
suggested addressing
the
problem
of
the
relation between
energy
and fre-
quency
by
introducing
what
were
later
to be
called "adiabatic
invariants."[17]
The
paper
by
Einstein
and Stern
aroused
widespread
interest and stimulated theo-
retical
as
well
as
experimental
research.[18]
Pierre Weiss drew Einstein's attention
to
measurements
by
Pierre
Curie
on
the
paramagnetic susceptibility
of
oxygen as
evi-
dence for
the
existence of
a
zero-point
energy.[19]
But
in the fall
of
1913
Einstein
[13]Stern
received
his
doctorate
in
physical chemistry
from
the
University
of Breslau. For
a
contemporary comment
by
Einstein
on
his
collaboration
with Stern,
see
his
Gutachten
zu
dem
Habilitationsgesuch
des
Herrn
Dr. O. Stern,
15 July
1913 (see
Vol.
5,
Doc.
452).
For later
recollections
by
Stern,
see
the
typescript
of
Res
Jost's
interviews with
Stern, 25
November and
2
December
1961,
SzZE Mediathek.
[14]See
typescript
of
Res
Jost's interviews with
Stern,
25
November and
2
December
1961,
SzZE
Mediathek,
pp.
6-7. See also
Segre 1973,
pp.
216-217.
[15]See
Einstein and
Hopf
1910b (Vol. 3,
Doc.
8).
[16]See,
also for
the
following,
Einstein
et
al.
1914a
(Vol. 3,
Doc.
27),
pp.
362-364.
[17]In
1913
Ehrenfest
independently
developed
the
approach
earlier considered
by
Lorentz
and
Einstein, and
also dealt
with the question
of
the
statistical distribution of rotational
fre-
quencies
(see Ehrenfest
1913, 1914).
For historical
discussions,
see
Klein,
M.
1970,
pp.
264-
273,
and Needell
1980, pp.
256-259.
[18]See
Eucken
1914,
pp.
400-405.
[19]See
the note
added
in
proof
to
Einstein and Stern
1913
(Doc. 11).
See
also
Klein, M.
1966 for
a
discussion of other
experiments
that seemed
to
support
the
existence of
zero-point
energy.