EINSTEIN
AND
STERN
ON
ZERO-POINT ENERGY
I
The
paper by
Einstein and Otto
Stern,
Einstein and Stern
1913
(Doc. 11) presents
the
results of their
study
of
some
ways
in
which the
zero-point
energy,
introduced
two
years
earlier
by
Max Planck
in his
"second
quantum
theory," might
affect
physical
phenomena[1] They
offered
two
arguments
in
favor of
accepting zero-point
energy
as
real.[2]
Planck had deduced the existence of
an
extra term in
the
energy
of
an
oscillator
of
frequency
v
that absorbs
energy continuously
but emits
energy
only
in
integral
multiples
of
hv. The
spectral
distribution of
black-body
radiation
is
unaffected
by
the
extra
energy,
whose
magnitude
is
hv/2 for each
oscillator,
and is
independent
of
temperature.
Einstein and Stern showed that
a
theory,
an
approximate
one,
of
the
energy
of
rotating
molecules which
incorporates
the
zero-point energy agreed quite
well with
Arnold Eucken's
recent measurements
of the
specific
heat of
hydrogen gas
at low
temperatures.
The
same
approximate theory
but with the
zero-point energy
omitted
led
to
a specific
heat
versus
temperature curve qualitatively as
well
as
quantitatively
different from the
experimental
behavior.
Einstein
and
Stern also
gave a
new
derivation of the Planck
radiation distribution
law,
a
derivation based
on
the
assumption
of
a
zero-point
energy,
but
making
no
assumption
of
discontinuity
at all. In
spite
of the
apparent
success
of this
paper,
Ein-
stein
soon
lost confidence
in
the
concept
of
zero-point energy
and
publicly
stated that
he
no
longer
believed
in it at
the second
Solvay Congress
in
late October
1913.[3]
II
Following
the
publication
of Einstein's work
on
the
specific
heat of
solid bodies in
1907,[4]
the
quantum hypothesis
had become
an
important
instrument
for
solving prob-
lems related
to the
atomistic
conception
of
matter.
One of those
problems,
which had
[1]See
Planck
1911a, 1911b, 1912,
1914a.
See,
e.g.,
Einstein
to Wilhelm
Wien,
17 May
1912
(Vol. 5,
Doc.
395),
for
an expression
of Einstein's
skeptical
attitude toward
this
theory.
For
a
historical discussion of Planck's second
theory, see
Kuhn
1978, chap. 10,
and Needell
1980, chap.
4.
[2]For
historical
accounts
of the Einstein-Stern
paper,
see Klein,
M.
1970,
pp.
265-267, and
Needell
1980,
pp.
252-256. See Eucken
1914,
pp.
374
and
400-405,
for
a
contemporary per-
spective on
Einstein and Stern's work
on
zero-point energy.
[3]See
Einstein's discussion remark
following
Max
Laue's lecture
(Doc.
22).
See also
Ein-
stein to
Ludwig Hopf,
2
November
1913
(Vol.
5,
Doc.
480),
in which
he states
that the
unten-
ability
of
the
zero-point energy
became clear
to
him
soon
after
the publication
of Einstein and
Stern
1913
(Doc.
11).
[4]Einstein 1907a
(Vol.
2,
Doc.
38).
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