EINSTEIN
ON
CRITICAL OPALESCENCE
285
after the
paper's publication, however,
the
relationship
between the
two
phenomena
remained unclear
to
Smoluchowski. In
1911
he
published
a
paper
in which
he claimed
that the blue color of the
sky
has
two
causes:
Rayleigh scattering
by
the molecules of
the
air,
and Smoluchowski-Einstein
scattering
by density
fluctuations.[16]
Einstein
immediately responded
to
this
paper, pointing
out
that
"a 'molecular
opalescence'
in
addition
to
the fluctuation
opalescence
does
not exist."[17]
Smoluchowski
readily
accepted
Einstein's
criticism.[18]
Statistical
physics
enters
Einstein's derivation of
a
formula for
light scattering by
density
fluctuations
through
his
use
of Boltzmann's
principle, just
as
it did
in
Smolu-
chowski's earlier work. This
approach
was
particularly
useful at
a
time when
no
deeper understanding
of
the
underlying
atomistic
processes causing phenomena
such
as
opalescence
was
available. In
fact,
the
use
of Boltzmann's
principle
had also
played
a
crucial role earlier
in
Einstein's contributions
to
quantum theory
and for similar
reasons.[19]
His
paper
on
critical
opalescence, therefore, begins
with what could
be
considered
a
paper
within
a
paper:
a
lengthy
introduction
developing
a
framework
for
statistical
physics
that
is essentially
based
on
Boltzmann's
principle.[20]
This introduc-
tory
section became
a
pioneering
contribution
to
statistical
thermodynamics,
a
theory
dealing
with
statistical fluctuations without
using
an
explicit
atomistic
framework.[21]
The
first
major improvement
to
Einstein's
analysis
of
density
fluctuations
came
with
the work of Ornstein and Zernike
in 1915.
They pointed
out
that
density
fluctuations
in
different volume elements
must be
correlated and
that
the
range
of these correla-
tions increases
rapidly
as
the critical
point is approached.
As
a
consequence,
Ein-
stein's
implicit assumption
of
statistically independent
fluctuations
in
separate
vol-
ume
elements had
to
be
modified.[22]
But this
discovery
was
just
one more
step
in
a
rapidly growing
field-the
study
of
critical phenomena-that
would
radically change
the
understanding
of statistical
physics.[23]
Einstein's work
on
critical
opalescence,
comprising
both
his ideas
on
the foundations of statistical
physics
and
his
derivation
of
a
formula for
light scattering
by
density fluctuations,
thus became
one
of the
starting points
for several
major
research traditions
in
twentieth-century
physics.
[16]See
Smoluchowski
1911, Appendix.
[17]"Es
existiert also nicht
neben
der
von
Ihnen erklärten
Schwankungs-Opaleszenz
noch
eine 'Molekular-Opaleszenz...'."
Einstein
to
Marian
von
Smoluchowski, 27
November
1911.
[18]See
Marian
von
Smoluchowski to
Einstein, 12
December
1911.
[19]For historical
accounts
of this
role,
see
the editorial
note in Vol.
2,
"Einstein's
Early
Work
on
the
Quantum Hypothesis," pp.
134-148,
and
Klein,
M.
1964, 1974.
[20]Einstein
commented
on
the inclusion of
this
lengthy
first part in
the letter of submission
to
Wien; see
Einstein
to
Wilhelm
Wien,
7
October
1910.
[21]For
the
development
of statistical
thermodynamics, see,
e.g.,
the historical literature
refer-
ences
in Tisza and
Quay
1963.
[22]See Ornstein and
Zernike
1915, pp.
794-795,
fn. 1.
[23]For studies of critical
opalescence
that
can
be
considered
a
more
direct continuation of
Einstein's
approach
than the work
by
Ornstein and
Zernike,
see
Rocard
1933.
For
comparisons
of the
two
approaches,
see
Klein,
M. and Tisza 1949
and Fisher
1964.
For
introductions
to
the modern
understanding
of the
subject
that also
provide
overviews
of
its
historical
develop-
ment,
see
also Münster
1965
and
Stanley
1971.