EINSTEIN ON CRITICAL OPALESCENCE
Einstein's
paper
on
critical
opalescence explains
the
optical
effects
that
occur near
the
critical
point
of
a
gas
and
near
the critical
point
of
a
binary
mixture of
liquids.
In
spite
of
its
title,
the results of
this
paper
fail to hold,
as
Einstein
points
out, in
the immediate
vicinity
of the critical
point
but
are,
on
the other
hand,
valid far
away
from
it.
They
thus extend
Rayleigh's
earlier studies of the blue color of the
sky[1]
and relate this
phenomenon to
the
density
fluctuations of
the
light-scattering
medium
that
cause
critical
opalescence.
Einstein's research
on
critical
opalescence
and
the blue
of
the
sky
follow
his studies of Brownian motion and add
to
the
evidence
provided by
these
studies for the atomistic constitution of
matter.[2]
In
1908
Smoluchowski
published
a
paper
on
critical
opalescence
in
the
Annalen
that
had
appeared
the
year
before in Polish.[3]
Not
long
after the
publication
of the
German
version,
he received
a
postcard
in
which Einstein asked for
reprints
of
his
papers.[4]
While
it
is
unclear whether
or
not
Einstein's
request
indicates
his
intent
to
work
on
critical
opalescence already
at
that
time,
Einstein's
paper
of
1910
evidently
takes Smoluchowski's work
as
its
point
of
departure.
In
his
paper
Smoluchowski
sketched
an
explanation
of critical
opalescence by density
fluctuations of the
me-
dium,
but
he
did
not
derive
a
quantitative
formula for the
light scattering
due
to
these
fluctuations.[5]
Such
a
quantitative
formula
was
first
presented
by
Keesom
in
a
foot-
note to
a
joint paper
with
Kamerlingh
Onnes.[6]
Following
a
suggestion
by
Einstein,
Keesom later
published
a
paper on
the
argument
by
which
he
had obtained
his
formula.[7]
This
argument,
however, went
little
beyond
what Smoluchowski had al-
ready
arrived
at,
and
it
was
left to
Einstein
to
rigorously
derive
a
formula for
light
scattering
by
density
fluctuations
on
the basis of Maxwell's
theory
of
electro–
[1]See,
also for
references to
earlier
work, Rayleigh 1899.
[2]For historical
analyses
of Einstein's work
on
critical
opalescence, see
Teske 1969
and Pais
1982, pp.
100-104.
[3]Smoluchowski
1907,
1908.
[4]See Einstein
to
Marian
von
Smoluchowski,
11
June
1908.
[5]He
restricted himself
to
mentioning Rayleigh's
formula for
light scattering
and
to
generally
comparing
the
phenomena
of critical
opalescence
and the blue color of the
sky.
For
a
detailed
account
of the historical
development
of Smoluchowski's
work,
see
Teske 1977.
[6]Kamerlingh
Onnes
and
Keesom
1908b,
English version,
pp.
621-622,
fn.
2;
this
footnote
does
not
appear
in
the Dutch version. The results
in
this section
are
derived
directly
from
Maxwell's
equations.
That Keesom
was
the author
is
clear from
a
letter
by
Heike
Kamerlingh
Onnes
to W. H. Julius, 24
November
1911,
NeUU,
Archief Julius
I,
27a.
Einstein
was
already
familiar with the work
by Kamerlingh
Onnes and Keesom before
his visit
to Leiden
in
Febru-
ary 1911;
see
Einstein
to Kamerlingh Onnes,
31
December
1910.
[7]See Keesom
1911, p.
597,
fn.
2.