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.