xx

INTRODUCTION

TO VOLUME

2

in his work

on

Brownian motion combine statistical

physical concepts

he

had

re-

cently investigated

with

concepts

from the

theory

of

diffusion familiar to him from

his work

on

molecular

forces.[21]

As

a consequence,

he not

only gave

the first

satisfactory explanation

of

Brownian motion

as a

stochastic

process,

but

also de-

veloped

a new

method for the determination

of

molecular dimensions,

based

on

related

techniques,

and

completed

a

doctoral dissertation

on

this

topic.[22]

Einstein

emphasized

that

the existence and

properties

of

stochastic fluctuations

represented

a

critical

test

of

the

kinetic

theory

of

heat,

which

was

still

challenged

by

a

number

of

scientists.

His theoretical studies

helped

to

stimulate much

experimental

work

by

Perrin and others

that

effectively

served

to

put

such doubts to

rest.

Initially,

Einstein believed

black-body

radiation to be the

only system

for which

energy

fluctuations

are

empirically significant.

In 1904 he

applied

the

thermody-

namic

approach developed

for mechanical

systems

to the

energy

fluctuations

of

"a

radiation-filled

space"

("ein

Strahlungsraum"),

with

encouraging

results.[23]

The

following year,

Einstein returned

to

the

problem

of

black-body

radiation,

us-

ing thermodynamic

methods combined with

Boltzmann's

principle

to show that,

in the

high

v/T

limit,

the

entropy

of

radiation

varies with its

volume

in

the

same

way

as

does the

entropy

of

a system

of

particles.

Such considerations led

him

to

formulate the heuristic

viewpoint

that radiant

energy,

like matter and

electricity,

is

quantized.[24]

In 1907 he extended the

quantum hypothesis

to the vibrational

energy

of

solids.

He

was

thus able to

explain a long-standing anomaly

in the

theory

of

specific

heats

of

solids,

which had led to serious doubts about the kinetic

theory

of

heat.

Begin-

ning

about

1911,

with the first

experimental

confirmations

of

Einstein's

theory

of

specific

heats,

this work

played an important

role in

persuading many

physicists

of

the basic

significance

of

the

quantum

hypothesis.[25]

In 1909 he

applied

both of

his methods for

treating

fluctuations in

an investigation

of

black-body

radiation

based

on

Planck's

law. He used

a thermodynamic approach,

based

on

the inver-

sion

of Boltzmann's

principle,

to

investigate energy

fluctuations;

and

a

stochastic

approach, examining

the Brownian motion

of

a

small mirror in

equilibrium

with

the radiation, to

investigate pressure

fluctuations. As noted

above,

the

results of

[21]

See the

editorial

notes,

"Einstein

on

Brownian Motion,"

pp.

206-222, and "Ein-

stein

on

the Nature

of

Molecular Forces,"

pp.

3-8.

[22] See the

editorial note,

"Einstein's

Disser-

tation

on

the

Determination

of

Molecular Di-

mensions,"

pp.

170-182.

[23]

See

Einstein

1904

(Doc. 5), pp.

360-362.

This

success

of

methods

developed

for

systems

with

a

finite number

of

degrees

of

freedom when

applied

to radiation

may

have

encouraged

Ein-

stein

to

treat radiation

itself

as

such

a

system (see

Einstein

1905i

[Doc. 14], pp.

132-133).

[24]

See the editorial note,

"Einstein's

Early

Work

on

the Quantum Hypothesis,"

pp.

134-

148.

[25]

For

a

discussion

of

the

important

role

of

the

quantum theory

of

specific heats,

see

Klein

1965,

and Kuhn

1978,

pp.

210-220.