EARLY WORK ON QUANTUM HYPOTHESIS 139

of

the

system.[36]

If

the

entropy

of

a system

is

given as a

function

of

its

macroscopic

state

variables,

then

Boltzmann's

principle,

in

the form

W

=

exp(S/k), can

be used

to

calculate

the

probability

of

a

state,

and hence

of

the fluctuations

of

any

state variable. In 1909

Einstein used this method to calculate the fluctuations

in

the

energy

of

black-body

radia-

tion

in

a given region

of

space.[37]

The stochastic

method,

used in the

same

paper

to cal-

culate fluctuations in the

pressure

of

radiation, is

based

on

his work

on

Brownian motion.

Pressure

fluctuations maintain the Brownian motion

of

a

small mirror

moving

through

the

radiation

field,

in the face

of

the

retarding

force exerted

on

the mirror

by

the

average

radiation

pressure.[38]

The results

of

these two fluctuation calculations

are

discussed

in the

next section.

Einstein's

work

on relativity

also contributed to the

development

of

his views

on

the

nature

of

light. By eliminating

the

concept

of

the ether and

showing

that

a

flux

of radiant

energy

transfers inertial

mass,

the

theory

of

relativity

demonstrated that

light no longer

need be treated

as a

disturbance

in

a hypothetical

medium,

but could be

regarded as com-

posed

of

independent

structures,

to which

mass

is

attributed.[39]

III

Among

Einstein's

papers on

the

quantum hypothesis,

the 1905

paper

is

unique

in

arguing

for the notion

of

light

quanta

without

using

either the formal

apparatus

of

his statistical

papers

or

Planck's

law.[40]

As noted in the

previous

section,

Einstein demonstrated

that

only

the

limiting

form

of Planck's

formula

for small values

of

v/T

is

consistent

with the

accepted

foundations

of

statistical mechanics and

electrodynamics.

At the

other

extreme,

at which

Wien's

distribution law

holds,

"the

theoretical foundations

we

have utilized

.

. .

fail

. . .

completely"

("die

von uns

benutzten theoretischen

Grundlagen

. . .

versagen

. . .

vollständig").[41]

As he

explained

later that

year,

this failure

"seems

to

me

to have

its basis

in

a

fundamental

incompleteness

of

our physical

concepts"

("scheint

mir

in

einer

elementaren Unvollkommenheit

unserer physikalischen Anschauungen

ihren Grund

zu

ha–

[36]

The method

is

first discussed

in

Einstein

1907b

(Doc. 39).

[37]

See Einstein 1909b

(Doc. 56),

pp.

188-

189. The

equation

for the

energy

fluctuations

that results from

Boltzmann's

principle

is

equiv-

alent

to

one

that Einstein derived earlier from the

canonical distribution in Einstein 1904

(Doc. 5),

pp.

359-360,

as a simple thermodynamic argu-

ment shows. Einstein

evidently preferred a

for-

mula not

dependent on

the canonical distribution

for the

application

to

black-body

radiation.

[38]

See

Einstein

1909b

(Doc. 56),

pp.

189-

190,

and Einstein 1909c

(Doc.

60),

pp.

497-

498. For

a

discussion

of

the stochastic

method,

see

the editorial

note,

"Einstein

on

Brownian

Motion,"

pp.

213-215.

[39]

The conclusions

are implicit

in

some

of

Einstein's

earlier

papers

but

are

first made

ex-

plicit

in Einstein 1909c

(Doc. 60).

For discus-

sion

of

the elimination

of

the

ether

and the iner-

tia

of

energy,

see

the editorial

note,

"Einstein

on

the

Theory

of

Relativity,"

pp.

253-274.

[40]

A

year

later Einstein

explained

that ini-

tially

he had

regarded

Planck's

theory as

form-

ing

"in

a

certain

sense an

antithesis" ("in

ge-

wisser

Beziehung

ein

Gegenstück") to

his

own

work

(Einstein

1906d

[Doc. 34], p. 199).

While

"Gegenstück"

can

also

mean

"complement,"

the

context

in which

it is

used here

suggests

"antithesis."

[41]

Einstein

1905i

(Doc. 14),

p.

137.