146 EARLY WORK ON QUANTUM

HYPOTHESIS

several

considerations,

from which it follows for

me

that not

only

the mechanics

of

molecules,

but also Maxwell-Lorentz

electrodynamics

cannot be

brought

into

harmony

with the

[Planck]

radiation formula.

einige Betrachtungen, aus

denen für mich

hervorgeht,

dass nicht

nur

die Mole-

kularmechanik

sondern auch die

Maxwell-Lorentz'sche

Elektrodynamik

mit

der

Strahlungsformel

nicht in

Einklang gebracht

werden

kann.[84]

After

replying

in turn to Ritz and

Jeans,[85]

Einstein

stated,

more clearly

than he had

pre-

viously

done

so,

what he

regarded as

the deviations from

proper

statistical foundations in

Planck's

derivation

of

the radiation

law.[86]

The

major

novelties

of

the

paper,

however,

are

two

arguments

for the existence

of

light quanta

based

upon

the

analysis

of

fluctuations in

black-body

radiation. As noted in section

II,

Einstein did not

apply

his

canonical

fluctua-

tion formula,

perhaps

to forestall doubts about the

applicability

of

this

formula

to radia-

tion.[87]

Instead,

he

applied an equivalent

formula based

on

Boltzmann's

principle,

a prin-

ciple

he held

to be

universally

valid. In addition to

energy fluctuations,

Einstein calculated

fluctuations

in the radiation

pressure

by

studying

the Brownian motion

of

a

small, two–

sided

mirror

in

a

radiation-filled

cavity.[88]

In

both

instances,

Planck's

law

yields

expres-

sions for the fluctuations that

are

the

sum

of

two

terms,

which

"behave

like fluctuations

(errors)

which arise from

causes independent

of

one

another"

("sich

verhalten

wie

Schwankungen

(Fehler),

welche voneinander

unabhängigen

Ursachen

entspringen").[89]

One

of

the

terms,

which dominates at low

frequencies,

Einstein

interpreted as

due to

the

interference

of

independent,

random

waves;

the

other,

which dominates at

high frequen-

cies,

he

interpreted as

due to

"complexes

of

energy

hv

of

small extension,

moving

inde-

pendently

of

one

another"

("von

einander

unabhängig beweglichen, wenig

ausgedehnten

Komplexen von

der

Energie

hv").[90]

It

is

not

enough

to

assume

that

the emission and

absorption

of

light

take

place

via

energy quanta;

the structure

of

the radiation

itself

shows

evidence

of

such

quanta. Although light quanta

cannot

be

deduced from

Planck's

law,

he

concluded,

"one

can

indeed assert that the

quantum theory

offers

...

the

simplest

inter-

pretation" ("[m]an

kann aber wohl

behaupten,

daß die

Quantentheorie

die

einfachste

Interpretation

.

.

.

liefert")

of

this

law.[91]

1909.

Presumably

the

"question"

("Sache")

to

which he refers is

the

"Strahlungsproblem"

in

the title

of

the

paper.

[84]

Einstein to Hendrik

Lorentz,

30 March

1909.

[85]

See

Einstein

1909b

(Doc. 56), pp.

185-

187.

Einstein's

response

to

Ritz occasioned

a re-

joinder

by

Ritz,

Ritz

1909,

and

a

joint

statement

of their

disagreement,

Ritz

and

Einstein

1909

(Doc.

57).

[86]

See

Einstein

1909b

(Doc. 56),

pp.

187-

188.

[87]

Einstein raised the

question

of

the

appli-

cability

of

statistical mechanics

to

thermal radia-

tion in

Einstein

1909b

(Doc. 56),

p.

186. Ein-

stein

and

Hopf

1910a, 1910b

dispose

of

such

doubts.

[88]

Einstein later stated that in 1905 he knew

Maxwell's

theory

leads

to

an

incorrect

expres-

sion

for

the fluctuations

of

the radiation

pressure

on a

mirror

(see

Einstein to Max

von Laue,

17

January

1952).

[89]

Einstein 1909b

(Doc. 56),

p.

190.

[90]

Einstein

1909b

(Doc. 56),

p.

190.

[91]

Einstein

1909b

(Doc. 56),

p.

191.