178 DOC.

3

RESPONSE TO PLANCK 1910A

Fernwirkungstheorie hatte,

mit der Maxwellschen Theorie

vereinbar

ist;[8]

dies

will ich

nächstens einmal

im

Zusammenhang

mit anderem veröffent-

lichen.

Wenn die

Faraday-sche

Veranschaulichung

bei

der

Entwickelung

der

Elektrodynamik

auch

wichtige

Dienste

geleistet hat,

so

kann daraus

nach

meiner

Meinung

nicht

gefolgert werden,

dass

sie stets

mit allen Einzelheiten

beibehalten werden müsse

AD.

[19 241].

In the hand of Mileva Einstein-Maric

(GyB, Slg.

Darmst.,

F

le 1908

[7]).

[1]Dated

on

the

assumption

that

it

was

written before

18 January

1910,

when the

manuscript

for Planck

1910a

was

received

by

Annalen

der

Physik.

[2]The

published

version

is

Planck

1910a;

this

passage appears

on p.

762.

"des emittierenden

Lichtes" should

be

"des emittierten Lichtes."

[3]In

his

paper

Planck

argues

that

it

is unnecessary

to

introduce the

assumption

of

a

disconti-

nuity

for the

treatment

of

the

electromagnetic

radiation

in

a

vacuum,

but that this

assumption

should

be

limited

to

the

treatment

of

the

interaction between

elementary

oscillators and radia-

tion

(see

Planck

1910a,

p.

768, propositions

4

and

5).

[4]According

to Planck,

who discusses Einstein's

treatment

of fluctuations

as presented

in

Einstein

1909b

(Vol. 2,

Doc.

56),

the statistical

average

values

characterizing black-body

radia-

tion enclosed

in

a

cavity

do

not

depend

on

the material

properties

of the

cavity,

while

the

fluctuations around these

average

values

actually might

(see

Planck

1910a, pp. 762-763).

Hence,

following

Planck's idea

that

the emission of radiation

is

quantized

but that

its

propaga-

tion

in

empty space

is

described

by

Maxwell's

equations,

there should also

be,

as

Einstein

points

out

in the

following,

a

dependence

of the statistical

properties

of radiation

(which

in

Einstein's

understanding

include

its fluctuations)

on

the

size

of

the cavity or, in

other

words,

on

the distance from the

emitting wall.

[5]In

§7

of

Einstein 1909b

(Vol.

2,

Doc.

56),

Einstein

had determined the

momentum

fluctua-

tions of

a

mirror

moving

in

black-body

radiation in

two

steps:

he

first presented

an

expression

for the radiation

pressure

that

is

derived within the

framework

of

classical electrodynamics

and

does therefore

not explicitly

contain Planck's

constant; he

then

inserted into

this

expression

Planck's

formula for the

energy density

of

black-body

radiation. Planck's criticism had focused

on

the first

step

of this

derivation, which,

according

to Planck,

does

not

take into

account

a

possible

role of

h in

the emission

process.

For

Planck,

such

a

dependence

seemed

likely,

since

the total

expression

for the

momentum fluctuations,

that

is,

the

expression

obtained after

Einstein's second

step,

does

indeed

depend

on

h

(see

Planck

1910a,

pp. 762-763).

The

"dimen-

sional consideration"

("Dimensionalbetrachtung")

mentioned

in

this

context

by

both Einstein

and

Planck

is

a

reference

to

§10

of Einstein

1909b

(Vol.

2,

Doc.

56),

which

is not

directly

concerned with fluctuations but contains

a

heuristic

argument

for

an

expression

of

the

energy

density

of

black-body

radiation that

is compatible

with Planck's formula.

[6]Einstein's

belief

that

the

relationship

between fluctuations and interference

in

classical

electrodynamics is possibly

worth

studying

may

have been

one

of the

starting

points

for his

collaboration with

Ludwig Hopf;

see

Einstein and

Hopf 1910a

(Doc.

7)

and Einstein

and

Hopf

1910b (Doc.

8).

[7]In

his

paper,

Planck

argues

that

the

"frequency" ("Schwingungszahl")

of

an

electrostatic

field is

zero

and that therefore the

energy

of the

field

should consist of

infinitely many energy

quanta

of

value

zero.

He

expresses

doubts

that

under such circumstances

a

finite,

directed

field

quantity

can

still be

defined

(Planck 1910a,

p. 764).

[8]Einstein had earlier referred

to

action-at-a-distance theories

in

Einstein

1909c

(Vol.

2,

Doc.

60), p.

499. See

also Einstein

to

Michele

Besso, 31

December

1909,

for details of what Einstein

had

in

mind.