88

DOC.

18

REPLY TO LAUE

Doc.

18

Response

to

a

Paper

by

M.

von

Laue: "A Theorem

in

Probability

Calculus and Its

Application

to

Radiation

Theory"1

by

A.

Einstein

[p. 879]

[1]

In the

paper quoted,

Laue

brings

the mathematical foundation

of

radiation statistics

into

a

form

which,

as

to

precision

and

beauty,

leaves

nothing

to be desired.

However,

as

far

as

the

application

of

these

foundations

to

radiation

theory

is

concerned,

it

seems

to

me

that he

has fallen

victim

to

a

critical

error

which

requires urgent

correction. Laue claims that the coefficients in

a

Fourier

expansion,

as

they occur

in

the local oscillations of natural

radiation,

need

not

be

statistically

independent

of

each

other.

If

this claim

were

justified,

one

would

really

have

a

very promising

method

to

overcome

the difficulties

that

are

manifest in the theoretical

"indigestibility"

of all

laws

in which

Planck's "h"

plays an important

role. This

was precisely

the

reason

that

motivated

me

five

years ago

to

investigate

this

question

in

more

detail in

a published

[2] paper,

co-authored with

L.

Hopf.

The result of this

not

quite

flawlessly

executed

paper

is

recognized by

Laue

as

a

correct conclusion from the basic

assumptions

made in

it.

What Laue denies is the

permissibility

of these basic

assumptions,

which

can

be

phrased

as

follows:

If

I

obtain

a

completely

disordered radiation

(i.e.,

statistically mutually

independent

Fourier

coefficients) by

superimposing an

infinite number

of

completely

given

identical radiations such that the total

phases

of this

superimposed conglomer-

ate

are

chosen

at random,

then natural radiation

must

a

fortiori

be

statistically

disordered.

This basic

assumption appeared

to

me, then,

as

evident. The

fact, however,

that

[p.

880] an

experienced expert,

such

as

Laue,

does

not

share this

opinion proves

the

opposite.

I

shall,

therefore,

in what follows

give

a

proof

that is free

of

said

assumption

and

which-as I

hope-will

irrefutably

demonstrate that

our

theory

of undulation

definitely

demands the mutual statistical

independence

of the Fourier coefficients.

However,

before

I enter

into this

proof,

I want

to show

why

the considerations in

parts

II

and III of Laue's

paper

are,

in

my opinion,

not

a convincing proof.

Laue considers radiation

from

a large

number

of resonators that emit

orthogonal

to

a layer

(of

thickness

cr),

over

which

they

are

irregularly

distributed. In

part

II

of

his

paper

he

assumes

that all of these resonators oscillate

simultaneously

and under

the

same law;

and in

part

III,

that the oscillations of all resonators

are governed by

Translator's

note. Typographical

errors

occurring

in the

original

have been corrected

in this

translation.

See

notes {1}-{3}

and note

[3].