394

CONSTITUTION

OF

RADIATION

nonuniformities.

I

shall

add

that another consideration

concerning

the

spatial

distribution

of

the

energy

yields results that

agree

quite well with

the

above

consideration

concerning

the spatial distribution

of

the

momentum.

As

far

as

I

know,

it

has

not yet

been

possible

to

formulate

a

mathemati-

cal

theory

of radiation that

would do

justice both

to

the

undulatory

structure

and to

the

structure

inferred

from

the first

term

of the

above

formula

(quantum

structure).

The

difficulty

lies

mainly

in the fact that the fluctu-

ation properties

of

radiation,

as

expressed

by

the

above formula,

offer

few

formal clues

on

which to

build

a

theory.

Imagine

that the diffraction

and

interference

phenomena are

not

yet

known,

but that

one

knows

that the

average

magnitude

of

the

irregular fluctuations

of

the radiation

pressure

is deter-

mined

by

the

second term of

the

above

formula,

where

v

is

a

parameter

of

unknown

significance

that determines the color.

Who

would

have

sufficient

imagination

to construct

the

wave

theory

of

light

on

such

a

basis?

Still, for the time

being

the

most

natural

interpretation

seems

to

me

to

be

that the

occurence

of

electromagnetic

fields of light is associated with

singular points

just like the

occurence

of

electrostatic fields

according

to

[31]

the electron

theory.

It is

not

out

of

the

question

that in

such

a

theory

the

entire

energy

of the

electromagnetic

field

might

be

viewed

as

localized in

these singularities,

exactly like in the old

theory

of

action

at

a

distance.

[32]

I

more or

less

imagine

each such singular

point

as

being

surrounded

by

a

field

of

force

which has

essentially the character of

a

plane

wave

and

whose

ampli-

tude decreases with the distance

from

the

singular point. If

many

such

sin-

gularities

are

present

at

separations

that

are

small

compared

with the

dimen-

sions

of

the field of force

of

a

singular point, then

such

fields

of

force

will

superpose,

and their

totality will

yield

an

undulatory

field

of

force

that

may

differ

only

slightly

from

an

undulatory

field

as

defined

by

the

current

electromagnetic theory

of

light.

I

am

sure

it

need

not

be particu-

larly

emphasized

that

no

importance

should

be

attached

to

such

a

picture

as

long

as

it

has

not

led

to

an

exact theory.

All

I

wanted

is briefly

to

indicate with its

help

that the

two

structural properties

(the

undulatory

structure

and the

quantum

structure)

simultaneously displayed

by

radiation

according to

the

Planck formula should

not be

considered

as

mutually

incompatible.