DOC.

163

MAY 1909

123

phenomena

differs from the

theory

used

so

far.

If

we

could

only

understand

the

relation

e

=

hv

somehow!

In

this connection,

it is

of interest that

according

to

the

relativity

theory,

the

energy

(e)

and

frequency (v)

of

a

monochromatic

light complex

propagating

in

a

specific

direction

change

with

the

change

of

the

coordinate

system

in such

a manner

that

e/v

remains

constant.[5]

As

far

as

the

light

quanta

are

concerned,

it

seems

that

I did

not

express myself

clearly.

For

I

am

not at

all

of the

opinion

that

light

has to be

thought

of

as

being

composed

of

mutually independent quanta

localized in

relatively

small

spaces.

To be

sure,

this would be the

most

convenient

way

to

explain

the Wien

end of

the

radiation

formula.

But the

splitting

of

light rays

on

the

surfaces

of

refracting

media

already

makes

this

approach

absolutely

inadmissible.

A

light ray splits,

but

a

light

quantum

cannot

split

without

a

change

in

frequency.

I

enjoyed very

much

your

explanation

of the

difficulties

that

arise

for the

quantum

theory

from

the

phenomena

of interference

and

sharpness

of

image.

I

see

from

it how

acutely you

have

thought

about these

things

which have

already

given

me

such

a

headache.

As I said

already,

in

my

opinion

we

should not

even

think of

constructing

light

out

of

discrete,

mutually independent

points.

This

is, more or

less,

how

I

imagine

the

thing:

According

to Maxwell's

equations,

a wave process

propagating

in

a given

direction

that neither

extends into

infinity

perpendicularly to

its

direction of

propagation

nor

becomes infinite in

each

plane

of

equal phase

is out

of the

question. By

virtue of the

expansion

in all

directions,

the

energy

of each

wave

system

seeks to

expand over

larger

and

larger

volumes.

This

is

the feature

of

our

present theory

of

light

that

seems

to

me

to be

wrong.

Instead, I believe

that

the

light groups

around

singular[6]

points

in

a

way

similar to

what

we are

accustomed

to

assume

for

the

electrostatic

field.[7]

Thus,

I

think

of

a

single light

quantum

as a

point

surrounded

by a greatly

extended

vector field

that

somehow

decreases

with distance.

The

point is

a

singularity

without

which

the

vector

field

cannot

exist.

I

wouldn't

know to

say

whether

one

has to envision

a simple

superposition

of the

vector fields when

many

light

quanta

with

mutually

overlapping

fields

are

present.

In

any

case,

in

order

to

determine

the

processes

one

would also have

to have

equations

of motion

for the

singular

points

in

addition

to

the differential

equations

for

the

vector

field,

if

mathematical

singularities

are

introduced. The

energy

of

the

electromagnetic

field-at least

in

the

case

of

sufficiently

diffuse

radiation-should

be related, in

some way or

another,

to

the number of these

singular

points. Absorption

would

take

place

only

in association with

the

disappearance

of

such

a

singular point

or

degeneration

of the radiation

field

belonging

to this

point.[8] By

specifying

the

motions

of

all

singularities

one

would

completely

determine

the vector

field,

so

that the number

of

variables

necessary

for the

characterization of radiation

would be

finite.

In the

case

of the

decomposition

of

a ray

at

the

boundary

of

two

media

one

would have

to

assume

the formation of

new singular

points

and

the

disappearance

of those that

have

been