DOC.

38

QUANTUM

THEORY OF RADIATION

221

somewhat the still unclear

processes

of

emission and

absorption

of

radiation

by

matter. I

made

a

few

hypotheses

about the emission and

absorption

of

radiation

by

molecules,

which

suggested

themselves from

a

quantum-theoretic point

of

view,

and

thus

was

able

to

show that

molecules under

quantum theoretically

distributed states

at

temperature equilibrium

are

in

dynamical equilibrium

with Planck's radiation.

By

this

procedure,

Planck's formula

(4)

followed in

an

amazingly simple

and

general

manner.

It resulted from the condition that the distribution

of

molecules

over

their

states

of the inner

energy,

which

quantum theory

demands, must

be the sole result

of

absorption

and

emission of radiation.

If

the

hypotheses

which

I

introduced about the interaction between radiation and

matter

are

correct, they

must

provide more

than

merely

the correct

statistical

distribution

of

the inner

energy

of

the molecules.

Because, during absorption

and

emission

of radiation there

occurs

also

a

transfer of

momentum

upon

the molecules.

This transfer

effects

a

certain

distribution

of velocities

of

the

molecules, by way

of

the

mere

interaction between radiation and the molecules. This distribution must be

identical to the

one

which results from the mutual collision of the

molecules, i.e.,

it

must be identical with the Maxwell distribution. One has to demand that the

mean

kinetic

energy

of

a

molecule

(per

degree

of

freedom)

in

a

Planck field of radiation

of

temperature

T is

equal

to

kT-2;

this

must

hold

independently

of the

absorbed

or

emitted

frequencies

and the nature of the molecules considered. We want to show in

the

present paper

that this

far-reaching

demand is indeed satisfied in

a

quite

general

manner.

In this

way our simple hypotheses

about the

elementary processes

of

emission and

absorption gain

new

support.

In order

to

achieve the result mentioned

above,

we

have to

supplement

to

some

[p.

49]

extent the

hypotheses upon

which

our

earlier work

was

based because

they

relate

only

to the

exchange

of

energy.

There arises the

question:

Does the molecule receive

an impulse

when it absorbs

or

emits the

energy

e?

For

example,

let

us

look

at

emission from the

point

of

view

of

classical

electrodynamics.

When

a

body

emits the

radiation

e

it suffers

a

recoil

(momentum)

e/c

if

the entire amount

of

radiation

energy

e

is emitted in the

same

direction.

If, however,

the emission is

a

spatially symmetric

process, e.g.,

a

spherical

wave,

no

recoil at all

occurs.

This alternative also

plays

a

role in

the

quantum theory

of radiation. When

a

molecule absorbs

or

emits the

energy

e

in

the

form

of

radiation

during

the transition between

quantum theoretically

possible

states,

then this

elementary process can

be viewed either

as a

completely

or

partially

directed

one

in

space,

or

also

as

a

symmetrical (nondirected) one.

It

turns out

that

we

arrive

at

a theory

that

is

free

of

contradictions, only

if

we

interpret

those

elementary

processes

as

completely

directed

processes.

Herein lies the main result of the

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