DOC. 24 RESPONSE TO

QUESTION

BY REIßNER 277

be another

symmetric

four-dimensional

expression

for the conservation

laws,

other

than

(9b).

But

equation (9b)

can

indeed elicit the doubts

expressed by

Mr. Reißner.

According

to

(9b),

the

equations

for the

momentum

of the static

gravitational

field

in the absence of material

processes

have the

following

form:

d

fp-j

+

d

^2

+

_

Q

dx

dy

dz

The

equilibrium

of

the static

gravitational

field

is

reduced here to

an equilibrium

exclusively

of

surface forces, whereas, indeed,

a

kind of

volume

forces should exist

in

the

gravitational

field, since,

according

to

the basic

assumptions

of the

theory,

the

gravitational

field would be

expected

to act

on

its

own

"energetic components"

tov

just

as

it

acts

on

the

corresponding energetic components

3!ov

of

matter.

It should be

noted, however,

that the

possibility

of such

a

representation

does

not

imply anything

about the

physical

nature

of the

effects under consideration.

All that

the

possibility

of such

a

representation

does

say

is

that the

momentum

law

is

valid.

When Mr. Reißner

says

that,

for the basic idea of the

theory

not to

be

abandoned,

the

existence

of

an

energy

density

of

a

static

gravitational

field

must

have

as a

consequence

a

transfer

of

momentum

from the

gravitational

field

to

itself,

then

I

agree

with him.

But this

momentum

transfer

must

be

compensated

by

the effects

(momentum

transfer)

of

pressure forces,

because otherwise the

momentum

law would

be

violated. Volume forces and surface forces

are

not

separable

in the

momentum

conservation

law for the

gravitational field,

and the

momentum

law

requires

that all

forces be reducible

to

surface

forces.3

But

on

the other

hand,

one

must

demand of the

theory

that the

energetic

components

of

a gravitational

field

belonging

to

a

closed

system

make

exactly

the

same

contribution

to

the

gravitational

mass

of the whole

system

as

do the

energetic

components

of the

matter

constituting

the

system.

The

theory actually

satisfies this

condition,

as

is evident

from the

following.

In

a

formerly gravitation-free

space

(

dguv/dxo

=

0

)

a

we place a

static material

system

X

,

the

energetic components

of which

belong

in

part

to

the

gravitational

field

produced

by

the

parts

of

X

.

If

one

sets

3In

electrostatics,

for

example,

the fact that all forces

acting on

matter

can

be

represented by

Maxwellian stresses does not

permit

the conclusion that

no

volume forces

actually

act

on

the

matter; rather,

this is

merely a

mode

of

representation

that makes the

validity

of

the

principle

of

reaction evident.

[6]