DOC.

18

DISCUSSION OF DOC.

16

229

Born:

I

would like

to

address

a

question

to Mr. Einstein, namely,

how fast does

[22]

the effect

of

gravitation propagate according

to

your

theory.

It is not obvious

to

me

that this would

happen

with

the

velocity

of

light;

this

must

be

a

very complicated

relationship.

Einstein: It is

extraordinarily simple

to

write down the

equations

for the

case

where the disturbances

one

places

into the field

are

infinitesimal. In that

case

the

g

differ

only infinitesimally

from those that would be

present

without that

disturbance;

disturbances

propagate

then with the

same

velocity

as light.

Born: But

things are surely very complicated

in the

case

of

great

disturbances?

Einstein:

Yes,

this

is

a

mathematically complicated problem.

In

general,

it

is

difficult

to

find

exact

solutions

of

the

equations,

since the

equations are

not

linear.

Jäger: Einstein should tell

us

how

he

envisions

the execution of the crucial

gas.

A

gas, or perhaps

bettter,

a liquid

under the influence

of

volume

forces, like,

e.g.,

gravity, can

reach

a

state

of

equilibrium only

because

an

equation

of

state holds between

the volume and the

pressure.

Thus,

an equation

of

state is

probably

also

necessary

in

empty space, say

between the

gradients

of

the

velocity

of

light

and certain

stresses

to be fabricated

according

to

Maxwell's

procedure.

For

example,

in the

case

of

centrally symmetric

fields such

a

condition

amounts

to

an equation

of

state

between the

energy density

and stresses in

empty space.

Following

the

analogy

of

Maxwell's

system

for

electrodynamic

stresses,

Mr. M.

Abraham has worked

out

roughly

how

one

must conceive this in

terms

of formulas

(International Congress

of

Mathematicians.

Cambridge. Aug.

1912).

I

have

only one [20]

criticism,

and this takes

us straight

to the heart

of

my question.

For in Abraham's

representation,

the volume forces associated with the field

energy

density

of

a space

free

of

ponderable mass go

to

zero,

and this

may

not

be

if

every

form

of

energy possesses mass

and thus also

gravity,

which claim

Mr. Einstein has made the

centerpiece

of

his

system

of

gravitation.

Has Mr. Einstein

replaced

Abraham's above-mentioned

system

of

stresses

by

another

one,

in which

even

the field

energy density

of

empty space

is

affected

by gravitational

forces that achieve

equilibrium

with

stresses

of

the

Maxwellian kind

by

the latter's

opposing

a

deformation

of

the

field,

e.g., a change

in the

energy density?

In this

way

the field

energy

of

empty space acquires

certain elastic

properties!

Furthermore,

the

gravitational

forces

of

empty space

differ from those

of

matter by

virtue

of

the fact

that,

in the static

case,

the former

always

achieve

equilibrium

with the

quasi-Maxwellian stresses, even

without the aid

of

momentum

or energy

flux,

while the

gravitational

forces

of

discrete bodies reach

equilibrium

without the

production

of

momentum

or

other external forces. From what other

equation

of

state

connecting

the

velocity

of

light

with stresses within matter must this result?

Were Mr.

Einstein to take

a position on

this

question,

it

would

surely provide

welcome

enlightenment

for

many

other

readers

of his

works.

[21]

H.

Reißner.