DOC.

436

JANUARY

1918 443

By presupposing

these

equations,

we

have Euclidean

geometry

not when all

matter

disappears,

as was

earlier

the

case,

but

when

a

very specific

value

is

prescribed

for

the material

tensor,

a

value which results from

the

equations

-Aduv =-K,

(t).

(2)

The

Tuv's

are

determined from it such

that

only

the

diagonal

terms occur,

that

is,

all

equivalent

to

one

another.

(A

cancels

out.)

Equations

(2)

are

valid

upon presupposing

a

coordinate

system

S

in which

guv

=

duv

throughout;

in such

a

system,

p(dx1/ds)2

=

...

=

p(dx4/ds)2

should

apply,[3]

that is

matter

ought

to

appear

to

be

moving

with

reference

to

S

at

the

velocity

of

light.

However,

this contradicts

experience, according

to which

an

approximate

Eu-

clidean

geometry

can

be observed

in

a

coordinate

system

against

which matter

is

at

rest.-One

could

take

the

pressure

into account in

the material

tensor,

but

this

is

no

substantial

improvement;

it

seems

most

likely

to work

with internal

tensions.

Indeed,

Tuv

is interpreted

as

the

el[ectro]m[a]g[netic]

energy tensor;

hence

the

equality

of

the

diagonal

terms

probably

means

that

we

have

a

matter

consisting

in

pure el.mg.

pressure

energy.

In

any case, your

consideration

is

tailored

to

ponderable

matter,

and the

material

tensor

has

always

been

pdxudzu/dsds.

This tensor

originates

from the

gen-

eralization of Euler’s

equations

of

motion and has

nothing

to

do with

tensions;

inviscid fluids exist. It indicates the

density

and

velocity

distributions,

it has

more

similarity

to

kinetic

energy

than

to stress

energy.

If this tensor

is

retained

then,

precisely

because

density

and

velocity

occur

in

it,

the

possibility immediately

arises of

constructing your

static

world, by

inserting

T44

=

T

=

p

in

(1).

Yet,

the

difficulty

with

Euclidean

geometry

presents itself,

although I

do not know for

sure

whether it

really

is

a difficulty.

If this tensor is not retained and is

replaced

with

one

taken from

the

elasticity,

shall

we

say,

the latter

difficulty

can

perhaps

be

avoided,

but

I

do

not

know at

present

how

it

would

then

have

to

be inserted

specifically

in order to

obtain

your

or

de Sitter’s world

(T44 =

const

?,

Tuv

=

0).[4]

I

would be

very obliged

to

you

if

you

would

kindly clarify

these

questions

for

me.

With best

regards, yours truly,

R.

Humm,

stud[ent].