594

DOCS.

566,

567

JUNE

1918

has

to set

xa

=

n/2,

c

=

2,

R

=

Kp0/3_

in formula

(35)

there

in order

to have de

2

V

3

Sitter’s

ds2.[12]

Formula

(35)

relates,

of

course,

to

the

interior

of

the

sphere

at rest

considered

by

Schwarzschild of

gravitating liquid

of

constant

density.

Formula

(30)

is

thus

applicable,

which

yields p

=

-p0,

hence

a

steady

pull.[13]

Obliging regards

from

yours

most

truly,

Klein.

P.S.

I

think

I

can

set

your

letter

of

9 June[14] straight

now.

The

ÄB's

are

strictly

equal

to

zero

for

a

#

4,

the

corresp.

Axa’s

are

arbitrarily

small

against

Ax4.[15]

567. To

Felix

Klein

[Berlin,

20

June

1918]

Esteemed

Colleague,

You

are

entirely right.

De

Sitter’s world

is,

in and of

itself,

free of

singulari-

ties

and its

space-time points

are

all

equivalent.[1]

A

singularity

comes

about

only

through

the

substitution

providing

the

transition to the static form of

the

line el-

ement. This

substitution

changes

the

analysis-situs

relations. Two

hypersurfaces

t

=

t1

and

t

= t2

intersect

each

other

in

the

original represention,

whereas they do not

intersect

each

other

in

the

static

one.[2]

This

is

related

to

the fact

that, for

the

physi-

cal

interpretation,

masses are

necessary

in

the static

conception

but

not

in

the

former

one.[3]

My

critical remark about

de Sitter’s solution needs

correction;

a

singularity-free

solution for

the

gravitation

equations

without

matter

does in

fact

exist.[4]

However,

under

no

condition could

this

world

come

into

consideration

as

a

physical possibility.

For in

this

world,

time t cannot be defined in such

a

way

that the

three-dimensional slices t

=

const. do not intersect

one

another and

so

that

these slices

are

equal

to

one

another

(metrically).[5]

With

sincere

thanks

for

your

fine

and

illuminating

letter,

yours truly,

A.

Einstein.

Recipients

note

on

the

verso:

“Did

Weyl

appear? Appointment regarding

the

building

plans

of

the Math. Inst.”