552

DOC. 43

COSMOLOGICAL CONSIDERATIONS

Published

in

Königlich Preußische

Akademie der

Wissenschaften

(Berlin).

Sitzungsberichte

(1917):

142-152. Submitted

8 February 1917, published 15 February

1917. A

manuscript frag-

ment

of

p.

5

of the

text

[2

079.1] is

preserved.

It

corresponds to

that

portion

of

sec.

2

of the

published paper

that

begins

on p.

146

at "[Grenz]bedingungen"

and ends

on p.

147

with "so

besäße

er

nach dieser"

in

the

penultimate paragraph

of

sec.

2.

[1]For

historical

background to

this

paper,

see

the Introduction.

[2]Einstein

was

already thinking

about the

problem regarding

the choice of the

boundary

conditions

at infinity

in

the

spring

of

1916 (see

Einstein

to

Michele

Besso,

14 May 1916,

where

he also mentions the

possibility

of the world

being

finite).

[3]See Einstein 1915h

(Doc.

24),

p.

833,

for

a

discussion of the

boundary

conditions

in

the

"planetary problem."

[4]This

difficulty

in

the Newtonian

theory

of

gravitation

is

also discussed

in

Einstein 1917a

(Doc. 42), pp.

71-72. There it

is

also mentioned that modifications

in

the

gravitational poten-

tial had been

proposed

in

the late nineteenth

century

in

order

to overcome

this

difficulty (see

Seeliger

1895 and

Neumann,

C.

1896;

see

also North

1965,

chap. 2,

for

a

historical

discussion).

[5]"\"

should be

"M."

[6]This statement

summarizes Einstein's

interpretation

of "Mach's

Principle."

See

Einstein

1916c

(Doc. 29),

note 4,

for

more on

the role that Mach's ideas

played

in

Einstein's

thinking;

see

also Einstein's

comments

on

the

relativity

of inertia

(and

on

the

present paper

in

general)

in

Einstein

to

Felix

Klein, 26

March

1917.

[7]Jakob

Grommer

(1879-1933)

was

Einstein's occasional collaborator until

1928

(see

Pais

1982,

pp.

487-488).

[8]See

De Sitter

1916,

p.

503

(p.

531 in

the

English translation),

fn.

2,

in

which De Sitter

criticizes the

boundary

condition

given

above.

As De

Sitter

points

out,

the footnote

was

added

to

the

paper on

29 September

1916

after

a

conversation with Einstein.

[9]De

Sitter

1916.

The

paper

was

actually

submitted

at

the

meeting

of

the

Amsterdam Acad-

emy

of Sciences of

30 September 1916.

This

paper,

which criticized Einstein's

rejection

of

absolute

space

and his attribution

of inertia

to

distant

masses,

as

expounded

in

Einstein 1916e

(Doc. 30),

was

the

start

of

a

controvery

between

De

Sitter and Einstein

on

the

relativity

of

rota-

tion and the

nature

of inertia. The discussion

was

carried

on

in

published papers

as

well

as

in

correspondence

(see Vol.

8

for the Einstein-De Sitter

correspondence

from the

years

1916-

1918).

For historical

discussions,

see

North

1965, chap. 5, Kerszberg

1987, 1989a, 1989b,

and

Eisenstaedt 1993.

[10]Einstein

refers

to

the fact that

in

Schwarzschild and Droste's

exact

solution of the field

equations a

single

mass

generates

a

gravitational

field

in all

space

(see Schwarzschild

1916a

and Droste

1916).

See

also Einstein's discussion of this

point

in

Einstein

to

Karl Schwarz-

schild,

9

January

1916.

[11]The

reference

is

to

eq.

(5)

on p.

146.

[12]"Linsenelement" should

be

"Linienelement."

[13]See,

e.g.,

Einstein

1916g

(Doc. 32),

eq. (1).

[14]"(14)"

should be

"(13)."

[15]The

factor

T2

in

the last

expression

should be

in

front of the

square root.

[16]From astronomical data Einstein

concluded

to

a

value of

R

of

107 light-years,

whereas

the size of the visible universe

was

estimated

at 104

light-years (see, e.g.,

Einstein

to

Michele

Besso,

after

9

March

1917,

and Einstein

to

Paul

Ehrenfest, 14

February 1917,

for his

com-

ments).

Not

long

after the

publication

of this

paper,

both Erwin Freundlich and Felix Klein

pointed

out

to

Einstein that

an

elliptical geometry

could have been chosen instead of

the

spher-

ical

geometry

considered here

(see

Einstein

to

Felix

Klein, 26

March

1917,

in

which Einstein

acknowledges

the

comments

and claims that both

geometries give

the

same

relation between

radius and

mean

density).