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).