XX
INTRODUCTION TO VOLUME
6
other
Mach's
principle.
That
Einstein turned
to
cosmology
so soon
after the
completion
of
general relativity can
also be understood from the fact that
cos-
mology
is
an
integral part
of
general relativity,
in
the
sense
that the
geometric
structure
of
the
universe
is not
given
a
priori,
as
in
Newtonian
cosmology,
but
must fit
into the framework of the
general theory. Cosmological
consider-
ations
appear
already
in Einstein 1916e
(Doc.
30).
Indeed,
the
argument giv-
en
in the
introductory part
of this
paper
concerning
two
spheres,
one
of which
is
rotating,
touches
directly on
Mach's
principle.
The
physical cause
needed
to
explain
the
difference in
shape
between the
rotating sphere
and the
non-
rotating one
is
found in the
presence
of distant
masses; making
absolute
space
responsible,
as
Newton
did,
is
"a
purely fictitious cause,
not
something
ob-
servable."[23]
According
to
Einstein,
empty space
cannot
have
a
geometrical
structure,
and
a single
isolated
mass
cannot
have inertia
or impose a
structure
on
space
at
infinity.
It
was
precisely
this conviction that Einstein took
as
the
starting point
for
his
paper
on
cosmology
(Einstein 1917b [Doc. 43]).
The
consequence
of
Ein-
stein's version of Mach's
principle
is
that
at
infinity
the
components
of the
metric
tensor
should
degenerate:
for
an
isotropic
field the
spatial components
become
zero,
whereas the timelike
component goes
to
infinity.
It turned
out
to
be
impossible
to
realize these conditions for
centrally symmetric
static
fields. Einstein's
way
out
was
to postulate
a
universe that
is
spatially
finite,
closed,
and
static,
with
a
uniform
mass
distribution,
a
universe
in
which
no
boundary
conditions
are
needed.
In
order
to
do
so,
however,
Einstein had
to
modify
his
field
equations
to
include what became known
as
the
"cosmolog-
ical constant." In this
way
Einstein had
incorporated
the Machian ideas
as
well
as
he
could, without, however,
completely solving
the
problem
of rela-
tivity
of rotation.
The
paper
marks the
beginning
of
a
discussion between Einstein and the
Dutch
astronomer
Willem de Sitter
on
the
relativity
of rotation and
the
rela-
tivity
of
inertia,
carried
out
in
correspondence
as
well
as
in
published pa-
pers.[24]
A
major topic
of discussion
was
De
Sitter's
own
cosmological
solu-
tion,
which showed
that
an
empty
universe
can
exhibit
global curvature.
Although
the existence
of
such
a
solution
was a
serious blow
to
Einstein's
ideas
on
the
relativity
of
inertia,
he did
not
abandon his views
on cosmology.
[23]"eine bloß fingierte
Ursache,
keine beobachtbare Sache." Einstein 1916e
(Doc. 30),
p.
771.
[24]See
the
correspondence
between Einstein and De Sitter in
Vol.
8;
see
also
Kerszberg
1989b for
an
analysis
of the
Einstein-De
Sitter
controversy
and North 1965 and Eisenstaedt
1993 for historical discussions of the later
developments
outlined
in
this
paragraph.