DOC.
488
MARCH
1918 509
of the Earth around
its
own
axis
reliably
through
purely
terrestrial
observations
(with
Foucault’s
pendulum); we
are
going
to be able to
say absolutely:
the Earth
rotates
around this and this
axis,
at
this
and
this rotation
velocity. By
contrast,
if
your
theory is
correct
(which
I
do not
doubt)
it could not be
demonstrated
that the Earth
has
a
curvilinear motion in
space
around
the
Sun. For
the
effect
of
the
Sun’s
gravitational field
always exactly compensates
all the
influences of
the
orbit’s curvature.
So
one
would
probably
say,
if
only
terrestrial
observations
could be made:
the Earth
is
motionless in
space
and rotates
only
around
its
own
axis.
It
is
very interesting
to note
here,
though,
that
this
relativity
of
the
gravitational
field[8]
is
valid
only
when
the
Sun’s
gravitational
field
within
the
region
accessible
to
us
for
performing
terrestrial
observations
is
regarded
as con-
stant.
Phenomena
originating
from
a
change
in
the
Sun’s gravitational field
with
distance
within
the
range
of
the
Earth’s
diameter,
for
example
the
precession
of
the Earth’s rotational
axis,
would
likewise
have to be ascertainable from
purely
terrestrial
observations. Let
us assume
for
a
moment
that
Foucault’s
pendulum
experiment
could be conducted with such
precision
that
the
precessional
motion
of
the Earth’s
axis
were
detected,
then
one
would
certainly
have
a
purely
terres-
trial
observation
that
would
prove
the
inadequacy
of
the
conception
of
an
Earth
motionless in
space, only
rotating
around its
own
axis. The
principle
of
the
rel-
ativity
of
the
gravitational field is
thus attached
to
the
condition
that
a
certain
limit in
observational
precision
must be
presupposed,
as
I
have also
explained
in
my
Göttingen
lectures;[9]
it
really
is
a
very
wonderful
theorem,
though,
all
the
same.
If
we assume
this
condition
valid,
we can
then
arrive at
the
assertion: “the
Earth
describes
a
curvilinear orbit”
only
when
we
can
extend
the
observations
over a
large enough region
in
space
in which
the
solar
gravitational field is
cer-
tainly
no
longer
constant,
hence
through
the
entire
region
delimited
by
the Earth’s
orbit. If
we can
peer
about
as
far into
the
universe from
our
Einsteinian
coupé
(it
must
then,
obviously, actually
lose
its
coupé
designation!),
then-but
also
only
then-we
can
determine
absolutely
that the
motionless-Earth
hypothesis
is
false.
Generally,
this
can
also be
expressed
thus: If
not
the
entire universe
were
accessible
to
our
observations,
but rather
only
a
thin
“world
tube” delimited
by
geodesic
world
lines,
which
is
so narrow
that
in its interior
the
geodesic
lines still
form
a
“coordinate
grid”
(if
I
may express myself
in
this concise
manner
after
my
discussion in
the
Göttingen
lectures),
then
nothing
can
be concluded
about
the
form of
this tube
from
observations;
it
can
be
regarded
as
straight
or
also
as
curved in
any
manner
you
like.
The construction
of
an
“absolute
coordinate
system,”
in which
the
world-line
tube
just
considered
is
also
assigned
a
specific
shape,
is
possible only
when
the
region
accessible to observation
is
so
large
that
one can
say
with
certainty
whether
or
not
the
geodesic
lines form
a
coordinate
grid.