96 DOC.
3
STATICS OF GRAVITATIONAL FIELD
equivalent
to
a
system
at rest
in which there
is
a
mass-free static
gravitational
field3
of
a specific
kind. The
spatial
measurement
of K is carried
out
by
means
of
measuring
rods
that-when
compared
with
one
another
in
a
state
of
rest at
the
same
location in K-possess the
same
length;
the laws of
geometry
shall hold for
lengths
so
measured,
hence also for relations between the coordinates
x,
y,
z
and other
lengths.
This
stipulation
is
not
permitted
as a
matter
of
course;
in
fact, it
contains
physical assumptions
that
might possibly
prove to
be
wrong;
for
example,
they
most
probably
do
not
hold in
a
uniformly rotating system
in
which, owing
to
the Lorentz
contraction,
the ratio of the circumference
to
the diameter would have
to
be different
[5]
from
n
if
our
definition
were
applied.
The
measuring
rod
as
well
as
the coordinate
axes are
to
be conceived
as rigid
bodies. This is
permitted despite
the fact
that,
according
to
the
theory
of
relativity,
the
rigid body
cannot
possess
real existence. For
[6] one can imagine
the
rigid measuring body being replaced by
a
great
number of
nonrigid
bodies
arranged
in
a row
in such
a
manner
that
they
do
not exert any
pressure
on
each other in that each is
supported separately.
We
imagine
that the time
t
in
system
K is
measured
by
clocks
so
constituted and
so
rigidly arrayed
at
the
spatial points
of the
system
K that the time
span-measured
by
them-that
is needed
for
a
light ray
to
get
from
a
point A
to
a point
B
of the
system
K does
not
depend on
the
time
of
emission of the
light ray
at A.
Furthermore,
it will
turn out
that
simultaneity can
be
defined in
a
consistent
manner by postulating that,
with
respect
[7]
to
the
setting
of the
clocks,
all
light rays
that
pass
a
point A
of K have the
same
propagation velocity
at
A independently
of
their direction.
We
now
imagine
that the reference
system
K
(x, y, z, t)
is observed from
a
nonaccelerated
reference
system (of constant
gravitation potential)
2(£,
rj,
(, t). We
postulate
that the x-axis coincides
permanently
with the
£-axis
and that the
y-axis
is
permanently parallel
to the
n-axis,
while the z-axis is
permanently parallel
to
the
C-axis.
This
stipulation
is
possible
on
the
assumption
that the
state
of acceleration
has
no
influence
on
the
shape
of K with
respect
to
E.
We take this
physical
assumption
as our
basis. It follows from this that for
arbitrary
T
we
must
have
n
=
y,
(1)
C
=
z,
so
that it
only
remains for
us
to
find out the relation that obtains between
E
and
T
on
the
one
hand,
and
between
x
and t
on
the other. Let the
two
reference
systems
coincide
at
time
T
=
0;
then the
substitution
equations
that
we are
seeking
must be
of the form
3One has
to
imagine
that the
masses
that
generate
this field
are
situated
at
infinity.
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