262 DOC.
21
THEORY OF RELATIVITY
Further,
it
can easily
be
seen
that,
according
to
the
general
theory
of
relativity,
the
gravitational
field
must
have
a
much
more
complicated
structure
than
according
to
Newton's
theory.
For if
one assumes
that K'
is in uniform rotation
with
respect
to
the inertial
system K,
then the
motion of material
points
relative
to K' is
such
that
their acceleration
depends
not
only
on
their
position (centrifugal force)
but also
on
their
velocity
(Coriolis force).
[24]
Further,
from the
fact
of
the Lorentz
construction,
which
was
derived above
as
a
consequence
of the
special theory
of
relativity,
one can
draw the conclusion that
the
possibilities
for
arranging practically rigid
bodies with
respect
to
K'
are
not
accurately
described
by
Euclidean
geometry
and
that the rate
of
identically
constructed clocks
depends
on
the location.
Thus,
a
geometry
and kinematics
that
are
independent
of the
rest
of
physics
do
not
exist
in
the
general theory
of
relativity,
since the behavior of
measuring
rods and clocks
is
determined
by
the
gravitational
field.
It
is
thanks
to
this circumstance that the
general theory
of
relativity
entails
a
much
more
profound change
in the
theory
of
space
and time than does the
special
theory
of
relativity.
For
according
to the
latter,
the
spatial
and
temporal
coordinates
have
a
direct
physical meaning:
between
two
points
(x1, y1, z1)
and
(x2,
y2,
z2)
of the
coordinate
system,
one can
lay
down
a
rigid measuring
rod of
length
x2
-
X12
+
(y2
-
y1)f
+
(z2
-
ztf,
and the time difference
t2
- t1
of
two events
taking place
at
the
same
point
of the
coordinate
system can
be measured
directly by a
clock
(of
identical construction for
all
points)
set
up
at
this
point
(or
in
its
immediate
vicinity).
Such
a
direct
physical
meaning
cannot
be ascribed
to
the coordinates
in
the
general theory
of
relativity.
To
be
sure,
the
totality
of
events, i.e.,
of
the
point
events, is
arranged
in
a
four-dimensional continuum
(space-time)
in
this
theory
as
well,
but the behavior of
measuring
rods and clocks
(the
geometry
or
the metric
in
general)
in
this continuum
is
determined
by
the
gravitational
field;
the latter
is
thus
a physical
state
of
space
that
simultaneously
determines
gravitation, inertia,
and the metric. Herein lies the
deepening
and the unification that the foundation of
physics
underwent due
to
the
general theory
of
relativity.
Quantitative Verification
In remarkable
contrast to
the
profound conceptual change
that the foundation of
physics
underwent due
to
the
general
theory
of
relativity,
the difference between the
quantitatively
verifiable assertions of
the
new
and the old
theory
is
slight.
Besides the