148
DOC. 30 FOUNDATION
OF GENERAL RELATIVITY
For
the
laws
of
geometry, even
according
to the
special theory
of relativity,
are
to
be
interpreted directly
as
laws
relating
to
the
possible
relative
positions
of solid bodies
at rest;
and, in
a
more
general way,
the
laws of
kinematics
are
to be inter-
preted
as
laws
which
describe
the relations
of
measuring
bodies
and
clocks.
To two
selected
material
points
of
a
stationary rigid body
there
always corresponds
a
distance
of
quite
definite
length,
which
is
independent of
the
locality
and
orientation of
the
body,
and is also
independent
of
the time.
To
two selected
positions
of
the hands
of
a
clock at
rest
relatively
to
the
privileged
system
of
reference there
always
corresponds
an
interval
of
time
of
a
definite
length,
which
is
independent
of
place
and
time.
We
shall
soon
see
that the
general theory
of
relativity
cannot
adhere
to
this
simple
physical interpretation
of
space
and
time.
§
2.
The Need
for
an
Extension
of
the Postulate
of
Relativity
[7]
In
classical mechanics,
and
no
less
in the
special theory
of
relativity,
there
is
an
inherent
epistemological
defect which
was,
perhaps
for
the first
time,
clearly
pointed
out
by
Ernst
Mach. We
will
elucidate it
by
the
following
example:-Two
fluid
bodies
of
the
same
size
and nature hover
freely
in
space
at
so great
a
distance
from
each other and
from all
other
masses
that
only
those
gravitational
forces need be
taken into
account
which arise
from the interaction
of different
parts
of
the
same
body.
Let the
distance between
the
two
bodies be
invariable, and
in
neither
of
the
bodies
let there be
any
relative
movements of
the
parts
with
respect
to
one
another.
But let either
mass,
as judged by an
observer
at
rest
relatively
to
the other
mass,
rotate
with
constant
angular
velocity
about the
line
joining
the
masses.
This is
a
verifi-
able
relative motion
of
the two
bodies. Now
let
us
imagine
that
each
of
the
bodies has been
surveyed by
means
of
measuring
instruments
at rest
relatively
to
itself,
and let the
surface of
S1
prove
to
be
a sphere,
and that
of
S2
an ellipsoid
of
revolution.
Thereupon
we
put
the
question-What
is
the
reason
for this
difference
in the
two
bodies?
No
answer can