DOC. 42 SPECIAL AND GENERAL RELATIVITY
333
90
Relativity
edge
of the
disc,
so
that
they
are
at rest
relative
to
it. We
now
ask ourselves whether both clocks
go
at
the
same
rate
from the
standpoint
of the
non-rotating
Galileian
reference-body K. As
judged
from this
body,
the clock
at
the
centre
of the
disc has
no
velocity,
whereas the clock
at
the
edge
of the
disc
is
in
motion relative
to
K in
consequence
of the rotation.
According
to
a
result
obtained
in Section
12,
it
follows
that the latter
clock
goes
at
a
rate
permanently
slower than that of the clock
at
the
centre
of the
circular
disc,
i.e.
as
observed
from
K.
It
is
obvious
that the
same
effect
would be
noted
by
an
observer
whom
we
will
imagine sitting alongside
his
clock
at
the
centre
of
the circular disc.
Thus
on
our
circular
disc, or, to
make the
case
more
general,
in
every gravitational field,
a
clock
will
go
more
quickly
or
less
quickly, according to
the
position
in
which the clock
is
situated
(at rest).
For this
reason
it
is not
possible
to
obtain
a
reasonable definition of time with the
aid
of
clocks
which
are
arranged at rest
with
respect to
the
body
of
reference.
A
similar
difficulty presents
itself when
we
at-
tempt to apply
our
earlier definition of
simultaneity
in
such
a
case,
but
I
do
not
wish
to go any
farther into this
question.
Moreover,
at
this
stage
the definition of the
space
co-
ordinates
also
presents
insurmountable difficulties. If the
ob-
server
applies
his
standard
measuring-rod (a
rod
which
is
short
[46]
as
compared
with the radius of the
disc)
tangentially
to
the
edge
of
the
disc,
then,
as
judged
from
the Galileian
system,
the
length
of this
rod will
be
less
than
1,
since,
according
to
Section
12,
moving
bodies suffer
a
shortening
in
the direction
of the motion.
On the other
hand,
the
measuring-rod
will
not
experience
a
shortening
in
length,
as
judged
from
K,
if
it
is