320
DOC.
71
PRINCETON LECTURES
THE GENERAL
THEORY
along
the
diameter,
then,
if
K' does
not rotate
relatively
to
K, we
shall
have
But if
K'
rotates
we
get a
different result.
Suppose
that
at
a
definite time
t,
of K
we
determine the
ends of all
the
rods.
With
respect to
K all the
rods
upon
the
periphery
experience
the Lorentz
contraction,
but the rods
upon
the
diameter do
not experience
this
contraction
(along
their
lengths!).*
It therefore
follows
that
It
therefore
follows
that
the laws of
configuration
of
rigid
bodies
with respect
to K' do
not
agree
with
the
laws of
configuration
of
rigid
bodies
that are
in accord-
ance with Euclidean geometry.
If,
further,
we
place
two
similar
clocks
(rotating with K'),
one
upon
the
periphery,
and the other at
the
centre
of the circle,
then, judged
from
K,
the clock on the
periphery
will go slower
than
the clock
at the centre. The
same
thing must take
place,
judged from K',
if we do
not
define
time with respect
to K'
in a wholly
unnatural
way,
(that
is,
in such a way
that
the
laws
with respect
to
K' depend explicitly upon the
time). Space and
time,
therefore, cannot
be
defined
with respect
to K' as
they
were in
the
special
theory
of
relativity with respect
to
inertial
systems. But,
accord-
ing
to the
principle
of
equivalence, K' may
also be
con-
sidered
as a system
at
rest,
with respect
to
which there
is
a
gravitational
field (field of
centrifugal
force,
and
*These
considerations assume
that
the behavior of rods and
clocks
depends only upon velocities,
and
not upon accelerations, or, at least,
that
the influence of acceleration does not counteract
that
of velocity.
[80]
[81]
U/D =
T.
U/D
T.
[60]