348
DOC.
17
THE THEORY
OF
RELATIVITY
velocity
of
light,
it will
collapse
to
a
plane. However,
as
judged
by
a
comoving
observer,
the
body
retains,
before
and
after,
its
spherical shape; on
the other
hand,
to
the observer
moving
with
the
body,
all
noncomoving
objects
appear,
in
exactly
the
same
way,
contracted in the direction of the relative motion.
This
result
loses
very
much
of
its
oddness
if
one
considers that
this
assertion about the
shape
of
a moving
body
has
quite
a
complicated meaning since,
according
to what has
been
said
above,
this
shape can
be
ascertained
only
with
the
aid
of determinations of
time.
The
feeling
that
this
concept,
"the
shape
of the
moving body,"
has
an
immediately
obvious
meaning is
due to the
fact
that
in
our day-to-day
experience
we are
accustomed
to
encountering
only
such velocities
of motion that
are
practically infinitely
small
compared
with
the
velocity
of
light.
And
now a
second
purely
kinematic
consequence
of
the
theory
that strikes
us as even
more
peculiar.
We
imagine
that there
is
given
a
clock
capable
of
indicating
the
time
of
a
reference
system
k,
provided
that
it
is arranged
at rest relative to this
system.
It
can
be
proved
that
this
same clock,
when
set
into uniform motion
relative to
the reference
system k, runs slower, as
judged
from
the
system
k,
in such
a
way
that
when
the time
reading
of the
clock has
increased
by
1,
the
clocks
of the
system
k
indicate
that,
with
respect
to
the
system k,
there
has
elapsed
the time
1
1--
N
c2
Thus,
the
moving
clock
runs more
slowly
than the
same
clock when in state
of
rest with
respect
to k.
One
must
imagine
that
one
determines the
rate
of the
clock in
a
state
of
motion
by comparing,
from time
to
time,
the
position
of
the
hands of
this clock with
the
positions
of
the
hands of
those clocks at
rest
relative to
k that
measure
the
time relative
to k and
that the
moving
clock
under consideration
is just
then
passing
by.
Were
we
to succeed in
making
the
clock
move
with
the
velocity
of
light-we would be able to
make it
move
with
a velocity
approximating
the
velocity
of
light
if
we
had
sufficient
force-the
hands of the
clock,
as
judged
from
k,
would
move
forward
infinitely
slowly.
The
thing is
at its
funniest
when
one
imagines
that the
following
is
being
done:
One
imparts
to this clock
a
very
great
velocity (almost
equal
to
c),
then
lets it
fly
on
in
uniform
motion,
and after the
clock has
covered
a
long
stretch,
one
imparts
to it
a
momentum in
the
opposite
direction,
so
that
it returns to
the
point
from which it has
been launched. It then
turns out
that the
positions
of the
clock's
hands
have
hardly
changed
during
the
clock's
entire
trip,
while
an
identically
constituted
clock
that
remained
at
rest at
the
launching point during
the entire
time
changed
the
setting
of
its
hands
quite
substantially.
It should be added that
whatever holds
for
this
clock,
which
we
introduced
as a simple
representation
of
all
physical
phenomena,
holds also
for
closed
physical