DOC.
21
THEORY OF RELATIVITY 257
l
=
l'
.
1

 \
c2
This
means
the
following.
If
a
rod
possesses
the
length
l'
when measured
at rest,
then,
if
it
moves
with
velocity v along
its
axis, it
will
possess
the smaller
length
1
=
1'
1

V2/c2
for
a
noncomoving
observer,
whereas for
a
comoving
observer,
it will,
as
always,
have
the
length
l'.
The
greater
the
velocity v
of the
moving
rod
is
chosen
to
be,
the smaller the
length
l.
If
v approaches
the
velocity
of
light c,
then
the
length
of the rod
approaches
the value
zero.
For values of
v
that exceed the
velocity
of
light,
our
result becomes
meaningless;
such velocities of motion
are
not
possible
according
to
the
theory
of
relativity.
One
sees
that the abovementioned
hypothesis
of
H. A.
Lorentz and
FitzGerald,
which
was
advanced
in
order
to
explain
Michelson's
experiment,
follows
as a
consequence
of the
theory
of
relativity.
On the other
hand,
according
to
the
latter,
bodies
at rest
relative
to
Kevaluated
from
K'will
display
exactly
the
same
contraction
as
bodies
at rest in K'
if these
are
evaluated
from
K.
The
Rate
of
Moving
Clocks
A
further
important consequence
of
our
equations
is
obtained
as
follows. Let
a
clock
with
a
second hand be located
at
the
origin
of K'. For this clock
we
always
have
x'
=
0,
and the clock strikes the seconds
at
times t'
=
0,
1,
2, 3,
etc.
The first and the
fourth of
our
equations yield
the
following
values for the times
t
of these strokes:
0
1
2
t
=
,
etc.
1

v
N
1
y2
c2
N
ly2
c2
Thus,
evaluated from
K,
the time between
two
strokes of the clock
is
equal
to
t
=

1
,
and thus
longer
than
one
second.
A
clock
traveling
with the
velocity
v runs
slowerjudged
from
a
noncomoving
systemthan
the
same
clock when
it
does
not
travel.
Generalizing,
one can
conclude:
Every
event in
a
physical system
slows down
if the
system
is set
into translational motion. But this
slowing
occurs
only
from the
standpoint
of
a
noncomoving
coordinate
system
(observer). [12]