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
non-comoving
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 above-mentioned
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
K-evaluated
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
l-y2
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
slower-judged
from
a
non-comoving
system-than
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
non-comoving
coordinate
system
(observer). [12]
Previous Page Next Page