256 DOC.
21
THEORY OF RELATIVITY
X
-
vt
x
=
1
-
V
N
y'
=
y
z' =
z
V
t
-
t'
=
1
-
N
Relativity
of Time
The last of these
equations
shows
that,
in
general,
the
equality
of time values
(simultaneity)
of
two events
with
respect
to K
does
not
result in the
equality
of time
values
(simultaneity)
of the
same
events
with
respect
to
K'.
Thus,
the absolute
meaning
of
simultaneity
is lost.
Contraction
of
Moving
Bodies
in the
Direction
of Motion
We ask further: How
great
is
the
length
l
of
a
rod-as
observed
from the
system
K-that
is at
rest
with
respect
to K',
is oriented
parallel
to
the
x'-axis,
and
possesses
the
length
l' with
respect
to
K'? The first of the
equations provides
the
answer3
3For
both ends of the
rod,
that
is,
the x-coordinates
of
the
rod ends
satisfy
the
equations
x1 -
vt
x1
=
,
x2' =
x2
- Vt
,
which
yield
after subtraction:
*2
~
V
=
*2
"
xl
or
i=v i
-
i
-
N
N