DOC.
23
145
locations
they
happen
to
occupy;
hence,
these clocks
are
"synchronous
in
the
system
at
rest."
We
further
imagine
that
each clock has
an
observer
co-moving
with
it,
and
that
these observers
apply to
the
two
clocks
the criterion for
synchronism
formulated
in
§1. Suppose
a
ray
of
light
starts
out
from
A
at time1
tA,
is
reflected
from
B
at
time
tB,
and
arrives
back
at
A
at
time
t'A.
Taking
into
account
the principle of the
constancy
of the velocity
of
light,
we
find
that
and
t
t
-
VAB
B
~
A
~
V
-
v
V
t
-
riB
lA
XB
~
V
+ v
'
where
rAB
denotes the
length
of the
moving
rod,
measured
in the
system
at
rest.
The
observers
co-moving
with the
moving
rod would
thus find
that the
two
clocks
do
not
run
synchronously
while the observers in the
system
at rest
would
declare
them
synchronous.
Thus
we
see
that
we
must
not
ascribe absolute
meaning
to
the
concept
of
simultaneity;
instead,
two events
that
are
simultaneous
when
observed
from
some
particular
coordinate
system can
no
longer
be
considered
simultaneous
when
observed
from
a
system
that is
moving
relative
to
that
system.
§3.
Theory
of
transformation of
coordinates
and
time
from
a
system
at
rest to
a
system
in
uniform
translational
motion
relative
to
it
Let
there
be
given two
coordinate
systems
in the
space
"at
rest,"
i.e.,
two
systems
of three
mutually
perpendicular rigid material lines
issuing from
one
point. Let
the
X-axes
of the
two
systems
coincide
and
their
Y-
and
Z-axes
be
parallel.
Each
system
shall
be supplied
with
a
rigid
measuring
rod
and
a
number
of clocks,
and the
two measuring
rods
and
all the clocks of the
two systems
should
be exactly alike.
1"Time"
here
means
both "time of
the
system at
rest"
and
"the
position of the
hands
of the
moving
clock
located
at
the
place
in question."