142
ELECTRODYNAMICS OF MOVING
BODIES
It
might
seem
that
all difficulties involved in the definition of
"time"
could
be
overcome by
my
substituting
"position
of
the small
hand
of
my
clock"
for "time."
Such
a
definition is
indeed
sufficient if time
has to be
defined
exclusively
for the
place
at which
the clock is located; but the definition
becomes
insufficent
as soon as
series
of
events occurring at
different
locations
have to be
linked
temporally,
orwhat
amounts to
the
sameevents
[9] occurring
at places remote from
the clock
have to be
evaluated
temporally.
To
be
sure,
we
could content ourselves with
evaluating
the time of the
events
by
stationing
an
observer with the clock
at
the coordinate
origin, and
having him assign
the
corresponding
clockhand
position to each
light
signal
that
attests to
an
event to
be
evaluated
and
reaches
him
through
empty
space.
But
as we
know
from
experience,
such
an
assignment
has
the
drawback
that it is
not
independent
of
the
position of
the observer
equipped
with the clock.
We
[10]
arrive
at
a
far
more
practical
arrangement
by
the
following
consideration.
If
there
is
a
clock
at point
A
of
space,
then
an
observer located
at
A
can
evaluate the time
of
the
events
in the
immediate
vicinity of
A
by
finding
the clockhand
positions
that
are
simultaneous with these
events.
If there is
also
a
clock
at
point
Bwe should
add,
"a
clock
of exactly the
same
consti
tution
as
that
at
A"then the
time of
the
events
in the
immediate
vicinity
of
B
can
likewise
be
evaluated
by
an
observer located
at
B.
But
it is
not
possible
to compare
the
time
of
an
event
at
A
with
one
at
B
without
a
further
stipulation;
thus far
we
have only
defined
an
"Atime" and
a
"Btime"
but
not
a
"time"
common
to
A
and
B.
The
latter
can now
be
determined
by
establishing
by
definition
that the "time"
needed
for the
light
to
travel
from
A
to
B
is
equal to
the "time" it
needs
to
travel
from
B
to
A.
For,
suppose
a
ray
of
light leaves
from
A
toward
B
at
"Atime"
tA,
is reflected
from
B
toward
A
at
"Btime"
tB,
and
arrives
back at
A
at "Atime"
t'A.
The two
clocks
are
synchronous
by
definition if
tB 
tA =
t'A

tB.
We
assume
that
it
is
possible
for this definition of
synchronism
to be
free
of
contradictions,
and
to
be
so
for arbitrarily
many
points, and
that the
following
relations
are
therefore
generally
valid: