DOC.
17
THE THEORY OF RELATIVITY
345
the
clock at
the
origin
of k
notes
the time
at which
he received
notice
of the
event in
question
by means
of
a
ray
of
light,
this
time
will
not
be the
time
of the
event itself,
but
a
time
greater
than the latter
by
the
velocity
of
propagation
of the
light ray
from
the
event to
the
clock.
If
we
knew
the
velocity
of
propagation
of
light
relative to
the
system
k
in
the direction under
consideration,
it would be
possible
to
determine the time of
the
event
using
the
above
clock;
but the
velocity
of
light can
be
measured
only
if the
problem
of
the
determination of
time,
which
we
are
now
discussing,
has
been
solved.
To
measure
the
velocity
of
light
in
a given
direction,
we
would have to
measure
the
distance
between
points
A
and
B,
between
which
the
light ray
propagates,
and
further,
the
time
of the
emission
of the
light
at A
and the time of the
arrival
of the
light
at B.
Thus,
time
would have to
be measured
at
different
locations; however,
this
can
be
done
only
if
the
definition of time
we are
seeking
has
already
been
given.
But
if it
is
impossible
in
principle
to
measure a velocity,
in
particular
the
velocity
of
light,
without
recourse
to
arbitrary
stipulations,
then
we are
justified
in
making
further
arbitrary
stipulations
regarding
the
velocity
of
light.
We
shall
now
stipulate
that the
velocity
of the
propagation
of
light
in
vacuum
from
some
point
A to
some
point
B
is
the
same as
that
from B to A.
By
virtue of
this
stipulation
we are
indeed
in
a
position
to
regulate
identically
constructed
clocks
that
we
have
arranged at
various
points
at rest relative to
the
system
k.
For
example, we
will set
the
clocks at
the
points
A and B in
such
a
manner
that the
following
will obtain:
If
a ray
of
light
sent from A
toward
B at time
t
(measured
by
the
clock at
A)
arrives at B at
time
t
+ a
(measured
by
the
clock at
B),
then,
conversely,
a
ray
sent from B toward A at time
t (measured
by
the
clock
at
B)
must
arrive at
A at
time
t
+
a
(measured
by
the
clock at
A).
This
is
the rule
according
to which all clocks
arranged
in
the
system
k
must
be
regulated.
If
we
follow
this
rule,
we
achieve
a
determination of time
from
the
standpoint
of the
measuring
physicist.
That
is
to
say,
the
time
of
an
event
is equal
to
the
readings
of the
clocks
located
at
the
place
of the
event
that
are regulated according
to
the rule
we
just
described.
Since all this sounds
self-evident, one may
wonder
what
is particularly
remarkable
about the result
we
have
obtained. What
is
remarkable
is
the
fact
that,
in
order
to
obtain
time
readings
with
a
perfectly
definite
meaning,
this
rule refers
to
a system
of
clocks
that
is
at rest
relative
to
an exactly specified
coordinate
system
k.
We
have not
merely
obtained
a
time,
but
a
time
that refers
to
the coordinate
system
k,
or
to the
system
k
together
with
the
clocks set
up
at rest
relative
to
k.
Of
course,
we can carry
out
exactly
the
same
operations
if
we
have
another
system
k' that
is
moving uniformly
relative
to
k.
We
can
distribute
throughout
space
a
system
of
clocks relative to this
coordinate
system
k',
but
in such
a
way
that
all
of them
move together
with
k'. We
can
then
regulate
these
clocks,
which
are
at rest
relative
to k',
exactly according
to
the rule
described before. If
we
do
this, we
obtain
a
time
with
respect
to
the
system
k'
as
well.