DOC.
2 RELATIVITY
AND
ITS CONSEQUENCES
127
well
use
light rays
propagating through
the
vacuum or through
a
homogeneous
medium
at rest with
respect
to A
and
B.
It
does not
make
any
difference whether
we
choose
this
or
that
kind
of
signals.
If
two kinds
of
signals were
to
produce discrepant results,
we
would have to
conclude
that,
for
at least
one
of the
two kinds
of
signals,
the condition
of
equivalence
of the
paths
AB
and
BA
was
not
satisfied.
Still,
of
all
the
signals
that
can
be
used,
we
are going
to
prefer
those that
make
use
of
light rays
propagating
in
the
vacuum,
because the
synchronization
requires
that the
path
out and
the
path
back be
equivalent,
and
in
our case
this
equivalence is
satisfied
by
definition, since,
by
virtue of the
principle
of the
constancy
of the
velocity
of
light, light
in
the
vacuum always propagates
with
the
velocity
c.
Hence
we
will have to
synchronize our
clocks in such
a way
that the time
spent
by
a signal
traveling
from A to B
be
equal
to
the
time
spent
by an
identical
signal
traveling
from B
to A.
Now
we possess
a
well-defined
method
by
which to
synchronize
two clocks with
respect
to
each other. Once the
synchronization
has
been
done,
we
will
say
that the
two
clocks
are
in
phase. If, step
by step, we
regulate
clock B
against
clock
A,
clock C
against
clock B
...,
we
obtain
a
series
of
clocks such
that
any
of them
is
in
phase
with
the
preceding one.
Moreover,
any
two
nonconsecutive
clocks in
the
series must also
be
in
phase
by
virtue of the
principle
of the
constancy
of the
velocity
of
light.
The
totality
of the
readings
of
all
of these
clocks in
phase
with
one
another
is
what
we
will call
the
physical
time.
By an elementary
event
we
will
understand
an
event
that
is supposed
to be
concentrated
in
one point
and
is
of
infinitely
short duration.
By
the
time coordinate
of
an elementary
event
we
will
understand the
indication,
at
the instant of the event's
occurrence,
of
a
clock
that
is
situated
infinitely
close to
the
point
at which
the
event
takes
place.
An
elementary
event
is
thus
defined
by
four
coordinates, namely
the
time
coordinate
and
the three
coordinates that define
the
spatial
position
of
the
point
in which
the
event is supposed to
be concentrated.
Thanks
to
our physical
definition of
time, we can give a
perfectly
defined
meaning
to
the
concepts
of
simultaneity
and
nonsimultaneity
of
two
events occurring
at locations
removed from
one
another. In the
same
way,
the introduction of the coordinates
x, y,
z
of
a spatial
point
gives a
completely
defined
meaning
to
the
concept
of
position.
Thus,
for
example,
to
say
that the
abscissa
of
a
point
P
situated
on
the
axis is
x,
is
the
same
as saying
that
we
must hit
upon
the
point
P
if,
starting
from
the
origin,
we
apply,
with
a
ruler,
a
unit
length
x
times
along
the
axis.
We
proceed
in
the
same way
to
fix
the
position
of
a
point
if
all
three coordinates
x, y, z
are
different
from
zero, except
that the
operations
are a
little
more
complicated.
Be
it
as
it
may,
the
specification
of the