126
DOC. 2
RELATIVITY AND
ITS CONSEQUENCES
degree
of
accuracy
desired. But
we
cannot
obtain
in this
manner a
definition of
time
useful to
a
physicist,
because
we
did not
say
what
the
position
of
the clock
hands
should
be
at
a given
instant of time
at
different
spatial points.
We
forgot
to
synchronize our
clocks,
and
it
is
clear that the
intervals
of
time
elapsed during some
event have
a
certain
extension
that
will
vary considerably
as
the
event
occupies
this
or
that
point
in
space.
Suppose,
for
example,
that
we are studying
the motion of
a
material
point
whose
trajectory
passes
through the points
A,
B,
C
....
At
the
moment when
the point passes
through
A, we
will note
the instant
tA,
indicated
by
the
clock
located
at this
point.
In
the
same way we
will
register
the
instants
tB,
tc,
...
of the
passage
through
the
points
B,
C
....
Since
the coordinates of
the
points
A, B,
C,... on
the axes
of
the system
S
can
be obtained
directly-by
performing
measurements
with
a graduated measuring rod,
for
example-then,
by relating
the coordinates
xA, yA,
zA
...
of the
points
A,
B, C,
...
to
the instants
tA, tB,
tc
,
we can
obtain the coordinates
x, y,
z
...
of the
moving
material
point
as
a
function of
a
variable
t,
which
we
will call time.
It
is
clear
that the
form of
this function will
depend
essentially on
the
way
the
clocks
had been
set
before
they
were
placed at
their
respective
locations.
To
get
a complete
physical
definition of
time, we
have to
take
an
additional
step:
We
have
to
say
in what
manner
all
of
the clocks
have
been
set at
the
start
of the
experiment.
We
will
proceed
as
follows:
First, we
furnish
ourselves with
a
means
of
sending
signals,
be
it from A to
B,
or
from
B to A. This
means
should be
such
that
we
have
no reason
whatsoever
to believe
that the
phenomena
of
signal
transmission
in
the direction
AB will differ in
any way
whatsoever from the
phenomena
of
signal
transmission
in
the direction
BA.
In that
case
there
is, obviously, only one way
of
regulating
the
clock at B
against
the
clock at A in such
a manner
that the
signal
traveling
from A to B would
take the
same
amount
of time-measured
with
the
clocks
described
above-as
the
signal traveling
from
B to A.
If
we
denote
by
tA
the
reading
of the
clock at A at
the
moment
signal
AB leaves
A
tB
" B " AB
arr.
at B
tB'
" B "
BA
leaves B
tA'
" A " AB
arr.
at A
then
we
have to
set
the
clock at
B
against
that
at A in such
a
way
that
t
-
t
=
t '
-
tB' B
A A
.
For these
signals we can
use,
for
example,
sound
waves
that
propagate
between
A
and
B
through
a
medium that
is
at rest with
respect
to
these
points.8
We
can
just as
8The medium must
be
at rest-or at
the
very
least must not have
any velocity
component
in
the
direction
AB-so
that the
paths
AB and
BA
can
be
equivalent.
[12]