DOC.
2
RELATIVITY AND
ITS
CONSEQUENCES
125
propagation
relative
to
a system
S' that
is
in
uniform translational motion
with
respect
to
the
first
system. Applying
the rule of addition of
velocities
(the
rule of the
parallelogram
of
velocities),
we
will
generally
find
a velocity
different from
c;
in
other
words,
the
principle
of the
constancy
of the
velocity
of
light
that
is
valid with
respect
to
S
is not valid with
respect
to
S'.
So
that the
theory
based
on
these
two
principles
should
not
lead
to
contradictory
results,
one
must
renounce
the
customary
rule of addition of
velocities
or,
better,
replace
it with
another rule.
Well
founded
as
this
rule
may
seem
to
be
at first
glance,
it conceals
no
less
than
two
arbitrary
hypotheses,
which
consequently, as
we
shall
see,
hold
sway
over
all
of
kinematics.
It
is
these
hypotheses
that made
us
think
that, with
the
aid
of the
transformation
equations
(1),
the
incompatibility
of Lorentz's
theory
with
the
principle
of
relativity
can
be demonstrated.
The
first
hypothesis
we
wish to discuss
concerns
the
physical
notion of
time
measurement.
To
measure
time,
we
use
clocks.
What
is
a
clock?
By
a
clock
we
understand
any
thing
characterized
by a
phenomenon
passing
periodically through
identical
phases
so
that
we
must
assume,
by
virtue of the
principle
of
sufficient reason,
that
all
that
happens
in
a given
period is
identical
with all
that
happens
in
any
arbitrary
period.7
If the
clock
comes
in
the form of
a
mechanism that
is
provided
with clock
[11]
hands,
then
to
mark the
positions
of the
clock's
hands
is
tantamount to
counting
the
number of
moments
elapsed.
By definition,
to
measure
the
time interval
during
which
an
event
takes
place
means
to count
the number of
time
periods
indicated
by
the
clock
from the
beginning
till
the end of the
event in
question.
The
meaning
of
this
definition
is
perfectly
clear
as
long
as
the
clock
is
sufficiently
close to
the
place
at which
the
event
occurs, so
that the
clock and
the
event
can
be
observed
simultaneously. If, on
the
contrary,
the
event
is
taking place
in
some corner
far
away
from the
clock,
then
it will
no
longer
be
possible
to
establish
immediately a
correspondence
between the different
phases
of
the
event,
and the different
positions
of
the
clock's hands.
The
definition
is
therefore
deficient
and
needs
to
be
completed.
Until
now one
has
completed
it
unawares.
To determine the time
at each
point
in
space, we
can
imagine
it
populated
with
a
very
great
number of
clocks
of
identical construction.
Let
us
consider the
points
A,
B,
C,
...,
each
of
which
is
furnished
with
a
clock
and
is
referred
to
a system
in
nonaccelerated
motion
with
the
aid
of
time-independent
coordinates.
We
will
now
be
able to know
the
time at
any
of
the locations at which
we
choose
to
put
a
clock.
If
we
choose
a sufficiently
large
number of
clocks, so
that
we can
ascribe to each
of them
a
sufficiently
small
domain, we
will be able to
fix
any
instant
whatsoever,
at
any
location in
space,
to
any
7Thus,
we
postulate
that
two identical
phenomena
are
of the
same
duration. The
perfect
clock
thus
defined
plays a
role
in
the
measurement
of
time
that
is
analogous
to
the role
played by
the
perfect
solid
body
in
the
measurement
of
lengths.