DOC.
47
303
in
7 may
be neglected.
Since
we are
going
to
restrict ourselves
to
that
case,
we
do not
have
to
assume
that the acceleration
has
any
influence
on
the
shape
of the
body.
We now
consider
a
reference
system
E
that is
uniformly
accelerated
relative
to
the nonaccelerated
system S
in the direction of the latter's
X-axis.
The
clocks
and
measuring
rods of
E,
examined at rest,
shall
be
identical with the clocks
and
measuring
rods
of
S. The
coordinate
origin
of
E
shall
move
along
the X-axis of
S,
and
the
axes
of
E
shall
be
perpetually
parallel
to
those of
S.
At
any
moment
there
exists
a
nonaccelerated reference
system
S'
whose
coordinate
axes
coincide with the
coordinate
axes
of
E
at
the
moment
in
question
(at
a
given
time t'
of
S').
If the coordinates of
a
point event
occurring at
this time
t'
are
£,
n,
(
with
respect to
E,
we
will
have
x =
(
y'
= v
=
C
because in accordance with
what
we
said
above,
we are
not
to
assume
that
acceleration affects the
shape
of
the
measuring
instruments
used
for
measuring
E, n,
C.
We
shall also
imagine
that the clocks
of
E
are
set at
time t'
of
S' such
that their
readings
at
that
moment equal
t'.
What
about the
rate
of
the clocks in the
next
time
element
r?
First of
all,
we
have to
bear in
mind
that
a
specific effect of
acceleration
on
the
rate
of the clocks of
E
need not be
taken into
account,
since it
would have to be
of the order
r2.
Furthermore, since the effect of
the velocity attained
during
r on
the
rate
of the clocks is
negligible, and
the distances traveled
by
the clocks
during
the
time
r
relative
to
those
traveled
by
S'
are
also of the order
r2,
i.e.,
negligible,
the
readings
of
the
clocks of
E
may
be
fully
replaced
by
readings
of the clocks of
S'
for
the time
element
r.
From
the
foregoing
it follows that, relative
to E,
light
in
vacuum
is
propagated during
the
time element
r
with the universal
velocity
c
if
we
define
simultaneity
in the
system
S' which is
momentarily
at
rest
relative
[95]