DOC.
47 265
It follows further that the addition of the light
velocity
c
and
a
"sublightvelocity" yields
again
the light velocity
c.
The
addition
theorem
of velocities also
yields
the interesting
conclusion
that there
cannot
exist
an
effect that
can
be used
for arbitrary
signaling and
that is
propagated
faster than light in
vacuum.
For
example,
[27]
let
there be
a
material
strip
stretched
along
the x-axis of
S,
relative
to
which
a
certain effect
(viewed
from
the material
strip)
propagates
with
velocity
W,
and
let there
be
two
observers,
one
in the point
x
=
0
(point
A)
and
one
in
the point
x
= X
(point
B)
of the x-axis,
who
are
at rest
relative
to
S. Let the observer
in
A
send
a
signal
by means
of the
[28]
above-mentioned effect
to
the
observer in
B
through
the material strip,
which
shall
not
be
at rest
but
shall
be
moving
in the
negative
x-direction
with velocity
v (
c).
As
a
consequence
of the first of
equations
(3),
the
signal will
then
be
transmitted
from
A
to
B
with
velocity
W-u/1-Wv/c2.
The
time
T
necessary
for this is then
¥v
T=*-irir-7?"11-
The
velocity
v can
assume any
value smaller than
c.
Hence,
if,
as we
have
assumed,
W
c, one can
always
choose
v
such
that
T
0.
This
result
means
that
we
would have
to
consider
as
possible
a
transfer
mechanism
whereby
the achieved effect
would precede
the
cause.
Even
though
this
result,
in
my
opinion,
does not
contain
any
contradiction
from
a
purely logical
point of
view,
it
conflicts
with the
character
of
all
our
experience
to such
an
extent
that this
seems
sufficient
to
prove
the
impossibility
of the
assumption
W c.
§6.
Application of
the
transformation equations
to
some
problems
in optics
[29]
Suppose
the light
vector
of
a
plane
light
wave
propagated
in
vacuum
is
proportional
to
sin u
i
_
ix
+
mv
+ nz
[30]
with
respect
to
the
system
S,
and to