DOC.
53
AUGUST
1907 37
propagate,
thus,
a
kind of
group
velocity,
which
is, as you
noted,
in
certain
cases a
superluminal
velocity.
But this
velocity
ceases
to have
the character
of
a signal velocity
as
soon
as
absorption
becomes noticeable.
By signal velocity
I
understand the
following.
If
an initially
closed
shutter
at
the
location
A
opens
from the time
t0,
and
if
the
first
light
arrives at B
through
the shutter
at
time
tl,
then
I
understand
by signal velocity
the
quantity
distance
A
-
B
t1h *t0
This
quantity is
what
matters; it follows from
the
theory
of
relativity
(and,
more
generally,
from Maxwell's
theory)
that
this
quantity
cannot be
a
superluminal
velocity.
As
soon as
absorption is present (to
be
more
precise,
if
dK
=
k2^-k1
0),[2]
your
group
velocity
cannot be
regarded
as a signal velocity
in
the
sense
just
defined.
For
if
we
plot
the
amplitudes
as
functions of time for
the
cross
sections
x
=
0 and
x
=
l
for
the
case
K1
=
k2
=
0,
then
we
obtain
a
picture
similar
to
that sketched here.
In
both
cross
sections the
amplitude
passes
through
zero.
Obviously,
we
also
obtain
a
possible
process
if
we assume
that the
amplitude
in
x
=
0 vanishes
up
to t
=
t0,
and
in
x
=
l
up
to
t
=
t1,
while the
right
part
of
the
curve
is
retained. From
this
one can
see
that
in this
case
the
group
velocity
obtained
by you
can
also be
regarded
as a
signal
velocity
in
the
sense
indicated.
x
=
0: