36
DOCS.
52,
53
AUGUST
1907
other
volume
elements of the
same
electron. Therefore
my argument
does
not
hold
here.
Further, I
now
know for
sure
that
the
expression
for the
group
velocity
that
you
gave,
and
that
I
at
first
accepted
owing
to
an
incorrect
argument,
holds
only
for
nonabsorbing
bodies.[5]
If
no
error
has
slipped
into
my
calculation,
the
matter
stands
as
follows.
Let the
group
velocity
V be
defined
as
the
velocity
with which
a
position
of
zero
amplitude propagates
along
a wave
train.
Further,
let
(p
be
a
(generally
complex
function
of
such
kind that the dielectric
constant
e'
(which
is
complex
in
absorptive
bodies)
used in
Drude's
textbook[6]
on optics
is
p
(co
),
if
0)
denotes
the 27r-fold
frequency.
If
we
set[7]
xsjy(x)
=
\|/0c),
then
A
=
^(G
-
jß)
(where
L
denotes
the
velocity
of
light,
and
ß
a
real
constant),
if
ß is
chosen
such
that
X00
~
jß)
becomes real.-
Be
that
as
it
may,
in
the
light
of Wiechert's results and the
simple
argument
presented
in
my
first
letter,[8]
a
velocity
of
propagation
of
a
light signal
with
superluminal
velocity
in
any
medium
seems
to
me
incompatible
with Maxwell's
theory
as long as
one
does not
assume
that electric
masses
in
different
volume
elements
also
influence each
other
by
forces other than
electromagnetic
forces.
A
more
detailed
analysis
of
this
matter
based
on
the
electromagnetic theory
of
dispersion
cannot
yield a
result that
would
contradict the
general
analysis.
With
best
regards,
yours truly,
A.
Einstein
53.
To
Wilhelm
Wien
Aeschi, 11 August
1907
Highly
esteemed Professor
Wien:
I
am
in
possession
of
your
letter
in which
you so kindly
reported
your
calculation
to
me.
This
calculation
agrees
in
principle
with
the
calculation
that
I
first
made.
I
agree
with
the calculation itself
as
well
as
with
the
consequences
that
you
draw from it
(up
to
a
slight
correction
in the
expression[1]
V
-
dv
dX,
which
is
given
at
the
end
of
the
dX
letter);
however,
the
following
should be
noted.
The
velocity
that
you
calculated
is
in fact
equal
to
the
velocity
with which
the
temporal
maxima
and
minima
of
the
amplitude
of
the
wave
train under
consideration