32
DOC. 49
JULY
1907
49.
To
Wilhelm
Wien
Bern, 23
August
[July]
1907[1]
Highly
esteemed Professor
Wien:[2]
You have
raised here
a
most
interesting
question!
Immediately
after
I
your
letter
I
threw
myself
into this
matter and have
arrived
at
the
following
preliminary
results.
1.
I
defined
as
the
"group
velocity"
U
the
velocity
with which
a
(slow) change
of
amplitude is
propagated;
this
is,
after
all,
the
quantity
at
issue. I
found
(for arbitrarily
strong absorption):
U
=
V
·
-
1
J +
X
dV
'
V dX
X
wavelength (in vacuum)
V
velocity
of
light
(in
the
medium)
which
agrees,
with
an
accuracy
for
the
present,
with
the
value
V
-
X
mentioned
by
you.
2.
In
my opinion,
there
is
a
with
the
principle
of
relativity
in
conjunction
with
the
principle
of
the
constancy
of
the
velocity
of
light
in
the
vacuum
if
for
a spec,
metal and
a
specific
color U L
(velocity
of
light
in
vacuum).
3.
The
propagation
of
an
electromagnetic
signal
with
superluminal
velocity
is
also
incompatible
with Maxwell's
theory
of
electricity
&
light.
This follows
from the results
of
a
study
by
Wiechert that
was
published
in
the Lorentz
Festschrift.[3]
In
this
study
it
is
shown
that
one
obtains
something
equivalent
to
Maxwell's
equations
if
one
introduces
certain
actions-at-a-distance that
propagate
with the
velocity
of
light
L in the
vacuum
and act from
one
electric
mass
to
the other.
Let
A be
a
point
from which
an
electromagn.
influence
can
emanate,
and
B
a
point
in which
the
influence
emanating
from
A
can
be
perceived.
Let
P,
Q, R,
etc. be
electromagnetically active, stationary
corpuscles
out
of
which
the
propagation-mediating
medium under
investigation
is
imagined
to
be
composed.
Let
an
influence
propagate
from A. An
action-at-a-distance
is hereby generated
in
AB
B
at
time unless
it
is compensated
by
processes
of
the
following
kind:
L
Emission in
A-from here action-at-distance
in
P-emission
in
P-excitation
in
Q
by
the
action-at-distance
from
P-etc.-excitation
in
B.
The
whole
process
can
be conceived
of
as
being
composed
of
such
indirect
actions
from
A
to B
and of the first-mentioned direct
action.
From
this
one can
easily
conclude
AB
that
at
least the
time
must
lapse
before the
first excitation in
B,
which
is to
say
that
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