Information Technology Reference
In-Depth Information
P
OSSIBILITY OF
S
UPERLUMINAL
S
PEED
IN
Q
UANTUM
R
EGION
E.Recami [2001] claimed in his paper that tunneling photons traveling in an evanescent
mode can move with superluminal group speed, which can be shown as follows;
The evanescent photon generated in quantum domain satisfies the following Klein-Fock-
Gordon equation given by
⎡
2
2
*
2
⎤
1
∂
m
c
−
+
∇
2
−
A
(
x
,
t
)
=
0
(1)
⎣
⎦
2
2
2
c
∂
t
h
where
c
is the light speed,
m
is an absolute value of the proper mass of the evanescent
photon and
h
is the Plank constant divided by
2
.
This equation has the solution for the photon traveling in an evanescent mode given by
Et
+
px
⎡
⎤
A
(
x
,
t
)
=
A
exp
−
(2)
⎣
⎦
0
h
which corresponds to the elementary particle with an imaginary mass
im
that travels at a
*
superluminal speed satisfying
2
2
2
2
*
4
E
=
p
c
−
m
c
(3)
where
E
is the energy of the superluminal particle and
p
is its momentum given
respectively as
2
m
c
*
E
=
(4)
2
2
v
/
c
−
1
and
m
v
p
=
*
(5)
2
2
v
/
c
−
1
Hence, it can be seen that tunneling photons traveling in an evanescent mode can move at a
superluminal speed.
By the pulse propagation experiment, Chu and Wong at AT&T Bell Labs measured
superluminal velocities for light traveling through the absorbing material [Brown,1995].
Furthermore Steinberg, Kwait and Chiao [1993] measured the tunneling time for visible light
through the optical filter consisting of the multilayer coating about
10
−
6
m thick.
