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.