MadSci Network: Physics |
Greetings:
Reference: S. Ramo, J. R. Winnery, T. Van Duzer, “Fields and Waves in
Communication Electronics, John Wiley & Sons, NY, 1967
Your question has to do with the leading edge of current research in
physics and
so my answer will be a bit long because in the future Mad Science will
receive
many more questions similar to yours and I will then refer them to
your question
for background information.
I located an article on the web which I have copied at the end of this
note.
The article covers the experiment the experiment mentioned in your
question
and is titled “The Speed of Light Is Exceeded in Lab”, and was
published in
the Washington Post on 7/21/00. As you can see from the comments in the
article made by the scientists that conducted the experiment and by
other
scientists commenting on the experiment, the results are not exactly
what the
average person understands it to be and to my mind the title of the
article is
misleading. Many experts question that the experiment actually
exceeds the
speed of light; however, it really becomes a matter of definition.
Is the article talking about the group velocity or the phase velocity
in the
experiment? The two velocities are blurred in the complex experiment
conducted
at the NEC Princeton Laboratory. While the phase velocity may exceed
the
speed of light, any useful information modulated on the wave
generally travels at
the group velocity. Most scientists consider the group velocity to
always be less
than the speed of light. The phase velocity is the velocity of
the
wave front of a
single, an undistorted sine wave at the frequency of interest. The
reference book
Ramo et al states: “The group velocity is often referred to as
the “velocity of
energy travel”. This concept has validity for many important cases,
but is not
universally true.” Other scientists simply state the group velocity is
the velocity
that useful information is transmitted. Recent experiments, such as
the one
described in the article, blur the distinction between group velocity
and phase
velocity and are the cause of many arguments between scientists and
engineers.
Certainly the experiment in which the speed of light is slowed down to
38 miles
per hour is a remarkable achievement. However, exceeding the speed of
light is
very suspect in view of Einstein’s Relativity Theory, which have held
up
remarkably well for over 90 years. However, scientists must keep an
open mind
on the subject and perhaps there are flaws in relativity, just as
relativity showed
the flaws in Newton’s Laws of Motion.
Many types of circuits have phase velocities that exceed the speed of
light. Since
the 1930s engineers have used waveguides as transmission lines for
microwave
radar and communications systems. Waveguides are made from metal pipes
with
circular, rectangular of elliptical cross-sectional openings. The
inside of the pipes
are about one half wavelength in diameter and the microwaves travel
through the
pipes reflecting from the walls in a cris crossing manner. More
recently fiber
optic transmission lines have extended waveguide theory to waveguides
transmitting laser light.
It is beyond the ability of this forum to discuss the models for phase
velocity and
group velocity used by scientists and engineers except to say that
placing
information, usually called modulation, on a carrier sine wave,
requires that a
band of sinusoidal frequencies with different amplitudes and phases be
transmitted. For example a single pulse of energy placed on a
microwave or laser
carrier wave requires a bandwidth of frequencies that is approximately
2 divided
by the pulse length to accurately transmit the pulse. Thus a one
microsecond
long pulse requires a band of frequencies two megahertz wide centered
about the
carrier frequency. A nanosecond pulse requires a 2 gigahertz wide band
of
frequencies centered about the carrier wave. Other forms of modulation
such as
amplitude modulation (AM), frequency modulation (FM) and pulse code
modulation (PCM) also require bands of frequencies about the carrier
wave.
These bands of frequencies are related to the group velocity for they
carry the
information being transmitted.
Perhaps a simple thought experiment that you can cutout and trace on
graph
paper that will help you understand the effects that we are
discussing. This
thought model is not exactly correct; however, it does help to
understand the
actual concepts of phase and group velocity.
Lets place two search lights or better yet lasers on two trucks back
to back, in mid-field
on a football field. We aim the beams backward and upward 60 degrees
from the
horizon so that the two beams cross each other above the trucks at a
60 degree
angle. We then view the experiment from a grandstand on the side
lines. We
have the trucks pull away from each other toward the opposite goal
lines at a
constant horizontal velocity and we measure the vertical velocity of
the
intersection of the two light beams. We find that the intersection
travels upward
at 2 times the velocity of the trucks! If we raise the beams on the
trucks to higher
elevation angles we will increase the vertical velocity of the
intersection to even
higher velocities. For example an elevation angle near 71 degrees give
a vertical
velocity 3 times greater than the horizontal velocity, 76 degrees
gives 4 times the
horizontal velocity and 79 degrees gives a vertical velocity 5 times
the horizontal
velocity. Also; that if the trucks velocity could approach one half of
speed of
light or greater, then the velocity of the intersection of the beams
would easily
exceed the speed of light! The intersection in our thought experiment
is the
phase velocity of our experiment.
Now how can we put information onto the intersection? For simplicity
lets say
that we will use simple digital modulation of the intersection. If we
turn both
beams on at full power we will have a digital one at the
intersection. If we will
turn both beams to one half power we will call it a digital zero at
the
intersection. To get this information to the intersection the full
power or half
power beams must travel up from the source on the truck at the speed
of light to
reach the intersection. If the intersection is moving faster than the
speed of light
the information will never reach the intersection. How can we make
this concept
work?
In our thought experiment we will add flat mirrors along each goal
line and the
mirrors will extend to a great height. This is the form of a 2
dimensional
waveguide. Now the beams from the trucks will reflect back and forth
and we
will have hundreds of intersections, all traveling in a vertical path
faster than the
speed of light (FTL). Now the digital modulation will not reach the
first faster
than light (FTL) intersection s; however, later intersections will be
launched after
the modulation and the phase velocity intersections will pass through
them and
modulate them. Now because the light beams that are traveling at the
speed of
light are zig-zaging back and forth, their vertical path length is
much longer
which reduces their velocity well below the speed of light. This is
exactly what
happens in a typical microwave wave guide and the reason that I picked
a 60
degree launch angle for our thought experiment. In a microwave
transmission
line the phase velocity is typically 1.5 to 2 times the speed of
light, while the
group velocity, the information velocity, moves in a manner similar to
our
thought experiment at a vertical velocity ranging from 50% to 60% of
the speed
of light in free space. Note, the two beams are traveling at the speed
of light;
however, there zig-zaging path slows the vertical component of their
velocity.
Actual cylindrical microwave wave guides are, depending on the
wavelength, from
1 to 10 centimeters in diameter and
the waves travel in three dimensional paths called modes through the
wave
guide. Fiber optic wave guides have identical modes to the microwave
guides
only the light guiding core of fiber optic waveguides are only 5
micrometers to
50 micrometers in diameter. A human hair is about 100 micrometers
thick!
The NEC experiment follows the same concepts as our thought experiment;
however, the scientists are using cryogenic temperatures and laser
cooling to
change the waveguide characteristics in real time as the pulsed light
signals
passes through them making the experiment very complex. They are also
changing
the index of refraction in the optical material in real time.You can find
answers
to laser cooling questions in the Mad Science Archives.
QUOTE
The Speed of Light Is Exceeded in Lab...07/21/00
By Curt Suplee
Washington Post Staff Writer
In a landmark experiment, scientists have broken the cosmic speed
limit,
causing a light pulse to travel at many times the speed of light--so
fast that the
peak of the pulse exited a specially prepared test chamber before it
even finished
entering it.
That seems to contradict not only common sense, but also a bedrock
principle of
Albert Einstein's theory of relativity, which sets the speed of light
in a vacuum,
about 186,000 miles per second, as the fastest that anything can go.
But the findings--the long-awaited first clear evidence of faster-than-
light
motion--are "not at odds with Einstein," said Lijun Wang, who with
colleagues
at the NEC Research Institute in Princeton, N.J., report their results
in today's
issue of the journal Nature.
"However," Wang said, "our experiment does show that the generally held
misconception that 'nothing can move faster than the speed of light'
is wrong."
Nothing with mass can exceed the light-speed limit. But physicists now
believe
that a pulse of light--which is a group of massless individual waves--
can.
To demonstrate that, the researchers created a carefully doctored
vapor of
laser-irradiated atoms that twist, squeeze and ultimately boost the
speed of light
waves in such abnormal ways that a pulse shoots through the vapor in
about
1/300th the time it would take the pulse to go the same distance in a
vacuum.
As a general rule, light travels more slowly in any medium more dense
than a
vacuum (which, by definition, has no density at all). For example, in
water, light
travels at about three-fourths its vacuum speed; in glass, it's around
two-thirds.
The ratio between the speed of light in a vacuum and its speed in a
material is
called the refractive index. The index can be changed slightly by
altering the
chemical or physical structure of the medium. Ordinary glass has a
refractive
index around 1.5. But by adding a bit of lead, it rises to 1.6. The
slower speed,
and greater bending, of light waves accounts for the more sprightly
sparkle of
lead crystal glass.
The NEC researchers achieved the opposite effect, creating a gaseous
medium
that, when manipulated with lasers, exhibits a sudden and precipitous
drop in
refractive index, Wang said, speeding up the passage of a pulse of
light. The
team used a 2.5-inch-long chamber filled with a vapor of cesium, a
metallic
element with a goldish color. They then trained several laser beams on
the atoms,
putting them in a stable but highly unnatural state.
In that condition, a pulse of light or "wave packet" (a cluster made
up of many
separate interconnected waves of different frequencies) is drastically
reconfigured as it passes through the vapor. Some of the component
waves are
stretched out, others compressed. Yet at the end of the chamber, they
recombine
and reinforce one another to form exactly the same shape as the
original pulse,
Wang said. "It's called re-phasing."
The key finding is that the reconstituted pulse re-forms before the
original intact
pulse could have gotten there by simply traveling though empty space.
That is,
the peak of the pulse is, in effect, extended forward in time. As a
result,
detectors attached to the beginning and end of the vapor chamber show
that the
peak of the exiting pulse leaves the chamber about 62 billionths of a
second
before the peak of the initial pulse finishes going in.
That is not the way things usually work. Ordinarily, when sunlight--
which, like
the pulse in the experiment, is a combination of many different
frequencies--passes through a glass prism, the prism disperses the
white light's
components.
This happens because each frequency moves at a different speed in
glass,
smearing out the original light beam. Blue is slowed the most, and
thus deflected
the farthest; red travels fastest and is bent the least. That
phenomenon produces
the familiar rainbow spectrum.
But the NEC team's laser-zapped cesium vapor produces the opposite
outcome.
It bends red more than blue in a process called "anomalous
dispersion," causing
an unusual reshuffling of the relationships among the various
component light
waves. That's what causes the accelerated re-formation of the pulse,
and hence
the speed-up.
The new results are almost precisely the reverse of a celebrated
experiment
reported last year, when Lene Hau, now at Harvard University, together
with
Stanford physicist S.E. Harris and others, created an ultra-cold gas
of sodium
atoms that reduced the speed of a light pulse to an amazing 38 miles
per
hour--slow enough to be honked at on the Beltway.
The new work by Wang, A. Kuzmich and A. Dogariu is also very different
from
other methods used recently to exceed the light-speed limit. Raymond
Y. Chiao
of the University of California at Berkeley, Aephraim M. Steinberg of
the
University of Toronto and others have shown that units of light,
called photons,
that "tunnel" through a mirror or opaque barrier apparently do so at
about 1.7
times the speed of light.
However, physicist Jon Marangos of Imperial College in London writes
in a
companion commentary that "the light pulses have always been distorted
in the
process, so interpreting these experiments has been difficult."
The NEC results, experts emphasized, do not violate the fundamental
law of
causality: Namely, that an effect cannot occur before its cause. Such
an irrational
outcome is captured in a famous limerick:
There was a young lady named Bright,
Whose speed was far faster than light;
She set out one day,
In a relative way,
And returned home the previous night.
That is not the case in the NEC experiment, the researchers said,
because all the
effects are explainable by traditional theories of wave behavior. The
initial pulse
is plainly the cause of the reconstituted pulse, even if the latter
travels faster.
Although the pulse in the new experiment clearly exceeded the speed of
light in a
vacuum, it did not convey any information--thus leaving intact the
belief of
virtually all experts that no meaningful signal or energy can exceed
light speed.
The NEC experiment, said Steinberg of Toronto, "comes closer than any
previous work at violating the thing about energy," but "of course,
it's still not
true." And although the leading edge of the pulse emerges from the
chamber in
1/300th the time that it would have taken in a vacuum, no information
was
actually conveyed.
For genuine information transfer, he said, "you can't talk about just
a single
pulse. You need two things that can be distinguished, even in
principle--two
different states."
In theory, the work might eventually lead to dramatic improvements in
optical
transmission rates. "There's a lot of excitement in the field now,"
said Steinberg.
"People didn't get into this area for the applications, but we all
certainly hope
that some applications can come out of it. It's a gamble, and we just
wait and
see."
END QUOTE
Best Regards, Your Mad Scientist
Adrian Popa
Try the links in the MadSci Library for more information on Physics.