|MadSci Network: Physics|
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
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.
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
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
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 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
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
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
Best Regards, Your Mad Scientist
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