Download Nothing Travels Faster Than Light

Nothing Travels Faster Than Light
Quantum Electronics Project
December 14th 2000
Jonathan Stone AP4: 94538441
Rory Ryan
AP4: 95307036
Introduction.
The speed of light is one of the fundamental constants of Physics. Measured at 300 million
metres per second, it is the universal speed limit and the cornerstone on which most of
Einstein’s theory of Relativity is based. By Einstein’s theory, no thing can travel faster than
light, as this would breach the principle of causality, which states that cause must precede
effect. If it were possible to send particles and objects faster than light we could expect
strange things to happen
For example, if we were to take a rifle a fire a bullet at 5 times the speed of light, by
Einstein’s theory, the bullet would be out of the gun and flying towards it target before the
trigger had even been pulled. And this is just the start. Scientists have dreamed up time
machines and paradoxes to state why it should and how it could be possible, all based on the
assumption that superluminal speeds are possible.
With the motivation of becoming the man to break the light speed barrier (and the man who
proved Einstein wrong!), many scientists have created experiments to try to propagate
particles superluminally. And although they have all claimed to have broken the speed of
light, most “Faster Than Light” experiments never seemed to rise above the clouds of doubt
and uncertainty that descended upon them when they were investigated thoroughly.
In 1974, a group of Australian scientists claimed that they had found cosmic ray particles that
travelled faster than light, only to find out that they were incorrect. In 1982, Gustav Nimtz
claimed to have transmitted Mozart’s 40th Symphony across his lab at many times the speed
of light but senior physicists rejected his experiment also. And there have been many others.
Needless to say, with this history, any new so-called superluminal experiments are met with a
certain degree of scepticism.
So, in July of this year, the world of science was gripped with the news that Dr Lijun Wang
and his research group working at NEC labs in the USA, had in fact achieved this
monumental feat, the grandmasters of physics wanted to take a closer look before committing
themselves. Entitled “Gain-Assisted Superluminal Light Propagation”, details of the
experiment were first sent to Nature in May 2000 and the article was published in the July
2000 issue.
With such a sensational title, it is no wonder that the global physics community wanted to
take a closer look at the Dr. Lijun Wang’s experiment. Wang and his team of scientists
claimed to have propagated a light pulse through a chamber of specially prepared Caesium
gas 310 times faster than the speed of light in a vacuum. But amidst the hype and headlines
claiming Einstein’s theory of Relativity had been violated just five years before its 100th
anniversary, Dr. Wang was quick to point out that the experiment was not at odds with
Relativity at all, and could be explained using existing laws of wave propagation.
In this project we will take a closer look at the “Gain Assisted SuperLuminality” experiment,
describing the underlying principles on which it is based, and drawing some conclusions as to
what possible uses it could have in the future.
(II) Fundamental Principles.
In this section we will describe some of the underlying concepts and principles that are
needed to fully understand the “Gain Assisted Superluminality” experiment.
Normal Dispersion and Anomalous Dispersion.
White light is composed of many millions of light waves of different wavelength. In a
vacuum all of these light waves travel at the same speed but in a dispersive medium, such as
air or glass, this is no longer true. In a dispersive medium, different wavelengths of light will
pass through with different velocities.
This is demonstrated in Figure 1 (a) below. As the white light travels through the (dispersive)
prism, each of the wavelengths passes through with it’s own wave velocity. This is because in
a dispersive medium, refractive index is a function of wavelength [1]. Longer wavelengths of
light such as red (700nm) will pass through more quickly, and will be deviated by a small
amount. Shorter wavelengths, such as blue light (400nm) will be deviated more as it passes
through more slowly. This effect is called “Normal” Dispersion.
Figure 1 [2]
(a)Normal Dispersion
(b)Anomalous Dispersion
In anomalous dispersion, however, there is an opposite effect. In a region of anomalous
dispersion, long wavelengths of light will pass through more slowly than shorter wavelengths.
This condition is demonstrated in Figure 1 (b) above. In this example, we show what would
happen if a prism exhibited anomalous dispersion properties.
The light is again dispersed (as in Normal dispersion), but this time the dispersion spectrum is
reversed. Longer wavelengths are deviated more than shorter wavelengths so now the red
appears at the bottom of the dispersion spectrum and the shorter wavelength blue appears at
the top. Anomalous dispersion is not naturally occurring in transparent materials. It has only
been found in (highly absorbing) opaque materials
In mathematical terms, the group refractive index in a region of anomalous dispersion is:
n g = n + v.
dn
dn
where v.
<0
dv
dv
Using this we find that the group velocity now becomes greater than the speed of light. This is
one of the most important fundamentals for understanding the Gain Assisted Superluminality
experiment.
Group Velocity.
A light pulse is composed of many constituent waves of varying wavelength (or frequency).
Consider, as an example, figure 2 (a). Wave 1, Wave 2 and Wave 3 are harmonic waves of
different wavelength. If we get a superposition of the three waves and all of the other
component waves of the light, we get a beat pattern similar to Figure 2 (b). The rate at which
the modulation envelope of this beat pattern advances is called the Group Velocity.
Wave Group
In a non-dispersive medium, the group velocity of the wave group (or beat) is equal to the
wave velocity of each of the component waves (i.e. light waves of all wavelengths travel the
same speed in a non-dispersive medium). This is not the same for a dispersive medium. In a
dispersive medium, such as glass, light waves of different wavelength travel at different
velocities. This means that the group velocity is also dependent on the refractive index of the
dispersing medium. We will see in the next section how this is important for superlumination.
(III) Experimental Description.
Wang’s experiment was carried out at NEC Labs in the USA. It is based on the wave
propagation nature of light and anomalous dispersion. Wang combines the results of previous
experiments based on anomalous dispersion and absorption gain lines, to successfully
propagate a 3.7 microsecond light pulse superluminally through a 6cm chamber of Caesium
gas. Here’s how he did it:
The fact that the group velocity could exceed c in a region of anomalous dispersion is nothing
new to physics. It is consistent with theory in modern optics textbooks. In a region of
anomalous dispersion, the rate of change of refractive index with increasing frequency is
negative. In mathematical terms,
v.
c
dn
> c [6]
< 0 and the Group Velocity becomes V g =
ng
dv
So, by propagating a wave through such a region it is possible to achieve a group velocity that
is greater than the speed of light.
But in previous attempts to demonstrate this, which were usually carried out with opaque
media, the pulse or wave-packet was severely absorbed and distorted as it passed through the
region of anomalous dispersion. The results therefore, were inconclusive, and could not be
taken as proof that the effect could work.
Wang’s experiment demonstrates that this it is in fact possible to achieve superluminality with
this anomalous dispersion effect and keep the pulse intact. He observed how the group
velocity index was greatly enhanced using a lossless normal dispersion region between two
closely spaced gain lines in an experiment entitled “Electromagnetically Induced
Transparency”[4]. The effect of enhancing the group velocity index meant that a pulse
passing through the medium would not experience any severe reshaping and the pulse should
remain intact. It was also known that pulses could be propagated superluminally in regions of
anomalous dispersion [3]. From this, Wang devised a means of creating a region of lossless
anomalous dispersion using Caesium.
Naturally occurring Caesium gas can exist in any one of 16 possible quantum mechanical
states called “Hyperfine ground state magnetic sub-levels”. In the “Gain Assisted
Superlumination” experiment, the Caesium atoms are pumped by two continuous wave lasers
using a technique called optical pumping, to one of these hyperfine states [2]. In this
hyperfine state, the Caesium gas has two absorption lines with a frequency separation of
1.9Mhz and a region of rapid decrease in refractive index with wavelength (or anomalous
dispersion) between these lines (shown in Figure 3 below). A third probe laser was used to
measure the refractive index and gain coefficients of the Caesium.
Figure 3 [2]
The green box in Figure 3 above indicates the region of frequencies Wang identified in the
Caesium gas for which a light wave will experience anomalous and lossless dispersion.
The pulse used for the experiment is a 3.7 microsecond, near-gaussian beam whose
bandwidth lies between the two gain peaks of the atomic Caesium gas. This pulse is
propagated into the caesium cell. As it passes through the Caesium cell, the pulse is
anomalously dispersed.
Figure 4
To view what is happening in the region of anomalous dispersion on a wave level, look at
Figure 4 above. The pulse is made up of many different wavelengths of light. In the
anomalous dispersion region the shorter wavelengths of light travel faster than the long
wavelengths. This changes the phase of the component waves in relation to each other and
causes them to rephase further along the line of propagation. Normally, a pulse is not allowed
to rephase further along its propagation but due to the properties of the medium it can be
done.
We can describe the passage of the pulse through the Caesium chamber in mathematical
terms. For a normal dispersive medium (where v.dn/dv >1 and ng>1) of length L, the delay
time experienced by light will be:
∆T =
(n g − 1) L
c
However, in a region of anomalous dispersion, the value of ng is less than 1, the transit time
for the light now becomes:
− ∆T =
(1 − n g ) L
c
So when ng <1, the delay time across the medium is negative. In other words the pulse appears
to leave the cell even before it has entered. Wang measured that the propagation time for the
pulse to pass through the cell was 62 nanoseconds quicker than it would have taken if the
chamber were a vacuum. A demonstration of this effect can be seen below in Figure 5[2]:
T1 - Pulse before entering chamber
T2 – Pulse passing through chamber
T3 – Pulse on the far side of chamber
Figure 5 (the full animation can be downloaded from Wang’s web site [2])
At time T1 the pulse travels toward the chamber. At time T2 the pulse is just entering the
chamber, yet it has already exited the far side due to the nature of the Caesium. The leading
edge of the pulse has been rephased further along the propagation line due to the anomalous
dispersion in the gas. At time T3 the pulse has exited the chamber superluminally. In distance
terms the advanced pulse would have travelled 19 metres past the chamber before the original
pulse would have exited the chamber. NB The diagrams in Figure 5 are greatly exaggerated
for the purpose of demonstration.
We do not presently know whether this effect can be used to speed up optical signalling.
Wang has applied for a patent, but there is an issue that still has not been resolved as to
whether the signal velocity (the speed at which a signal is transmitted using a light pulse) can
be faster than light. Most textbooks suggest that the signal velocity must always remain below
c even when travelling through a region of anomalous dispersion [6]. In this case it is
assumed that the signal velocity must stay at c. Wang published a document on the issue, in
which he ruled out superluminal signalling [7] but the discussion as to whether it will be
possible to send information faster than light is still ongoing.
(IV) Conclusion.
When Dr. Lijun Wang’s experiment was first released to the media, it was sensationalised
with headlines such as “Eureka! Scientists break the speed of light” [5]. The papers spoke of
how Wang and his team had broken the speed of light, proved Einstein “wrong” and showed
that there were inconsistencies in his theory of Relativity. This created a wrong impression of
what Wang was actually doing.
All aspects of the “Gain Assisted Superluminality” experiment can be explained by existing
laws of physics. No laws of physics were broken and no new laws were created. Even Wang
himself says that the experiment is not “at odds” with Relativity [2]. The prospect of
projecting light superluminally using anomalous dispersion had been with us well before
Wang embarked on this project.
Steven Chu and Stephen Wong, who were researching at Bells Labs at the time, had
previously carried out similar experiments with anomalous dispersion and group velocities in
1982 [3], which showed that light could be propagated superluminally. Wang just took his
work one step further.
Historically, these anomalous effects had only been seen in opaque materials, but Wang
showed that by manipulating Caesium gas with lasers and pumping it to a certain state, it was
possible to demonstrate these conditions in a transparent medium also.
So, what are the practical uses of this experiment, if we can’t build time machines or send
information into the past? When the experiment was originally unveiled in July 2000, it was
initially suggested that the superluminality effect could be used to speed up electronic
circuitry. Seeing as how that article was released nearly six months ago, I thought I’d mail Dr.
Wang for an update.
Dr Wang said, “it has not been used in any electronic equipment as yet”. So, at the present
moment, no real uses have come from the Gain assisted Superluminality experiment.
References:
1. “Gain Assisted Superluminal Light Propagation” – L.J.Wang, A Kuzmich and A.Dogariu.
2. Dr Lijun Wang’s web site - http://www.neci.nj.nec.com/homepages/lwan/gas.htm
3. “Linear Pulse Propagation in an absorbing medium” – S. Chu and S. Wong (1982)
4. “Electromagnetically Induced Transparency” S.E. Harris – Physics Today issue 50.
5. “Eureka! Scientists Break The Speed Of Light” – Sunday Times June 4 2000
6. “Optics” – Hecht.
7. “Signal velocity, Causality and quantum noise in Superluminal Light Pulse Propagation”L.J. Wang, A. Doragiu and A. Kuzmich.