Email: Ali A. Faraj |

Superluminal Light

**A Scientific Revolution in Progress**

In the
early 1900s, the opponents of Einstein’s Special Relativity put forward the
theoretical possibility of superluminal speeds of light in refractive media
with indices less than unity, the so-called fast-light media.

Despite its
hypothetical nature, this objection caused a quite stir among Einstein’s
supporters who devoted several sessions of their conferences to the problem.

Finally, A.
Sommerfeld and L. Brillouin came up with what was deemed at the time to be a
convincing theoretical demonstration that Relativistic causality is preserved
and superluminal speeds of light are not physically meaningful. Their proof
hinges entirely on a rather artificial distinction between two loosely defined
speeds of light, namely the phase speed and the group speed of pulses or
collections of elementary waveforms with various frequencies.

In recent
years, however, many experiments on fast-light media have shown that
superluminal speeds of light are real and the Sommerfeld-Brillouin supposed
proof is completely wrong.

The main
purpose of this paper is to investigate the far-reaching consequences of these
extraordinary experimental developments in physics and to evaluate the present
threat to the theory of Special Relativity.

**Experiments on Speed of Light**

Recent experiments on speed of light can be
listed into two categories, those involve subluminal speeds of light, and those
involve superluminal speeds of light.
An example of the subluminal category is the Hau experiment, in which a
subluminal speed of 17 ms^{-1}
is achieved. Among the
experiments of the superluminal category is the Nimtz experiment, in which
Mozart’s 40^{th} Symphony is sent at 4.7c to a microwave receiver.

In terms of their scientific and technological
merit, the two types of experiments are equally important. In addition, their
commercial potential makes both an attractive target for patent hunters. Can you imagine how much NASA is willing to
pay for speedy communication with its space robots in real time? Unfortunately, this gold-mine potential
renders the duplication of these experiments extremely difficult. Precise
specifications of the instruments used are absent. Experimental techniques are couched in nonsensical interpretations
of all sorts. And old-fashioned industrial secrecy clouds the practical aspects
of this very important subject.

Duplication and practical considerations aside,
the published results of the two categories of experiments are truly impressive
and earth shaking.

Theoretically, experiments of the subluminal
type present no obvious threat to conventional theories and their results can
be handled quite easily within the framework of the current paradigm.
Nonetheless, a few experiments of this category come dangerously close to the
phenomenon of frozen light, which for some unclear reason is considered by A.
Einstein to be incompatible with his theory.

Experiments of the superluminal category,
however, are radical and their positive outcome poses an immediate threat to
the theory of Special Relativity.

The following is a brief list of the crucial
experiments:

**1.** The Nimtz experiment:

In this experiment, a famous symphony of Mozart
is encoded in a microwave beam and
transmitted to a receiver at 4.7 times the speed of light. It’s a decisive
experimental refutation of the current attempts at redefining the speed limit
of Relativity as the limiting speed of information rather than limiting speed
of objects.

**2.** The Ranfagni experiment:

In this experiment, observed pulses of
reflected microwaves are clocked at up to 1.25c in open air. Thus, the
supposition that superluminal speeds of light are possible only inside
artificial optical materials is experimentally falsified. Light indeed can travel at superluminal
speeds in open air, and by simple inference, in vacuum as well.

**3.** The Wang experiment:

In this experiment, a laser pulse travels
through gas-filled cells at a record superluminal speed of 310c.

**4.** The Stenner experiment:

In this experiment, a refractive index of –19 ± 0.8 is inferred. It’s designed to investigate
the so-called velocity of information. A critical analysis of the Stenner
experiment will be given later in this discussion.

**5.** The Munday experiment:

In this experiment, superluminal speeds of light are achieved for the first time inside fibre optics.

**6.** The Thévenaz
experiment:

In this experiment, superluminal and subluminal
speeds of light are achieved inside fibre optics.

**2. Superluminality Versus Relativity**

The following equations are at the core of
Special Relativity:

** ****x' = (x -
vt) / [1 - (v ^{2} / c^{2})]^{½}**

** y' = y****
(2.2),**

** z' = z****
(2.3),**

** t' = [t - (vx / c ^{2})] / [1
- (v^{2} / c^{2})]^{½}**

**When
these Lorentz equations break down, the whole edifice of Einstein’s theory
breaks down as well. Logical paradoxes
and philosophical concepts of causality and the like are of secondary
significance in this regard.**

For speeds of reference frames and ponderable objects equal to or greater than the Maxwell speed of light, the Lorentz equations suffer an immediate mathematical breakdown. Put v ³ c in those equations; and see the results! This sort of mathematical failure is well known and well documented. No further elaboration is necessary.

The Situation is quite unfamiliar and totally different in the case of superluminal speeds of light. Above all, there is no mathematical breakdown of any kind. To the contrary, the Lorentz equations become more robust and less nonsensical, as they approach the Galilean limit with increasing speed of light.

In physics, however, the above situation is not as rosy as in mathematics. In fact, it’s dismal. Here is a summary of the Relativistic failures in the case of light superluminality:

** **(**1**)** **Although
speed of light in Lorentz equations can, in principle, have any value between
zero and infinity, the slightest deviation from its Maxwellian value puts
Special Relativity at odds with almost every experiment. Calculations of
momentum and energy fail. Electromagnetic calculations fail. Electrodynamics’
calculations fail. Mass-energy calculations fail. In brief, century-old,
parameter-fitted, and fine-tuned calculations of all sorts utterly fail.

(**2**) The failure of Relativistic calculations doesn’t stop there.
Calculations based on General Relativity fail as well. None of the three widely
publicized predictions of that theory can survive any change in the value of
speed of light.

(**3**) The most serious
threat, however, is not the one brought about by a single value. Given enough
time, it is not impossible through collective efforts to fix the problem of
failed calculations. What cannot be fixed, even in principle, is the problem of
value multiplicity. It took years to build one single Minkowskian space for
Special Relativity. Now imagine building not just one or two Minkowskian
spaces, but an infinite number of them, each equipped with its own space-time
paraphernalia!

(**4**) Two Minkowskian
spaces, one with lower value and one with higher value of speed of light, are
mutually exclusive. The two cannot coexist even in principle.

(**5**) Looking up from
a lower Minkowskian space at a higher Minkowskian one, nothing can make sense.
And if something there did make sense, that sense would be riddled with
absurdities and contradictions.

(**6**) Looking down
from a higher Minkowskian space at a lower one, everything down there does make
sense. All judgments that have been made in the space of lower status are
overturned or reduced in value. The lower speed of light itself becomes
relative and ordinary like any other speed in the lower space.

(**7**) Best of all or
worst of all depending on your point of view, absolute space and absolute time
rise in their full glory at infinity. From there, one can look back and dismiss
out of hand all that Relativist hard work as a waste of time and completely
worthless.

**3.
****Phase and Group Velocities**

The distinction between
phase and group velocities lies at the heart of most attempts at modifying
Special Relativity to meet the superluminal challenge.

These two types of velocity
have been defined and treated within the framework of the classical wave
theory, but so far no attempt is made to clarify their meaning in the context
of the current photon model.

The clearest treatment of
these two notions is given in the field of radio pulsars. Here, group velocity
C_{g} is defined as the velocity of propagation, at which a group of
waves of the same wavelength travels through the interstellar medium,

**Cg =
c[1 – (Nr _{0}**

where r_{0} is the
classical radius of the electron, N the electron density, and l the wavelength. For wave propagation in
plasmas,

**Cg =
c[1 – ****w**_{p}^{2}**/****w**^{2}**)]** (**3.2**),

where w_{p} is the plasma frequency, and w is the wave frequency.

The phase velocity Cp is the
velocity at which a wave expands, and is related to the group velocity by the
equation,

**C _{p}C_{g} = c^{2} ** (

Since the phase of a radio
wave oscillates at right angles to the direction of propagation, the phase
velocity plays no role in the wave displacement in the forward direction, and
hence it’s ignored in computing the delay t in travel time over a distance L,

**t =
(Nr _{0}c**

where n is the frequency of the wave. It can be seen
from this relation that a short-broad-band pulse arrives first at high
frequencies, and its energy is delivered across the receiver band for an
extended period of time.

The fore-mentioned definition
of group velocity must not be confused with other definitions of the term in
the published literature on Relativity. One of these definitions, for example,
refers to group velocity as the velocity of a group of points on the surface of
a spherical wave, which can under certain conditions expand at superluminal
speeds. The term ‘group velocity’ is also used to denote the apparent velocity
of patterns on a wave train of infinite extent. If, for instance, a wave train
of infinite extent traveling through a medium is observed long enough, then one
can pick out identical spatial patterns that appear to travel at superluminal
speeds. Since all experiments on superluminal propagation of light use highly
collimated laser light of finite extent, the last two types of group velocity
are irrelevant to the case under discussion.

Finally, a new definition
of the term ‘group velocity’ is given by M. D. Stenner and his team, in a
recent attempt to explain away the superluminal anomaly. This recent attempt is
the topic of the next section.

**4.
****The Stenner Experiment**

In a recent article by M.
D. Stenner et al, group velocity C_{g} is defined as the velocity of
the peak of a collection of elementary sinusoidal waveforms, each with a
distinct frequency w,

**Cg =
c/(n + ****w****dn/d****w****|**** ****w****=****w**_{0}**) =
c/n _{g} **(

where n_{g} is the
group index, w_{0} is the central frequency of the wave packet,
and dn/dw is the dispersion of an optical
material.

According to the above
article, the speed limit in Special Relativity must be redefined as the
limiting speed of information, rather than limiting speed of an object.

Using this reformulation of
Einstein’s postulate of constancy, Stenner and his team carry out an experiment
to see whether the velocity of information C_{i}, C_{i} = c as
desired, or C_{i} = C_{g}, which violates Relativistic
causality.

The following is a summary
of their experiment:

[**1**] It’s assumed
that for a typical optical material, there exists narrow spectral regions,
where dn/dw < 0, resulting in anomalous dispersion
and superluminal group velocity.

[**2**] A laser-driven
potassium vapor is used to obtain n_{g} = -19 ± 0.8, indicating a highly
superluminal regime and large advancement for a smooth gaussian-shaped pulse.

[**3**] It’s assumed
that information is encoded on an optical pulse by creating a point of
non-analycity, which always travels at c regardless of the other velocities
associated with the pulse.

[**4**] Two identical
optical pulses are used to estimate the location of the point of non-analycity
by turning on the pulse amplitude above the noise floor of the detection
instruments to a high (1) or low (0) value near the gaussian peak and for the
remainder of the pulse. The moment when a decision is made to switch between
the two symbols is assumed to be the point of non-analycity.

[**5**] It’s assumed
that the detection time of information is later than the time when information
is available at the detector, and this detection latency Dt depends on the characteristics of the medium,
the shape of the symbols, the detection algorithm, the noise in the detection,
and the bit error rate (BER) threshold.

[**6**] The purpose of
the current experiment is to make the detection latency Dt as small and as similar as possible for both
vacuum and advanced pulses. But achieving the limit Dt ® 0 is deemed impossible on the
assumption it requires the use of infinite energy and unrealistic optimal shape
symbols.

[**7**] An
integrate-and-dump matched filter technique is used to determine the bit error
rate (BER) for vacuum and advanced pulse pairs. A BER in the range between –40
and –25 ns is obtained.

[**8**] Placing the
detection threshold at BER = 0.1, the difference in detection time for the
vacuum and the advanced pulse pairs is obtained.

[**9**] It’s concluded
that the information detection time for pulses propagating through the
fast-light medium is longer than the detection time for the same information
propagating through vacuum, even though the group velocity is in the highly
superluminal regime for the fast-light medium.

[**10**] A mathematical
model based on Maxwell’s equations is reported to be analyzed to gain insight
about the detection latency, and the observations are deemed to be consistent
with Special Relativity for a medium where the group velocity is highly
superluminal.

The following points can be
made with regard to the Stenner experiment:

**1.** Compared to its precise definition
in the investigations of radio pulsars, group velocity defined as the velocity
of the pulse peak, though novel, is inadequate and inaccurate. That is because
any optical pulse composed of waves with various frequencies can lose its peak
upon traversing a dispersive medium. Group velocity, therefore, must be defined
in terms of one single frequency for each component of the optical pulse.
Defining ‘group velocity’ as the average propagation velocities for all the
pulse components would not work.

**2.** Equation #4 .1 for computing the
average group velocity breaks down at n = wdn/dw, signaling illogical or
non-physical assumptions have been explicitly or implicitly used in its
construction. In fact, the very notion of negative refractive index is
non-physical and logically absurd.

**3.** The redefinition of the speed
limit, imposed by the theory of Special Relativity, as limiting the speed of
information is clearly anthropomorphic. There is little evidence that physical
objects have any use for it, since their only language is the language of
energy and momentum.

**4.** Removing the limit imposed on the
speeds of physical objects presents far more serious threat to Relativistic causality
than removing the limit on that of information. That is because interactions
among physical objects are real events, while information encoded on optical
pulses is only the image of previous events. In principle, bits of information
can arrive at a particular detector in any conceivable order without any
violation of causality principle.

**5.** Digital encoding is not the only
available technique for encoding information on optical pulses. As a matter of
fact, analogue encoding is ideal for eliminating the arbitrariness of decision
making, and it should have been used in this experiment.

**6.** The implicit assumption of equating
detection latency of encoded information to reaction time for momentum and
energy delivery cannot be justified. Since it’s immediately evident that when a
wave with a high group velocity arrives, its energy and momentum are delivered
at the moment of its arrival regardless of the arrival time of any other
component of the optical pulse.

**7.** The experimenters fail to specify
the data reduction procedures that they used to reduce the original
observations in their report.

**8.** The experimenters fail to
investigate possible sources of error related to their experiment.

**9.** The experimenters strong
theoretical leaning towards preserving Relativistic causality could bias their
investigation and make them see what they want to see as opposed to what is
really out there.

**10.** The assumption that the vapor-cell
portion of the path for a pulse propagating through the cells is equivalent to
vacuum, when lasers are tuned far from the atomic resonance, is unjustified. A
pulse path as close as possible to vacuum should have been secured. Since this
basic requirement is not met, the reported finding of less detection latency in
vacuum is groundless.

**11.** The very claim that detection
latency is greater for signals with higher speeds than for signals with lower
speeds is logically untenable and absurd. It has no chance at all of being
realized in the physical world.

**12.** The finding of the Stenner experiment
is contradicted in a direct and dramatic way by the results of the Nimtz
experiment, in which the 40^{th} Symphony of Mozart is encoded and
transmitted at 4.7c.

In spite of the major flaws
listed above, the Stenner experiment confirms the results of previous
experiments concerning the phenomenon of superluminal light propagation. This
confirmation is a very important step towards developing some sort of general
consensus in this regard.

**5.
****Concluding Remarks**

The recent discovery of
superluminal light propagation has all the attributes of a major scientific
revolution. Long-held assumptions in physics are seriously threatened.
Textbooks are terribly out of date. Lovely dreams of writing the last decimal
are in tatters. Reactionary and pro-status-quo physicists are stunned and
utterly at loss. They don’t know what to do. In short, what was built to be the
one-thousand-year Reich of Relativity exists no more.

Even though Relativity and
the Quantum theory, from logical perspective, are equally absurd, experiments
on superluminality are designed and carried out almost entirely within the
framework of the latter theory. For this reason, the discovery of superluminal
light propagation is perceived as a victory for Bohr over Einstein. For the
first time ever, Einstein’s camp loses the battle of public relation and mass
media to Bohr’s camp. Clearly, the public is decidedly on the side of
superluminality and against the Relativists who increasingly look like
reactionaries and enemies of progress.

The battle between Einstein’s
camp and Bohr’s camp, however, is better pictured not as a battle between two
opposing schools or groups of people, but rather as a conflict between two
sealed compartments inside the head of average physicist. That is why it’s so
painful and difficult to resolve.

Nevertheless, there is one
feasible experiment, which can settle once and for all this controversial
issue. A number of laser reflectors is left on the moon by the Apollo mission.
Those reflectors are still in good working conditions. The average time of a
round trip for light from the earth to the moon and back is known to a
sufficient degree of accuracy, mainly through the use of those laser
reflectors. Now if, instead of laser, synchrotron light is used, the current
disagreement over superluminality can be decisively resolved. A round trip for
timed pulses of the synchrotron in less than half the time of that of the laser
is enough to convince everyone that the postulate of constant speed of light is
false. The main obstacle, here, is how to get a synchrotron facility and
astronomical observatory to collaborate effectively and carry out this crucial
experiment.

__References__

**1.** Smith, F. G., (1977). Pulsars.
Cambridge University Press.

**2.** Stenner, M. D., et al, “The Speed
of Information in a Fast-light Optical Medium”. Nature, VOL 425, October 16^{th}, 2003.

**3.** “Light pulses flout sacrosanct speed limit”:

http://www.sciencenews.org/articles/20000610/fob7.asp

**4.**
“Light that travels…faster than light”: http://i-newswire.com/pr43033.html

**5.**
“Speed of light broken with basic lab kit: http://www.newscientist.com/article.ns?id=dn2796

**6.**
“Laser smashes light-speed record”: http://physicsweb.org/articles/news/4/7/8

**7.** “Light exceeds its own speed limit”: http://hideinplainwebsite.com/Light
Exceeds Its Own Speed Limit.htm

__Related Papers__

(**1**) Restricted
Relativity: http://www.wbabin.net/physics/faraj3.htm

(**2**) Is c Constant by
Convention? http://www.wbabin.net/physics/faraj5.htm

(**3**) STR Fake Test
Theories: http://www.mrelativity.net/Papers/27/Faraj.htm