|Email: Ali A. Faraj|
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.
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 40th 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 - (v2 / c2)]½ (2.1),
y' = y (2.2),
z' = z (2.3),
t' = [t - (vx / c2)] / [1 - (v2 / c2)]½ (2.4).
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 Cg 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 – (Nr0l2 / 2p)] (3.1),
where r0 is the classical radius of the electron, N the electron density, and l the wavelength. For wave propagation in plasmas,
Cg = c[1 – wp2/w2)] (3.2),
where wp 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,
CpCg = c2 (3.3).
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 = (Nr0cn-2 / 2p)L (3.4),
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 Cg is defined as the velocity of the peak of a collection of elementary sinusoidal waveforms, each with a distinct frequency w,
Cg = c/(n + wdn/dw| w=w0) = c/ng (4.1),
where ng is the group index, w0 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 Ci, Ci = c as desired, or Ci = Cg, which violates Relativistic causality.
The following is a summary of their experiment:
 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.
 A laser-driven potassium vapor is used to obtain ng = -19 ± 0.8, indicating a highly superluminal regime and large advancement for a smooth gaussian-shaped pulse.
 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.
 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.
 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.
 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.
 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.
 Placing the detection threshold at BER = 0.1, the difference in detection time for the vacuum and the advanced pulse pairs is obtained.
 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.
 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 40th 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.
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 16th, 2003.
3. “Light pulses flout sacrosanct speed limit”:
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
(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