July 2001
by Robert Novella

Ephemeral and ubiquitous, light has been mystifying to man since the first homo-sapien pondered its existence countless millennia ago. It remains so to this day but science has taught us much in the intervening time. Of all its bizarre properties, the most self-evident is probably its vast speed. Light is so fast, in fact, that for centuries it was assumed to be infinite. We know better today. Over the years, hundreds of experiments have continually refined the accuracy of our measurements producing the accepted figure of 186,282.397 miles per second or about 670 million mph (in a vacuum)(Bova,2000). Thanks to the revelations of Einstein’s Relativity we came to believe that light travels at the cosmic speed limit of the universe, unsurpassable by any form of energy or matter. So established was this belief that it came as a shock to many when the headlines of major newspapers revealed in the past year that scientists have coaxed light to speeds in excess of 300 times its previously accepted value. The authors of these articles would have us believe this was a seminal event. Has yet another “fact” of science been proven wrong? Will we be communicating superluminally in the future? Closer examinations of these experiments and of light itself produce conclusions to the contrary.

In July 2000, Lijun Wang, along with his colleagues Alexander Kuzmich and Arthur Dogariu, published in the magazine “Nature” an article called “Gain-assisted superluminal light propagation” (2000). In it they describe their experiment in which a light pulse sped through a specially prepared chamber of cesium gas at 310 times the speed of light in a vacuum. Professor R.Y. Chiao at Berkely first predicted this phenomenon in 1993 and since then many researchers including Professor S. Chu at Stanford University have observed similar effects. Two of the distinguishing characteristics of this most recent experiment were the use of a non-opaque medium (the cesium) and the fact that the light pulse exiting the gas was very similar, although less intense, than the one that entered. This last fact is salient primarily because it makes the apparent superluminal signals much easier to confirm.

The experiment itself uses two lasers and a magnetic field to induce the cesium gas to enter a highly excited state. When conditions are just right, another laser beam, this one 3.7 microseconds in duration, enters the six-centimeter chamber filled with the cold gas. The light’s transit, through a vacuum, would be expected to be 0.2 nanoseconds but in this experiment it leaves the chamber 62 nanoseconds sooner than that. This has been calculated at 310 times the vacuum speed of light. To explain this, scientists point to the energetic state of the gas, which allows for an amplification or gain of wavelengths and one other absolutely crucial factor; anomalous dispersion.

Anomalous What?

Anomalous dispersion is a curious phenomenon that deals with how different frequencies of light react in certain media. But before we dive into this topic, we need to understand what refraction and normal dispersion are. Light has not one but many maximum velocities depending on the medium it’s propagating through. The absolute highest speed, of course, occurs in a vacuum. Other substances such as air, water, or glass slow down light to varying degrees depending on the density of the medium. When light hits an object at an angle, the decrease in speed also results in a bending or change in direction of the light propagation. These phenomena are the essence of refraction. We have all seen a stick placed in water at a certain angle, which appears as if the submerged portion was bent at an odd angle. This principle also explains the behavior of eyeglasses, telescopes, prisms and many other familiar objects. The ratio by which light is slowed in a medium is called the index of refraction. This slowing and bending of light depends not only on the index of refraction of the medium but can also be a function of the frequency of light itself. This frequency-dependent slowing of light in the same medium is called dispersion. For example, when light moves from air to water the higher frequency light (like blue or violet) bends more than the lower frequency light (like red and orange). A rainbow illustrates this principle like no other. Sunlight is refracted as it enters water droplets in the atmosphere. The higher the frequency of light the more it slows down and bends, the lower the frequency of light, the less it slows down and bends. This explains how the white light, which consists of all frequencies moving at the same speed, can be disassembled or dispersed into its component frequencies (colors), creating the beautiful spectral pattern we call a rainbow. During dispersion the index of refraction increases with angular frequency and since this is a common occurrence in nature it is called normal dispersion. In an anomalous dispersion medium, like the specially prepared cesium in the experiment, just the opposite occurs. In other words, the refractive index falls with increasing frequency. If water drops exhibited these properties, the colors of a rainbow would be inverted. We will see later how anomalous dispersion can have unusual and counterintuitive effects on light.

A Light History

Light propagates with such remarkable velocity that it is easy to assume that it must be infinitely fast. Aristotle (384-322 BC) was such a believer. In fact, he thought that it was simply wrong to even conceive of light as propagating phenomena at all (Zajonc, 1993). Those few of his contemporaries who disagreed with him could offer no evidence one-way or the other. Aristotle’s belief, like many of his beliefs, influenced those of others for many centuries to come.

Although Galileo Galilei (1564-1632) failed in his attempt to resolve this controversy, he distinguished himself in that he was the first to scientifically evaluate the speed of light in the early 1600’s. While not as well known as his apocryphal test of gravity at the Leaning Tower of Pisa, his lantern experiment at least had the distinction of actually being carried out (Walter, 1684). This research consisted of he and a colleague, separated by a mile or so, each on a hilltop and holding a covered lantern. When one lantern was manually uncovered, the other was as well when the light from the first reached it. By using the known distance and by timing the interval between the uncovering of the first lantern and the light from the second reaching the first, Galileo believed an estimate of the speed of light could be ascertained. Unfortunately, the one hundred-thousandth of a second journey was completely swamped by the glacial reaction time of the human participants. Galileo, however, would have demonstrated the finite speed of light had it been merely fast instead of mind-numbingly fast.

In the 1600’s, with no hard evidence for the finite speed of light, it was still widely believed to propagate with infinite speed. This was supported by observations of lunar eclipses in which there was no time lag of the position of earth’s shadow on the moon. Yet again, this was because light is just far too fast for humans, unaided by adequate technology, to tell the difference between finite (yet large) and infinite. Even Johannes Kepler (1571-1630) supported the status quo. His reasoning was that since light had no mass and resistance to motion, it therefore must have an infinite speed.

To resolve this problem what was needed was a way to experiment on light that involved distances far beyond that between hills or even the quarter million miles between the earth and the moon. This is exactly what Ole Romer (1644-1719) serendipitously did in1675. During his study of the Jupiter moon Io, he noticed that throughout the year the eclipse of Io by Jupiter slowly changed from being eight minutes late to being eight minutes early when compared to the predicted time. The easy conclusion would have been to doubt Newton’s theory of gravity; specifically its prediction of the constancy of orbital periods. Romer wisely decided not to pursue this course and instead used his experiment to reveal clues about the nature of light. Helping him in this regard was the fact that the cycles of waxing and waning orbital periods were approximately 12 months apart. Further, when the appearance of the eclipse was maximally late, the earth was at its furthest distance from Jupiter. He correctly concluded that this time difference had to be due to the transit time of light to earth at its varying distances from Jupiter. His approximations of light’s actual speed were off by twenty-five percent due to inaccurate estimates on intrastellar distances but science finally had hard evidence that light did not move with infinite speed. Surprisingly, so entrenched was the belief in an infinite speed for light that it took over fifty years for Romer’s conclusions to be widely accepted by the scientific community.

The next major increase in measurement accuracy was completely earthbound experimentally and was carried out by physicist Armand Fizeau (1819-1896) in 1849. His elegant experimental design was in fact similar to Galileo’s as if the latter had covered and uncovered his lantern over and over and over and reflected its light off a mirror eight kilometers away. To achieve this effect, Fizeau used a rotating disc with teeth. When spun at the appropriate speed so that the light bounced through a gap, off the mirror and back through the proper gap in the disc it was possible to deduce a figure for the speed of light that was within four percent of today’s accepted value. Over the years measurements became increasingly precise. Today, it has been estimated that we can achieve an accuracy that is better than one part per billion.

What is being measured here? What exactly is light anyway? In a way, of course, we are all intimately acquainted with this phenomenon since we are bathed in it, all day every day and we rely on it as a source of information about our world that far surpasses all others. Its true nature, like its velocity, has eluded elucidation since time immemorial. That all changed, however, in 1864 when James Clerk Maxwell (1831-1879) put forth his theory of electromagnetism. The two ostensibly disparate phenomena of electricity and magnetism were shown, in this theory, to be different manifestations of the more fundamental force, electromagnetism1. The key insight occurred when Maxwell realized that a changing magnetic field creates a changing electric field and so on and so on feeding off each other and traveling through space as an electromagnetic field2. When he calculated its speed, it was so close to the measured speed of light that he realized the two must be one and the same. So significant was Maxwell’s work that Nobel Laureate Richard Feynman believed that even ten thousand years from now it will be considered the most significant event of the 19th century (Zajunc, 1993). If it were possible to see a wave of electromagnetism we would see magnetic and electric fields oscillating at right angles to one another and its direction of propagation. What we call “light” is actually just a tiny slice of the entire electromagnetic spectrum. This slice is called visible light and it consists of the relatively small range of frequencies that the human eye is sensitive to (from 800 nanometers to 340 nm). The moving charges that produce visible light, like electrons, also produce other forms of electromagnetism that the unaided eye is blind to including radio, infrared, ultraviolet, microwaves, x-rays, and gamma rays3.

Phase and Group Velocity

There are other less well known aspects of light velocity that are absolutely crucial to understanding the significance of these recent faster-than-light experiments. There are actually different types of velocity that reveal themselves depending on which feature of light is being examined. One such feature is called phase velocity. This can be described as the speed of oscillation of the electric and magnetic fields that comprise light. Group velocity, by contrast, refers to the speed at which the entire wave packet or pulse of light travels. Since light normally consists of an ensemble of frequencies, phase velocity refers to the individual component waves and group velocity refers to the collection as a whole as they travel together interfering with each other and making their own unique pattern of waves. For a macroscopic analog in nature, picture a wave traveling on the ocean. Sometimes if you look closely you can see not only the main wave train moving, but also smaller waves being created at the back of the wave train, traveling through it, and then disappearing at the front.

In a vacuum these two phenomena propagate at the same speed but in any type of dispersive media in which speed changes with frequency, phase and group velocity can diverge. During normal dispersion, group velocity is always slower than phase velocity. This is analogous to a walking caterpillar. Its many legs and body segments create a wave-like motion (phase velocity) moving up its body, which is moving faster than the caterpillar as a whole (group velocity). In an anomalous dispersion medium this divergence can create unusual and counterintuitive wave effects. It is in this realm that group velocity can exceed the accepted speed of light. How is this possible? Try to picture the light before it enters the chamber. One way to do this is as many individual waves each with a different frequency or arrangement of peaks and valleys. Another way to envision it is as one composite wave variously called a wave packet or pulse, which is essentially the sum of all the individual waves. Where the peaks of the individual waves line up there is a very high peak in the composite wave. Conversely, where the valleys line up there is a very low valley in the composite. This is called constructive interference. As long as all the individual frequencies travel at the same speed, then the relative positions of all the peaks and valleys stay the same thereby creating a stable composite wave that does not move relative to the individual waves. In this case phase and group velocity are equal as it is in a vacuum. During anomalous dispersion, however, the index of refraction is lower as frequency increases and this does very weird things to group velocity. In this situation the individual waves are now moving relative to each other causing them to go in and out of phase. Since the highest peaks of the composite wave corresponds to where the individual waves are in phase and the places where that happens is now changing with time; the result is a pulse of light that can move with arbitrary speed, even faster than light. This how group velocity can enter the superluminal realm.

Causality and Relativity

Can this effect be used for superluminal communication? Has relativity been turned on its ear? Has causality been violated? No, no, and no (respectively). Why? Because the apparent superluminal motion is an artifact. Nothing; not mass nor energy nor information is traveling at the speed that the group velocity would have you believe. It is simply an artifact of the way the different frequencies of light from the individual waves are sliding in and out of phase. Nothing significant or tangible needs to move at the group velocity in order for its shape to manifest features that move at that speed. In the cesium experiment group velocity is like the shadow of phase velocity. If you shine a light on your moving hand, its shadow on a distant wall can move at a velocity greater than the hand itself. If you move the wall farther away and tilt it obliquely the shadow will move much much faster. The speed of light is not a limitation for such moving shadows. Indeed, faster than light motion is a rather common phenomenon yet is not a violation of relativity since mass/energy itself is not also moving at that speed. Therefore non-material points or features that do not transport energy are exempt from relativity’s prohibition. This is called the “motion of effects” (Steinberg, 2000) which includes other events like the moving point of intersection of a closing pair of scissors and a moving spot of laser light projected from the earth to the moon. In all of these examples there is no discrete object that is moving at that speed. There is no way to encode information in the speedy spot of light and there are no photons that are traveling greater than the speed of light as well. The same is true for the bizarre features of light in the cesium experiment. Wang and his colleagues themselves agree that fundamental laws of physics are not being overturned by their research. Indeed, on their FAQ website they argue the following:

“Our experiment is not at odds with Einstein’s special relativity. The experiment can be well explained using existing physics theories that are consistent with Relativity. In fact, the experiment was designed based on calculations using existing physics theories. (Wang, Kuzmich, Dogariu 2000)”

The scientific concept of causality is likewise not in danger of revision. The countless experiments involving relativity repeatedly confirm the notion of simultaneity in which two observers of two separate space-time events will disagree as to the event’s temporal relationship if no light signal could connect them moving at c (the speed of light) or less. If simultaneity were to fail, all of our views of causality would be defenestrated. Since there’s nothing even remotely close to the evidence that would be required to reject the principle that cause must precede effect, the conclusion is inevitable that signals cannot propagate faster than light. The researchers themselves agree that causality remains sacrosanct.

‘The observed superluminal light pulse propagation is not at odds with causality, being a direct consequence of classical interference between its different frequency components in an anomalous dispersion region. (Wang, Kuzmich, Dogariu 2000)”

I was pleasantly surprised by many of the non-technical articles describing Wang’s experiment because many quoted the researchers arguing that the fundamental tenets of science have not been called into question. But the writers, nevertheless and at best, misrepresented the research due to their unwarranted focus on the apparent superluminal results. As I’ve discussed, the real speed of light, the speed at which energy or information can move, was never in any real danger. But this is not even what the experiment was all about. The real novelty of the experiment was not the high group velocity nor was it the clever wave manipulation inherent in the anomalous dispersion. Both phenomena have been observed many times before. It was the fact that this event took place in a transparent medium; something that had never been accomplished before. This prosaic goal is not nearly as engaging as an artifact of the experiment that seemed to contradict a universally cherished tenet of science; the fact that the speed of light is not the ultimate speed limit. Obviously, very few newspapers would have sold if the headlines read: “Anomalous Dispersion Produced in a Transparent Medium”. But, if scientific research does not really warrant headlines in mainstream newspapers and other media then so be it. This kind of sensationalism of science does little for respect of and confidence in science itself and scientific decrees of the past and future.

References

1) Bova,Ben; “The Beauty of Light” John Wiley & Sons, Inc, 1988
2) Zajonc, Arthur; “Catching The Light: The Entwined History of Light and Mind”, Oxford University Press, 1993, pg 263
3) Essays of Natural Experiments made in the Academie del Cimento; translated by Richard Waler, London; 1684; p. 157
4) L. J. Wang, A. Kuzmich & A. Dogariu ; “Gain-Assisted Superluminal Light Propagation”, Nature 406, 277 – 279 (2000) © Macmillan Publishers Ltd.
5) L. J. Wang, A. Kuzmich & A. Dogariu, http://www.neci.nec.com/homepages/lwan/faq.htm. 2000
6) Steinberg, Aephraim M; “No thing goes faster than light”,http://physicsweb.org/article/world/13/9/3, 2000

Notes

1-In 1984 it was shown that electromagnetism and the weak forces are themselves manifestations of the yet more fundamental “electroweak” force.
2-There is, of course, another way to think of light that’s not wave-like but as discrete bundles of energy called photons. The wave and particle nature of light manifest themselves depending on the experiment being performed. Both are a legitimate way to conceptualize the nature of light. This is known as the wave-particle duality.
3-Gamma radiation is somewhat distinct in that only radioactive decay or nuclear reactions produce it.

Filed under: Pseudoscience, speed of light