Faster Than Light

By Wil McCarthy



Part I: Moving at the Speed of Light

It's not just a good idea, it's the law: 186,287 miles per second. The fact that sound waves travel at a finite speed--roughly 330 meters per second--has been known since ancient times. It's obvious, really, when you stand back a ways and observe the falling of a tree or the clapping of a pair of hands, and the sound arrives noticeably later than the sight itself. The fact that light waves also travel at finite speed is much harder to notice, because that speed is almost a million times faster.

But by the end of the Renaissance, astronomers--viewing events much more distant than a few hundred meters--had begun to suspect the truth. In 1676, the Danish astronomer Olaus Roemer observed that the orbital period of Jupiter's moons appeared to vary with the Earth's seasons. He reasoned that the time difference could be accounted for by motion of the Earth itself--towards Jupiter at one point in its orbit, and away from it at the other. (Imagine standing near a merry-go-round while a particular horse goes round and round, alternately approaching and retreating from you.) Using the crude range-to-Jupiter measurements available at the time, Roemer was able to estimate the speed of light to within an order of magnitude. His best guess was about a third of the actual answer, which isn't too bad under the circumstances. In fact, no significantly better methods for calculating "c" were devised until 173 years later, when French scientist Armande Fizcau placed a light source behind a slotted, spinning disc, and reflected the resulting flashes off a mirror placed eight kilometers away. His measurement was within 5 percent of the value we use today.

Around this time, experimenters began to notice another peculiar property of light: it behaved like a wave. If a rifle bullet travels a thousand meters per second, and a steam locomotive travels ten, then a bullet fired forward from a moving train goes 1010 meters per second, and one fired backward goes 990. Interestingly, though, a sound wave doesn't behave this way. The speed of sound varies with altitude and temperature and barometric pressure--the denser the air, the faster the speed--but for a given set of conditions the speed of sound is just that: the speed at which all sound travels, regardless of source.

Doppler effects affect us forever

The sound of our rifle shot (which is actually slower than the bullet itself) goes the same speed in both the forward and reverse directions, no matter how fast the train is going. Still, in the forward direction the sound waves crowd together as their source moves along behind them, meaning they will arrive more frequently in the ear of a listener, somewhere up ahead of the train. And since frequency is related to pitch, the listener interprets this difference as a higher-pitched sound. In the opposite direction, the sound waves are spread out, and the pitch is lower. This effect was first characterized by Christian Doppler in 1842, and is known today as the Doppler effect.

As Doppler himself realized, light is also subject to this effect, meaning it behaves more like a sound wave than a rifle shot. Now, sound waves are rhythmic disturbances in the air, which is clearly not the case for light waves. This led many researchers to hypothesize a much denser material--a fluid called "Ether"--through which light must propagate. Such a fluid would have to permeate every corner of space, from the interplanetary vacuum to insides of solid objects, including the planets themselves. This was a fairly weird suggestion, since we don't appear to be swimming around in any superdense fluid, but the discrepancy was cleared up by one additional hypothesis: that Ether did not interact with matter. That was weird, too, but at least it fit the facts.

Well, most of them.

One consequence of this theory is that it permits matter to travel faster than light, in exactly the same way that a rifle bullet can travel faster than its own sound waves. However, while astronomers had managed to locate some very speedy objects up there in the heavens, they could not find any superluminal ("faster than light") ones. Too, since the Earth was moving around the sun--and therefore through the stationary Ether--at some 18 miles per second, one side of the Earth should be facing into the oncoming Ether, while the opposite side faced away. So the starlight falling on one side should be sleeting in 36 miles per second faster than on the other. (A train moving through stationary air sees exactly this effect with sound waves.)

But in fact, this effect was not observed--there was no difference in the speed of light from one side of the Earth to the other. There was also no difference in the speed of light from a moving object than from a stationary one. The speed of light was the same for all observers, always. No superdense fluid could explain that. Instead, there seemed to be something fundamental in the structure of the universe, that made the speed of light an absolute. As a young Munich patent clerk pointed out in 1905, "E" apparently, for some reason, equaled "mc2." And that changed just about everything.

Einstein, tachyons and FTL, oh my!

This equation--Einstein's theory of relativity--tells us that to accelerate any mass to the speed of light requires an infinite amount of energy. The accelerated mass also experiences infinite time dilation, so that (for example) one second elapsing on a spaceship traveling at light speed equals infinity in the outside universe. Clearly these are not mere inconveniences--it's relativistically impossible for any material object to travel at the speed of light.

Another consequence of relativity--or more properly, of the early quantum theory Einstein developed at the same time--is that light, even though it's a wave, can sometimes act as a stream of particles, which we call photons. These can travel at "c"--the speed of light--because they have no mass, which sets a handy precedent: anything massless can travel that fast. But what about faster? Interestingly, the equations are symmetrical; it takes infinite energy to reach the speed of light, but not to exceed it, so while there's no way for a slower-than-light particle to become a faster-than-light one, a particle which starts out faster than light--and stays that way--is permitted by the theory. In 1967, physicist Gerald Feinberg even coined a name for such particles: the Greek word "tachyon" (roughly, "swift thing").

Do tachyons exist in the physical universe? If so, their masses would have to be imaginary, meaning a multiple of i, the square root of negative 1. That would be weird, and difficult to measure--no tachyon of any sort has ever been detected. Probably. But there is a subatomic particle--the neutrino--which has caused some scientists to wonder. Neutrinos are produced in great quantity by the nuclear reactions inside our sun, and every other in this star-spangled universe. They travel at or near the speed of light, meaning their mass--if they have one--must be something very close to zero. But it's hard to measure, and sometimes the sun's stormy surface kicks out a burst of neutrinos which we observe several seconds before an obviously related burst of photons. So yeah, the evidence is sparse, but it's tempting to speculate the neutrinos are maybe going a little bit faster than "c."

There are a few other things that can go faster than light, by virtue of not being "things" at all. The spot from a laser pointer is one example--shine it at the wall in front of you and you can make it move around quite rapidly. The farther the wall, the faster (and dimmer) the moving spot; shine it at a target thirty thousand miles away and you can easily move it faster than "c." The individual photons, of course, still move as slowly as ever--it's exactly like waving a firehose around so that the splash of its impact travels faster than the speed of the water through the hose. The splash is a process, not an object, so it isn't constrained by relativity.

Can we send messages faster than light this way? Alas, no. We could certainly shine a gigantic laser pointer at Alpha Centauri, then quickly snap it around to Vega, and anyone looking up at the night sky in those distant solar systems would see the ruby flash. But the only information that hops the gap from AC to V is, "I'll bet those other guys saw that flash, too," which in a mathematical sense is no information at all. The Einsteinian universe turns out to have some sharp restrictions against FTL transmissions.

Fortunately, there's more to our universe than even Einstein suspected. The burgeoning and highly weird field of quantum mechanics offers dazzling hints--and even hard experimental evidence--of faster-than-light phenomena, which we'll discuss here next month!

Part II: The Quantum Connection

Einstein saw the universe as a marvel of geometry--a sweeping four-dimensional structure whose curves, both cosmic and intimate, defined the force of gravity which held the whole thing together. Distant parts of this universe were isolated from one another by a "locality principle," which held that interaction between distant portions of the 4-D universe must be limited by the speed of light. Since the universe appeared (and still appears) to be expanding at a substantial fraction of that speed, this actually meant that some regions of the universe--on "opposite sides," as it were--could never see or detect each other at all! On a more practical note, it meant that the transmission of information over short distances--say, between neighboring planets or stars--was also limited to "c," the speed of light.

Science fiction has popularized the concept of "wormholes," which essentially are geometric deformations of the universe, like folds in a tablecloth, which bring two distant points into contact, allowing light or particles (or starships, yeah) to "skip over" the intervening distance. In fact, this idea originated with Einstein as well. However, this sort of bending and twisting requires such enormous and finely controlled gravity fields that we literally can't envision any technology that could accomplish it.

Fortunately, we may not need to: quantum mechanics--the study of time and space and matter/energy in the very tiniest of increments--reveals an even stranger universe, where similar shortcuts--free for anyone's use--are quite literally more common than dirt. These aren't wormholes, but more subtle effects like "quantum entanglements" between distant particles, which allow (in fact, force) them to interact instantaneously, regardless of the distance between them.

If you find this concept a bit baffling, don't worry--so do the most brilliant physicists. No one really knows what to make of all this, or where it might lead us someday. But for now we have some very cool findings to kick around.

Bell's ringing on the universe

The first of these is "Bell's Inequality," named for John S. Bell, who in 1964 devised an experiment which sent pairs of photons in opposite directions. The decay of a particle called a pion produces these photon pairs in a "singlet" state, meaning the spin of one photon (the rotation of its electric and magnetic fields) is opposite to the spin of the other. Thus, one photon "knows" the state of the other, even though the speed of light firmly isolates them from one another. But Bell found, somewhat alarmingly, that if he altered the spin of one photon by passing it through a polarizing filter, the other photon's spin changed as well. A signal (in fact, an action) was being transmitted instantaneously, or at least much faster than the photons themselves were traveling.

Unfortunately, by nature the spin of photons is random, so all this signal could actually do was turn one random sequence into a different random sequence. Unless the observer at the receiving end knew what the unmodified spin sequence "should" have been, there would be no way to tell if the incoming photons had been rotated or not. In a mathematical sense, no information was being transferred. This subtle but crucial distinction makes all the difference between a faster-than-light or "FTL" transmitter--what author Ursula K. LeGuin called an "ansible"--and a laboratory curiosity. Still, this experiment--a real shocker in its day, and still cutting-edge these 40 years later--proved for the first time that quantum entanglement was a physical phenomenon with bona fide FTL implications. The locality principle was dead.

More recently, a team from the NEC Research Institute in Princeton, N.J., made headlines last summer for a similarly staggering experiment, which purportedly coaxed a light beam--built up from photons of various colors--to exceed "c." This claim is somewhat misleading, though, and was further distorted by the media, who couldn't quite comprehend the explanation.

The "speed" of the beam, more precisely known as the "group velocity" of the assembled photons, is measured by the arrival time of its energy peaks, i.e., the instants when the beam is at its brightest. However, by staging the departure times for the colored photons, the researchers were able to manipulate that peak into traveling faster than the photons themselves. Imagine a race among three horses: one bearing a red banner, one a green and one a blue. Now imagine a giant "X" floating along among them, marking the center of mass of the three horses. (If they were supported by a three-way teeter-totter of some sort, this is the balance point where you'd stick the support post.) While they run, each horse raises and lowers its body at a slightly different rate, so the X bobs up and down at a frequency of its own--sometimes faster than the individual horses and sometimes slower.

If a "beam" of horses is measured by the high points of the X as it bobs along the track, then as the beam's frequency fluctuates, it creates peaks which, yes, may appear to move faster than the horses themselves. But it's a silly sort of measurement--you can't tape a message to the "X" and expect it to leap from peak to peak, outracing the horses, because these peaks are purely imaginary, an artifact of the peculiar way we've chosen to observe the race. Only the horses themselves are real. So despite all the headlines, this experiment was really no different from the radio "phase velocity" gimmicks of the early 20th century, where the frequencies of two carrier waves interacted to create a harmonic wave with apparently FTL peaks. But again, carrier waves don't convey information--it's the manipulation (or "modulation") of the waves which does. And those modulations travel--you guessed it--at the speed of light.

Slow light may speed the future

A bit more interesting was the recent "slow light" demonstration, by Dr. Lene V. Hau of Harvard University. We've known for a hundred years that the speed of light is slower through solids and liquids than through empty space. The "slowest" natural substance is diamond, which bogs light down to about 0.4c, or 40% of its vacuum speed. But in 1999, Hau and her team went nature one better, using a cloud of ultracold sodium atoms, held in a "coupled" state by a laser beam, to slow the photons of another laser beam down to less than three meters per second. In subsequent experiments they were able to reduce this speed still further, until finally, last month, they were able to stop the beam completely.

Stopping light with an ordinary barrier--say, a lens cap -- destroys the photons irretrievably. If they were carrying a signal, too bad; the signal is lost forever. Hau's apparatus does something quite different: when the coupling laser is turned off, the energy and quantum state of the signal photons are stored as a "spin" in the gaseous sodium atoms. Later, when the coupling laser is turned back on, the reconstructed signal beam emerges from the cloud, unchanged from its previous state. This isn't a trick or gimmick; the light actually slows down, and actually stops. The implications for optical computing are huge.

But while this lets us travel--even walk!--faster than "the speed of light" through a Hau cell, it isn't much use for interstellar communication.

For that we have to look deeper into the past. Before Hau and Bell there was Werner Heisenberg, whose 1925 "Uncertainty Principle" stated that a particle's momentum and position could not be precisely known at the same time. Not because of measurement difficulties, but because the math appears to forbid it. At first, this looked like a problem with the math, but it turns out there really is something slippery and unknowable about the universe at its lowest levels. If an electron, for example, is trapped in a device which constrains its velocity, its position begins to blur. It jumps from place to place, or partially occupies many places at once. It becomes a probability density function (a "wave") rather than a particle. That's quantum mechanics.

Anyway, the physical reality of the Uncertainty Principle is demonstrated by a phenomenon called "quantum tunneling," which actually permits a particle to jump, spontaneously, to places it couldn't reach by linear travel. As electronic components are made smaller and faster, they're increasingly plagued by "leakage" of tunneled electrons into unwanted areas. Other components--particularly those in quantum computers--are designed specifically to exploit this phenomenon.

The same trick works for photons; with a device called a waveguide, it's rather easy to create barriers across which microwave photons are incapable of traveling. But some small fraction of the photons can tunnel across it, appearing suddenly on the other side as if by magic. That's not the strange part. In 1992, Cologne University physicist Gunter Nimtz noticed that the time required for a photon to tunnel across such barriers was constant, regardless of the distances involved. In fact, if the distance was more than a few centimeters, the photon would leap across the gap faster than it could have traveled across it. Faster than "c." Faster than light.

Again, this was not a sleight of hand or trick of math: Nimtz actually broadcast Mozart's 40th symphony across a tabletop waveguide, and reconstructed on the other side an intelligible recording which had tunneled there at 4.7 times the speed of light. (Roughly 1 out of every 100,000 photons successfully tunneled across the barrier, a fraction which drops off exponentially as the barrier width increases.)

Bully for Nimtz, who certainly deserves a Nobel prize for his efforts. Unfortunately, at this point the universe's strangely predictable bookkeeping catches up with us again: the signal is carried by the tunneled photons in an "evanescent mode"--essentially the leading edge of a highly elongated photon. Imagine our horse race again, only this time the horses' noses are rushing out across the finish line, far ahead of their actual bodies. Since evanescent modes carry negative energy and cannot be directly observed until the peak of the photon (or the horse's center of mass) arrives behind them, their indirectly observable FTL effects once again can't carry information.


We may never find a way around these slippery barriers. In fact, there are so many barriers, everywhere we look, that many scientists have long considered the cause hopeless. Still, the example of Nimtz's photons is instructive: if a small fraction of them can tunnel across a waveguide or brick wall, maybe, possibly, some small fraction of FTL researchers can tunnel across the information barrier and build the ansible of our long and hopeful dreams. If so, then persistence really is the key, and we had better get busy.

Wil McCarthy is a rocket guidance engineer, robot designer, science fiction author and occasional aquanaut. He has contributed to three interplanetary spacecraft, five communication and weather satellites, a line of landmine-clearing robots, and some other "really cool stuff" he can't tell us about. His short fiction has graced the pages of Analog, Asimov's, Science Fiction Age and other major publications, and his novel-length works include Aggressor Six, the New York Times notable Bloom, and The Collapsium.

Articles original published in Labnotes

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