Speed freaks

New Scientist vol 180 issue 2417 - 18 October 2003, page 42

Can information travel faster than the speed of light? That all depends on how you measure it, says Valerie Jamieson
 

LIJUN WANG is no athlete, but he holds the record for the world's fastest moving thing. Wang and his colleagues at NEC's Research Institute in Princeton, New Jersey, have clocked laser pulses apparently travelling at a stunning 100 billion metres per second, 300 times as fast as the accepted speed of light in a vacuum, through a container filled with caesium gas. The pulses travelled so quickly, they emerged from the container even before they had struck it.

The experiment, which hit the headlines worldwide, sounded like a direct violation of the generally accepted maxim that nothing can go faster than light. "People have used a whole variety of experiments like this to claim 'look, it's moving faster than the speed of light'," says information theorist Seth Lloyd of the Massachusetts Institute of Technology in Cambridge.

But information theorists like Lloyd have a get-out clause. Nothing was really travelling faster than the speed of light. It only appeared to be doing so. Wang's pulse wasn't carrying any information. "You can't send information faster than the speed of light this way," says Lloyd. If you could, you would be able to transmit signals backwards in time and affect causality, the idea that cause must always precede an effect.

But how can Lloyd be sure? Wang had not tried to encode information on his pulse, but what if he had? When physicist Dan Gauthier of Duke University in Durham, North Carolina, heard about Wang's experiment in 2000, he asked information theorists what the speed limit of information was. He was shocked to find that no one actually knew.

The trouble is, no one can agree how to define the speed of information. "That really bothered me," says Gauthier. So with colleagues Michael Stenner, also at Duke, and Mark Neifeld at the University of Arizona in Tucson, he set about devising an experiment to measure it. The results are reported this week in Nature (vol 425, p 695).

Designing the experiment was surprisingly tricky, because we know almost nothing about the basic nature of information. For almost a century physicists have argued over how you define the speed of information. What is the difference between the speed of a signal carrying information and that of a mere light beam?

Nearly 150 years ago, the Austrian physicist Ludwig Boltzmann came up with some clues. Boltzmann realised that information is a real physical quantity, just as temperature and pressure are. The temperature of a gas measures the average energy of individual molecules, while pressure relates to the collective push of the molecules against the sides of a container holding the gas. The "entropy" or disorderliness of gas molecules relates to the lack of information about their positions and velocities. If you release a tiny vial of gas into a room, you can no longer pin down the position of a specific molecule to a place in space, in other words you lose information about the molecule's coordinates as the entropy increases. Every form of matter can, in principle, be used to send information, from massless photons to supermassive black holes. "When we send signals we are just piggy-backing on the inclination of physical systems to carry information around with them," says Lloyd. Everything from puffs of smoke and semaphore flags to radio waves and laser beams has been used to transmit signals.

Light speed ahead

Einstein showed that photons, the massless particles that make up light, radio signals and other electromagnetic waves, always travel at the speed of light, which is just shy of 300,000 kilometres per second in a vacuum. This cosmic speed limit is enshrined in equations of electromagnetism formulated by the Scottish physicist James Clerk Maxwell. To safeguard Maxwell's equations, Einstein concluded that the speed of light is always the same no matter how fast you are travelling. Even if you hitched a ride on a rocket travelling at 299,000 kilometres per second, you would see a light beam sent from behind you overtaking you at 300,000 kilometres per second.

Based on that argument, which is the cornerstone of Einstein's special theory of relativity, it might seem impossible that information could ever break the speed limit, because whatever is carrying the information cannot.

But it is not that simple. Back in 1905 when Einstein formulated his theory, he had no idea that information would turn out to be the important quantity that it is today. He therefore assumed that it did not matter whether the light or radio signals were being used as signals. "Einstein didn't talk about the speed of sending information," says Lloyd, "he only talked about sending light."

Special relativity only explains why the speed of light remains for ever out of our reach. Objects with the slightest hint of mass grow heavier as they speed up. And as you approach the speed of light, your rocket would become so massive that it would take an infinite amount of energy to accelerate actually up to the speed of light. But Einstein's theory does not rule out the possibility that there might be other exotic things that can naturally travel faster than the cosmic speed limit.

Because we do not fully understand what underlies information, some researchers have argued that the door is still open for information to travel faster than the speed of light. In 1967 Gerald Feinberg, a physicist at Rockefeller University in New York, showed that special relativity does not outlaw certain types of particles thought to have been created during the big bang from breaking the cosmic speed limit. If you could encode information in these "tachyons", you could send signals back in time. But no one has ever detected a tachyon, and many physicists doubt they exist.

The only other faster-than-light claims are due to experiments resembling Wang's. One of the first of these was carried out in 1993 by Raymond Chiao's group at the University of California at Berkeley. He showed that quantum mechanics allows pulses of light to appear to break the cosmic speed limit. According to quantum theory, when a particle of light called a photon hits an opaque wall there is a chance that it will tunnel through it rather than bounce back.

Chiao showed that photons in the pulse can travel faster than light when they tunnel through a filter made up of thin layers of titanium oxide and silica glass sandwiched together. He raced tunnelling photons against a light pulse sent through a vacuum. The tunnelling photons reached the detector first, and Chiao showed that to do so they seemed to have travelled through the filter 1.7 times as fast as the speed of light in a vacuum.

And last year Stefano Longhi at the Technical University in Milan teamed up with optical fibre manufacturer Corning to show that pulses can travel five times as fast as light in specially adapted glass fibres. Light usually slows down when it travels through optical fibres because it is continually absorbed and re-emitted by the glass. To counter this effect, Longhi and his colleagues carved structures that do a similar job to Chiao's filters in glass fibres of the sort used for phone lines.

Rather than use a filter, Wang and his colleagues simply fired their pulses at a container of caesium gas, which behaves like a filter because it can transmit, absorb or reflect photons.

Visual illusion

Despite the claims made about their experiments, Chiao, Wang and others insist that their results are not at odds with causality. Even though the pulses appeared to outrun the speed of light in a vacuum, the researchers argue that the effect is an illusion. It all boils down to the nature of the pulse. A pulse contains many light waves with slightly different frequencies, which add up to make a bell-shaped pulse with a central peak and tails extending ahead and behind.

When light passes through a filter, most of it gets absorbed and re-emitted by atoms. Light waves that aren't absorbed can either tunnel through the layers in the filter or bounce back off them. The first waves to be registered in the detector are the ones that took the fastest route. These processes sculpt the pulse, chopping off its trailing tail and whittling it down in size. So when the light pulse emerges from the filter, it looks as if it has jumped forward. If you base your measurements on the time the pulse arrives at the detector, you would conclude that the velocity of the pulse as a whole, its "group velocity", is greater than the speed of light.

But does any information encoded on the pulse travel at this group velocity? Can information go faster than light? Günter Nimtz at the University of Cologne in Germany believes it does. He famously encoded Mozart's symphony number 40 on a stream of microwaves, just as radio transmitters encode pop songs on radio waves. Normally radio and microwaves travel at the speed of light, but when Nimtz transmitted the signal through a tunnelling device he found the encoded microwaves travelled at 4.7 times the speed of light in a vacuum. When he decoded the signal, Mozart's masterpiece was still recognisable. This, he says, demonstrates that information really can travel faster than light.

To work out the amount of information in a signal, argues Nimtz, you must hear the entire signal. So the right way to measure the speed of information is to measure the speed of the whole pulse. In other words, Nimtz believes information travels at the group velocity.

And he thinks tunnelling filters created from layers of silicon and germanium placed in electronic circuits could ultimately speed up computers. At present the speed with which electrons zip through copper cables is limited to around two-thirds the speed of light due to the electrical resistance of the material. Nimtz believes tunnelling filters could boost slow-moving electrons travelling through them.

But Nimtz's views are controversial. According to Chiao, the arrival of the peak of the pulse does not necessarily correspond to the arrival of information. What he thinks is important is to know the very first moment new information arrives.

Nimtz and Chiao have argued for years about who is right. The trouble is, no one was able to test Chiao's definition of the speed of information. To do so, you would need to make a radio wave or light pulse that turns on in an instant. The trouble with the bell-shaped pulses that have been used up till now is that they turn on gradually. So you can't pinpoint the exact moment they arrive.

Gauthier and his colleagues came up with an alternative plan. Instead of clocking the front edge of the pulse, they devised a kind of two-letter "alphabet" using light. Their approach was inspired by Chiao, who proposed that information be encoded as a sharp step or sudden change in the intensity of a light pulse.

To make their alphabet, Gauthier and Stenner used a device called a waveform generator that allowed them to specify the exact form of light pulses. The leading edge of their "letters" looked identical - half a bell shape. Near the peak of the pulses, the researchers either switched the light off or cranked up its intensity, producing two very differently shaped pulses. The kinks in the pulse shape were the points that represent the information. So you only glean information about which pulse was sent when you detect the discontinuity.

To measure the speed of information, Gauthier and Stenner fired these pulses through a container of gas similar to the one that Wang's team had used at NEC and timed how long it took them to reach a detector. When they fired conventional bell-shaped pulses, like Wang's group they found the pulses apparently travelled nearly 20 times as fast as the speed of light. But they got a surprise when they launched the two letters into the gas.

Alphabetical order

Even though the leading edge and peak of the pulse travelled at superluminal speeds, the discontinuities travelled just shy of the cosmic speed limit. So the speed of information has nothing to do with the speed of the group of light waves in a pulse. Instead, it is measured by the speed of the part of the light pulse that is actually carrying information.

Further proof comes thanks to the fact that Gauthier and Stenner had different letters to play with. When they sent two different letters through the gas, they found the leading edges and the bell-shaped peaks always arrived at the detector neck and neck. So they could not tell the two letters apart until the discontinuity crossed the line. It is almost like watching the letters E and F moving out of a fax machine upside down. You wouldn't realise which one was coming out until the fax got to the end. This implies that what matters when it comes to encoding information are the discontinuities, not the group velocity. "It is a very nice piece of work," says Lloyd.

Although Gauthier's work solves one mystery, the argument over the true nature of information is bound to continue. The link between these experiments and the definition of information in terms of entropy - the disorderliness of a physical system - is still missing. In a further test, Gauthier has passed his "alphabetical" light pulses through an apparatus that slows the speed of light to walking pace. Will the discontinuities will slow down too, or will they continue to travel at the speed of light in a vacuum? The results have not been announced, but if the discontinuities do continue to travel at the speed of light, it will be one more sign that the information encoded on a pulse is fundamentally different to the group of light waves that make it up. Whatever light pulses appear to be doing, nature still respects the cosmic speed limit.

Valerie Jamieson
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