The Bit and the Pendulum: From Quantum Computing to M Theory--The New Physics of Information

By Tom Siegfried

"Funny, clear, deep, and right on target. [Siegfried] lets us get a handle on ideas that are essential for understanding the evolving world."
-K. C. Cole, author of The Universe and the Teacup
"An eager, ambitious book. A stimulating, accessible introduction to scientific theory."
-Dallas Morning News
An award-winning journalist surveys the horizon of a new revolution in science
Everything in the universe, from the molecules in our bodies to the heart of a black hole, is made up of bits of information. This is the radical idea at the center of the new physics of information, and it is leading to exciting breakthroughs in a vast range of science, including the invention of a new kind of quantum computer, millions of times faster than any computer today. Acclaimed science writer Tom Siegfried offers a lively introduction to the leading scientists and ideas responsible for this exciting new scientific paradigm.

• Language: English
• Publisher: Turner Publishing Company
• Release date: May 2, 2008
• ISBN: 9780470354230

Book preview

Chapter 1

Beam Up the Goulash

It’s always fun to learn something new about quantum mechanics.

—BENJAMIN SCHUMACHER

Had it appeared two months later, the IBM advertisement in the February 1996 Scientific American would have been taken for an April Fools’ joke.

The double-page ad, right inside the front cover, featured Margit and her friend Seiji, who lived in Osaka. (Margit’s address was not disclosed.) For years, the ad says, Margit shared recipes with Seiji. And then one day she e-mailed him to say, Stand by. I’ll teleport you some goulash.

Margit is a little premature, the ad acknowledged. But we’re working on it. An IBM scientist and his colleagues have discovered a way to make an object disintegrate in one place and reappear intact in another.

Maybe the twenty-third century was arriving two hundred years early. Apparently IBM had found the secret for beaming people and paraphernalia from place to place, like the transporters of the famous TV starship Enterprise. This was a breakthrough, the ad proclaimed, that could affect everything from the future of computers to our knowledge of the cosmos.

Some people couldn’t wait until April Fools’ Day to start making jokes. Robert Park, the American Physical Society’s government affairs officer, writes an acerbic (but funny) weekly notice of what’s new in physics and public policy that is widely distributed over the Internet. He noted and ridiculed the goulash ad, which ran not only in Scientific American but in several other publications, even Rolling Stone. He pointed out that IBM itself didn’t believe in teleporting goulash, citing an article in the IBM Research Magazine that said it is well to make clear at the start that teleportation has nothing to do with beaming people or material particles from one place to another.

So what’s going on? Park asked. There are several theories. One reader noted that many research scientists, disintegrated at IBM labs, have been observed to reappear intact at universities. ¹

Moderately embarrassed by such criticism, IBM promptly prepared an Internet announcement directing people to a World Wide Web page offering a primer on the teleportation research alluded to in the ad. Science fiction fans will be disappointed to learn that no one expects to be able to teleport people or other macroscopic objects in the foreseeable future, the Web explanation stated, even though it would not violate any fundamental law to do so. So the truth was out. Neither Margit nor IBM nor anybody else has the faintest idea how to teleport goulash or any other high-calorie dish from oven to table, let alone from orbit to Earth. That’s still science fiction. But the truth is stranger still. Serious scientists have in fact begun to figure out how, in principle, teleportation might work.

The story of teleportation begins in March 1993. In that month the American Physical Society held one of its two annual meetings (imaginatively known as the March meeting) in Seattle. Several thousand physicists showed up, most of them immersed in the study of silicon, the stuff of computer chips, or other substances in the solid state. There are usually a few out-of-the-mainstream sessions at such meetings, though, and this time the schedule listed one about the physics of computation.

Among the speakers at that session was Charles Bennett of IBM, an expert in the quantum aspects of computer physics. I had visited him a few years earlier at his lab, at the Thomas J. Watson Research Center, hidden away in the tree-covered hills a little ways north of New York City. And I’d heard him present talks on several occasions, most recently in San Diego, the November preceding the March meeting. When I saw him in Seattle, I asked if there was anything new to report. Yes! he enthusiastically exclaimed. Quantum teleportation!

This was a rare situation for a science journalist—covering a conference where a scientist was to present something entirely new. Most new results disseminated at such meetings are additional bits of data in well-known fields, or answers to old questions, or new twists on current controversies. Quantum teleportation was different. Nobody had ever heard of it before. It was almost science fiction coming to life, evoking images of Captain Kirk dematerializing and then reappearing on some alien world in Star Trek.

In retrospect, quantum teleportation should have been a bigger story. But it isn’t easy to get new developments in quantum physics on the front page of the newspaper. Besides, it was just a theoretical idea in an obscure subfield of quantum research that might never amount to anything, and it offered no real hope of teleporting people or even goulash. To try to make teleportation a news story would have meant playing up the science-fiction-comes-to-real-life aspect, and that would have been misleading, unwarranted sensationalism, or so I convinced myself. Instead I wrote about quantum teleportation for my weekly science column, which runs every Monday in the science pages tucked away at the back of Section D. My account appeared on March 29, the same day the published version of the research appeared in the journal Physical Review Letters. So if teleporting goulash ever does become feasible, March 29, 1993, will be remembered as the day that the real possibility of teleportation was revealed to the world. (Unless, of course, you’d prefer to celebrate on March 24, the day that Bennett presented his talk in Seattle on how to teleport photons.)

Teleporting Information

Almost two years later (and a year before the IBM goulash ad appeared), Samuel Braunstein, a quantum physicist at the Weizmann Institute in Israel, was asked to present a talk to the science-fiction club in Rehovot. What better topic, he thought, than quantum teleportation? News of this idea hadn’t exactly dominated the world’s media in the time since Bennett had introduced it in Seattle. But teleportation had attracted some attention among physicists, and the science-fiction connection provided a good angle for discussing it with the public.

Braunstein immediately realized, though, that talking about teleportation presented one small problem—it wasn’t exactly clear what teleportation really is. It’s no good just to say that teleportation is what happens when Scotty beams Kirk back up to the Enterprise. So Braunstein decided he had to start his talk by devising a teleportation definition. "I’ve seen Star Trek, he reasoned, so I figure I can take a stab at defining it."²

In the TV show, characters stood on a transporter platform and dissolved into a blur. They then reformed at their destination, usually on the surface of some mysterious planet. To Braunstein, this suggested that teleportation is some kind of instantaneous ‘disembodied’ transport. But hold the phone. Einstein’s laws are still on the books, and one of them prohibits instantaneous anything (at least whenever sending information is involved). Therefore, Braunstein decided, teleportation is just some kind of disembodied transport. That’s still a little vague, he realized, and it might include a lot of things that a science-fiction club surely didn’t have in mind. A fax, for example, transports the images on a sheet of paper to a distant location. And telephones could be thought of as teleporting sound waves. In both cases, there is a sort of disembodied transport. But neither example is really in harmony with the science-fiction sense of teleportation.

Teleporting, Braunstein decided, is not making a copy of something and sending the copy to somewhere else. In teleportation, the original is moved from one place to another. Or at least the original disintegrates in one place and a perfect replica appears somewhere else. A telephone line, on the other hand, merely carries a copy of sound waves, emitted and audible at point A, to a receiver at point B, where the sounds are regenerated. A fax machine spits the original sheet out into a waiting basket as a copy appears at some distant location. The original is not teleported—it remains behind.

But perhaps copying of some sort is involved in real teleportation, Braunstein suggested. Maybe Star Trek’s transporters work like a photocopy machine with too strong a flashlamp, vaporizing the original while copying it. The information about all the object’s parts and how they are put together is stored in the process and then sent to the planet below. The secret of teleportation, then, would lie not in transporting people, or material objects, but in information about the structure of whatever was to be teleported.

Somehow, then, the Star Trek teleporter must generate blueprints of people to be used in reconstructing them at their destination. Presumably the raw materials would be available, or perhaps the original atoms are sent along and then reassembled. In any case, the crew members vaporized on the transporter platform magically rematerialize into the same people because all the information about how those people were put together was recorded and transported.

Naturally this process raises a lot of questions that the script writers for Star Trek never answered. For example, just how much information would it take to describe how every piece of a human body is put together?

They might have asked the U.S. National Institutes of Health, which plans to construct a full 3-D model of the human body (computer-imaged to allow full visualization of all body parts, of course), showing details at any point down to features a millimeter apart. Such a model requires a lot of information—in terms of a typical desktop computer, about five hard drives full (at 2 gigabytes per hard drive). Maybe you could squeeze it all into a dozen CD-ROMs. In any case, it’s not an inconceivable amount for a computer of the twenty-third century, or even the twenty-first.

But wait. The NIH visible human is a not a working model. In a real human body, millimeter accuracy isn’t good enough. A molecule a mere millimeter out of place can mean big trouble in your brain and most other parts of your body. A good teleportation machine must put every atom back in precisely its proper place. That much information, Braunstein calculated, would require a billion trillion desktop computer hard drives, or a bundle of CD-ROM disks that would take up more space than the moon. And it would take about 100 million centuries to transmit the data for one human body from one spot to another. It would be easier, Braunstein noted, to walk.

So the information-copying concept did not seem very promising for teleportation, although the hang-up sounds more like an engineering problem than any barrier imposed by the laws of physics. Technically challenging, sure. But possible in principle.

Except for one thing. At the atomic scale, it is never possible to obtain what scientists would traditionally consider to be complete information. Aside from the practical problems, there is an inherent limit on the ability to record information about matter and energy. That limit is the Heisenberg uncertainty principle, which prohibits precise measurement of a particle’s motion and location at the same time. Heisenberg’s principle is not a mere inconvenience that might be evaded with sufficient cleverness. It expresses an inviolate truism about the nature of reality. The uncertainty principle is the cornerstone of quantum mechanics.

Quantum mechanics codifies the mathematical rules of the subatomic world. And they are not rules that were made to be broken. All the consequences predicted by quantum mathematics, no matter how bizarre, have been confirmed by every experimental test. Quantum mechanics is like Perry Mason—it never loses. And there is no court of appeal. So if quantum mechanics says you cannot physically acquire the information needed to teleport an object, you might as well give up. Or so it would seem. But in the decade of the 1990s, physicists have learned otherwise. You may not be able to teleport ordinary information. But there is another kind of information in the universe, concealed within the weirdness of quantum mechanics. This quantum information can be teleported. In fact, it is the marriage of information physics to quantum weirdness that makes teleportation possible, even if it’s not quite the sort of teleportation that Star Trek’s creator, Gene Roddenberry, had in mind.

So when the IBM ad writers mentioned objects that could already be teleported, they referred not to goulash or even anything edible, but to the most fundamental pieces of reality: objects described by the mathematics of quantum mechanics.

Quantum Objects

Understanding quantum objects is like enjoying a Hollywood movie—it requires the willing suspension of disbelief. These objects are nothing like rocks or billiard balls. They are fuzzy entities that elude concrete description, defying commonsense notions of space and time, cause and effect. They aren’t the sorts of things you can hold in your hand or play catch with. But they are important objects nonetheless—they could someday be used to decipher secret military codes, eavesdrop on sensitive financial transactions, and spy on confidential e-mail. And as the IBM ad suggested, the study of quantum objects could transform the future of computers and human understanding of the universe.

Typical quantum objects are the particles that make up atoms—the familiar protons and neutrons clumped in an atom’s central nucleus and the lightweight electrons that whiz around outside it. The most popular quantum objects for experimental purposes are particles of light, known as photons. A quantum object need not be a fundamental entity like a photon or electron, though. Under the right circumstances, a group of fundamental particles—such as an entire atom or molecule—can behave as a single quantum object.

Quantum objects embody all the deep mysteries of quantum mechanics, the most mysterious branch of modern science. Part of the mystery no doubt stems from the name itself, evoking the image of an auto repairman who specializes in a certain model of Volkswagen. But in quantum physics the term mechanics refers not to people who repair engines, but to the laws governing the motion of matter, the way classical Newtonian mechanics describes collisions between billiard balls or the orbits of the planets.

It is not easy to understand quantum mechanics. In fact, it’s impossible. Richard Feynman put it this way: Nobody understands quantum mechanics.³ Niels Bohr, who understood it better than anybody (at least for the first half of the twentieth century) expressed the same thought in a slightly different way, something to the effect that if quantum mechanics doesn’t make you dizzy, you don’t get it. To put it in my favorite way, anybody who claims to understand quantum mechanics, doesn’t.

To the extent that scientists do understand quantum mechanics, explaining it would require a book full of a lot of very sophisticated math. Many such books have already been written. Unfortunately, they don’t all agree on the best math to use or how to interpret it. It might seem, then, that understanding quantum mechanics and quantum objects is hopeless. But in fact, if you don’t worry about the details, quantum mechanics can be made ridiculously simple. You just have to remember three basic points: Quantum mechanics is like money. Quantum mechanics is like water. Quantum mechanics is like television.

Quantum Money

Historically, the first clue to the quantum nature of the universe was the realization that energy is quantized—in other words, energy comes in bundles. You can’t have just any old amount of energy, you have to have a multiple of the smallest unit. It’s like pennies. In any financial transaction in the United States the amounts involved have to be multiples of pennies. In any energy transaction, the amounts involved must be measured in fundamental packets called quanta.

Max Planck, the German physicist who coined the term quantum (from the Latin for how much), was the first to figure out this aspect of energy. An expert in thermodynamics, Planck was trying to explain the patterns of energy emitted by a glowing-hot cavity, something like an oven. The wavelengths of light emitted in the glow could be explained, Planck deduced, only by assuming that energy was emitted or absorbed in packets. He worked out the math and showed that the expectations based on his quantum assumption were accurately fulfilled by the light observed in careful experiments.

By some accounts, Planck privately suggested that what he had found was either nonsense or one of the greatest discoveries in physics since Newton. But Planck was no revolutionary. He tried to persuade himself that energy packets could merge in flight. That way light could still be transmitted as a wave; it had to break into packets only at the point of emission by some object (or absorption by another). But in the hands of Albert Einstein and Niels Bohr, Planck’s quanta took on a life beyond anything their creator had intended. Einstein proposed that light was composed of quantum particles in flight, and he showed how that idea could explain certain features of the photoelectric effect, in which light causes a material to emit electrons. Bohr used quantum principles to explain the architecture of the atom. Eventually it became apparent that if energy were not like money, atoms as we know them could not even exist.

Quantum Water

Planck announced the existence of quanta at the end of 1900; Einstein proposed that light was made up of quantum particles in 1905; Bohr explained the hydrogen atom in 1913. Then followed a decade of escalating confusion. By the early 1920s it was clear that there was something even weirder about quantum physics than its monetary aspect—namely, it was like water.

How in the world, physicists wondered, could Einstein be right about light being made of particles, when experiments had proven it to be made of waves? When they argued this point over drinks, the answer was staring them in the face (and even kissing them on the lips). Ice cubes. They are cold, hard particles, made of water. Yet on the oceans, water is waves.

The path to understanding the watery wave nature of quantum physics started in 1925 when Werner Heisenberg, soon to become the father of the uncertainty principle, had a bad case of hay fever and went off to the grassless island Heligoland to recover. Isolated from the usual distractions, he tried out various mathematical ways of describing the motion of multiple electrons in atoms. Finally one evening he hit on a scheme that looked promising. He stayed up all night checking his math and finally decided that he’d found a system that avoided all the previous problems. As morning arrived, he was still too excited to sleep. I climbed up onto a cliff and watched the sunrise and was happy, he later reported.⁴

Unwittingly, Heisenberg had reinvented a system of multiplication using arrangements of numbers called matrices. Only later, when he showed the math to his professor at the University of Göttingen, Max Born, was he told what kind of math he had invented. Now the learned Göttingen mathematicians talk so much about . . . matrices, Heisenberg told Niels Bohr, but I do not even know what a matrix is.⁵

Heisenberg’s version of quantum mechanics was naturally designated matrix mechanics. It treated quantum objects (in this case, eleetrons) as particles. The next year, the Austrian physicist Erwin Schrödinger, in the midst of a torrid love affair, found time to invent another description of electrons in atoms, using math that treated each electron as a wave. (Schrödinger’s system was creatively called wave mechanics.) As it turned out, both wave and matrix methods produced the same answers—they were mathematically equivalent—even though they painted completely different pictures of the electron.

Immediately physicists became suspicious. For years, Einstein had argued that light was made of particles, despite all the evidence that light was wavy. Now along comes Schrödinger, insisting that electrons (thought since 1897 to be particles) were really waves. And even before Schrödinger had produced his paper, the first experimental evidence of wavy electrons had been reported.

Bohr, who had merged quantum and atomic physics years earlier, was the first to devise an explanation for the double lives led by electrons and photons. In a famous lecture delivered in 1927, he presented a new view of reality based on a principle he called complementarity. Electrons—and light—could sometimes behave as waves, sometimes as particles—depending on what kind of experiment you set up to look at them.

Suppose you have an ice bucket containing H20. You don’t know whether the water is in the form of liquid or ice cubes, and you’re not allowed to look into the bucket. So you try an experiment to find out. You grab a pair of tongs and stick them into the bucket, and out come ice cubes. But if you dip in a ladle, you get liquid water.

An obvious objection arises—that the bucket contains cubes floating in liquid. But you try another experiment—turning the bucket upside down. Some of the time, ice cubes fall out, with no liquid. But on other occasions only liquid water spills out. Water, like electrons, can’t seem to make up its mind about how to behave. Quantum physics seems to describe different possible realities, which is why quantum mechanics is like television.

Quantum Television

TV signals ride on invisible waves. Emanating from transmitter towers or bouncing off of satellites in orbit, those waves carry comedy, drama, sports, and news from around the world into your living room every moment of the day. But you can’t hear or see or smell these waves. TV’s sights and sounds are just possibilities, not fully real until you turn the TV on and bring one of those intangible prospects to life.

Physicists view the subatomic world of quantum physics in a similar way. Atoms and smaller particles flutter about as waves, vibrating not in ordinary space but in a twilight zone of different possibilities. An electron is not confined to a specific orbit about an atom’s nucleus, but buzzes around in a blur. The math describing that electron’s motion says not where it is, but all the places it might be. In other words, the electron is simultaneously in many places at once, or at least that is one way of interpreting what the math of quantum mechanics describes. You can think of it as an electron in a state of many possible realities. Only when it is observed does the electron assume one of its many possible locations, much the way punching the remote control makes one of the many possible TV shows appear on the screen.

Another way of interpreting the math is to say that the quantum description of nature is probabilistic—that is, a complete quantum description of a system tells nothing for certain, but only gives the odds that the system will be in one condition or another. If you turn the quantum ice bucket upside down, you can predict the odds that it will come out liquid or cubes—say, 7 times out of 10 cubes, 3 times out of 10 liquid. But you can’t predict for sure what the outcome will be for any one try.

In a similar probabilistic way, for something as simple as the position of an electron, quantum mechanics indicates the odds of finding the electron in any given place. Quantum physics has therefore radically changed the scientific view of reality. In the old days of classical physics, Newton’s clockwork universe, particles followed predictable paths, and the future was determined by the past. But in the description of physical reality based on quantum mechanics, objects are fuzzy waves. The object we know as something solid and tangible might show up here, might show up there. Quantum math predicts not one future, only the odds for various different futures.

This is clearly the way life is for atoms and electrons. You simply cannot say, or even calculate, where an electron is in an atom or where it will be. You can only give the odds of its being here or there. And it is not here or there until you look for it and make a measurement of its position. Only then do you get an answer, and all the other possibilities just disappear. This is a difficult point to grasp, but it needs to be clear. It’s not just a lack of knowing the electron’s real position. The electron does not have a real position until somebody (or something) measures it. That’s why there is no avoiding the Heisenberg uncertainty principle. You can’t measure an electron’s velocity or position, just a range of possibilities.

It’s this probabilistic aspect of quantum mechanics that makes quantum information so mysterious, and so rich. And it’s an important part of the reason why quantum information makes teleportation possible.

Quantum Information

Everyday life is full of examples of information carriers—the electromagnetic waves beaming radio and TV signals, electrons streaming along telephone and cable TV lines, even quaint forms of information like ink arranged to form words and pictures. But whatever its form, information can be measured by bits and therefore described using the 1s and 0s of computer language. Whether information comes in the form of ink on paper, magnetic patterns on floppy disks, or a picture worth 10,000 kilobytes, it can always be expressed as a string of Is and 0s. Each digit is a bit, or binary digit, representing a choice from two alternatives—like a series of answers to yes-no questions, or a list of the heads-or-tails outcomes of repeatedly tossing a coin.

Quantum information, on the other hand, is like a spinning coin that hasn’t landed. A quantum bit is not heads or tails, but a simultaneous mix of heads and tails. It is a much richer form of information than, say, Morse code, but it is also much more fragile. Quantum information cannot be observed without messing it up—just like you can’t see whether a coin is heads or tails while it is still in the air. Looking at quantum information destroys it. In fact, it is impossible to copy (or clone) a quantum object, since making a copy would require measuring the information, and measurement destroys.

So you could not fax a copy of a quantum object—sending the information it contains to a distant location and retaining a copy for yourself. But in teleportation, as Braunstein pointed out, the original does not remain behind. There is no copy, only a disintegration and then reconstruction of the original. Perhaps a quantum object could be moved from one location to another without the need to measure (and thereby destroy) the information it contains. And that is exactly the strategy that Charles Bennett described at the March 1993 physics meeting in Seattle.

Quantum Teleportation

At the meeting, Bennett presented the paper for an international team of collaborators.* They had produced an intricate scheme for teleporting a quantum object. More precisely, they figured out how to convey all the quantum information contained by a quantum object to a distant destination, without transporting the object itself. It was kind of like the quantum equivalent of sending the Encyclopaedia Britannica from New York to Los Angeles, leaving the bound volumes of paper in New York and having only the ink materialize on fresh paper in L.A. Accomplishing this trick requires the sophisticated application of quantum technicalities. But to keep it as simple as possible, think of a quantum object as carrying information by virtue of the way that it spins. Say in this case the object in question is a photon, a particle of light. When unobserved, the photon’s spin is a mix of multiple possibilities, like all those possible TV channel signals streaming through your living room. You could picture the photon as spinning around an axis pointing in many different directions. (It would be as if the Earth’s North Pole could point toward many different constellations at once. For the sake of navigators everywhere, it’s a good thing that such multiple quantum possibilities are not detectable in systems the size of a planet.)

Anyway, measuring the photon freezes its spin in one of those directions, or states, destroying all the other possibilities. The destruction of all those different possible spin directions means a lot of information gets lost. In other words, a pure photon contains information about many directions; a measured photon contains information about only one direction. The trick of teleportation is to communicate all the possibility information contained in a pure photon that has not yet been observed. In other words, you can use teleportation to send a message without knowing what the message is.

So suppose Bennett’s favorite scientist, Bob at IBM, wants to study a photon produced in Los Angeles. He wants Alice, his colleague at UCLA, to send him all the information about that pure photon’s condition. This request poses a serious challenge for Alice. If she so much as looks at that particle she will obliterate most of the information it contains. She needs to find a way of sending information about the particle’s pristine condition to Bob without herself knowing what that condition is. Clearly, this is a job for quantum teleportation.

Bennett and his colleagues reasoned that the quantum information of the pure photon could be teleported if Alice and Bob had prepared properly in advance. The preparation scheme requires an atom that will emit twin photons and a way to send one of those photons to Bob and the other to Alice. They then save these twins for later use. These photon twins have a peculiar property—one of them knows instantly if something happens to the

Reviews for The Bit and the Pendulum

[tgraettinger_1 · Rating: 4 out of 5 stars]

This book was recommended reading for "The Science of Information: From Language to Black Holes". It includes a pretty good description of the info theory resolution of Maxwell's Demon. It also introduced me to the concept of "Statistical Complexity", apparently created by James Crutchfield. Skimmed through most of the rest. It was well written, but not focused enough on info theory for my tastes.

[drardavis · Rating: 4 out of 5 stars]

This is a well written survey of “modern” physics, as opposed to the “classical” physics that I learned in college years ago. It is a good place to start before trying to catch up with what has been happening in the last fifteen years.