by Michio Kaku
In 1905 Einstein had shown that waves of light can have particle-like properties; that is, they can be described as packets of energy called photons. But by the 1920s it was becoming apparent to Schrödinger that the opposite was also true: that particles like electrons could exhibit wavelike behavior. This idea was first pointed out by French physicist Louis de Broglie, who won the Nobel Prize for this conjecture. (We demonstrate this to our undergraduate students at our university. We fire electrons inside a cathode ray tube, like those commonly found in TVs. The electrons pass through a tiny hole, so normally you would expect to see a tiny dot where the electrons hit the TV screen. Instead you find concentric, wavelike rings, which you would expect if a wave had passed through the hole, not a point particle.)
One day Schrödinger gave a lecture on this curious phenomenon. He was challenged by a fellow physicist, Peter Debye, who asked him: If electrons are described by waves, then what is their wave equation?
Ever since Newton created the calculus, physicists had been able to describe waves in terms of differential equations, so Schrödinger took Debye’s question as a challenge to write down the differential equation for electron waves. That month Schrödinger went on vacation, and when he came back he had that equation. So in the same way that Maxwell before him had taken the force fields of Faraday and extracted Maxwell’s equations for light, Schrödinger took the matter-waves of de Broglie and extracted Schrodinger’s equations for electrons.
(Historians of science have spent some effort trying to track down precisely what Schrödinger was doing when he discovered his celebrated equation that forever changed the landscape of modern physics and chemistry. Apparently, Schrödinger was a believer in free love and would often be accompanied on vacation by his mistresses and his wife. He even kept a detailed diary account of all his numerous lovers, with elaborate codes concerning each encounter. Historians now believe that he was in the Villa Herwig in the Alps with one of his girlfriends the weekend that he discovered his equation.)
When Schrödinger began to solve his equation for the hydrogen atom, he found, much to his surprise, the precise energy levels of hydrogen that had been carefully catalogued by previous physicists. He then realized that the old picture of the atom by Niels Bohr showing electrons whizzing around the nucleus (which is used even today in books and advertisements when trying to symbolize modern science) was actually wrong. These orbits would have to be replaced by waves surrounding the nucleus.
Schrödinger’s work sent shock waves, as well, through the physics community. Suddenly physicists were able to peer inside the atom itself, to examine in detail the waves that made up its electron shells, and to extract precise predictions for these energy levels that fit the data perfectly.
But there was still a nagging question that haunts physics even today. If the electron is described by a wave, then what is waving? This has been answered by physicist Max Born, who said that these waves are actually waves of probability. These waves tell you only the chance of finding a particular electron at any place and any time. In other words, the electron is a particle, but the probability of finding that particle is given by Schrödinger’s wave. The larger the wave, the greater the chance of finding the particle at that point.
With these developments, suddenly chance and probability were being introduced right into the heart of physics, which previously had given us precise predictions and detailed trajectories of particles, from planets to comets to cannon balls.
This uncertainty was finally codified by Heisenberg when he proposed the uncertainty principle, that is, the concept that you cannot know both the exact velocity and the position of an electron at the same time. Nor can you know its exact energy, measured over a given amount of time. At the quantum level all the basic laws of common sense are violated: electrons can disappear and reappear elsewhere, and electrons can be many places at the same time.
(Ironically, Einstein, the godfather of the quantum theory who helped to start the revolution in 1905, and Schrödinger, who gave us the wave equation, were horrified by the introduction of chance into fundamental physics. Einstein wrote, “Quantum mechanics calls for a great deal of respect. But some inner voice tells me that this is not the true Jacob. The theory offers a lot, but it hardly brings us any closer to the Old Man’s secret. For my part, at least, I am convinced that He doesn’t throw dice.”)
Heisenberg’s theory was revolutionary and controversial—but it worked. In one sweep, physicists could explain a vast number of puzzling phenomena, including the laws of chemistry. To impress my Ph.D. students with just how bizarre the quantum theory is, I sometimes ask them to calculate the probability that their atoms will suddenly dissolve and reappear on the other side of a brick wall. Such a teleportation event is impossible under Newtonian physics but is actually allowed under quantum mechanics. The answer, however, is that one would have to wait longer than the lifetime of the universe for this to occur. (If you used a computer to graph the Schrödinger wave of your own body, you would find that it very much resembles all the features of your body, except that the graph would be a bit fuzzy, with some of your waves oozing out in all directions. Some of your waves would extend even as far as the distant stars. So there is a very tiny probability that one day you might wake up on a distant planet.)
The fact that electrons can seemingly be many places at the same time forms the very basis of chemistry. We know that electrons circle around the nucleus of an atom, like a miniature solar system. But atoms and solar systems are quite different; if two solar systems collide in outer space, the solar systems break apart and planets are flung into deep space. Yet when atoms collide they often form molecules that are perfectly stable, sharing electrons between them. In high school chemistry class the teacher often represents this with a “smeared electron,” which resembles a football, connecting the two atoms together.
But what chemistry teachers rarely tell their students is that the electron is not “smeared” between two atoms at all. This “football” actually represents the probability that the electron is in many places at the same time within the football. In other words, all of chemistry, which explains the molecules inside our bodies, is based on the idea that electrons can be many places at the same time, and it is this sharing of electrons between two atoms that holds the molecules of our body together. Without the quantum theory, our molecules and atoms would dissolve instantly.
This peculiar but profound property of the quantum theory (that there is a finite probability that even the most bizarre events may happen) was exploited by Douglas Adams in his hilarious novel The Hitchhiker’s Guide to the Galaxy. He needed a convenient way to whiz through the galaxy, so he invented the Infinite Improbability Drive, “a wonderful new method of crossing vast interstellar distances in a mere nothingth of a second, without all that tedious mucking around in hyperspace.” His machine enables you to change the odds of any quantum event at will, so that even highly improbable events become commonplace. So if you want to jet off to the nearest star system, you would simply change the probability that you will rematerialize on that star, and voilà! You would be instantly teleported there.
In reality the quantum “jumps” so common inside the atom cannot be easily generalized to large objects such as people, which contain trillions upon trillions of atoms. Even if the electrons in our body are dancing and jumping in their fantastic journey around the nucleus, there are so many of them that their motions average out. That is, roughly speaking, why at our level substances seem solid and permanent.
So while teleportation is allowed at the atomic level, one would have to wait longer than the lifetime of the universe to actually witness these bizarre effects on a macroscopic scale. But can one use the laws of the quantum theory to create a machine to teleport something on demand, as in science fiction stories? Surprisingly, the answer is a qualified yes.
THE EPR EXPERIMENT
The key to quantum teleportation lies in a celebrated 1935 paper by Albert Einstein
and his colleagues Boris Podolsky and Nathan Rosen, who, ironically, proposed the EPR experiment (named for the three authors) to kill off, once and for all, the introduction of probability into physics. (Bemoaning the undeniable experimental successes of the quantum theory, Einstein wrote, “the more success the quantum theory has, the sillier it looks.”)
If two electrons are initially vibrating in unison (a state called coherence) they can remain in wavelike synchronization even if they are separated by a large distance. Although the two electrons may be separated by light-years, there is still an invisible Schrödinger wave connecting both of them, like an umbilical cord. If something happens to one electron, then some of that information is immediately transmitted to the other. This is called “quantum entanglement,” the concept that particles vibrating in coherence have some kind of deep connection linking them together.
Let’s start with two coherent electrons oscillating in unison. Next, let them go flying out in opposite directions. Each electron is like a spinning top. The spins of each electron can be pointed up or down. Let’s say that the total spin of the system is zero, so that if the spin of one electron is up, then you know automatically that the spin of the other electron is down. According to the quantum theory, before you make a measurement, the electron is spinning neither up nor down but exists in a nether state where it is spinning both up and down simultaneously. (Once you make an observation, the wave function “collapses,” leaving a particle in a definite state.)
Next, measure the spin of one electron. It is, say, spinning up. Then you know instantly that the spin of the other electron is down. Even if the electrons are separated by many light-years, you instantly know the spin of the second electron as soon as you measure the spin of the first electron. In fact, you know this faster than the speed of light! Because these two electrons are “entangled,” that is, their wave functions beat in unison, their wave functions are connected by an invisible “thread” or umbilical cord. Whatever happens to one automatically has an effect on the other. (This means, in some sense, that what happens to us automatically affects things instantaneously in distant corners of the universe, since our wave functions were probably entangled at the beginning of time. In some sense there is a web of entanglement that connects distant corners of the universe, including us.) Einstein derisively called this “spooky-action-at-distance,” and this phenomenon enabled him to “prove” that the quantum theory was wrong, in his mind, since nothing can travel faster than the speed of light.
Originally, Einstein designed the EPR experiment to serve as the death knell of the quantum theory. But in the 1980s Alan Aspect and his colleagues in France performed this experiment with two detectors separated by 13 meters, measuring the spins of photons emitted from calcium atoms, and the results agreed precisely with the quantum theory. Apparently God does play dice with the universe.
Did information really travel faster than light? Was Einstein wrong about the speed of light being the speed limit of the universe? Not really. Information did travel faster than the speed of light, but the information was random, and hence useless. You cannot send a real message, or Morse code, via the EPR experiment even if information is traveling faster than light.
Knowing that an electron on the other side of the universe is spinning down is useless information. You cannot send today’s stock quotations via this method. For example, let’s say that a friend always wears one red and one green sock, in random order. Let’s say you examine one leg, and the leg has a red sock on it. Then you know, faster than the speed of light, that the other sock is green. Information actually traveled faster than light, but this information is useless. No signal containing nonrandom information can be sent via this method.
For years the EPR experiment was used as an example of the resounding victory of the quantum theory over its critics, but it was a hollow victory with no practical consequences. Until now.
QUANTUM TELEPORTATION
Everything changed in 1993, when scientists at IBM, led by Charles Bennett, showed that it was physically possible to teleport objects, at least at the atomic level, using the EPR experiment. (More precisely, they showed that you could teleport all the information contained within a particle.) Since then physicists have been able to teleport photons and even entire cesium atoms. Within a few decades scientists may be able to teleport the first DNA molecule and virus.
Quantum teleportation exploits some of the more bizarre properties of the EPR experiment. In these teleportation experiments physicists start with two atoms, A and C. Let’s say we wish to teleport information from atom A to atom C. We begin by introducing a third atom, B, which starts out being entangled with C, so B and C are coherent. Now atom A comes in contact with atom B. A scans B, so that the information content of atom A is transferred to atom B. A and B become entangled in the process. But since B and C were originally entangled, the information within A has now been transferred to atom C. In conclusion, atom A has now been teleported into atom C, that is, the information content of A is now identical to that of C.
Notice that the information within atom A has been destroyed (so we don’t have two copies after the teleportation). This means that anyone being hypothetically teleported would die in the process. But the information content of his body would appear elsewhere. Notice also that atom A did not move to the position of atom C. On the contrary, it is the information within A (e.g., its spin and polarization) that has been transferred to C. (This does not mean that atom A was dissolved and then zapped to another location. It means that the information content of atom A has been transferred to another atom, C.)
Since the original announcement of this breakthrough, progress has been fiercely competitive as different groups have attempted to outrace each other. The first historic demonstration of quantum teleportation in which photons of ultraviolet light were teleported occurred in 1997 at the University of Innsbruck. This was followed the next year by experimenters at Cal Tech who did an even more precise experiment involving teleporting photons.
In 2004 physicists at the University of Vienna were able to teleport particles of light over a distance of 600 meters beneath the River Danube, using a fiber-optic cable, setting a new record. (The cable itself was 800 meters long and was strung underneath the public sewer system beneath the River Danube. The sender stood on one side of the river, and the receiver was on the other.)
One criticism of these experiments is that they were conducted with photons of light. This is hardly the stuff of science fiction. It was significant, therefore, in 2004, when quantum teleportation was demonstrated not with photons of light, but with actual atoms, bringing us a step closer to a more realistic teleportation device. The physicists at the National Institute of Standards and Technology in Washington, D.C., successfully entangled three beryllium atoms and transferred the properties of one atom into another. This achievement was so significant that it made the cover of Nature magazine. Another group was able to teleport calcium atoms as well.
In 2006 yet another spectacular advance was made, for the first time involving a macroscopic object. Physicists at the Niels Bohr Institute in Copenhagen and the Max Planck Institute in Germany were able to entangle a light beam with a gas of cesium atoms, a feat involving trillions upon trillions of atoms. Then they encoded information contained inside laser pulses and were able to teleport this information to the cesium atoms over a distance of about half a yard. “For the first time,” said Eugene Polzik, one of the researchers, quantum teleportation “has been achieved between light—the carrier of information—and atoms.”
TELEPORTATION WITHOUT ENTANGLEMENT
Progress in teleportation is rapidly accelerating. In 2007 yet another breakthrough was made. Physicists proposed a teleportation method that does not require entanglement. We recall that entanglement is the single most difficult feature of quantum teleportation. Solving this problem could open up new vistas in teleportation.
“We’re talking about a beam of about 5,000 particl
es disappearing from one place and appearing somewhere else,” says physicist Aston Bradley of the Australian Research Council Centre of Excellence for Quantum Atom Optics in Brisbane, Australia, who helped pioneer a new method of teleportation.
“We feel that our scheme is closer in spirit to the original fictional concept,” he claims. In their approach, he and his colleagues take a beam of rubidium atoms, convert all its information into a beam of light, send this beam of light across a fiber-optic cable, and then reconstruct the original beam of atoms in a distant location. If his claim holds up, this method would eliminate the number one stumbling block to teleportation and open up entirely new ways to teleport increasingly large objects.
In order to distinguish this new method from quantum teleportation, Dr. Bradley has called his method “classical teleportation.” (This is a bit misleading, since his method also depends heavily on the quantum theory, but not on entanglement.)
The key to this novel type of teleportation is a new state of matter called a “Bose Einstein condensate,” or BEC, which is one of the coldest substances in the entire universe. In nature the coldest temperature is found in outer space; it is 3 K above absolute zero. (This is due to residual heat left over from the big bang, which still fills up the universe.) But a BEC is a millionth to a billionth of a degree above absolute zero, a temperature that can be found only in the laboratory.
When certain forms of matter are cooled down to near absolute zero, their atoms all tumble down to the lowest energy state, so that all their atoms vibrate in unison, becoming coherent. The wave functions of all the atoms overlap, so that, in some sense, a BEC is like a gigantic “super atom,” with all the individual atoms vibrating in unison. This bizarre state of matter was predicted by Einstein and Satyendranath Bose in 1925, but it would be another seventy years, not until 1995, before a BEC was finally created in the lab at MIT and the University of Colorado.
