Science Matters

by Robert M. Hazen

  There is a useful analogy that will help you think about measurement in the quantum domain. Suppose there was a long, dark tunnel in a mountain and you wanted to know whether there was a car in the tunnel. Suppose further that you couldn’t go into the tunnel yourself or shine a light down it—that the only way you could answer your question was to send another car down that tunnel and then listen for a crash. If you heard a crash, you could certainly say that there was another car in the tunnel. You couldn’t say, however, that the car was the same after your “measurement” as it was before. The very act of measuring—in this case the collision of one car with the other—changes the original car. If you then sent another car down the tunnel to make a second measurement, you would no longer be measuring the original car, but the original car as it has been altered by the first measurement.

  In the same way, the fact that to make a measurement on an electron requires the same sort of disruptive interaction means that the electron (or any other quantum particle) must be changed whenever it is measured. This simple fact is the basis for the uncertainty principle and, in the end, for many of the differences that exist between the familiar world and the world of the quantum.

  The uncertainty principle is a statement that says, in effect, that the changes caused by the act of measurement make it impossible to know everything about a quantum particle with infinite precision. It says, for example, that you cannot know both the position (where something is) and velocity (how fast it’s moving) exactly—the two pieces of data that are significant in describing any physical object.

  The important thing about the uncertainty principle is that if you measure the position of a tiny particle with more and more precision, so that the error becomes smaller and smaller, the uncertainty in velocity must become greater to compensate. The more care you take to know one thing, the more poorly you know the other. The very act of measuring changes the thing you are measuring, so you must always be uncertain about something.

  THE WAVE FUNCTION

  The fact that one cannot measure a quantum system without changing it leads to an extremely important conclusion about the way that such systems must be described. Suppose that large objects, like airplanes, behaved the way electrons do. Suppose you knew that an airplane was flying somewhere in the Midwest and you wanted to predict where it would be a few hours later. Because of the uncertainty principle, you couldn’t know both where the plane was and how fast it was going, and you’d have to make some compromise. You might, for example, locate the plane to within 50 miles and its velocity to within 100 miles per hour.

  If you now ask where the plane will be in two hours, the only answer you can give is, “It depends.” If the plane is traveling 500 miles per hour, it will be 1,000 miles away; if it’s traveling 400 miles per hour, it will be only 800 miles away. And since we don’t know exactly where the plane started, there is an additional uncertainty about its final location.

  One way to deal with this problem is to describe the final location of the plane in terms of probabilities: there’s a 30 percent chance it will be in Pittsburgh, a 20 percent chance it will be in New York, and so on. You could, in fact, draw a graph that would show the probable location of the plane at any point east of the Mississippi. For historical reasons, a collection of probabilities like this is called the “wave function” of the plane.

  We normally don’t worry about wave function for airplanes, because in the everyday world the amount of change caused by a measurement is so small as to be negligible, so the uncertainties in the plane’s position and speed are tiny. In the quantum world, however, every measurement causes appreciable change in the object being measured, and hence everything has to be described in terms of probabilities and wave functions. It was this unpredictable aspect of the quantum world that troubled Albert Einstein and caused him to remark that “God does not play dice with the universe.” (His old friend Niels Bohr is supposed to have replied, “Albert, stop telling God what to do.”)

  WAVES OR PARTICLES?

  We all run into trouble when we try to visualize a quantum object like an electron. Our inventory of mental images is limited to the sorts of things we can see in our familiar world, and unfortunately, electrons just don’t fit anywhere on our mental file cards. Nowhere is this problem of visualization more difficult than in discussion of particles and waves in the quantum world.

  In our normal world, energy can be transferred by particle or by wave, as you can see by thinking about a bowling alley. Suppose there was one pin standing at the other end and you wanted to knock it down. You would have to apply energy to the pin to do this, of course, and might choose to expend some energy to get a bowling ball moving, and then let the ball roll down the alley and knock the pin over. This process involves a particle—the bowling ball—carrying energy from you to the pin. Alternatively, you could set up a line of pins and then knock the first one over. It would knock over the second, which would knock over the third, and so on like dominoes until the final pin fell. In this case, the energy would be transmitted by the wave of falling pins, and no single object travels from you to your target.

  When scientists started to explore the subatomic world, they naturally asked, “Are electrons particles or are they waves?” After all, an electron transfers energy, and if energy can be transferred only by particles and waves, then the electron must be one or the other.

  Unfortunately, things aren’t that simple. Experiments performed on electrons have found that in some situations they seem to act as particles, in other situations as waves. Similarly, something we normally consider to be a wave—light, for example—can appear to be a particle under certain circumstances. In the early years of the twentieth century, this seemingly inexplicable behavior was called “wave-particle duality” and was supposed to illustrate the strangeness of the quantum world.

  There is, however, nothing particularly mysterious about “duality.” The behavior of electrons and light simply tells us that in the quantum world, our familiar categories of “wave” and “particle” do not apply. The electron is not a wave, and it’s not a particle—it’s something else entirely. Depending on the experiment we do, we can see wave-like or particle-like behavior. The wave-particle problem lies not with nature, but with our own minds.

  Suppose you were a Martian who, for some reason or other, had been able to pick up radio broadcasts from Earth only in the French and German languages. You might very well come up with a theory that every language on Earth was either French or German. Suppose then that you came to Earth and landed in the middle of an American city. You hear English for the first time, and you note that some of the words are like French and some are like German. You would have no problem if you realized that there was a third type of language of which you had been previously ignorant, but you could easily tie yourself in philosophical knots if you didn’t. You might even develop a theory of “French-German duality” to explain the new phenomenon.

  In the same way, as long as we are willing to accept that things at the atomic level are not like things in our everyday world, no problem arises with the question of whether things are waves or particles. The correct answer to the wave-particle question is simply “none of the above.”

  Of course, this means that we cannot visualize what an electron is like—we can’t draw a picture of it. For creatures as wedded to visual imagery as we are, this is deeply troubling. Physicists and nonphysicists alike rebel and try to make mental images, whether they are “real” or not. The authors are no different, and, for the record, we imagine the electron as something like a tidal wave, located in one general area, like a particle, but with crests and troughs, like a wave.

  The length of the “tidal wave” associated with different kinds of particles varies tremendously. That of an electron, for example, is smaller than that of an atom, while a photon of ordinary visible light is about three feet long. Viewed this way, both “waves” like light and “particles” like electrons have the same basic structur
e. The distinction in classical physics between wave and particle turns out to be a meaningless distinction in the quantum world.

  THE ATOM—QUANTUM

  MECHANICS IN ACTION

  The most important role quantum mechanics plays in science is explaining how the atom is put together. In the last chapter we described the peculiar property of electrons in the Bohr atom to adopt fixed orbits. These fixed orbits are a consequence of quantized electron energies. Electrons can only have certain precise energies, and any quantum leap between orbits must correspond exactly to the difference in orbital energies. Each quantum leap by one electron leads to the absorption or the production of one photon.

  Electrons moving up and down in their orbits are analogous to a person moving up and down a staircase: It requires energy to climb, and energy is released upon descent. And, like a person on a staircase, an electron cannot be found between “steps”—in other words, it can be found only in allowed orbits.

  Although it is tempting to think of electrons in orbits as particles, little lumps of matter, scientists often picture them in terms of their wave functions. The peak in the electron “wave,” corresponding to the highest probability of finding the electron, is at the place where the electron would be located if we pictured it as a particle.

  Lasers

  From grocery lines to rock concerts, compact discs to the most advanced weaponry, lasers pervade our world and have changed the ways we use light.

  “Laser” is an acronym for Light Amplification by Stimulated Emission of Radiation, an imposing name for a remarkable de vice. Lasers work like this: You start off with a collection of atoms, each with an electron in a high-energy orbit. The chromium atoms in crystals of ruby serve this function in many red lasers. Photons with exactly the same energy as the excited electrons are focused on those special atoms. When one of these photons comes near an atom it “stimulates” the electron in the atom to jump down, emitting another photon in the process—one that is not only of the same wavelength as the original, but is precisely aligned, crest to crest, trough to trough. The two photons now pass through the material, stimulating other atoms until a flood of precisely aligned photons results. In this way, one photon “amplifies” itself.

  The energy needed to get the atoms into an excited state in the first place, and to get them to go back to it after they have emitted a photon, can be added to the system in many ways. Typically, scientists “pump” a laser by subjecting the material to heat, to a beam of energetic electrons, or to a bright light, from something like a flashbulb or even another laser.

  Two precisely aligned mirrors at each end of the laser material cause the photons to move back and forth millions of times. Engineers design laser mirrors to allow a small fraction (maybe 5 percent) of the photons to escape on each bounce, and these leftover photons form the laser beam.

  QUANTUM ENTANGLEMENT

  In the 1930s, Albert Einstein proposed a paradox that, to him, illustrated the fact that quantum mechanics, with its emphasis on probabilistic interpretations, could not possibly be the correct way to describe the subatomic world. His thought experiment was very simple: Suppose an atom emitted two particles back to back, and suppose further that we know that if one particle is spinning clockwise, the other must be spinning counterclockwise. If we write the wave function for either particle, it would be a combination of probabilities for these two directions of spin. The rules of quantum mechanics say that we have to describe the particles this way—each particle can have either spin until we make a measurement.

  Einstein pointed out, however, that if we waited until the particles were far apart from each other—too far to allow a light signal to get from one to the other—and measured the spin of one particle, then we would know the spin of the other. In other words, measuring the spin of one particle would determine the spin of the other, even though no signal could pass between the two and no measurement was made on the second one. He regarded this as proof that quantum mechanics could not be the final theory of matter.

  This proposal led to a strange series of events. In 1964, the Irish physicist John Bell proved a theorem that showed that there were certain experiments that would show unequivocally whether Einstein was right or not, and in the 1970s those experiments were done, showing that in spite of the apparent paradox, quantum mechanics was right. It was about this time that the term “quantum weirdness” was born.

  Today we understand that if two particles interact at some point in time (such as Einstein’s two emitted particles), then their wave functions are never really separate from each other. Scientists use the term “quantum entanglement” to describe this phenomenon. Because of quantum entanglement, we can’t measure only one of the particles in the pair—the measurement will always involve both. In the language of theoretical physics, we now understand that quantum mechanics, unlike ordinary Newtonian mechanics, is not a “local” theory, and that some quantum particles can never be separated from each other, no matter how far apart they are.

  FRONTIERS

  Quantum Teleportation

  As strange as it may seem, quantum entanglement has not only been verified in the laboratory, but is being developed for a number of practical applications, of which quantum teleportation is one. It works this way: Imagine that you have a pair of entangled particles—call them photons, just for the sake of definiteness. Suppose further that you give each member of the pair to a different person. Traditionally, these people are called Alice and Bob, a joking reference to a 1970s movie titled Bob and Carol and Ted and Alice.

  Now suppose that Alice takes another photon—call it the test photon—and lets it interact with her member of the entangled pair. She can then tell Bob what the result of that measurement was (a phone call will do), and Bob can then re-create the test photon in his laboratory using his member of the entangled pair. Thus, the test photon was destroyed (or at least changed) in Alice’s lab and an identical photon was created in Bob’s. We say that the photon was teleported to emphasize that no photon ever traveled directly from Alice to Bob.

  In 1997, physicist Anton Zeilinger of the University of Vienna used this technique to teleport the first visual image. (It was a photograph of the Venus of Willendorf, a stone age fertility statue found in Austria.)

  Entanglement may also turn out to be an important phenomenon in the area of cryptography. If you think about the situation of Bob and Alice described above, you realize that it is absolutely secure. It would do an eavesdropper no good to intercept the call from Alice to Bob, because without one of the entangled photons he could not reconstruct Alice’s test photon. Furthermore, if he tried to intercept an entangled photon, the uncertainty principle guarantees that he would have to change it in the process, which would be readily detectable. Thus, quantum entanglement holds the prospect of serving as the basis for absolutely secure communications.

  Quantum Computing

  One way of thinking about a particle described by a wave function is to imagine that the particle is actually in all possible states simultaneously. (In technical jargon, we say that the wave function is a “superposition of all possible states.”) The key idea behind the new field of quantum computing is that if we let each of those superposed states perform a part of a calculation and add everything up at the end, we will have a system capable of doing calculations much more rapidly than they could be done in a conventional machine.

  Think of this analogy: One way of reading a page of this book would be to give one sentence each to a series of readers, then assemble the output from those readers at the end of the process. This would clearly take less time than having one reader go through the page sentence by sentence. In the same way, the hope of people trying to develop a quantum computer is that the states involved in the superposition will play the same role as the readers in our analogy, producing computers of unparalleled power.

  We do not have a working quantum computer at this point, but scientists have succeeded in building parts of such a machine
(what are called logic gates) and have hopes of proceeding farther in the future.

  CHAPTER SIX

  Chemical Bonding

  NOTHING Beats Margees Pennsylvania applesauce bread.

  2 cups all-purpose flour

  ¾ cup sugar

  1 teaspoon baking powder

  1 teaspoon baking soda

  1 teaspoon cinnamon

  ½ teaspoon nutmeg

  1 teaspoon vanilla

  ½ cup shortening

  1 cup applesauce

  2 eggs

  Combine all ingredients in large mixing bowl. Beat at medium speed until well blended. Grease a 9“x 5” loaf pan on the bottom only, and pour in mixture. Bake at 350°F for 55 to 60 minutes, until a toothpick comes out clean. Loosen the edges with a spatula and remove from the pan. Cool before slicing.

  Scientists like to cook up new recipes. Early in 1986 two scientists made history (and won the Nobel Prize) by mixing and grinding ordinary elements like copper, oxygen, and a couple of others in just the right proportions, and baking them at just the right temperature just long enough to produce a nondescript black wafer about the size of an aspirin tablet. That little black disk turned out to be the first of an entirely new kind of superconductor, a material with extraordinarily valuable electrical properties.

  How is it possible that ingredients as different as flour, eggs, salt, and applesauce can combine to form a delicious loaf of bread? How can commonplace elements as different as copper and oxygen become a priceless black disk? The answer lies in the atoms—the building blocks of everything around us. Atoms combine in countless ways to form materials with every imaginable property. But in every case: