The God Particle

by Leon Lederman

  Now in principle the same experiment can be carried out with electrons. In a way this is what Davisson did at Bell Labs. Using electrons, the experiment also results in an interference pattern. The screen is covered with tiny Geiger counters, which click when an electron hits. The Geiger counter detects particles. To check that the counters are working, we put a thick piece of lead over slit two: no electrons can penetrate. Now all Geiger counters click if we wait long enough for some thousands of electrons to pass through the remaining open slit. But when two slits are open, some columns of Geiger counters never click!

  Wait a minute. Hold it. When one slit is closed, the electrons, squirting through the other slit, spread out, some going to the left, some straight, some to the right, causing a roughly uniform pattern of clicks across the screen, just as Young's yellow light resulted in a broad bright line in his one-slit experiment. In other words, the electrons behave, logically enough, like particles. But if we remove the lead and let some of the electrons go through slit two, the pattern changes and no electrons reach those columns of Geiger counters corresponding to the dark fringe locations. Now the electrons are acting like waves. Yet we know they are particles because the counters are clicking.

  Maybe, you might argue, two or more electrons are passing simultaneously through the slits and simulating a wave interference pattern. To verify that no two electrons are passing simultaneously through the slits, we reduce the rate of electrons to one per minute. Same patterns. Conclusion: electrons going through slit one "know" that slit two is open or closed because they change their patterns in each case.

  How do we come up with this idea of "smart" electrons? Put yourself in the place of the experimenter. You have an electron gun, so you know you're shooting particles at the slits. You also know that you end up with particles at the destination, the screen, because the Geiger counters click. A click means particle. So, whether we have one slit or two slits open, we begin and end with particles. However; where the particles land depends on whether one or two slits are open. So a particle going through slit one seems to know whether slit two is open or closed, because it appears to change its path depending on that information. If slit two is closed, it says to itself, "Okay, I can land anywhere on the screen." If slit two is open, it says, "Uh-oh, I have to avoid certain bands on the screen in order to create a fringe pattern." Since particles can't "know," our wave-particle ambiguity has created a logical crisis.

  Quantum mechanics says we can predict the probability of the electrons' passage through slits and subsequent arrival at the screen. The probability is a wave, and waves exhibit two-slit interference patterns. When both slits are open, the xy probability waves can interfere to result in zero probability (y = 0) at certain places on the screen. The anthropomorphic complaint of the previous paragraph is a classical hangover; in the quantum world, "How does the electron know which slit to go through?" is not a question that can be answered by measurement. The detailed point-by-point trajectory of the electron is not being observed, and therefore the question "Which slit did the electron go through?" is not an operational question. Heisenberg's uncertainty relations also solve our hangup by pointing out that if you try to measure the electron's trajectory between the electron gun and the wall, you totally change the motion of the electron and destroy the experiment. We can know the initial conditions (electron fired from gun); we can know the results (electron hits some position on screen); we cannot know the path from A to B unless we are prepared to screw up the experiment. This is the spooky nature of the new world in the atom.

  The quantum mechanics solution, that is, Don't worry! We can't measure it, is logical enough, but not satisfying to most human minds, which strive to understand the details of the world around us. For some tortured souls, this quantum unknowability is still too high a price to pay. Our defense: this is the only theory we know now that works.

  NEWTON VS. Schrödinger

  A new intuition must be cultivated. We spend years teaching physics students classical physics, then turn around and teach them quantum theory. It takes graduate students two or more years to develop quantum intuition. (You, lucky reader are expected to perform this pirouette in the space of just one chapter.)

  The obvious question is, which is correct? Newton's theory or Schrödinger's? The envelope, please. And the winner is ... Schrödinger! Newton's physics was developed for big things; it doesn't work inside the atom. Schrödinger's theory was designed for micro-phenomena. Yet when the Schrödinger equation is applied to macroscopic situations it gives results identical to Newton's.

  Let's look at a classic example. The earth orbits the sun. An electron orbits—to use the old Bohr language—a nucleus. The electron, however, is constrained to specific orbits. Are there only certain allowable quantum orbits for the planet earth around the sun? Newton would say no, the planet can orbit wherever it wants. But the correct answer is yes. We can apply the Schrödinger equation to the earth-sun system. Schrödinger's equation would give the usual discrete set of orbits, but there would be a huge number of them. In using the equation, you'd plug the mass of the earth (instead of the mass of the electron) into the denominator, so the orbital spacings out where the earth is, say, 93 million miles from the sun, would end up so small—say, one every billionth of a billionth of an inch—as to be in effect continuous. For all practical purposes, you end up with the Newtonian result that all orbits are allowed. When you take the Schrödinger equation and apply it to macro objects, it changes in front of your very eyes to... F = ma! Or thereabouts. It was Roger Boscovich, by the way, in the eighteenth century who surmised that Newton's formulas were simply approximations that were good over large distances but wouldn't survive in the microworld. So our graduate students do not have to discard their mechanics books. They may get a job with NASA or the Chicago Cubs, plotting rocket reentry trajectories or pop-ups with good old Newtonian equations.

  In quantum theory, the concept of orbits, or of what the electron is doing in the atom or in a beam, is not useful. What matters is the result of a measurement, and here quantum methods can only predict the probability of any possible result. If you measure where the electron is, say in the hydrogen atom, your result could be a number, the distance of the electron from the nucleus. You do this, not by measuring a single electron but by repeating the measurement many times. You get a different result each time, and finally you draw a curve graphing all the results. It is this graph that can be compared to the theory. The theory cannot predict the result of any given measurement. It is a statistical thing. Going back to my cloth-cutter analogy, if we know that the average height of freshmen at the University of Chicago is 5 foot 7, the next new freshman might still be 5 foot 3 or 6 foot 1. We cannot predict the height of the next freshman; we can only draw a kind of actuarial curve.

  Where it gets spooky is in predictions of a particle's passage through a barrier or the decay time of a radioactive atom. We prepare an identical setup many times. We shoot a 5.00 MeV electron at a 5.50 MeV potential barrier. We predict that 45 times out of 100 it will penetrate. But we can't ever be sure what a given electron will do. One gets through; the next one, identical in every way, does not. Identical experiments have different results. That's the quantum world. In classical science we stress the importance of replicating experiments. In the quantum world, we can replicate everything except the result.

  In the same way, take the neutron, which has a "half-life" of 10.3 minutes, meaning that if you start with 1,000 neutrons, half have disintegrated in 10.3 minutes. But a given neutron? It can decay in 3 seconds or 29 minutes. Its exact time of decay is unpredictable. Einstein hated this idea. "God does not play dice with the universe," he said. Other critics said, suppose there is, in each neutron or each electron, some mechanism, some spring, some "hidden variable" that makes each neutron different, like human beings, who also have an average lifetime. In the case of humans, there are plenty of not-so-hidden things—genes, clogged arteries, and so on—which in principle can b
e used to predict an individual's day of demise, barring falling elevators, disastrous love affairs, or an out-of-control Mercedes.

  The hidden-variable hypothesis has been essentially disproven for two reasons: no such variables have shown up in all the billions of experiments done on electrons and new, improved theories related to quantum-mechanics experiments have ruled them out.

  THREE THINGS TO REMEMBER ABOUT QUANTUM MECHANICS

  Quantum mechanics can be said to have three remarkable qualities: (1) it is counterintuitive; (2) it works; and (3) it has aspects that made it unacceptable to the likes of Einstein and Schrödinger and that have made it a source of continuing study in the 1990s. Let's touch on each of these.

  1. It is counterintuitive. Quantum mechanics replaces continuity with discreteness. Metaphorically, instead of a liquid being poured into the glass, it is very fine sand. The smooth hum you hear is the beating of huge numbers of atoms on your eardrums. Then there is the spookiness of the double-slit experiment, already discussed.

  Another counterintuitive phenomena is "tunneling." We talked about sending electrons toward an energy barrier. The classical analogue is rolling a ball up a hill. If you give the ball enough initial push (energy), it will go over the top. If the initial energy is too low, the ball will come back down. Or picture a roller coaster with the car stuck in a trough between two terrifying rises. Suppose the car rolls halfway up one rise and loses power. It will slide back down, then almost halfway up the other side, then oscillate back and forth, trapped in the trough. If we could remove friction, the car would oscillate forever, imprisoned between the two insurmountable rises. In quantum atomic theory such a system is known as a bound state. However, our description of what happens to electrons aimed at an energy barrier or an electron trapped between two barriers must include probabilistic waves. It turns out that some of the wave can "leak" through the barrier (in atomic or nuclear systems the barrier is either an electrical or a strong force), and therefore there is a finite probability that the trapped particle will appear outside the trap. This was not only counterintuitive, it was considered a major paradox, since the electron on its way through the barrier would have negative kinetic energy—a classical absurdity. But with evolving quantum intuition one responds that the condition of the electron "in the tunnel" is not observable and therefore not a question for physics. What one does observe is that it does get out. This phenomenon, called tunneling, was used to explain alpha-radioactivity. It is the basis of an important solid state electronic device known as a tunnel diode. Spooky as it is, this tunnel effect is essential to modern computers and other electronic devices.

  Point particles, tunneling, radioactivity, double slit anguish—all of these contributed to the new intuitions that quantum physicists needed as they fanned out in the late 1920s and '30s with their new intellectual armaments to seek unexplained phenomena.

  2. It works. As a result of the events of 1923–1927, the atom was understood. Even so, in those pre-computer days, only simple atoms—hydrogen, helium, lithium, and atoms in which some electrons are removed (ionized)—could be properly analyzed. A breakthrough was made by Wolfgang Pauli, one of the wunderkinder, who understood the theory of relativity at the age of nineteen and became the "enfant terrible" of physics as an elder statesman.

  A digression on Pauli is unavoidable at this point. Noted for his high standards and irascibility, Pauli was the conscience of physics in his time. Or was he just candid? Abraham Pais reports that Pauli once complained to him that he had trouble finding a challenging problem to work on: "Perhaps it's because I know too much." Not a brag, just a statement of fact. You can imagine that he was tough on assistants. When one new young assistant, Victor Weisskopf, a future leading theorist, reported to him at Zurich, Pauli looked Weisskopf over, shook his head, and muttered, "Ach, so young and already you are unknown." After some months, Weisskopf presented Pauli with a theoretical effort. Pauli took one glance and said, "Ach, that isn't even wrong!" To one postdoc he said, "I don't mind your thinking slowly. I mind your publishing faster than you think." No one was safe from Pauli. In recommending a fellow to be assistant to Einstein, who was, in his later years, deep into the mathematical exotica of his fruitless quest for a unified field theory, Pauli wrote: "Dear Einstein, This student is good, but he does not clearly grasp the difference between mathematics and physics. On the other hand, you, dear Master; have long lost this distinction." That's our boy Wolfgang.

  In 1924 Pauli proposed a fundamental principle that explained the Mendeleev periodic table of the elements. The problem: we build up the atoms of the heavier chemical elements by adding positive charge to the nucleus and electrons to the various allowed energy states of the atom (orbits, in the old quantum theory). Where do the electrons go? Pauli announced what has become known as the Pauli exclusion principle: no two electrons can occupy the same quantum state. Originally an inspired guess, the principle turned out to be a consequence of a deep and lovely symmetry.

  Let's see how Santa, in his workshop, makes the chemical elements. He has to do this right because he works for Her, and She is tough. Hydrogen is easy. He takes one proton—the nucleus. He adds an electron, which occupies the lowest possible energy state—in the old Bohr theory (which is still useful pictorially) the orbit with the smallest allowed radius. Santa doesn't have to be careful; he just drops the electron anywhere near the proton and it "jumps" eventually to this lowest "ground" state, emitting photons on the way. Now helium. He assembles the helium nucleus, which has two plus charges. So he needs to drop in two electrons. And with lithium it takes three electrons to form the electrically neutral atom. The issue is, where do these electrons go? In the quantum world, only certain states are allowed. Do they all crowd into the ground state, three, four, five ... electrons? This is where the Pauli principle comes in. No, says Pauli, no two electrons can be in the same quantum state. In helium, the second electron is allowed to join the first electron in the lowest energy state only if it spins in the opposite sense to its partner. When we add the third electron, for the lithium atom, it is excluded from the lowest energy level and must go into the next lowest level. This turns out to have a much larger radius (again a la Bohr theory), thus accounting for lithium's chemical activity—namely, the ease with which it can use this lone electron to combine with other atoms. After lithium we have the four-electron atom, beryllium, in which the fourth electron joins the third in its "shell," as the energy levels are called.

  As we proceed merrily along—beryllium, boron, carbon, nitrogen, oxygen, neon—we add electrons until each shell is filled. No more in that shell, says Pauli. Start a new one. Briefly, the regularity of chemical properties and behaviors all comes out of this quantum buildup via the Pauli principle. Decades earlier, scientists had derided Mendeleev's insistence on lining the elements up in rows and columns according to their characteristics. Pauli showed that this periodicity was precisely tied to the various shells and quantum states of electrons: two can be accommodated in the first shell, eight in the second, eight in the third, and so on. The periodic table did indeed contain a deeper meaning.

  Let's summarize this important idea. Pauli invented a rule for how the chemical elements change their electronic structure. This rule accounts for the chemical properties (inert gas, active metal, and so on), tying them to the numbers and states of the electrons, especially those in the outermost shells, where they are most readily in contact with other atoms. The dramatic implication of the Pauli principle is that if a shell is filled, it is impossible to add an additional electron to that shell. The resistive force is huge. This is the real reason for the impenetrability of matter. Although atoms are way more than 99.99 percent empty space, I have a real problem in walking through a wall. Probably you share this frustration. Why? In solids, where atoms are locked together via complicated electrical attractions, the imposition of your body's electrons on the system of "wall" atoms meets Pauli's prohibition on having electrons too close together. A bullet is able
to penetrate a wall because it ruptures the atom-atom bonds and, like a football blocker, makes room for its own electrons. Pauli's principle also plays a crucial role in such bizarre and romantic systems as neutron stars and black holes. But I digress.

  Once we understand atoms, we solve the problem of how they combine to make molecules, for example, H20 or NaCl. Molecules are formed via the complex of forces among electrons and nuclei in the combining atoms. The arrangement of the electrons in their shells provides the key to creating a stable molecule. Quantum theory gave chemistry a firm scientific base. Quantum chemistry today is a thriving field, out of which has come new disciplines like molecular biology, genetic engineering, and molecular medicine. In materials science, quantum theory helps us explain and control the properties of metals, insulators, superconductors, and semiconductors. Semiconductors led to the discovery of the transistor, whose inventors fully credit the quantum theory of metals as their inspiration. And out of that discovery came computers and microelectronics and the revolution in communications and information. And then there are masers and lasers, which are complete quantum systems.

  When our measurements reached into the atomic nucleus—a scale 100,000 times smaller than the atom—the quantum theory was an essential tool in that new regime. In astrophysics, stellar processes produce such exotic objects as suns, red giants, white dwarfs, neutron stars, and black holes. The life story of these objects is based on quantum theory. From the point of view of social utility, as we have estimated, quantum theory accounts for over 25 percent of the GNP of all the industrial powers. Just think, here are these European physicists obsessed with how the atom works, and out of their efforts come trillions of dollars of economic activity. If only wise and prescient governments had thought to put a 0.1 percent tax on quantum technological products, set aside for research and education ... Anyway, it does indeed work.