The God Particle

by Leon Lederman

  Bohr's theory, developed between 1913 and 1925, is now referred to as the "old quantum theory." Planck, Einstein, and Bohr had each taken a step to flout classical physics. All had firm experimental data that told them they were right. Planck's theory beautifully agreed with the black body spectrum, Einstein's with detailed measurements of photoelectrons. In Bohr's mathematical formula one finds such quantities as the electron's charge and mass, Planck's constant, some it's, numbers like 3, and an important integer (the quantum number) that enumerated the energy states. All of these, when factored together; provided a formula from which all the spectral lines of hydrogen could be calculated. It was in remarkable agreement with the data.

  Rutherford loved Bohr's theory but raised the question of when and how the electron decides to jump from one state to another—something Bohr didn't discuss. Rutherford remembered a previous puzzle: when does a radioactive atom decide to decay? In classical physics, every action has a cause. In the atomic domain that kind of causality doesn't seem to appear. Bohr recognized the crisis (which wasn't really solved until Einstein's 1916 work on "spontaneous transitions") and pointed out a direction. But the experimenters, still exploring the phenomena of the atomic world, found a number of things that Bohr hadn't counted on.

  When the American physicist Albert Michelson, a precision fanatic, examined the spectral lines more closely he noticed that each of the hydrogen lines was actually two narrowly spaced lines—two wavelengths that were very close together. This doubling of lines means that when an electron is ready to jump down, it has a choice of two lower energy states. Bohr's model didn't predict the doubling, which was called "fine structure." Arnold Sommerfeld, a contemporary and associate of Bohr, noticed that the velocity of electrons in the hydrogen atom is a significant fraction of the velocity of light and should be treated in accordance with Einstein's 1905 theory of relativity. He made the first step toward joining the two revolutions, quantum theory and relativity. When he included the effects of relativity, he noted that where the Bohr theory predicted one orbit, the new theory predicted two closely spaced orbits. This explained the doubling of the lines. In carrying out this calculation, Sommerfeld introduced a "new abbreviation" of some constants that frequently appeared in his equations. It was 2πe2/hc, which he abbreviated with the Greek letter alpha (α). Don't worry about the equation. The interesting thing is this: when one plugs in the known numbers for the electron's charge, e, Planck's constant, h, and the velocity of light, c, out pops a = 1/137. There's that 137 again, a pure number.

  Experimenters continued to add pieces to the Bohr model of the atom. In 1896, before the discovery of the electron, a Dutchman, Pieter Zeeman, put a Bunsen burner between the poles of a strong magnet and placed a lump of table salt in the burner. He examined the yellow light from sodium with a very precise spectrometer he had constructed. Sure enough, in the magnetic field the yellow spectral lines became broader, meaning that the magnetic field actually splits the lines. This effect was confirmed by more precise measurements up through 1925, when two Dutch physicists, Samuel Goudsmit and George Uhlenbeck, came up with a bizarre suggestion that the effect could be explained only by giving the electrons the property of "spin." In a classical object, say a top, spin is the rotation of the top around its axis of symmetry. Electron spin is the quantum analogue.

  All of these new ideas, though valid by themselves, were rather ungracefully tacked on to the 1913 Bohr atomic model, like products picked up at a custom-car shop. With these accoutrements, the now greatly aggrandized Bohr theory, like an old Ford retrofitted with air conditioning, spinner hubcaps, and fake tailfins, could account for a very impressive amount of precise and brilliantly achieved experimental data.

  There was only one problem with the model. It was wrong.

  A PEEK UNDER THE VEIL

  The crazy-quilt theory initiated by Niels Bohr in 1912 was running into increasing difficulties when a French graduate student in 1924 uncovered a crucial clue. This clue, revealed in an unlikely source, the turgid prose of a doctoral dissertation, would, in three dramatic years, yield a totally new conception of reality in the microworld. The author was a young aristocrat, Prince Louis-Victor de Broglie, sweating out his Ph.D. in Paris. De Broglie was inspired by a paper by Einstein, who in 1909 was mulling over the significance of his light quanta. How could light behave like a swarm of energy bundles—that is, like particles—and at the same time exhibit all the behaviors of waves, such as interference, diffraction, and other properties that require a wavelength?

  De Broglie thought that this curious dual character of light might be a fundamental property of nature that could be applied to material objects such as electrons as well. In his photoelectric theory, following Planck, Einstein had assigned a certain energy to a quantum of light, related to its wavelength or frequency. De Broglie then invoked a new symmetry: if waves can be particles, then particles (electrons) can be waves. He devised a way to assign electrons a wavelength related to their energy. His idea immediately hit pay dirt when he applied it to electrons in the hydrogen atom. An assigned wavelength gave an explanation for Bohr's mysterious ad hoc rule that only certain radii are allowed to the electron. It's totally obvious! It is? Sure. If in a Bohr orbit the electron has a wavelength of some teensy fraction of a centimeter, then only those orbits are allowed in which an integral (whole) number of wavelengths can fit around the circumference. Try this crude visualization. Go get a nickel and a handful of pennies. Place the nickel (the nucleus) on a table and arrange a number of pennies in a circle (the electron orbit) around the nickel. You'll find you need seven pennies to make the smallest orbit. This defines a radius. If you want to use eight pennies you are forced to make a bigger circle, but not any bigger circle; only one radius will do it. Larger radii will permit nine, ten, eleven, or more pennies. You can see from this dumb example that if you restrict yourself to whole pennies—or whole wavelengths—only certain radii are allowed. To get circles in between requires overlapping the pennies, and if they represent wavelengths, the waves wouldn't connect up smoothly around the orbit. De Broglie's idea was that the wavelength of the electron (the diameter of the penny) determines the allowed radii. Key to his concept was the idea of assigning a wavelength to the electron.

  De Broglie, in his dissertation, speculated as to whether electrons would demonstrate other wavelike effects such as interference and diffraction. His faculty advisers at the University of Paris, though impressed by the young prince's virtuosity, were nonplused by the notion of particle waves. One of his examiners, wanting an outside opinion, sent a copy to Einstein, who wrote back this compliment about de Broglie: "He has lifted a corner of the great veil." His Ph.D. thesis was accepted in 1924 and eventually earned him a Nobel Prize, making de Broglie the only physicist up to that time to win the Prize on the basis of a dissertation. The biggest winner, though, was Erwin Schrödinger, who saw the real potential in de Broglie's work.

  Now comes an interesting pas de deux of theory-experiment. De Broglie's idea had no experimental support. An electron wave? What does it mean? The necessary support appeared in 1927, in, of all places, New Jersey—not a Channel island but an American state near Newark. Bell Telephone Laboratories, the famous industrial research institution, was engaged in a study of vacuum tubes, an ancient electronic device used before the dawn of civilization and the invention of transistors. Two scientists, Clinton Davisson and Lester Germer, were bombarding various oxide-coated metal surfaces with streams of electrons. Germer, working under Davisson's direction, noticed that a curious pattern of electrons was reflected from certain metal surfaces that had no oxide coating.

  In 1926 Davisson traveled to a meeting in England and learned about de Broglie's idea. He rushed back to Bell Labs and began to analyze his data from the point of view of wave behavior. The patterns he observed fit precisely with the theory of electrons behaving as waves whose wavelength was related to the energy of the bombarding particles. He and Germer rushed to publish. They were none t
oo soon. In the Cavendish Laboratory, George P. Thomson, son of the famous J. J., was carrying out similar research. Davisson and Thomson shared the 1938 Nobel Prize for first observing electron waves.

  The filial affection of J. J. and G. P. is, incidentally, amply documented in their warm correspondence. In one of his more emotional letters, G. P. gushed:

  Dear Father,

  Given a spherical triangle with sides ABC ...

  [And, after three densely written pages of the same]

  Your son, George

  So now a wave is associated with an electron whether it is imprisoned in an atom or traveling in a vacuum tube. But what is there about this electron that waves?

  THE MAN WHO DIDN'T KNOW BATTERIES

  If Rutherford was the prototypical experimenter, Werner Heisenberg (1901–1976) qualified as his theoretical counterpart. He would have fit I.I. Rabi's definition of a theorist as one who "couldn't tie his own shoelaces." One of the most brilliant students in Europe, Heisenberg almost failed his Ph.D. orals at the University of Munich when one of his examiners, Wilhelm Wien, a pioneer in the study of black body radiation, took a dislike to him. Wien started asking practical questions, like how does a battery work? Heisenberg had no idea. Wien, after grilling him with more questions about experimentation, wanted to flunk him. Cooler heads prevailed, and Heisenberg got off with the equivalent of a gentleman's C.

  His father was a professor of Greek at Munich, and as a teenager Heisenberg had read the Timaeus, which includes all of Plato's atomic theory. Heisenberg thought Plato was nuts—his "atoms" were little cubes and pyramids—but he was fascinated with Plato's basic tenet that one can never understand the universe until the smallest components of matter are known. Young Heisenberg decided to devote his life to studying the smallest particles of matter.

  Heisenberg tried hard to picture the Rutherford-Bohr atom in his mind and kept coming up empty. Bohr's electron orbits were like none he could imagine. The cute little atom that would become the Atomic Energy Commission's logo for so many years—a nucleus with electrons circling in "magic" radii without radiating—just didn't make any sense. Heisenberg realized that Bohr's orbits were merely constructs that made the numbers come out right and got rid of or (better) finessed classical objections to the Rutherford model of the atom. But real orbits? No. Bohr's quantum theory didn't go far enough in discarding the baggage of classical physics. The unique way in which space in the atom permitted only certain orbits required a more radical proposition. Heisenberg came to realize that this new atom was fundamentally not visualizable. He developed a firm guide: do not deal with anything that can't be measured. Orbits can't be measured. Spectral lines, however, can be. Heisenberg wrote a theory called "matrix mechanics," based on mathematical forms called matrices. His methods were difficult mathematically, and even more difficult to visualize, but it was clear that he had made a major improvement in Bohr's old theory. In time, matrix mechanics repeated all the successes of the Bohr theory without the arbitrary magic radii. Heisenberg's matrices went on to new successes where the old theory failed. But physicists found the matrices hard to use.

  And then came the most famous vacation in the history of physics.

  MATTER WAVES AND THE LADY IN THE VILLA

  A few months after Heisenberg completed his matrix formulation, Erwin Schrödinger decided he needed a holiday. It was about ten days before Christmas in the winter of 1925. Schrödinger was a competent but undistinguished professor of physics at the University of Zurich, and all college teachers deserve a Christmas holiday. But this was no ordinary vacation. Leaving his wife at home, Schrödinger booked a villa in the Swiss Alps for two and a half weeks, taking with him his notebooks, two pearls, and an old Viennese girlfriend. Schrödinger's self-appointed mission was to save the patched-up, creaky quantum theory of the time. The Viennese-born physicist placed a pearl in each ear to screen out any distracting noises. Then he placed the girlfriend in bed for inspiration. Schrödinger had his work cut out for him. He had to create a new theory and keep the lady happy. Fortunately he was up to the task. (Don't become a physicist unless you are prepared for such demands.)

  Schrödinger had begun his career as an experimenter but had switched to theory rather early on. He was old for a theorist, thirty-eight that Christmas. Obviously, there are lots of middle-aged, even elderly, theorists around. But they usually do their best work in their twenties, then retire, intellectually speaking, in their thirties to become "elder statesmen" of physics. This shooting-star phenomenon was especially true during the heyday of quantum theory, which saw Paul Dirac, Werner Heisenberg, Wolfgang Pauli, and Niels Bohr all crafting their finest theories as very young men. When Dirac and Heisenberg went to Stockholm to accept their Nobel Prizes, they were, in fact, accompanied by their mothers. Dirac once wrote:

  Age is of course a fever chill

  That every physicist must fear.

  He's better dead than living still

  When once he's past his thirtieth year.

  (He won his Nobel for physics, not for literature.) Fortunately for science, Dirac didn't take his own verse to heart, living well into his eighties.

  One of the items Schrödinger took with him on vacation was de Broglie's paper on particles and waves. Working feverishly, he extended the quantum concept even further. He didn't just treat electrons as particles with wave characteristics. He came up with an equation in which electrons are waves, matter waves. A key actor in Schrödinger's famous equation is the Greek symbol psi, or ψ. Physicists are fond of saying that the equation thus reduces everything to psi's (sighs). ψ is known as the wave function, and it contains all we know or can know about the electron. When Schrödinger's equation is solved, it gives ψ as it varies in space and changes with time. Later the equation was applied to systems of many electrons and eventually to any system requiring a quantum treatment. In other words, the Schrödinger equation, or "wave mechanics," applies to atoms, molecules, protons, neutrons, and, especially important to us today, clusters of quarks, among other particles.

  Schrödinger was out to rescue classical physics. He insisted that electrons were truly classical waves, like sound waves, water waves, or Maxwell's electromagnetic light and radio waves, and that their particle aspect was illusory. They were matter waves. Waves were well understood, simple to visualize, unlike the electrons in the Bohr atom, jumping willy-nilly from orbit to orbit. In Schrödinger's interpretation, ψ (really the square of ψ, or ψ2) described the density distribution of this matter wave. His equation described these waves under the influence of the electrical forces in the atom. For example, in the hydrogen atom, Schrödinger's waves clump in places where the old Bohr quantum theory talked orbits. The equation gave the Bohr radii automatically, with no adjustments, and provided the spectral lines, not only for hydrogen but for the other elements as well.

  Schrödinger published his wave equation within weeks after he left the villa. It was an immediate sensation, one of the most powerful mathematical tools ever devised to deal with the structure of matter. (By 1960, more than 100,000 scientific papers had been published based on the application of Schrödinger's equation.) He wrote five more papers in quick succession; all six papers were published in a six-month period that was among the greatest bursts of creativity in scientific history. J. Robert Oppenheimer called the theory of wave mechanics "perhaps one of the most perfect, most accurate, and most lovely man has discovered." Arthur Sommerfeld, the great physicist and mathematician, said Schrödinger's theory "was the most astonishing among all the astonishing discoveries of the twentieth century."

  For all of this, I personally forgive Schrödinger for his romantic dalliances which, after all, are of concern only to biographers, sociological historians, and envious colleagues.

  A WAVE OF PROBABILITY

  Physicists loved Schrödinger's equation because they could solve it and it worked. Although Heisenberg's matrix mechanics and Schrödinger's equation both seemed to give the correct answers, most phy
sicists seized on the Schrödinger method since this was a good old differential equation, a warm and familiar form of mathematics. A few years later it was shown that the physical ideas and numerical consequences of Heisenberg's and Schrödinger's theories were identical. They were just written in different mathematical languages. Today a mixture of the most convenient aspects of both theories is used.

  The only problem with Schrödinger's equation was that his interpretation of the "wave" was wrong. It turned out that the thing could not represent matter waves. There was no doubt it represented some sort of wave, but the question was, what's waving?

  The answer was provided by the German physicist Max Born, still in that eventful year 1926. Born insisted that the only consistent interpretation of Schrödinger's wave function is that ψ2 represents the probability of finding a particle, the electron, at various locations. ψ varies in space and time. Where ψ2 is large, the electron has a large probability of being found. Where ψ = 0, the electron is never found. The wave function is a wave of probability.

  Born was influenced by experiments in which a stream of electrons is directed toward some sort of energy barrier. This could be, for example, a wire screen connected to the negative terminal of a battery, say at −10 volts. If the electrons have an energy of only 5 volts, they should be effectively repelled by the "10-volt barrier" in the classical view. If an electron's energy is larger than that of the barrier it will penetrate the barrier like a ball thrown over a wall. If its energy is less than that of the barrier the electron is reflected, like a ball thrown against the wall. However Schrödinger's quantum equation indicates that some of the ψ-wave penetrates and some of the wave is reflected. This is typical light behavior. Pass a store window and you see the goodies displayed, but you also see a dim image of yourself. Light waves are both transmitted through and reflected by the glass. Schrödinger's equation predicts similar results. But we never see a fraction of an electron!