The God Particle

by Leon Lederman

  Not satisfied that he has enough proof, he hits on using the idea of conservation of energy. He captures the cathode rays in a metal block. Their energy is known; it is simply the electrical energy given to the particles by the voltage from the battery. He measures the heat generated by the cathode rays, and notes that in relating the energy acquired by the hypothetical electrons to the heat generated in the metal block, the ratio elm appears. In a long series of experiments, Thomson gets a value for elm (2.0 × 1011 coulombs per kilogram), that is not very different from his first result. In 1897 he announces the result: "We have in the cathode rays matter in a new state, a state in which the subdivision of matter is carried very much further than in the ordinary gaseous state." This "subdivision of matter" is an ingredient in all matter and is part of the "substance from which the chemical elements are built up."

  What to call this new particle? Stoney's term "electron" was handy, so electron it became. Thomson lectured and wrote about the corpuscular properties of cathode rays from April to August 1897. This is known as marketing your results.

  There was still one puzzle to be solved: the separate values of e and m. Thomson was in the same fix as Weichert a few years earlier. So he did something clever. Noting that the elm of this new particle was about a thousand times bigger than that of hydrogen, the lightest of all the chemical atoms, he realized that either the electron's e was much bigger or its m was much smaller. What's it to be: big e or little m? Intuitively, he went with little m—a brave choice, for he was guessing that this new particle had a tiny mass, far smaller than that of hydrogen. Remember, most physicists and chemists still thought that the chemical atom was the indivisible a-tom. Thomson now said that the glow in his tube was evidence of a universal ingredient, a smaller constituent of all chemical atoms.

  In 1898 Thomson went on to measure the electric charge of his cathode rays, thus indirectly measuring the mass as well. He used a new technique, the cloud chamber, invented by his Scottish student C. T. R. Wilson in order to study the properties of rain, not a rare commodity in Scotland. Rain happens when water vapor condenses on dust to form drops. When the air is clear, electrically charged ions can stand in for dust, and that's what happens in a cloud chamber. Thomson measured the total charge in the chamber using an electrometric technique and determined the individual charge on each droplet by counting them and dividing the total.

  I had to build a Wilson cloud chamber as part of my Ph.D. thesis, and I've hated the technique ever since, hated Wilson, hated anyone who had anything to do with this contrary and mulelike device. That Thomson got the correct value of e and hence a measurement of the mass of the electron is miraculous. And that's not all. During the whole process of pinning down this particle, his dedication had to be unwavering. How does he know the electric field? Does he read the label on the battery? No labels. How does he know the precise value of his magnetic field in order to measure velocity? How does he measure the current? Reading a pointer on a dial has its problems. The pointer is a bit thick. It may shiver and shake. How is the scale calibrated? Is it meaningful? In 1897 absolute standards were not catalogue items. Measuring voltages, currents, temperatures, pressures, distances, time intervals were all formidable problems. Each required a detailed knowledge of the workings of the battery, the magnets, the meters.

  Then there was the political problem: how to convince the powers that be to give you the resources to do the experiment in the first place. Being the boss, as Thomson was, really helped. And I left out the most crucial problem of all: how to decide which experiment to do. Thomson had the talent, the political know-how, the stamina, to carry through where others had failed. In 1898 he announced that electrons are components of the atom and that cathode rays are electrons that have been separated from the atom. Scientists thought the chemical atom was structureless, uncuttable. Thomson had torn it apart.

  The atom was split, and we had found our first elementary particle, our first a-tom. Do you hear that giggle?

  5. THE NAKED ATOM

  There's something happening here.

  What it is ain't exactly clear.

  —Buffalo Springfield

  ON NEW YEAR'S EVE 1999, while most of the world prepares for the last blowout of the century, physicists from Palo Alto to Novosibirsk, from Cape Town to Reykjavik, will be resting, having exhausted themselves almost two years earlier celebrating the one hundredth anniversary (in 1998) of the discovery of the electron—the first truly elementary particle. Physicists love to celebrate. They'll celebrate any particle's birthday, no matter how obscure. But the electron, wow! They'll be dancing in the streets.

  After its discovery, the electron was frequently toasted in its birthplace, the Cavendish Laboratory at Cambridge University, with: "To the electron, may it remain forever useless!" Fat chance. Today, less than a century later; our entire technological superstructure is based upon that little fellow.

  Almost as soon as the electron was born, it began causing problems. It still perplexes us today. The electron is "pictured" as a sphere of electric charge that spins rapidly around an axis, creating a magnetic field. J. J. Thomson struggled mightily to measure the electron's charge and mass, but now both quantities are known to a high degree of precision.

  Now for the spooky features. In the curious world of the atom, the radius of the electron is generally taken to be zero. This gives rise to some obvious problems:

  If the radius is zero, what spins?

  How can it have mass?

  Where is the charge?

  How do we know the radius is zero in the first place?

  Can I get my money back?

  Here we meet the Boscovich problem face to face. Boscovich solved the problem of "atoms" colliding by making them into points, things with no dimension. His points were literal mathematicians' points, but he allowed these point particles to have conventional properties: mass and something we call charge, the source of a field of force. Boscovich's points were theoretical, speculative. But the electron is real. Probably a point particle, but with all other properties intact. Mass, yes. Charge, yes. Spin, yes. Radius, no.

  Think of Lewis Carroll's Cheshire Cat. Slowly the Cheshire Cat disappears until all that's left is its smile. No cat, just smile. Imagine the radius of a spinning glob of charge slowly shrinking until it disappears, leaving intact its spin, charge, mass, and smile.

  This chapter is about the birth and development of the quantum theory. It is the story of what happens inside the atom. I begin with the electron, because a particle with spin and mass but no dimension is counterintuitive to us humans. Thinking about such stuff is a kind of mental pushup. It might hurt the brain a bit because you'll have to use certain obscure cerebral muscles that may not have had much use.

  Still, the idea of the electron as point mass, point charge, and point spin does raise conceptual problems. The God Particle is intimately tied to this structural difficulty. A deep understanding of mass still escapes us, and the electron in the 1930s and '40s was the harbinger of these difficulties. Measuring the size of the electron became a cottage industry, generating Ph.D.'s galore, from New Jersey to Lahore. Through the years, increasingly sensitive experiments gave smaller and smaller numbers, all consistent with zero radius. It's as if God took the electron in Her hand and squeezed it as small as She could. With the large accelerators built in the 1970s and '80s, the measurements became ever more precise. In 1990 the radius was measured at less than .000000000000000001 inches or, scientifically, 10−18 centimeters. This is the best "zero" physics can supply ... so far. If I had a good experimental idea as to how to add a zero I'd drop everything to try to get it approved.

  Another interesting property of the electron is its magnetism, which is described by a number called the g-factor. Using quantum theory, the electron's g-factor is calculated to be:

  2 × (1.001159652190)

  And what calculations! It took skilled theorists years and impressive amounts of supercomputer time to come up with this number.
But this was theory. For verification, experimenters devised ingenious methods for measuring the g-factor with equivalent precision. The result, obtained by Hans Dehmelt of the University of Washington:

  2 × (1.001159652193)

  As you can see, we have verification to almost twelve places. This is a spectacular agreement of theory and experiment. The point here is that the calculation of the g-factor is an outgrowth of quantum theory, and at the heart of quantum theory lies what are known as the Heisenberg uncertainty principles. In 1927 a German physicist proposed a startling idea: that it is impossible to measure both the speed and the position of a particle to arbitrary precision. This impossibility is independent of the brilliance and the budget of the experimenter. It is a fundamental law of nature.

  And yet, despite the fact that uncertainty is woven into the very fabric of quantum theory, it churns out predictions, such as the g-factor above, that are accurate to eleven decimal places. Quantum theory is a prima facie scientific revolution that forms the base rock on which twentieth-century science flourishes ... and it starts with a confession of uncertainty.

  How did the theory come about? It's a good detective story, and as in any mystery, there are clues—some valid, some false. There are butlers all over the place to confuse the detectives. The city cops, the state police, the FBI collide, argue, cooperate, fall apart. There are many heroes. There are coups and countercoups. I'll give a very partial view, hoping to convey a sense of the evolution of ideas from 1900 until the 1930s, when the very mature revolutionaries put the "finishing" touches on the theory. But be forewarned! The microworld is counterintuitive: point masses, point charges, and point spins are experimentally consistent properties of particles in the atomic world, but they are not quantities we can see around us in the normal macroscopic world. If we are to survive together as friends through this chapter, we have to learn to recognize hangups derived from our narrow experience as macro-creatures. So forget about normal; expect shock, disbelief. Niels Bohr, one of the founders, said that anyone who isn't shocked by quantum theory doesn't understand it.

  Richard Feynman asserted that no one understands quantum theory. ("So, what do you want from us?" say my students.) Einstein, Schrödinger, and other good scientists never accepted the implications of the theory, yet in the 1990s, elements of quantum spookiness are considered crucial to an understanding of the origin of the universe.

  The armory of intellectual weapons that the explorers carried with them into the new world of the atom included Newtonian mechanics and Maxwell's equations. All macroscopic phenomena seemed to be subject to these powerful syntheses. But the experiments of the 1890s began to trouble the theorists. We've already discussed cathode rays, which led to the discovery of the electron. In 1895 Wilhelm Roentgen discovered x-rays. In 1896 Antoine Becquerel accidentally discovered radioactivity, when he stored photographic plates near some uranium in a desk drawer. Radioactivity soon led to a concept of lifetimes. Radioactive stuff decayed over characteristic times whose average could be measured, but the decay of a particular atom was unpredictable. What did this mean? No one knew. Indeed, all of these phenomena defied explanation by classical means.

  WHEN THE RAINBOW ISN'T ENOUGH

  Physicists were also beginning to look closely at light and its properties. Newton, using a glass prism, had shown that he could replicate the rainbow by spreading white light out into its spectral composition, the colors going from red at one end of the spectrum to violet at the other one color graduating smoothly into another. In 1815 Joseph von Fraunhofer, a skilled craftsman, greatly refined the optical system used to observe the colors emanating from the prism. Now when one squinted through a small telescope, the spread-out colors appeared in exquisite focus. With this instrument—bingo!—Fraunhofer made a discovery. The splendid colors of the sun's spectrum were overlaid by a series of fine dark lines, seemingly irregularly spaced. Fraunhofer eventually recorded some 576 of these lines. What did they mean? In Fraunhofer's time light was known to be a wave phenomenon. Later James Clerk Maxwell would show that light waves are electric and magnetic fields and that a crucial parameter is the distance between wave crests, the wavelength, which determines color.

  Knowing wavelengths, we can assign a numerical scale to the band of colors. Visible light ranges from deep red, at 8,000 angstrom units (.00008 cm), to deep violet, at about 4,000 angstrom units. Using such a scale, Fraunhofer could locate precisely each of the fine dark lines. For example, one famous line known as Hα, or "aitch-sub-alpha" (if you don't like aitch-sub-alpha, call it Irving), has a wavelength of 6,562.8 angstrom units, in the green, close to the middle of the spectrum.

  Why do we care about these lines? Because by 1859 the German physicist Gustav Robert Kirchhoff had found a deep connection between these lines and the chemical elements. This fellow heated up various elements—copper, carbon, sodium, and so on—by putting them in a hot flame until they glowed. He energized various gases in tubes and used even more improved viewing apparatus to examine the spectra of light emitted by these glowing gases. He discovered that each element emitted a characteristic series of very sharp, bright-colored lines superimposed on a darker glow of continuous colors. Inside the telescope was an engraved scale, calibrated in wavelengths, so that the location of each bright line could be pinpointed. Because the line spacings were different for each element, Kirchhoff and his accomplice, Robert Bunsen, were able to fingerprint elements by their spectral lines. (Kirchhoff needed someone to help him heat up the elements; who better than the man who invented the Bunsen burner?) With some skill, researchers could identify small impurities of one chemical element embedded in another. Science now had a tool to examine the composition of anything that gives off light—for example, the sim, and indeed, in time, the distant stars. By finding spectral lines not previously recorded, scientists discovered a lode of new elements. In the sun a new element called helium was identified in 1878. It wasn't until seventeen years later that this star-born element was discovered on earth.

  Think of the thrill of discovery when the light from the first bright star was analyzed ... and was found to be made of the same stuff we have here on earth! Since starlight is very faint, it took great telescopic and spectroscopic skill to study its patterns of colors and lines but the conclusion was unavoidable: the sun and stars are made of the same stuff as the earth. In fact, we've yet to find an element in space that we don't have here on earth. We are all star material. For any overarching concept about the world in which we live, this discovery is clearly of incredible significance. It reinforces Copernicus: we are not special.

  Ah, but why was Fraunhofer, the guy who started all this, finding those dark lines in the sun's spectrum? The explanation was soon forthcoming. The hot core of the sun (white, white hot) emitted light of all wavelengths. But as this light filtered through the relatively cool gases at the sun's surface, those gases absorbed the light of just those wavelengths that they like to emit. So Fraunhofer's dark lines represented absorption. Kirchhoff's bright lines were light emissions.

  Here we are in the late 1800s, and what do we make of all this? The chemical atoms are supposed to be hard, massy, structureless, uncuttable a-toms. But each one seems to be capable of emitting or absorbing its own characteristic series of sharp lines of electromagnetic energy. To some scientists, this screamed one word, "structure!" It was well known that mechanical objects have structures that resonate to regular impulses. Piano or violin strings vibrate to make musical notes in their crafted instruments, and wineglasses shatter when a large tenor sings the perfect note. Bridges could be set into violent motion by the unfortunate beat of marching soldiers. Light waves are just that, impulses with a "beat" equal to the velocity divided by the wavelength. These mechanical examples raised the question: if atoms had no internal structure, how could they display resonant properties such as spectral lines?

  And if atoms had a structure, what would Newton's and Maxwell's theories say about it? X-rays, radioactivity, the electron,
and spectral lines had one thing in common. They couldn't be explained by classical theory (although many scientists tried). On the other hand, none of these phenomena flatly contradicted classical Newton/Maxwell theory either. They just couldn't be explained. But as long as there was no smoking gun, there was hope that some smartass kid eventually could find a way to save classical physics. That never happened. Instead, the smoking gun finally materialized. In fact, there were at least three smoking guns.

  SMOKING GUN NO. 1: THE ULTRAVIOLET CATASTROPHE

  The first observational evidence that flatly contradicted classical theory was "black body radiation." All objects radiate energy. The hotter they are, the more energy they radiate. A living, breathing human emits about 200 watts of radiation in the invisible infrared region of the spectrum. (Theorists emit 210 watts and politicians go to 250.)

  All objects also absorb energy from their surroundings. If their temperature is higher than the surroundings, they cool because they radiate more energy than they absorb. "Black body" is the technical term for an ideal absorber, one that absorbs 100 percent of the radiation hitting it. Such an object, when cold, appears black because it reflects no light. Experimenters like to use a black body as a standard for measuring emitted radiation. What is interesting about the radiation from such an object—a piece of coal, an iron horseshoe, a toaster wire—is the color spectrum of the light: how much light it gives off at the various wavelengths. As we heat these objects, our eyes perceive a dull red glow at first, then, as the objects get hotter, bright red, then yellow, then blue-white, then (lots of heat!) bright white. Why do we end up with white?