The God Particle: If the Universe Is the Answer, What Is the Question?

by Leon Lederman

  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?

  The shift of the color spectrum means that the peak intensity of the light is moving, as the temperature is raised, from infrared to red to yellow to blue. As the peak moves, the distribution of light among the wavelengths broadens. By the time the peak is at the blue, so many of the other colors are being radiated that the hot body appears to our eyes as white. White hot, we say. Today astrophysicists are studying the black body radiation left over from the most incandescent radiation in the history of the universe—the Big Bang.

  But I digress. In the late 1890s, the data on black body radiation were getting better and better. What did Maxwell's theory say about these data? Catastrophe! It was just wrong. Classical theory predicted the wrong shape for the curve of distribution of light intensity among the various colors, the various wavelengths. In particular, it predicted that the peak quantity of light would always be emitted at the shortest wavelengths, toward the violet end of the spectrum and even into the invisible ultraviolet. This is not what happens. Hence "the ultraviolet catastrophe," and hence the smoking gun.

  Initially, it was believed that this failure of the application of Maxwell's equations would be solved by a better understanding of how electromagnetic energy was generated by the radiating matter. The first physicist to appreciate the significance of this failure was Albert Einstein in 1905, but the stage was set for the master by another theorist.

  Enter Max Planck, a Berlin theorist in his forties, who had had a long career in physics and was an expert on the theory of heat. He was smart, and he was professorial. Once, when he forgot which room he was supposed to lecture in, he stopped by the department office and asked, "Please tell me in which room does Professor Planck lecture today?" He was told sternly, "Don't go there, young fellow. You are much too young to understand the lectures of our learned Professor Planck."

  In any case, Planck was close to the experimental data, much of which had been acquired by colleagues in his Berlin laboratory, and he was determined to understand them. He made an inspired guess at a mathematical expression that would fit the data. Not only did it fit the distribution of light intensity at any given temperature, but it agreed with the way the curve (the distribution of wavelengths) changed as the temperature changed. For future events it is important to emphasize that a given curve allows one to calculate the temperature of the body emitting the radiation. Planck had reason to be proud of himself. "Today I made a discovery as important as that of Newton," he boasted to his son.

  Planck's next problem was to tie his lucky educated guess to some law of nature. Black bodies, so the data insisted, emitted very little radiation at short wavelengths. What "law of nature" could result in a suppression of the short wavelengths so beloved by classical Maxwell theory? A few months after publishing his successful equation, Planck hit on a possibility. Heat is a form of energy, and thus the energy content of the radiating body is limited by its temperature. The hotter the object, the more energy available. In classical theory this energy is distributed equally among the different wavelengths, BUT (get goose pimples, damn it, we are about to discover quantum theory) suppose the amount of energy depends on the wavelength. Suppose short wavelengths "cost" more energy. Then, as we try to radiate shorter wavelengths, we run out of available energy.

  Planck found that to justify his formula (now called the Planck law of radiation) he had to make two explicit assumptions. He said, first, that the energy radiated is related to the wavelength of the light, and second, that discreteness is inextricably linked to this phenomenon. Planck could justify his formula and keep peace with the laws of heat by assuming that the radiation was emitted in discrete bundles or "packets" of energy or (here it comes) "quanta." Each bundle's energy is related to the frequency via a simple connection: E = hf. A quantum of energy £ is equal to the frequency, f, of the light times a constant, h. Since frequency is inversely related to wavelength, the short wavelengths (or high frequencies) cost more energy. At any given temperature, only so much energy is available, so high frequencies are suppressed. This discreteness was essential to get the right answer. Frequency is the speed of light divided by the wavelength.

  The constant that Planck introduced, h, was determined by the data. But what is h? Planck called it the "quantum of action," but history calls it Planck's constant, and it will forevermore symbolize the revolutionary new physics. Planck's constant has a value, 4.11 × 10−15 eV-second, for what it's worth. Don't memorize. Just note that it's a very small number, thanks to the 10−15 (15 places past the decimal point).

  This—the introduction of the notion of a quantum or bundle of light energy—is the turning point, although neither Planck nor his colleagues understood the depth of this discovery. The exception was Einstein, who did recognize th
e true significance of Planck's quanta, but for the rest of the scientific community it took twenty-five years to sink in. Planck's theory disturbed him; he didn't want to see classical physics destroyed. "We have to live with quantum theory," he finally conceded. "And believe me, it will expand. It will not be only in optics. It will go in all fields." How right he was!

  As a final comment, in 1990 the Cosmic Background Explorer (COBE) satellite transmitted back to its delighted astrophysicist masters data on the spectral distribution of the cosmic background radiation that pervades all of space. The data, of unprecedented precision, fit the Planck formula for black body radiation exactly. Remember, the curve of distribution of light intensity allows one to define the temperature of the body emitting the radiation. Using the data from the COBE satellite and Planck's equation, the researchers were able to calculate the average temperature of the universe. It's cold here: 2.73 degrees above absolute zero.

  SMOKING GUN NO. 2: THE PHOTOELECTRIC EFFECT

  Now we zip over to Albert Einstein, working as a clerk in the Swiss Patent Office in Bern. The year is 1905. Einstein obtained his Ph.D. in 1903 and spent the next year brooding about the system and the meaning of life. But 1905 was a good year for him. He managed to solve three of the outstanding problems of physics that year: the photoelectric effect (our topic), the theory of Brownian motion (look it up!), and, oh yes, the special theory of relativity. Einstein understood that Planck's guess meant that light, electromagnetic energy, was being emitted in discrete globs of energy, hf, rather than in the classical idyll of emission, one wavelength continuously and smoothly changing to another.