by James Gleick
Ghosts and Worms
The problem of gravity had the finest pedigree—it came in a direct line of descent from Einstein’s greatest work—yet it lay outside the mainstream of high-energy theoretical physics in the early 1960s. As the general theory of relativity neared its fiftieth anniversary, some relativists and mathematical physicists continued to struggle with the natural problem of trying to create a quantum theory of gravitation—to quantize the gravitational field, as the fields associated with other forces had been quantized. It was difficult, involuted work. A quantum field theory of Einsteinian gravitation meant, as Gell-Mann said, a “quantum mechanical smearing of space-time” itself. No experimental evidence demanded that gravity must be quantized, but physicists did not wish to imagine a world in which some fields obeyed the laws of quantum mechanics and others did not.
The difficulty, from an experimentalist’s perspective, was that gravity was so weak compared to the other forces. A bare handful of electrons can create a palpable electromagnetic force, while it takes a mass as great as the earth to create the gravity that draws a leaf from a tree. The orders of magnitude separating these forces strain the imagination and cause immense mathematical difficulties for theorists trying to reconcile them. The difference is 1042, a number that defied even Feynman’s ability to find illustrative analogies. “The gravitational force is weak,” he said at one conference, introducing his work on quantizing gravity. “In fact, it’s damned weak.” At that instant a loudspeaker demonically broke loose from the ceiling and crashed to the floor. Feynman barely hesitated: “Weak—but not negligible.”
He had begun with Einstein’s theory and simply started calculating, as he had done in electrodynamics. He pushed his way into different corners of the problem in original fashion. The late 1950s were a time when relativity specialists were confused about the nature of gravitational radiation, and the high levels of mathematical rigor they demanded were blocking them from the right approximations. To Feynman it seemed straightforward that gravitational waves were real. Once again he began with a palpable physical intuition and charged forward. He found answers—decisive, he believed—to questions that relativists argued about: Do gravity waves carry energy? (Yes, he showed.) Can gravity waves be detected by small-scale measurements inside the wavelength? (No, he argued. “Only beyond the wave length can a clear proof of waves be found,” he wrote Victor Weisskopf when he heard that his old friend was interested in his gravity work. “I have not seen any plans for any such experiments, except by crackpots.”) For the sake of argument, at least, he refused to abandon altogether the possibility that gravity could not be quantized after all. “Maybe gravity is a way that quantum mechanics fails at large distances. Isn’t it interesting to live in our time and have such wonderful puzzles to work on?” He wrote down Feynman diagrams and computed integrals, and he could see that he was producing answers that could not be right. The probabilities did not add up to one. Yet he realized—with a combination of physical and diagrammatic intuition—that he could make up the deficits all at once if he resorted to a gimmick. He had to add “ghosts,” fictitious particles that would circle around the Feynman diagrams, appearing just long enough to form loops and then vanishing once more into mathematical oblivion. It was a curious idea, but it worked, and he reported it in Warsaw, Poland, at a conference on gravitation in July 1962.
The subject was on the eve of a rebirth, when discoveries from astrophysicists and theories from relativists would come together in a shower of black holes, white dwarfs, quasars, and other cosmological treasures. Feynman himself continued his gravitational work for years. He applied the gauge-symmetry machinery known as Yang-Mills. He made an influential contribution without ever reaching a complete enough theory to publish whole. For the moment, he found no more joy in a gathering of relativists than in the conclaves on high-energy physics he was temporarily fleeing. One of the speakers began seriously: “Since 1916 we have had a slow, rather painful accumulation of minute technical improvements… . I think that the attempt to continue obtaining such minute improvements constitutes a legitimate and fascinating part of mathematical physics. If something really exciting turns up, fine… .” The American physicists mingled uneasily with their Russian counterparts. They teased each other about searching their rooms for microphones; Feynman actually took apart his telephone at the Grand Hotel and decided that if it contained no bugs the Poles were wasting wire. He was overheard during a break baiting one of the Russians: “What have you ever done in physics, Ivanenko?”
“I’ve written a book with Sokolov.”
“How do I know what you contributed to it? Ivanenko, what is the integral of e to the minus x squared from minus to plus infinity?” Silence. “Ivanenko, what is one and one?” Feynman was dismayed by the work offered up. His own presentation drew little immediate notice, though his “ghosts,” extended by other theorists, later became crucial to modern theory. “I am learning nothing,” he wrote home in frustration, and he gave Gweneth a scathing taxonomy of pretentious science:
The “work” is always: (1) completely un-understandable, (2) vague and indefinite, (3) something correct that is obvious and self-evident, worked out by a long and difficult analysis, and presented as an important discovery, or (4) a claim based on the stupidity of the author that some obvious and correct fact, accepted and checked for years is, in fact, false (these are the worst: no argument will convince the idiot), (5) an attempt to do something, probably impossible, but certainly of no utility, which, it is finally revealed at the end, fails or (6) just plain wrong. There is a great deal of “activity in the field” these days, but this “activity” is mainly in showing that the previous “activity” of somebody else resulted in an error or in nothing useful or in something promising.
He never had liked crowds in science. “It is like a lot of worms trying to get out of a bottle by crawling all over each other.”
Dissatisfied though Feynman remained, his Warsaw talk marked the beginning of a turn toward his path integrals as a fundamental approach to the deepest of cosmological issues. Neither he nor other theorists had relied on this viewpoint in the high-energy physics of the late 1950s. Much later, however, some physicists applied path integrals to the very structure of space-time. They sought to unify its conceivable topologies by, in a sense, summing over all possible universes. Gell-Mann himself speculated that Feynman’s path integrals might prove to be more than a method, more than an equivalent alternative formulation: “the real foundation of quantum mechanics and thus of physical theory.”
Room at the Bottom
So little of modern physics seemed dedicated to the world of human scales. High-energy theorists had skipped far down a ladder of sizes, past the merely microscopic into a realm of the unimaginably small and short-lived. “Miniaturization” was a catchword of the day, but tininess meant something more modest to engineers and manufacturers than to particle physicists. The transistor, invented just over a decade before at the Bell Telephone Laboratories, was becoming a commodity. Transistors meant radios, battery-powered, with brittle plastic casings, small enough to fit in one’s hand. Researchers were beginning to consider ways of further reducing suitcase-sized devices like tape recorders. Electronic computers that had filled large rooms could now be squeezed into cabinets barely larger than an automobile. It occurred to Feynman that engineers had barely begun to imagine the possibilities. “There is a device on the market, they tell me,” he said at the end of 1959, when the American Physical Society held its annual meeting at Caltech, “by which you can write the Lord’s Prayer on the head of a pin. But that’s nothing… .” On toward the atom, he urged them. “It is a staggeringly small world that is below.”
That same pinhead could hold the twenty-four volumes of the Encyclopaedia Britannica, pictures and all, if the encyclopedia were reduced 25,000 times in each direction. A modest reduction, considering that the barely visible dots making up a halftone photoengraving would still contain a thousand or so
atoms. For writing and reading this tiny Britannica, he proposed engineering techniques within the limits of contemporary technology: reversing the lenses of an electron microscope, for example, and focusing a beam of ions to a small spot. At this scale, the world’s entire store of book knowledge could be carried about in a small pamphlet. But direct reduction would be crude, he continued. Telephones and computers had given rise to a new way of thinking about information, and in terms of raw information—allowing six or seven “bits” per letter and a generous one hundred atoms per bit—all the world’s books could be written in a cube no larger than a speck of dust. His audience, unaccustomed to lectures of this kind at American Physical Society meetings, was enthralled. “Don’t tell me about microfilm!” Feynman declared.
He had several reasons for thinking about the mechanics of the atomic world. Although he did not say so, he had been pondering the second law of thermodynamics and the relationship between entropy and information; at atomic scales came the threshold where his calculations and thought experiments took place. The new genetics also brought such issues to the surface. He talked about DNA (fifty atoms per bit of information) and about the capacity of living organisms to build tiny machinery, not just for information storage but for manipulation and manufacturing. He talked about computers: given millions of times more power, they would not just calculate faster but would reveal qualitatively different abilities, such as the ability to make judgments. “There is nothing I can see in the physical laws that says the computer elements cannot be made enormously smaller than they are now,” he said. He talked about problems of lubrication, and he talked about the realm where quantum-mechanical laws would take over. He envisioned machines that would make smaller machines, each of which would make machines that were smaller still. “It doesn’t cost anything for materials, you see. So I want to build a billion tiny factories, models of each other, which are manufacturing simultaneously, drilling holes, stamping parts, and so on.” He concluded by offering a pair of one-thousand-dollar prizes: one for the first microscope-readable book page shrunk 25,000 times in each direction, and one for the first operating electric motor no larger than a 1/64th-inch cube.
Caltech’s magazine Engineering and Science printed Feynman’s talk, and it was widely reprinted elsewhere. (Popular Science Monthly retitled it “How to Build an Automobile Smaller than This Dot.”) Twenty years later there was a name for the field Feynman had been trying to invent: nanotechnology. Nanotechnologists, partly inspired and partly crackpot, made tiny silicon gears with carefully etched teeth and displayed them proudly in their microscopes; or imagined tiny self-replicating robot doctors that would swim through one’s arteries. They thought of Feynman as their spiritual father, although he himself never returned to the subject. In the crude mechanical sense, tiny machines seemed a feature of a future just as distant as in 1959. The mechanical laws of physics meant that friction, viscosity, and electrical forces did not scale down as neatly as Feynman’s imagined billion tiny factories. Wheels, gears, and levers tended to glue themselves together. Tiny machines had come into being, storing and manipulating information even more efficiently than he had predicted. But they were electronic, not mechanical, using quantum mechanics, not fighting it. Not until 1985 did Feynman have to pay the thousand dollars for tiny writing: a Stanford University graduate student, Thomas H. Newman, spent a month shrinking the first page of A Tale of Two Cities onto silicon by almost exactly the technique Feynman had outlined.
The tiny motor did not take so long. Feynman had underestimated existing technology. A local engineer, William McLellan, read the Engineering and Science article in February. By June, when he had not heard any more, he decided he had better make the motor himself. It took two months of working in his spare time, using a watchmaker’s lathe and a microdrill press, drilling invisible holes and wrapping 1/2000th-inch copper wire. Tweezers were too crude. McLellan used a sharpened toothpick. The result was a one-millionth-horsepower motor.
One day in November he visited Feynman, who was working alone in a Caltech laboratory. McLellan brought his equipment in a large wooden box. He saw Feynman’s eyes glaze; too many cranks had turned up, typically bringing toy automobile engines that they could hold in the palm of a hand. But McLellan opened his box and pulled out a microscope.
“Uh-oh,” Feynman said. He had neglected to make any arrangements for funding the prize. He sent McLellan a personal check.
All His Knowledge
He could not let go of the simple questions. He had spent much of a lifetime assembling a picture of how the world worked, how atoms and forces conjoined to create ice crystals and rainbows. In conjuring a world of miniature machines, he continued to work out possibilities at the level of long-lived molecules, not ephemeral strange particles. He had made himself a member of the community of theoretical physics, and he accepted their goals and their rhetoric: he had told the American Physical Society apologetically that miniaturization was not “fundamental physics (in the sense of, ‘What are the strange particles?’).” Indeed, his community now assigned a kind of intellectual primacy to phenomena that could be observed only in the searing less-than-an-instant of a particle collision. But a part of him still preferred to give fundamental a different definition. “What we are talking about is real and at hand: Nature,” he wrote to a correspondent in India, who had, he thought, spent too much time reading about esoteric phenomena.
Learn by trying to understand simple things in terms of other ideas—always honestly and directly. What keeps the clouds up, why can’t I see stars in the daytime, why do colors appear on oily water, what makes the lines on the surface of water being poured from a pitcher, why does a hanging lamp swing back and forth—and all the innumerable little things you see all around you. Then when you have learned what an explanation really is, you can then go on to more subtle questions.
The first plank in every Caltech undergraduate education was a two-year required course in basic physics. By the 1960s the institute administration recognized a problem. The course had grown stale. Too much ancient pedagogy lingered in it. Bright young freshmen arrived from their high schools around the country, ready to tackle the mysteries of relativity and strange particles, and were plunged into the study of—as Feynman put it—“pith balls and inclined planes.” There was no main lecturer; the course met in sections taught by graduate students. The administration decided in 1961 to revise the course from the bottom up and asked Feynman to take it on for one year. He would have to lecture twice a week.
Caltech was not alone; nor was physics. The pace of change in modern science had accelerated as most college syllabuses had hardened. It was no longer possible, as it had been a generation before, to bring undergraduates up to the live frontier of a field like physics or biology. Yet if quantum mechanics or molecular genetics could not be integrated into undergraduate education, science risked becoming a historical subject. Many first-year physics courses did begin with history: physics in ancient Greece; the pyramids of Egypt and the calendars of Sumeria; medieval physics through nineteenth-century physics. Virtually all began with some form of mechanics. A typical program went:
1. Historical Development of Physical Science
2. Present Status of Physical Science
3. Kinematics: The Study of Motion
4. The Laws of Dynamics
5. Application of the Laws of Motion: Momentum and Energy
6. Elasticity and Simple Harmonic Motion
7. Dynamics of Rigid Bodies
8. Statics of Rigid Bodies
and so on, until in its final weeks the course would reach
26. Atoms and Molecules
in time to touch upon Nuclear Physics and Astrophysics. Caltech was still using a generation-old text by its own luminary, Robert Millikan, that remained soundly mired in the physics of the eighteenth and nineteenth centuries.
Feynman began with atoms, because that was where his own understanding of the world began—not the world of quantum mec
hanics but the quotidian world of floating clouds and colors shimmering in oily water. Moments after nearly two hundred freshmen entered the hall for his first lecture in the fall of 1961, they heard these words from the grinning physicist striding back and forth upon the stage:
So, what is our over-all picture of the world?
If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.
Imagine a drop of water, he said. He took them on a tour inward through the length scales, magnifying the drop until it was forty feet across, then fifteen miles across, then 250 times larger still, until the teeming molecules came into view, each with a pair of hydrogen atoms stuck like round arms upon a larger oxygen atom. He discussed the contrary forces holding the molecules together and forcing them apart. He described heat as atoms in motion … pressure … expansion … steam. He described ice, with its molecules held in a rigid crystalline array. He described the surface of water in air, absorbing oxygen and nitrogen and giving off vapor, and he immediately raised issues of equilibrium and disequilibrium. Instead of Aristotle and Galileo, instead of levers and projectiles, he was building a tangible sense of how atoms create the substances around us and why substances behave as they do. Solution and precipitation, fire and odor—he kept moving, displaying the atomic hypothesis not as a reductive end point but as a road toward complexity.
