by James Gleick
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 mechanics 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.
If water—which is nothing but these little blobs, mile upon mile of the same thing over the earth—can form waves and foam, and make rushing noises and strange patterns as it runs over cement; if all of this, all the life of a stream of water, can be nothing but a pile of atoms, how much more is possible? … Is it possible that the “thing” walking back and forth in front of you, talking to you, is a great glob of these atoms in a very complex arrangement … ? When we say we are a pile of atoms, we do not mean we are merely a pile of atoms, because a pile of atoms which is not repeated from one to the other might well have the possibilities which you see before you in the mirror.
He found that he was working harder than at any time since the atomic bomb project. Teaching was only one of his goals. He realized also that he wished to organize his whole embracing knowledge of physics, to turn it end over end until he could find all the interconnections that were usually, he believed, left as loose ends. He felt as though he were making a map. In fact, for a while he considered actually trying to draw one, a diagram—a “Guide to the Perplexed,” as he put it.
A team of Caltech physics professors and graduate students scrambled to keep up, week after week, designing problem sets and supplementary material, as his guide to the perplexed took shape. They met with him at lunch after each lecture to piece together what Feynman had spun from as little as a single sheet of cryptic notes. Despite the homespun lyricism of his voice, the stress on ideas rather than technique, he was moving quickly, and his fellow physicists had to work to keep up with some of his leaps.
As every physics course recapitulated the subject’s history, so did Feynman’s, but instead of surveying the Sumerians or the Greeks he chose—in his second lecture—to sum up “Physics before 1920.” Less than a half-hour later he was on to a quick tour of quantum physics and then the nuclei and the strange particles according to Gell-Mann and Nishijima. This was what many students wanted to hear. Yet he did not want to leave them with the easy sense that here, at the microlevels, lay the most fundamental laws or the deepest unanswered questions. He described another problem, crossing the artificial boundaries that divide scientific disciplines, “not the problem of finding new fundamental particles, but something left over from a long time ago.”
It is the analysis of circulating or turbulent fluids. If we watch the evolution of a star, there comes a point where we can deduce that it is going to start convection, and thereafter we can no longer deduce what should happen… . We cannot analyze the weather. We do not know the patterns of motions that there should be inside the earth.
No one knew how to derive this chaos from the first principles of atomic forces or fluid flow. Simple fluid problems were for textbooks, he told the freshmen.
What we really cannot do is deal with actual, wet water running through a pipe. That is the central problem which we ought to solve some day.
Feynman designed his lectures as self-contained dramas. He never wanted to end by saying, “Well, the hour is up, we will continue this discussion next time …” He timed his diagrams and equations to fill the sliding two-tier blackboard so definitively that an image of the final chalk tableau seemed to have been in his head from the start. He chose grand themes with tentacles that spread into every corner of science: Conservation of Energy; Time and Distance; Probability … Before a month was out he introduced the deep and timely issue of symmetry in physical laws. His approach to the conservation of energy was revealing. This principle was never far from the consciousness of a working theoretical physicist, yet most textbooks let it arise in passing, toward the end of chapters on mechanical energy or thermodynamics. First they would note that mechanical energy is not conserved, since friction inevitably drains it away. Not until the Einsteinian equivalence of matter and energy does the principle fully come into its own.
Feynman took the conservation of energy as a starting point for discussing conservation laws in general (as a result, his syllabus managed to introduce the conservation of charge, baryons, and leptons weeks before reaching the subject of speed, distance, and acceleration). He put forward an ingenious analogy. Imagine, he said, a child with twenty-eight blocks. At the end of every day, his mother counts them. She discovers a fundamental law, the conservation of blocks: there are always twenty-eight.
One day she sees only twenty-seven, but careful investigation reveals one under the rug. Another day she finds twenty-six—but a window is open, and two are outside. Then she finds twenty-five—but there is a box in the room, and upon weighing the box and weighing individual blocks she surmises that three blocks are inside. The saga continues. Blocks vanish beneath the dirty water of a bathtub, and further calculations are needed to infer the number from the rising water level. “In the gradual increase in the complexity of her world,” Feynman said, “she finds a whole series of terms representing ways of calculating how many blocks are in places where she is not allowed to look.” One difference, he warned: in the case of energy, there are no blocks—just a set of abstract and increasingly intricate formulas which must always, in the end, return the physicist to his starting point.
With the vivid analogies and large themes immediately came computation. In the same one-hour lecture on the conservation of energy, Feynman had his students calculating
potential and kinetic energy in a gravitational field. A week later, when he introduced the uncertainty principle of quantum mechanics, he not only conveyed the philosophical drama of this “inherent fuzziness” in the description of nature but also leapt through the calculation of the probability density of an undisturbed hydrogen atom. He still had not reached the basics of speed, distance, and acceleration.
No wonder his colleagues found their nerves jangling as they tried to write problem sets. Before a half-year was gone, he was teaching an uncompromising version of the geometry of relativistic space-time, complete with particle diagrams, geometrical transformations, and four-vector algebra. For college freshmen this was difficult. Along with the mathematics Feynman tried to convey a feeling for how he visualized such problems, placing his “brain” into his diagrams like Alice plunging through the Looking-Glass. He tried to make his students imagine the apparent width and depth of an object:
They depend upon how we look at it; when we move to a new position, our brain immediately recalculates the width and the depth. But our brain does not immediately recalculate coordinates and time when we move at high speed, because we have had no effective experience of going nearly as fast as light to appreciate the fact that time and space are also of the same nature.
The students were sometimes terrified. Yet Feynman also returned to the standard fare of an introductory physics course. When he covered centers of mass and spinning gyroscopes, experienced physicists realized that he was giving the students not just the mathematical methods but also original, physical understanding. Why does a spinning top stand upright on your fingertip and then, as gravity pulls its axis downward, slowly circle about? Even physicists felt they were learning the why for the first time when they heard Feynman explain that the gyroscope began by “falling” an invisibly small distance … (He did not want to leave the students thinking a gyroscope was a miracle: “It is a wonderful thing, but it is not a miracle.”)
No realm of science was out of bounds. After consulting with experts in other fields, he gave two lectures on the physiology of the eye and the physiochemistry of color vision, making a profound connection between psychology and physics. He described the view of time and fields that arose from advanced and retarded potentials, his graduate work with Wheeler. He delivered a special lecture on the principle of least action, beginning with his high-school memories of his teacher Mr. Bader—how does a ball know what path to follow?—and ending with least action in quantum mechanics. He devoted an entire lecture to one of the simplest of mechanical gadgets, the ratchet and pawl, the sawtoothed device that keeps a watch spring from unwinding—but it was a lesson in reversibility and irreversibility, in disorder and entropy. Before he was done he had linked the macroscopic behavior of the ratchet and pawl to the events occurring at the level of its constituent atoms. The history of one ratchet was also the thermodynamic history of the universe, he showed:
The ratchet and pawl works in only one direction because it has some ultimate contact with the rest of the universe… . Because we cool off the earth and get heat from the sun, the ratchets and pawls that we make can turn one way… . It cannot be completely understood until the mystery of the beginnings of the history of the universe are reduced still further from speculation to scientific understanding.
The course was a magisterial achievement: word was spreading through the scientific community even before it ended. But it was not for freshmen. As the months went on, the examination results left Feynman shocked and discouraged. Still, when the year ended, the administration pleaded with him to keep on for a second year, teaching the same students, now sophomores. He did, finally trying to teach a thorough subcourse in quantum mechanics, again reversing the conventional order. Another Caltech physicist, David Goodstein, said long afterward, “I’ve spoken to some of those students in recent times, and in the gentle glow of dim memory, each has told me that having two years of physics from Feynman himself was the experience of a lifetime.” The reality was different:
As the course wore on, attendance by the kids at the lectures started dropping alarmingly, but at the same time, more and more faculty and graduate students started attending, so the room stayed full, and Feynman may never have known he was losing his intended audience.
This was the world according to Feynman. No scientist since Newton had so ambitiously and so unconventionally set down the full measure of his knowledge of the world—his own knowledge and his community’s. With intensive editing by other physicists, chiefly Robert B. Leighton and Matthew Sands, the lectures became the famous “red books”—the three-volume Feynman Lectures on Physics. Colleges and universities worldwide tried to adopt them as textbooks and then, inevitably, gave them up for more manageable and less radical alternatives. Unlike true textbooks, however, Feynman’s volumes continued to sell steadily a generation later.
Adorning each volume was a picture of Feynman in shirtsleeves, gleefully pounding a bongo drum. He came to regret that. “It is odd,” he said after hearing himself introduced yet again as a bongo player, “but on the infrequent occasions when I have been called upon in a formal place to play the bongo drums, the introducer never seems to find it necessary to mention that I also do theoretical physics. I believe that is probably because we respect the arts more than the sciences.” And when yet another request came in for a copy of the photograph—from a Swedish encyclopedia publisher who wished to “give a human approach to a presentation of the difficult matter that theoretical physics represents”—he exploded. “Dear Sir,” he scrawled,
The fact that I beat a drum has nothing to do with the fact that I do theoretical physics. Theoretical physics is a human endeavor, one of the higher developments of human beings—and this perpetual desire to prove that people who do it are human by showing that they do other things that a few other humans do (like playing bongo drums) is insulting to me.
I am human enough to tell you to go to hell.
The Explorers and the Tourists
“When you have learned what an explanation really is,” Feynman had said, “you can then go on to more subtle questions.”
Creeping philosophy. What is an explanation? Science and scientists had commandeered the practice of explanation, but the theory they left mainly to philosophers. The why seemed to fall in their domain. “With this question philosophy began and with this question it will end,” Martin Heidegger had recently said, “provided that it ends in greatness and not in an impotent decline.” Feynman, who believed that the impotent decline was well under way in the academies that supported philosophers, realized that he had had to develop a view of what constituted explanation, what legitimized explanation, and which phenomena did and did not require explanation.
His understanding of explanation did not depart far from the modern philosophical mainstream, though its jargon of explanans and explanandum was an alien language to him. Like most philosophers, he found explanations most satisfactory when they called upon a generalizing, underlying “law.” A thing is the way it is because other things of its kind are all that way. Why does Mars travel around the sun in an ellipse? Feynman explained—and ventured deep into philosophical territory—in an invited lecture series at Cornell University in 1964. He began by speaking, nominally, about the law of gravitation. In reality his subject was explanation itself.
All satellites travel in elliptical orbits. Why? Because objects tend to travel in a straight line when left alone (the law of inertia) and the combination of that unchanging motion and a force exerted toward a center of gravity—by the law of gravitation—creates an ellipse. What validates the law of gravitation? Feynman expressed the scientist’s modern view, a blend of the pragmatic and the aesthetic. He cautioned that even so beautiful a law was provisional: Newton’s law of gravitation gave way to Einstein’s, and a necessary quantum modification eluded physicists even now.
That is the same with all our other laws—they are not exact. There is always an edge of mystery, always a place where
we have some fiddling around to do yet. This may or may not be a property of Nature, but it certainly is common to all the laws as we know them today.
Yet in its unfinished form the law of gravitation explained so much. To a practicing scientist, that validated it. The same small parcel of mathematics explained Tycho Brahe’s nightly observations of the planets in the sixteenth century and Galileo’s measurements of balls rolling down inclined planes, timed against the beat of his own pulse. The planets are falling, Newton reasoned; the moon feels the same force as an earthly projectile, the force weakening with the square of the distance. A law is not a cause—philosophers still wrestled with this distinction—yet it is more than merely a description. It precedes the thing explained, not in time but in generality or in profundity. The same law explained the earth’s symmetrically bulging tides, rising both toward and away from the moon, and the newly measured orbits of the moons of Jupiter. It made new predictions that scientists could confirm or disprove with experiments on balls hanging delicately in a laboratory or observations of majestically rotating galaxies a hundred million million times larger. “Exactly the same law,” Feynman said, and added—having struggled to find the right wording—
Nature uses only the longest threads to weave her pattern, so each small piece of the fabric reveals the organization of the entire tapestry.
