Quantum Man: Richard Feynman's Life in Science (2 page)

PART I

The Paths to Greatness

Science is a way to teach how something gets to be known, what is not known, to what extent things are known (for nothing is known absolutely), how to handle doubt and uncertainty, what the rules of evidence are, how to think about things so that judgments can be made, how to distinguish truth from fraud, and from show.

—Richard Feynman

CHAPTER
1

Lights, Camera, Action

Perhaps a thing is simple if you can describe it fully in several different ways without immediately knowing that you are describing the same thing.

—R
ICHARD
F
EYNMAN

C
ould one have guessed while he was still a child that Richard Feynman would become perhaps the greatest, and probably the most beloved, physicist of the last half of the twentieth century? It is not so clear, even if many of the incipient signs were there. He was undeniably smart. He had a nurturing father who entertained him with puzzles and instilled a love of learning, encouraging his innate curiosity and feeding his mind whenever possible. And he had a chemistry set and displayed a fascination with radios.

But these things were not that uncommon for bright youngsters at the time. In most fundamental respects Richard Feynman appeared to be a typical smart Jewish kid from Queens growing up after the First World War, and it is perhaps that simple fact as much as anything else that colored his future place in history. His mind was extraordinary, yes, but he remained firmly grounded in reality, even as he was driven to explore the most esoteric realms of our existence. His disrespect for pomposity came from an early life in which he was not exposed to it, and his disrespect for authority came not only from a father who nurtured this independence but also from an early life in which he was remarkably free to be a child, to follow his own passions, and to make his own mistakes.

Perhaps the first signal of what was to come was Feynman’s literally indefatigable ability to concentrate on a problem for hours at a time, so much so that his parents began to worry. As a teenager, Feynman made practical use of his fascination with radios: he opened a small business fixing them. But unlike conventional repairmen, Feynman would delight in solving radio problems not merely by tinkering, but by thinking.

And he would combine this remarkable ability to focus all of his energy on a problem with an innate talent as a showman. His most famous radio repair, for example, involved an episode where he paced back and forth thinking while the broken radio shrieked in front of its owner whenever it was first turned on. Finally young Feynman pulled out two tubes and exchanged them, solving the problem. My suspicion is that Feynman let the whole thing last longer than it needed to, just for effect.

In later life almost exactly the same story would be told again. But this one originated when a skeptical Feynman was asked to examine a puzzling photograph from a bubble chamber—a device where elementary particles would leave visible tracks. After thinking for a while, he placed his pencil down on a precise spot in the picture and claimed that there must be a bolt located right there, where a particle had had an unanticipated collision, producing results that otherwise had been misinterpreted. Needless to say, when the experimenters involved in the claimed discovery went back to their device and looked at it, there was the bolt.

The showmanship, while contributing to the Feynman lore, was not important to his work however. Neither was his fascination with women, which also emerged later. The ability to concentrate, combined with an almost superhuman energy that he could apply to a problem, was. But the final essential icing on the cake, when combined with the former two characteristics, ultimately ensured his greatness. It involved simply an almost unparalleled talent for mathematics.

Feynman’s mathematical genius began to manifest itself by the time he was in high school. While a sophomore he taught himself trigonometry, advanced algebra, infinite series, analytical geometry, and differential and integral calculus. And in his self-learning, the other aspect of what made Feynman so unique began to materialize: he would recast all knowledge in his own way, often inventing a new language or new formalism to reflect his own understanding. In certain cases necessity was the mother of invention. When typing out a manual on complex mathematics, in 1933, at the age of fifteen, he devised “typewriter symbols” to reflect the appropriate mathematical operations, since his typewriter did not have keys to represent them, and created a new notation for a table of integrals that he had developed.

Feynman entered MIT with the intent to study mathematics, but it was a misplaced notion. Even though he loved mathematics, he forever wanted to know what he could “do” with it. He asked the chairman of the mathematics department this question and got two different answers: “Insurance estimates,” and “If you have to ask that, then you don’t belong in mathematics.” Neither resonated with Feynman, who decided mathematics wasn’t for him, so he switched to electrical engineering. Interestingly, this switch seemed too extreme. If mathematics was without purpose, engineering was too practical. Like the soup in the Goldilocks tale, however, physics was “just right,” and by the end of his freshman year Feynman had become a physics major.

The choice of course was an inspired one. Feynman’s innate talents allowed him to excel in physics. But he had another talent that mattered even more perhaps, and I don’t know if it was innate or not. This was intuition.

Physical intuition is a fascinating, ephemeral kind of skill. How does one know which avenue of approach will be most fruitful to solve a physics problem? No doubt some aspects of intuition are acquired. This is why physics majors are required to solve so many problems. In this way, they begin to learn which approaches work and which don’t, and increase their toolkit of techniques along the way. But surely some aspect of physical intuition cannot be taught, one that resonates at a certain place and time. Einstein had such intuition, and it served him well for over twenty years, from his epochal work on special relativity to his crowning achievement, general relativity. But his intuition began to fail him as he slowly drifted away from the mainstream of interest in quantum mechanics in the twentieth century.

Feynman’s intuition was unique in a different way. Whereas Einstein developed completely new theories about nature, Feynman explored existing ideas from a completely new and usually more fruitful perspective. The only way he could really understand physical ideas was to derive them using his own language. But because his language was usually also self-taught, the end results sometimes differed radically from what “conventional” wisdom produced. As we shall see, Feynman created his own wisdom.

But Feynman’s intuition was also earned the hard way, based on relentless labor. His systematic approach and the thoroughness with which he examined problems were already evident in high school. He recorded his progress in notebooks, with tables of sines and cosines he had calculated himself, and later on in his comprehensive calculus notebook, titled “The Calculus for the Practical Man,” with extensive tables of integrals, which again he had worked out himself. In later life he would amaze people by proposing a new way to solve a problem, or by grasping immediately the heart of a complex issue. More often than not this was because at some time, in the thousands of pages of notes he kept as he worked to understand nature, Feynman had thought about that very problem and explored not just one, but a host of different ways of solving it. It was this willingness to investigate a problem from every vantage point, and to carefully organize his thinking until he had exhausted all possibilities—a product of his deep intellect and his indefatigable ability to concentrate—that set him apart.

Perhaps
willingness
is the wrong word here.
Necessity
would be a better choice. Feynman needed to fully understand every problem he encountered by starting from scratch, solving it in his own way and often in several different ways. Later on, he would try to imbue this same ethic to his students, one of whom later said, “Feynman stressed creativity—which to him meant working things out from the beginning. He urged each of us to create his or her own universe of ideas, so that our products, even if only answers to assigned classwork problems, would have their own original character—just as his own work carried the unique stamp of his personality.”

Not only was Feynman’s ability to concentrate for long periods evident when he was young, but so was his ability to control and organize his thoughts. I remember having a chemistry set when I was a kid and I also remember often randomly throwing things together to see what would happen. But Feynman, as he later emphasized, “never played chaotically with scientific things.” Rather he always carried out his scientific “play” in a controlled manner, always attentive to what was going on. Again, much later, after his death, it became clear from the extensive notes he took that he carefully recorded each of his explorations. He even considered at one point organizing his domestic life with his future wife along scientific lines, before a friend convinced him that he was being hopelessly unrealistic. Ultimately, his naivete in this regard disappeared, and much later he advised a student, “You cannot develop a personality with physics alone. The rest of life must be worked in.” In any case, Feynman loved to play and joke, but when it came to science, starting early on and continuing for the rest of his life, Feynman could be deadly serious.

He may have waited until the end of his first year of university to declare himself a physics major, but the stars aligned when he was still in high school. In retrospect, what might have been the defining moment occurred when his high school teacher, Mr. Bader, introduced him to one of the most subtle and wonderful hidden mysteries of the observable world, a fact that had built on a discovery made three hundred years before he was born by a brilliant and reclusive lawyer-turned-mathematician, Pierre de Fermat.

Like Feynman, Fermat would achieve public recognition late in life for something that was unrelated to his most substantial accomplishments. In 1637, Fermat scrawled a brief note in the margin of his copy of
Arithmetica
, the masterpiece by the famous Greek mathematician Diophantus, indicating that he had discovered a simple proof of a remarkable fact. The equation
x
n
+
y
n
=
z
n
has no integer solutions if
n
>2 (for
n
= 2, this is familiar as the Pythagorean theorem relating lengths of the sides of a right triangle). It is doubtful that Fermat really possessed such a proof, which 350 years later required almost all of the developments of twentieth-century mathematics and several hundred pages to complete. Nevertheless, if Fermat is remembered at all today among the general public, it is not for his many key contributions to geometry, calculus, and number theory, but rather for this speculation in the margin that will forever be known as
Fermat’s last theorem
.

Twenty-five years after making this dubious claim, Fermat did present a complete proof of something else, however: a remarkable and almost otherworldy principle that established an approach to physical phenomena that Feynman would use later to change the way we think about physics in the modern world. The issue to which Fermat turned his attention in 1662 involved a phenomenon the Dutch scientist Willebrord Snell had described forty years earlier. Snell discovered a mathematical regularity in the way light is bent, or refracted, when it crosses between two different media, such as air and water. Today we call this Snell’s law, and it is often presented in high school physics classes as yet one additional tedious fact to be memorized, even though it played a profoundly important role in the history of science.

Snell’s law pertains to the angles that a light ray makes when transmitted across the surface between two media. The exact form of the law is unimportant here; what is important is both its general character and its physical origin. In simple terms, the law states that when light goes from a less dense to a more dense medium, the trajectory of the light ray is bent closer to the perpendicular to the surface between the media (see figure).

Snell’s law

Now, why does the light bend? Well, if light were made up of a stream of particles, as Newton and others thought, one could understand this relationship if the particles speed up as they move from one medium to the other. They would literally be dragged forward, moving more effectively in a direction perpendicular to the surface they had just crossed. However, this explanation seemed fishy even at the time. After all, in a more dense medium any such particles would presumably encounter a greater resistance to their motion, just as cars on a road end up moving more slowly in heavy traffic.

There was another possibility, however, as the Dutch scientist Christiaan Huygens demonstrated in 1690. If light were a wave and not made of particles, then just as a sound wave bends inward when it slows down, the same would occur for light if it too slowed down in the denser medium. As anyone familiar with the history of physics knows, light does indeed slow down in denser media, so that Snell’s law provides important evidence that light behaves, in this instance, like a wave.