INTRODUCTION

To understand why Richard Feynman was such a great teacher, it is important to appreciate his remarkable stature as a scientist. He was indeed one of the outstanding figures of twentieth-century theoretical physics. His contributions to that subject are central to the whole development of the particular way in which quantum theory is used in current cutting-edge research and thus to our presentday pictures of the world. The Feynman path integrals, Feynman diagrams, and Feynman rules are among the very basic tools of the modern theoretical physicist—tools that are necessary for the application of the rules of quantum theory to physical fields (e.g., the quantum theory of electrons, protons, and photons), and which form an essential part of the procedures whereby one makes these rules consistent with the requirements of Einstein’s Special Relativity theory. Although none of these ideas is easy to appreciate, Feynman’s particular approach always had a deep clarity about it, sweeping away unnecessary complications in what had gone before. There was a close link between his special ability to make progress in research and his particular qualities as a teacher. He had a unique talent that enabled him to cut through the complications that often obscure the essentials of a physical issue and to see clearly into the deep underlying physical principles.

Yet, in the popular conception of Feynman, he is known more for his antics and buffoonery, for his practical jokes, his irreverence towards authority, his bongo-drum performing, his relationships with women, both deep and shallow, his attendance at strip clubs, his attempts, late in life, to reach the obscure country of Tuva in central Asia, and many other schemes. Undoubtedly, he must have been extraordinarily clever, as his lightning quickness at calculation, his exploits involving safe-cracking, outwitting security services, deciphering ancient Mayan texts—not to mention his eventual Nobel Prize—clearly demonstrate. Yet none of this quite conveys the status that he unquestionably has amongst physicists and other scientists, as one of the deepest and most original thinkers of this century.

The distinguished physicist and writer Freeman Dyson, an early collaborator of Feynman’s at a time when he was developing his most important ideas, wrote in a letter to his parents in England in the spring of 1948, when Dyson was a graduate student at Cornell University, “Feynman is the young American professor, half genius and half buffoon, who keeps all physicists and their children amused with his effervescent vitality. He has, however, as I have recently learned, a great deal more to him than that. ...” Much later, in 1988, he would write: “A truer description would have said that Feynman was all genius and all buffoon. The deep thinking and the joyful clowning were not separate parts of a split personality.... He was thinking and clowning simultaneously.”¹ Indeed, in his lectures, his wit was spontaneous, and often outrageous. Through it he held his audiences’ attention, but never in a way that would distract from the purpose of the lecture, which was the conveying of genuine and deep physical understanding. Through laughter, his audiences could relax and be at ease, rather than feel daunted by what might otherwise be somewhat intimidating mathematical expressions and physical concepts that are tantalizingly difficult to grasp. Yet, although he enjoyed being center stage and was undoubtedly a showman, this was not the purpose of his expositions. That purpose was to convey some basic understanding of underlying physical ideas and of the essential mathematical tools that are needed in order to express these ideas properly.

Whereas laughter played a key part of his success in holding an audience’s attention, more important to the conveying of understanding was the immediacy of his approach. Indeed, he had an extraordinarily direct no-nonsense style. He scorned airy-fairy philosophizing where it had little physical content. Even his attitude to mathematics was somewhat similar. He had little use for pedantic mathematical niceties, but he had a distinctive mastery of the mathematics that he needed, and could present it in a powerfully transparent way. He was beholden to no one, and would never take on trust what others might maintain to be true without himself coming to an independent judgment. Accordingly, his approach was often strikingly original whether in his research or teaching. And when Feynman’s way differed significantly from what had gone before, it would be a reasonably sure bet that Feynman’s approach would be the more fruitful one to follow.

Feynman’s preferred method of communication was verbal. He did not easily, or often, commit himself to the printed word. In his scientific papers, the special “Feynman” qualities would certainly come through, though in a somewhat muted form. It was in his lectures that his talents were given full reign. His exceedingly popular “Feynman Lectures” were basically edited transcripts (by Robert B. Leighton and Matthew Sands) of lectures that Feynman gave, and the compelling nature of the text is evident to anyone who reads it. The Six Not-So-Easy Pieces that are presented here are taken from those accounts. Yet, even here, the printed words alone leave something significantly missing. To sense the full excitement that Feynman’s lectures exude, I believe that it is important to hear his actual voice. The directness of Feynman’s approach, the irreverence, and the humor then become things that we can immediately share in. Fortunately, there are recordings of all the lectures presented in this book, which give us this opportunity—and I strongly recommend, if the opportunity is there, that at least some of these audio versions are listened to first. Once we have heard Feynman’s forceful, enthralling, and witty commentary, in the tones of this streetwise New Yorker, we do not forget how he sounds, and it gives us an image to latch on to when we read his words. But whether we actually read the chapters or not, we can share something of the evident thrill that he himself feels as he explores—and continually re-explores—the extraordinary laws that govern the workings of our universe.

The present series of six lectures was carefully chosen to be of a level a little above the six that formed the earlier set of Feynman lectures entitled Six Easy Pieces (published by Addison Wesley Longman in 1995). Moreover, they go well together and constitute a superb and compelling account of one of the most important general areas of modern theoretical physics.

This area is relativity, which first burst forth into human awareness in the early years of this century. The name of Einstein figures preeminently in the public conception of this field. It was, indeed, Albert Einstein who, in 1905, first clearly enunciated the profound principles which underlie this new realm of physical endeavor. But there were others before him, most notably Hendrik Antoon Lorentz and Henri Poincaré, who had already appreciated most of the basics of the (then) new physics. Moreover, the great scientists Galileo Galilei and Isaac Newton, centuries before Einstein, had already pointed out that in the dynamical theories that they themselves were developing, the physics as perceived by an observer in uniform motion would be identical with that perceived by an observer at rest. The key problem with this had arisen only later, with James Clerk Maxwell’s discovery, as published in 1865, of the equations that govern the electric and magnetic fields, and which also control the propagation of light. The implication seemed to be that the relativity principle of Galileo and Newton could no longer hold true; for the speed of light must, by Maxwell’s equations, have a definite speed of propagation. Accordingly, an observer at rest is distinguished from those in motion by the fact that only to an observer at rest does the light speed appear to be the same in all directions. The relativity principle of Lorentz, Poincaré, and Einstein differs from that of Galileo and Newton, but it has this same implication: the physics as perceived by an observer in uniform motion is indeed identical with that perceived by an observer at rest.

Yet, in the new relativity, Maxwell’s equations are consistent with this principle, and the speed of light is measured to have a definite fixed value in every direction, no matter in what direction or with what speed the observer might be moving. How is this magic achieved so that these apparently hopelessly incompatible requirements are reconciled? I shall leave it to Feynman to explain—in his own inimitable fashion.

Relativity is perhaps the first place where the physical power of the mathematical idea of symmetry begins to be felt. Symmetry is a familiar idea, but it is less familiar to people how such an idea can be applied in accordance with a set of mathematical expressions. But it is just such a thing that is needed in order to implement the principles of special relativity in a system of equations. In order to be consistent with the relativity principle, whereby physics “looks the same” to an observer in uniform motion as to an observer at rest, there must be a “symmetry transformation” which translates one observer’s measured quantities into those of the other. It is a symmetry because the physical laws appear the same to each observer, and “symmetry,” after all, asserts that something has the same appearance from two distinct points of view. Feynman’s approach to abstract matters of this nature is very down to earth, and he is able to convey the ideas in a way that is accessible to people with no particular mathematical experience or aptitude for abstract thinking.

Whereas relativity pointed the way to additional symmetries that had not been perceived before, some of the more modern developments in physics have shown that certain symmetries, previously thought to be universal, are in fact subtly violated. It came as one of the most profound shocks to the physical community in 1957, as the work of Lee, Yang, and Wu showed, that in certain basic physical processes, the laws satisfied by a physical system are not the same as those satisfied by the mirror reflection of that system. In fact, Feynman had a hand in the development of the physical theory which is able to accommodate this asymmetry. His account here is, accordingly, a dramatic one, as deeper and deeper mysteries of nature gradually unfold.

As physics develops, there are mathematical formalisms that develop with it, and which are needed in order to express the new physical laws. When the mathematical tools are skillfully tuned to their appropriate tasks, they can make the physics seem much simpler than otherwise. The ideas of vector calculus are a case in point. The vector calculus of three dimensions was originally developed to handle the physics of ordinary space, and it provides an invaluable piece of machinery for the expression of physical laws, such as those of Newton, where there is no physically preferred direction in space. To put this another way, the physical laws have a symmetry under ordinary rotations in space. Feynman brings home the power of the vector notation and the underlying ideas for expressing such laws.

Relativity theory, however, tells us that time should also be brought under the compass of these symmetry transformations, so a four-dimensional vector calculus is needed. This calculus is also introduced to us here by Feynman, as it provides the way of understanding how not only time and space must be considered as different aspects of the same four-dimensional structure, but the same is true of energy and momentum in the relativistic scheme.

The idea that the history of the universe should be viewed, physically, as a four-dimensional space-time, rather than as a three-dimensional space evolving with time is indeed fundamental to modern physics. It is an idea whose significance is not easy to grasp. Indeed, Einstein himself was not sympathetic to this idea when he first encountered it. The idea of space-time was not, in fact, Einstein’s, although, in the popular imagination it is frequently attributed to him. It was the Russian/German geometer Hermann Minkowski, who had been a teacher of Einstein’s at the Zurich Polytechnic, who first put forward the idea of four-dimensional space-time in 1908, a few years after Poincaré and Einstein had formulated special relativity theory. In a famous lecture, Minkowski asserted: “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of unity between the two will preserve an independent reality.”²

Feynman’s most influential scientific discoveries, the ones that I have referred to above, stemmed from his own space-time approach to quantum mechanics. There is thus no question about the importance of space-time to Feynman’s work and to modern physics generally. It is not surprising, therefore, that Feynman is forceful in his promotion of space-time ideas, stressing their physical significance. Relativity is not airy-fairy philosophy, nor is space-time mere mathematical formalism. It is a foundational ingredient of the very universe in which we live.

When Einstein became accustomed to the idea of space-time, he took it completely into his way of thinking. It became an essential part of his extension of special relativity—the relativity theory I have been referring to above that Lorentz, Poincaré, and Einstein introduced—to what is known as general relativity. In Einstein’s general relativity, the space-time becomes curved, and it is able to incorporate the phenomenon of gravity into this curvature. Clearly, this is a difficult idea to grasp, and in Feynman’s final lecture in this collection, he makes no attempt to describe the full mathematical machinery that is needed for the complete formulation of Einstein’s theory. Yet he gives a powerfully dramatic description, with insightful use of intriguing analogies, in order to get the essential ideas across.

In all his lectures, Feynman made particular efforts to preserve accuracy in his descriptions, almost always qualifying what he says when there was any danger that his simplifications or analogies might be misleading or lead to erroneous conclusions. I felt, however, that his simplified account of the Einstein field equation of general relativity did need a qualification that he did not quite give. For in Einstein’s theory, the “active” mass which is the source of gravity is not simply the same as the energy (according to Einstein’s E=mc²); instead, this source is the energy density plus the sum of the pressures, and it is this that is the source of gravity’s inward accelerations. With this additional qualification, Feynman’s account is superb, and provides an excellent introduction to this most beautiful and self-contained of physical theories.

While Feynman’s lectures are unashamedly aimed at those who have aspirations to become physicists—whether professionally or in spirit only—they are undoubtedly accessible also to those with no such aspirations. Feynman strongly believed (and I agree with him) in the importance of conveying an understanding of our universe—according to the perceived basic principles of modern physics—far more widely than can be achieved merely by the teaching provided in physics courses. Even late in his life, when taking part in the investigations of the Challenger disaster, he took great pains to show, on national television, that the source of the disaster was something that could be appreciated at an ordinary level, and he performed a simple but convincing experiment on camera showing the brittleness of the shuttle’s O-rings in cold conditions.

He was a showman, certainly, sometimes even a clown; but his overriding purpose was always serious. And what more serious purpose can there be than the understanding of the nature of our universe at its deepest levels? At conveying this understanding, Richard Feynman was supreme.

 

ROGER PENROSE

December 1996