Quantum Leaps

The following sections are included:

• Table of Contents
• A Frontispiece
• Acknowledgements
• An Introduction

In the fall of 1957, I began what turned out to be a two-year membership at the Institute for Advanced Study in Princeton. This was a banner time for physics. In 1956, the Chinese-born American physicists T.D.Lee and C.N.Yang noted in several papers that what is called “parity symmetry” — the symmetry between left and right handed descriptions—a cornerstone of physics up to that point—had never been tested in the sort of weak interactions that are responsible for the instability of many elementary particles and atomic nuclei. They proposed several experiments, and when these were performed they demonstrated that, in these interactions, the symmetry was indeed violated. This was a sensational discovery and all of us were gripped by its implications. In the fall of 1957, Lee and Yang, who were both at the Institute, were awarded the Nobel Prize for Physics. Soon after my arrival at the Institute I studied the membership roster. There were several physicists whose work I had studied and admired, but I came across a name that really surprised me—Reinhold Niebuhr…

On August 30, 1983, the Dalai Lama and a delegation of Tibetan monks visited CERN. “CERN” is an acronym for the name ‘Conseil Europé en pour la Recherche Nuclé aire’ although in the official name, the word ‘Organisation’ has now replaced ‘Conseil’. CERN, which is on the border between France and Switzerland just outside of Geneva, is the largest laboratory in the world devoted to the physics of elementary particles. It is an international organization in every sense, although I am not aware of any Tibetans who have ever worked there, at least as scientists. Why the Dalai Lama chose to make this visit is somewhat mysterious to me, although accounts of his boyhood describe his interest in taking apart and putting together machines to see how they worked. In any event, on this occasion there were something like thirteen Tibetan monks. CERN, which is used to receiving delegations, arranged a formal lunch for the Tibetans and a corresponding number of people from the laboratory. One of them was my friend, the late John Bell who died suddenly of a cerebral hemorrhage in the fall of 1990 at the age of sixty-two. But some months before Bell’s death, I had had the chance to discuss the Dalai Lama’s visit at some length with him…

Niels Bohr had great difficulty in the actual writing of a paper, or in giving a lecture for that matter. One would be tempted to say that it was some curious form of dyslexia. This was especially true in his mature years as his output became more and more philosophical—less mathematical. To deal with this, Bohr hired assistants, part of whose job was to act as sounding boards and amanuenses. When none of these assistants were available, he pressed anyone who seemed both qualified and at hand into this duty. One of these people was the late Abraham Pais. He wrote about this experience in his biography of Bohr, Niels Bohr’s Times. Pais writes, “Bohr devoted tremendous effort and care to the composition of his articles. However, to perform the physical act of writing, pen or chalk in hand, was almost alien to him. He preferred to dictate. On one of the few occasions that I actually did see him write himself, Bohr performed the most remarkable act of calligraphy I shall ever witness.” “ … as we were discussing the address that Bohr was to give on the occasion of the tercentenary celebration of Newton’s birth, Bohr stood in front of the blackboard (wherever he dwelt, a blackboard was never far) and wrote down some general themes to be discussed. One of them had to do with the harmony of something or other. So Bohr wrote down the word ‘harmony’”…

In the fall of 1947, I entered Harvard College as a seventeen-year-old freshman. I had no real ideas about my future, except that I was quite sure that it would have nothing to do with science. I had no interest in science. But at that time the President of the university was James Bryant Conant, a chemist who had played a very important role in the creation of nuclear weapons. This experience had left him with a good deal of concern about this new force in the world. One manifestation of this was the notion that every Harvard graduate should have some sort of scientific education. He knew, of course, that most of us would not have careers in science, but we might well have careers where we would have to make decisions that involved science. So under the rubric of “General Education” a set of natural science courses had been instituted which presented non-mathematical surveys of different scientific fields. Every Harvard graduate was required to pass one of them unless he—there were no ‘she’s—was a science major. You also had to be able to swim two laps of a twenty-five-yard long pool. Faced with the former obstacle, I consulted the Harvard Confidential Guide to Courses—a small booklet produced and sold by the undergraduate newspaper, the Harvard Crimson—to find out which course was considered the easiest. The vote among the undergraduates who took the various courses and compared notes was unanimous that it was Natural Sciences 3, taught by the late historian of science, I. Bernard Cohen…

When I finished taking Philipp Frank’s course on the foundations of modern physics in the spring of 1958, one thing had become clear to me: if I really wanted to have any kind of understanding I needed to learn some mathematics. Professor Frank, after his formal lecture, made as I said in the last chapter, “a certain interval”, which was followed by a question period during which he would have a chance to expand on some things “for those of you who know a little of mathematics.” I still remember his solving the elementary differential equation that described the decay of a particle. I had no idea what he was doing or how it led to the exponential answer. I also had no idea what I was doing except that I wanted to learn “a little of mathematics.” On how I would use this later in life, I was clueless. I had some friends who were taking the introductory course in calculus. Indeed, one of them showed me his homework papers. The grader had made some extremely witty remarks. It turned out to have been Tom Lehrer who became one of the foremost musical satirists of the 20^th century…

In 1907, Einstein published a paper in the Annalen der Physik in which he tied up some loose ends left over from his great 1905 paper on the special theory of relativity—“special” because it did not deal with accelerated motions. I will describe one of the loose ends in more modern language. Suppose that the theory of relativity is valid, but suppose there exist particles that can move faster than light. Such hypothetical particles are now called “tachyons.” We must be clear about something. An ordinary particle like an electron, assuming the theory of relativity is correct, can never be accelerated to the speed of light, let alone faster. Tachyons always move at speeds greater than light. It turns out that this does not violate the theory of relativity but it leads to very strange behavior indeed…

I went through a chess playing phase. I was never good enough so that it became an obsession, but I did study and take a few lessons. I played chess hustlers—and still do—in Washington Square Park in Greenwich Village in New York. The first time I met Stanley Kubrick I discovered that he had been, somewhat before my time, one of those chess hustlers. This led to a match of 25 games—which he won—while he was filming 2001. My account of this in The New Yorker led to a commission from Playboy magazine to cover the Bobby Fischer-Boris Spassky match in Iceland. I tell you this because of a missed opportunity. One time when I was visiting my parents in Rochester I learned that the International Grandmaster Samuel Reshevsky was giving an exhibition. Reshevsky had dominated American chess for several decades and was one of my heroes. He was going to play a simultaneous match with some forty players, each one paying a few dollars for the privilege. I signed up…

When I started this exploration I had no idea where it would lead; that we would go from Auden to the Dalai Lama and on to communist ideology. The riches of the quantum theory are so vast that I am sure that we are closer to the beginning than to the end. But here are two of my favorite quotations, one from Bohr and the other from Feynman. They are a good note to end on…

There are no new discoveries that involve the quantum theory itself. This is unfortunate, because then we might have some experimental guidance as to how to modify the theory. There is some agreement among thoughtful students of the subject that there is no entirely satisfactory interpretation of the quantum theory. This has provoked a thoughtful practitioner like Freeman Dyson to propose that the theory only applies to probabilistic predictions of the future, but that the past is not probabilistic so the quantum theory does not apply to it. It happened and should be described classically. Dyson argues that there is no way in the standard quantum theory to formulate the statement that that atom decayed yesterday at 4 :P.M. I don’t think many other physicists are willing to go this far. But I would like here to explain the discontents that many of us feel and which were so well summarized by the late John Bell…