King of the Quantum

As Abraham Pais makes clear in his careful study, many of the scientists who encountered Niels Bohr even briefly came away with a remarkable impression. My own took place in 1958, when new elementary particles were appearing, in a bewildering profusion, from both cosmic rays and accelerator experiments. These were pre-quark days, so there was no theoretical model within which to fit this unexpected data. Things were so desperate that J. Robert Oppenheimer—I think he was kidding—suggested that a Nobel-like prize be given to an experimental physicist who did not discover a new particle.

In the confusion, a rumor arrived at The Institute for Advanced Study in Princeton, where I was then working, that Werner Heisenberg and Wolfgang Pauli had discovered a Theory of Everything. Each generation of theoretical physicists thinks it has discovered a Theory of Everything. By this time, Heisenberg’s physics were thought to be a bit over the hill, but Pauli, who died in 1958, was still considered one of the most brilliant and skeptical theoretical physicists who had ever lived. When Pauli said, as he occasionally did, that a paper was so bad that it was not even wrong, it generally sank without a trace. That Pauli had taken part in such an enterprise gave people pause.

Pauli was invited to lecture on his work with Heisenberg at Columbia University in late January 1958. A group of us came to New York from Princeton to hear him. I recall sitting next to Freeman Dyson during the lecture. Not long after the talk began, Dyson said to me, “It is like watching the death of a noble animal.” He had seen at once that the new theory was hopeless. What none of us then knew was that Pauli was to die of cancer a few months later. Before his death he turned against the theory and was circulating a cartoon, of his own devising, which showed only a blank canvas and a caption, in Heisenberg’s voice, which read, “I can paint like Titian—only a few details are missing.”

Niels Bohr was also at the lecture, a big man who reminded me of a Saint Bernard, dressed in an elegant dark suit with a vest. After Pauli had finished his lecture, Bohr was called upon to comment. I believe it was Pauli who remarked, perhaps in jest, that the theory may, at first, look “somewhat crazy.” Bohr then replied that the problem was that it was not crazy enough. Unlike quantum mechanics, say, it did not have the divine madness of great physics. At this point, Pauli and Bohr began stalking each other around the large demonstration table in front of the lecture hall. When Pauli appeared in front of the table he would say to the audience that the theory was sufficiently crazy, and when it was Bohr’s turn to stand in front of the table, he would say it wasn’t. The encounter of two of the giants of modern physics was an uncanny and unforgettable spectacle.

Abraham Pais’s new biography of Bohr begins with a somewhat different version of this event emphasizing his own talk with Bohr after the lecture. In his introductory chapter, oddly entitled “A Dane for all seasons,” Pais raises, again in the guise of an anecdote, one of the most fascinating questions a biographer of Bohr must deal with; namely, what was the lasting significance of Bohr’s work in physics. Pais describes a conversation he had with someone he describes as “one of the best and best-known physicists of my own generation.” The otherwise unidentified scientist says to Pais, “You knew Bohr well,” to which Pais replied, “I did.” “Then tell me,” Pais’s interlocutor goes on, “What did Bohr really do?”

The same physicist could not have asked the same question about Einstein, the subject of Pais’s splendid biography, Subtle is the Lord, for the answer would be simple: Einstein created twentieth-century physics. In addition, one can read Einstein’s original papers written at the beginning of this century, and later, with the pleasure of discovering the genius of the man, to say nothing of learning physics that is still relevant and valid. Einstein’s 1905 paper on relativity, for example, written when he was twenty-six, seems as fresh and clear and correct now as when it was first written. Only last spring, as I read for the first time the three papers Einstein wrote in the mid-1920s on certain kinds of quantum-mechanical gasses, I marveled that anyone could see as far as he did. If Einstein had written only these three papers he would have still been one of the greatest physicists of this century.

On the other hand, I cannot imagine anyone but a historian of science reading Bohr’s original papers. Not only are they densely written—as Pais, and others, have pointed out, the act of composition caused Bohr terrible anguish—but they also seem dated. The philosophical papers, of which Bohr was, it seems, especially proud, are almost unreadable today. I once asked the late I.I. Rabi what he thought of Bohr’s philosophical contributions to quantum mechanics. He said:

This work was his life. There was no point in trying to tell him that I thought it was irrelevant to the sort of things that an experimenter actually does in the laboratory. I felt that in this he was very profound about things that don’t really matter. But one was not going to tell him that.

There is something ironic and peculiar about all of this. Einstein was, in the deepest sense, a “classical” physicist. His sensibilities were formed during the nineteenth century and he never was able to accept the quantum mechanical view of reality. Bohr, on the other hand, was the guiding hand in creating this reality—the sounding board and mentor for Heisenberg, Pauli, Dirac, Schrödinger, and the rest of the inventors of quantum mechanics.¹ Yet, when one reads Bohr on quantum mechanics, with rare exceptions he seems almost wholly obscure when compared to Einstein. No one put this more clearly than my friend, the late John Bell, who, among all the present generation of physicists, thought the most deeply about quantum theory. Bell once said to me.

I feel that Einstein’s intellectual superiority over Bohr in this instance [the quantum theory of measurement] was enormous; a vast gulf between the man who saw clearly what was needed and the obscurantist. So for me, it is a pity that Einstein’s idea [of classical, causal, reality] doesn’t work. The reasonable thing just doesn’t work.²

This having been said, why is Bohr in many people’s reckoning, after Einstein, the most important physicist of this century? Pais’s book is especially good at answering this question. As he showed in his book on Einstein, he is very skilled at describing both the physics and the surrounding historical setting. This should not be confused with popular science writing. I do not believe that Pais’s historical vignettes can be read with much understanding by the non-physicist. The problem here is more acute than the one that confronts the Einstein biographer. Einstein was dealing with fundamental issues of space and time, while much of Bohr’s work was highly technical and the parts of it dealing with quantum mechanics were immensely subtle. Not only that, but some of what Bohr published turned out to be totally wrong. While one may argue that some of Einstein’s very last work came close to the “not even wrong” category, for close to thirty years everything the man published was brilliant. This means that Pais is forced, in Bohr’s case, to explain not only Bohr’s correct physics, but also his incorrect physics. I cannot imagine many non-specialists getting much out of this exercise.

Bohr’s great work was done in 1913, when he was twenty-eight. He had just returned to Denmark after a postdoctoral appointment in Manchester. His teacher in Manchester was the great New Zealand-born experimental physicist Ernest Rutherford. Rutherford, and his young collaborators, had, a few years earlier, discovered the atomic nucleus. Two of them, Hans Geiger (he of the counter) and Ernest Marsden, had been set the task of scattering so-called α-particles, actually helium nuclei, produced when radioactive decays of heavy elements take place. They are then scattered by thin foils of gold. Much to their astonishment, some of the α-particles were scattered backward, as if they had struck something hard within the gold atom. They had in fact struck the gold’s atomic nucleus. Before this, the most common view of the atom was that it was a fuzzy ball of electric charges. The α-particles were predicted to pass straight through it, like bullets through fog. Instead, some of them bounced backward.

It took some twenty-five years before it was established that the nucleus consisted of relatively massive neutrons and protons with the lighter particles, electrons, circulating outside it. But almost from the beginning, it was realized that the new model of the atom’s nucleus was in serious conflict with classical physics. An accelerated electron radiates, and hence loses energy. How then could matter be stable? Why didn’t the atoms simply collapse? Moreover, according to the classical picture, the electron radiation would be entirely chaotic. But, in fact, it was emitted in beautiful spectral lines which were, in the simplest cases, related to one another by elegant mathematical formulas, which had been discovered empirically.

Bohr resolved these two problems with one masterstroke. In our present language, he “quantized” the electron orbits. This means that he put forward the hypothesis that the electron, as it moved around the nucleus, could move only in special orbits. We now refer to them as Bohr orbits. The orbit with the least energy, the so-called ground state, was assumed to be absolutely stable. When an electron transited from one orbit to another—made a quantum jump—quanta of radiation were given off, with an energy determined by the energy difference between the orbits. Since the allowed orbits follow discrete patterns, so does the radiation.

All of this might have been dismissed as so much speculation if Bohr had not been able to make it quantitative. (In this I am reminded of Kepler, who was saved from the worst sort of Pythagorean mysticism by his determination to produce a quantitatively accurate description of the orbit of Mars.) Using his quantization, Bohr was able to compute the magnitude of the frequencies emitted, as well as their interrelations. When a tiny discrepancy between Bohr’s predicted values and the measured values showed up, he was also able to account for it as an effect of the relatively slow motion of the ponderous nucleus. When Einstein heard of these results he remarked, “This is an enormous achievement. The theory of Bohr must then be right.”

Bohr’s atom, with its classical orbits, quantized in space, has become one of the defining images of the atomic age. We see drawings of it everywhere. Yet it does not correspond at all to the modern quantum mechanical understanding of the atom. It is part of what is now known as the “old” quantum theory—an uneasy marriage between classical pictures of the atom and quantum conditions. From the time Bohr published his papers until the mid-1920s, when the “new” quantum theory was invented, this ungainly structure was elaborated ad infinitum. One is reminded of Ptolemy’s attempt to save the geocentric cosmology by adding more and more epicyclical planetary orbits, all of which were replaced when Kepler introduced a single elliptical planetary orbit around the sun.

Volumes have been written about the invention of the new quantum theory. Pais gives a useful summary of the new theory, with many references. From everything I have read, I am persuaded that it was Heisenberg who had the first truly quantum mechanical mind. He recognized that Bohr’s orbits were, in a certain sense, irrelevant. One cannot observe an electron making an atomic orbit. The act of observation destroys the orbit—“we murder to dissect”—since the electron is knocked out of the atom. This realization was later canonized by Heisenberg in his uncertainty principles. What one can observe are the spectral lines. Heisenberg concentrated on these, making a kind of calculus which became known as matrix mechanics. It was a Faustian bargain, since to accept this calculus was to give up visualizing the orbits. About the same time, Schrödinger invented what appeared to be a second quantum theory, in which the electron is described as a packet of waves. At first, people like Einstein who wanted to cling to classical realism were very pleased with this version of the theory, since it appeared that the waves could be visualized. This hope faded when the Heisenberg and Schrödinger theories were shown to be mathematically equivalent. Max Born then demonstrated that the Schrödinger wave packets had to be interpreted as packets of probability. The Bohr orbits become regions of space where the presence of the electrons is highly probable.

Niels Bohr’s role in all of this was, in a certain sense, Socratic. By the mid-1920s, he had been given his own institute for theoretical physics in Copenhagen—it was officially opened in 1921. So he was in the position of inviting the new breed of quantum theorists to Copenhagen to work out their ideas. In these sessions, Bohr was relentless. On one occasion, the exhausted Schrödinger was forced to take refuge in his bedroom, only to be followed there by Bohr, still arguing. Out of this came what is known as the Copenhagen interpretation of the quantum theory, which, curiously, does not seem to have been written down systematically anywhere. Two key elements were “correspondence” and “complementarity.” Correspondence refers to the requirement that the quantum theory have a classical limit, in the sense that the experiments described by quantum mechanics ultimately depend on the use of classical measuring instruments. Once again Bell put the issue succinctly:

I disagree with a lot of what Bohr said. But I think he said some very important things which are absolutely right and essential. One of the vital things that he always insisted on is that the apparatus [the measuring instrument used to measure wave and particle phenomena] is classical. For him there was no way of changing that. There must be things we can speak of in a classical way. For him it was inconceivable that you could extend the quantum formalism to include the apparatus.³

One can always attempt to describe an individual measuring instrument using the quantum mechanics of its atoms and molecules, but then this description must refer to another classical apparatus on the next level in the hierarchy. At the end of the day, the language we use is classical, Bohr would argue, and it must be. It is the only language we know.

Complementarity, which became for Bohr a general philosophical principle, was conceived in response to the particle-wave duality of matter. An object such as an electron can exhibit both particle and wave characteristics depending on the experimental arrangement used to measure its properties. On their face, these properties appear to exclude one another. Waves can pass through each other—modifying the patterns—while particles, as usually understood, cannot. Bohr noted that these properties are not really contradictory, but rather complementary, since they can never be realized conjointly in a single apparatus.

Each experimental setup reveals a distinctive facet of the electron. The Heisenberg uncertainty principles, it turns out, prevent contradictory facets of physical phenomenon from being realized simultaneously. But Bohr was not satisfied with limiting the idea of complementarity to physics. He thought he saw it virtually everywhere, for example in instinct and reason, free will, love, and justice, to name only a few of his applications. Pais remarks that he finds this way of viewing things “liberating.” I have always found that such attempts at extending the principle lead to a dead end.

I have also found the Copenhagen interpretation increasingly obscure, no doubt because of the influence of my friend John Bell. The question that is unanswered within quantum mechanics itself is to what it is supposed to apply. It is all very well to talk about different kinds of “classical” apparatus, but what are they? How many atoms does it take to construct such an apparatus? As Bell put it,

It is very strange in Bohr that, as far as I can see, you don’t find any discussion of where the division between his classical apparatus and the quantum system occurs. Mostly you will find [in Bohr] that there are parables about things like a walking stick—if you hold it closely it is part of you, and if you hold it loosely it is part of the outside world. He seems to have been extraordinarily insensitive to the fact that we have this beautiful mathematics, and we don’t know which part of the world it should be applied to.⁴

Most physicists of Pais’s generation, especially those who were exposed directly to Bohr—including, for example, Victor Weisskopf, Robert Oppenheimer, Rudolf Peierls, John Wheeler, and Pais himself—do not appear to have much sympathy for these issues. They tend to believe that, insofar as these questions are interesting, they were settled in the 1930s in Copenhagen. I once saw Oppenheimer reduce a young physicist nearly to tears by telling him that a talk he was delivering on the quantum theory of measurement at the Institute was of no interest, since all the problems had been solved by Bohr and his associates two decades earlier. In his book Pais writes,

By 1960 the non-relativistic quantum mechanics of a few particles in an external potential was a closed chapter to Bohr, as to most physicists.

Given this attitude, clearly Pais’s book is not the place to turn to learn about why more and more physicists are becoming dissatisfied with the conventional formulation of quantum mechanics. A reader who has the technical background to follow Pais’s book would do well to supplement it with, for example, John Bell’s Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, 1987).

This does not mean that there are ineluctable problems in applying the quantum theory to actual physical systems. Quantum theory has, so far, given us the answer to any question we have asked of it. I am constantly reminded of a story Dyson told me, many years ago, concerning his then young children. His daughter was explaining to her younger brother that she could now row a boat because she understood how the “rowers” worked. To this her brother replied that he did not understand how the “rowers” worked, but could row the boat anyway.

Bohr’s early success in physics made him a celebrated figure in Denmark. He rapidly became a smiling public man. Unlike Einstein, he established a school, and was successful in raising money to keep it running. One cannot imagine Einstein applying for grants, or heading scientific associations. Nor can one imagine Einstein seeking out world leaders like Churchill and George Marshall to discuss his ideas about an open world in which knowledge of nuclear weapons would be freely exchanged between the US and the USSR and other countries. Bohr got a sympathetic hearing from Roosevelt at least on their first meetings, and a very unsympathetic hearing from Churchill, who decided that Bohr, with his talk of sharing secrets, was a dangerous subversive. Oppenheimer once told me that he had thought of writing a play that he was going to call “The Day That Roosevelt Died.” His point was that if Roosevelt had lived a little longer, some of Bohr’s ideas about an open world might have gotten farther. In particular, the nuclear arms race with the Soviet Union, from which just now we seem to be emerging, might have been averted. This seems to me questionable. Andrei Sakharov’s memoirs as well as other studies of the period make one suspect that no amount of good will on Roosevelt’s part would have persuaded Stalin not to try to build the bomb. Sakharov wrote:

The Soviet government (or, more properly, those in power: Stalin, Beria and company) already understood the potential of the new weapon and nothing could have dissuaded them from going forward with its development. Any US move toward abandoning or suspending work on a thermonuclear weapon would have been perceived either as a cunning, deceitful maneuver or as evidence of stupidity or weakness.

Pais denies that Bohr was naive in his attempt to avoid a nuclear arms race. I think his discussion of this and several other matters, as I have tried to suggest, suffers from the common failing of biographers, which is to fall in love with their subjects. Pais is more candid than most. At the beginning of his book he remarks, “It may be well to state that I loved Bohr. I have tried to exercise restraint in regard to these sentiments, which may or may not shine through in what follows.” One of Bohr’s complementary antinomies was love versus justice. In this book, love tilts the scales. Bohr was such a complex figure that, as good as this biography is, there is still room for a further evaluation, in which the scales might from time to time tilt in a different direction.