The Uncertain Scientist

Werner Heisenberg was undoubtedly one of the greatest physicists of this century. In 1925, at the age of twenty-three, he wrote the paper that laid the foundations of quantum mechanics on which all subsequent generations have built. This was not just an extension or elaboration of the work of others, but an unexpected, radical new departure, which abandoned the basic notions of the old “classical” physics, such as that of electrons moving in orbits, replacing them by a much more abstract description.

In the public mind many advances in science are attributed to famous scientists, but in most cases the famous discoverer has completed a structure that was already developing, and without him someone else would sooner or later have done the same. Heisenberg’s paper was so original that, if he had not been around, it might have taken a very long time for the idea to occur to some other physicist; so this is one of the cases in which the personal attribution is justified. It is true that less than a year later Erwin Schroedinger published his theory of wave mechanics, which turned out to be identical in content to Heisenberg’s quantum mechanics. But we needed both points of view to develop a real understanding of the physical world.

Heisenberg was born in 1901 into an academic family. He was in his teens in Munich after the First World War, when a strong youth movement was emerging, and he became an enthusiastic member. Long hikes and campfire discussions of poetry, philosophy, religion, and music appealed to him. He learned to appreciate the beauty of nature: love for the countryside was part of the patriotism that was a strong emotion throughout his life. He became a youth leader, and formed a close friendship with a group of younger boys with whom he continued his long walks well after he became a famous and established scientist.

Another early interest was music; he was a highly gifted pianist, and it was even suggested that he might choose music as a career. But he was more strongly attracted to mathematics and physics; as a schoolboy he was fascinated by the theory of relativity. At the University of Munich he first tried to enroll in the study of mathematics, but he was put off by the mathematics professor, Ferdinand Lindemann, and he joined instead the theoretical physics group under Arnold Sommerfeld, then the greatest teacher of the subject. Sommerfeld immediately recognized Heisenberg’s unusual ability. Another student in the group, Wolfgang Pauli, a year his senior, became a lifelong friend.

Heisenberg was introduced to the intricacies of the quantum theory of Niels Bohr and Arnold Sommerfeld, which had successfully explained many facts about atoms, but had also had many failures and contained internal inconsistencies. He wrote his first paper in 1922, barely a year after entering the university. During Sommerfeld’s absence on leave he went to Göttingen to work with Max Born, and later returned there as Born’s assistant. He met Niels Bohr, and visited him in Copenhagen. This became another close and lasting relationship, in spite of the difference in their ages.

The next few years were a time of great activity and great confusion in atomic physics. New discoveries of phenomena and regularities showed up the inadequacies of the existing quantum theory and the need for new ideas. Bohr, Born, Pauli, and Heisenberg were among the people struggling to find a way forward, and, by intense correspondence and personal discussion, assisted and criticized each other in these attempts, but to no avail. This continued until the situation was revolutionized by Heisenberg’s paper of 1925.

All those who were able to understand the novel and difficult ideas in his paper recognized that here was the long-awaited breakthrough. The Bohr-Sommerfeld theory, accepted before Heisenberg’s paper, described electrons in the atom as revolving around the nucleus in orbits, like planets around the sun, as in classical mechanics; but only certain selected orbits were allowed. Radiation was emitted when an electron jumped from one orbit to another, and the energy loss of the electron determined the frequency (color) of the radiation. The theory predicted correctly the existence of sharp lines in atomic spectra, and their positions in the case of hydrogen, the simplest atom. But it encountered difficulty in dealing with more complex atoms, as well as many other problems. Heisenberg discarded the concept of orbits, which could not in principle be observed—this was made more precise later through his uncertainty principle—and he proposed that the physicist should deal only with observable things. This meant concentrating not on single orbits, but on the emitted radiation, which comes from a jump between two orbits, so that he was talking of two states of the atom at a time.

Many physicists started to elaborate and apply the new theory. In Göttingen Born and his collaborator Pascual Jordan perfected the mathematical formulation of Heisenberg’s scheme; they recognized that Heisenberg had reinvented a system known to mathematicians as “matrix calculus,” but unfamiliar to most physicists. Pauli in Hamburg managed to apply the new theory to the hydrogen atom, and showed that it gave the correct answers, while Paul Dirac in England reproduced and extended the theory in his own original presentation.

Schroedinger’s wave mechanics started from a very different approach, but it also gave correct results and appeared at first to be an alternative theory. It soon proved to be the same as Heisenberg’s, although expressed in a different language. Heisenberg was at first reluctant to accept it, but soon saw that Schroedinger’s equations were easier to handle for most purposes, and he started to use them himself. Schroedinger, however, believed that the waves in his theory were tangible waves, like waves on water, or sound waves. To Bohr and Heisenberg this view was untenable. The waves spread all over space, and Schroedinger’s interpretation could not account for the fact that when we look for an electron, we always find it concentrated at one point. Also, if there are several electrons, the wave function must give us the probability of their all having various positions, and this cannot be done by a real wave in space. But after many heated discussions Bohr and Heisenberg failed to convince Schroedinger. The correct view, as finally expressed by Max Born, was that the intensity of the waves determines the probability with which the electron will be found at a given point in space.

Thus physics cannot specify the exact position of a particle; its position is a matter of chance, with only probabilities being the subject of the physicist’s description. This conclusion led Heisenberg to his “uncertainty principle,” which has to do with the accuracy with which different attributes of a physical object can be known; the more precisely we want to know the position of a particle, the more uncertain must be its velocity, because the act of observation causes an unknown change in the velocity. Bohr had reached similar conclusions, and was a little annoyed with Heisenberg, because he would have preferred to state the argument in his own way.

In October 1927, when he was not yet twenty-six, Heisenberg was elected professor of theoretical physics at Leipzig, and became the successful leader of a group of students and more senior collaborators. His infectious enthusiasm and his simple and unpretentious manner no doubt reflected the qualities that had early engaged his sympathies in the youth movement. (As one of his students in 1928 and 1929 I had occasion to appreciate these qualities.) He continued to make original and important contributions to physics, although after the early Thirties his projects were less successful.

After Hitler came to power in 1933 Heisenberg found the effects of the regime on academic life, on science, and on life generally deplorable, but he decided to remain in Germany because of his patriotism, and because he felt a duty to do what he could to mitigate the regime’s evil effects. During the war he worked on the German atomic-energy project, which failed to get any results. His actions during that period have caused intense controversy, which continues, and to which I shall have to return.

After the war he conceived the ambitious idea of finding a single equation which would describe all the particles of physics and their interplay, but though he claimed at times partial success, the scheme never got off the ground. He was, however, instrumental in rebuilding German physics, and in arguing for Germany’s having nuclear power, but not nuclear weapons. He also participated in the creation of CERN, the European nuclear research center in Geneva.

David C. Cassidy has made a monumental effort to give us in 669 pages, including eighty-eight pages of notes, a full, personal, and scientific biography. The early chapters cover family background, childhood, and adolescence. They present a lively and, as far as I can judge, very fair picture of the young Heisenberg and his environment. With Heisenberg’s start in physics, the story includes many accounts of the physics to which he was exposed, and of his own work. Unfortunately, Cassidy’s account of the physics is much too difficult for the nonphysicist reader. He uses technical terms and jargon without restraint, and includes equations that most lay readers could not follow even if they knew what the symbols meant. For the physicist, on the other hand, there is not much to learn. Most physicists will be familiar with the concepts developed in 1925; they might not know all the details of the arguments in quantum theory before Heisenberg’s paper, but what is said is much too brief to satisfy any curiosity. Besides, the physicist will notice many errors. ¹

The atmosphere of the years of confusion before 1925, with their frustration, their cooperation and disagreements between the theorists, comes across very well, even though it is not possible to understand what they were arguing about. But Cassidy’s account of the debates with Schroedinger does not distinguish clearly (1) the debate over Schroedinger’s wave mechanics as opposed to Heisenberg’s matrix mechanics (which was soon settled when both came to be used interchangeably) from (2) Schroedinger’s claim of the tangible reality of the waves (which it took him a long time to abandon).

On the controversies about Heisenberg’s behavior during the Hitler period, Cassidy is clear and reasonable. The first question asked by many is: Why did Heisenberg stay in Germany, when he was opposed to much of what the system was doing, and why did he make so many compromises with the system? Cassidy’s answer, with which I agree, is that Heisenberg was strongly patriotic. He also had some sympathy for the idea of a national renewal put forward by Hitler, since the social system did not seem to be working under the Weimar republic. But he is on record as strongly disapproving of the sacking of “non-Aryans” and liberals, and the attacks on “Jewish,” as opposed to “German,” physics.

He often sought the advice of Max Planck, the elder statesman of physics, who felt it his duty to remain in his post as head of the Kaiser Wilhelm Society, the main body supporting research, to use his influence to prevent the Nazis’ worst excesses. In fact there was little he could do; his attitude is well characterized by a remark once made by Robert Oppenheimer, in reference to his own past, “As long as I ride on this train, it will not go to the wrong destination.”

Cassidy criticizes Heisenberg for trying to help his own students and others in his immediate circle and not anybody outside, but there were limits to what one could do under the system without great personal risk. Once he had decided to remain in Nazi Germany, he could hardly avoid making concessions to the regime. Not everybody could be like Max von Laue, who kept out of sight and made as few concessions as possible (it is said that he never left the house without carrying two packages or a briefcase and a package, so he had no hand free to give the Hitler salute). This was not a possible way of life for Heisenberg, who wanted to continue being active as a leader in science.

He never openly opposed the Nazi system, but he was outspoken when it came to the attacks on modern physics by Johannes Stark and other fanatical supporters of “German” physics, even though this exposed him to virulent personal denunciation. This culminated in an attack on him in a Nazi newspaper, and he was, as a result, turned down for the appointment to the chair in Munich, for which he was the favored candidate. He complained to Himmler, whose organization sponsored the paper, asking if this attack represented the official line, in which case he would feel obliged to resign his chair in Leipzig. It took a long time before the reply came that such an attack did not have official approval, and would not be allowed to happen again. Indeed the attacks on him ceased, to his gratification, though this result was not achieved without cost. While he was allowed to teach relativity, he had to promise not to mention the name of Einstein. Cassidy thinks that in this struggle, Heisenberg was concerned solely with his personal honor and standing, but it is hard to tell whether or how far he was also thinking of the standing and reputation of his subject and his profession.

Another important controversy centers on the question why the German scientists did not produce an atom bomb. Robert Jungk² and Walter Kaempfert of The New York Times have claimed that the German scientists were inhibited by moral scruples. Others, including Sam Goudsmit in his book Alsos³ (though he later withdrew some of his statements) and Jeremy Bernstein in his April 1991 review in these pages of Victor Weisskopf’s autobiography,⁴ claim that the failure was owing to incompetence. Bernstein quotes Paul Lawrence Rose’s assertion that Heisenberg did not know the difference between a bomb and a reactor, and he mentions, though without endorsing it, a rumor that the Germans planned to drop a reactor as a weapon.

Cassidy rightly dismisses most of these stories. Heisenberg and the other German scientists, after beginning research on an atom bomb, genuinely believed that there was no chance of completing the manufacture of a weapon during the war, and indeed even the American project did not produce the first bomb until after the end of the war in Europe. As a result German scientists did not press the government for a crash program, and that explains the limited resources that were allocated to the project and its slow pace.

It is true that they overestimated the difficulties, because they never made a careful estimate of the critical size needed for a fast chain reaction, and therefore tended to overestimate the size of a weapon. It is also true that there were many errors of judgment in their work. For example, they excluded graphite as a moderator to slow down the neutrons because of a mistaken finding that it absorbed too many neutrons (not, as Cassidy says, that it was ineffective in slowing them down). This failure is often blamed on Walther Bothe, who is alleged to have made “wrong” measurements. In fact his measurements were correct; but the “pure” graphite he was using contained impurities in amounts that were too small to be detected chemically, but were fatal for the absorption of neutrons. In the same situation, Fermi and his collaborators in the US guessed that further purification would improve the results. Another bad judgment was Heisenberg’s insis tence on using uranium plates, rather than rods or cubes of uranium, in the face of theoretical and experimental demonstration that rods or cubes were more effective.

While the Allied scientists were driven by the fear that Nazi Germany might get there first, the Germans arrogantly felt sure nobody could do better than they. But their view that Germany could not make a weapon before the end of the war was no doubt right. They were relieved that they did not have to make a moral judgment.

Would they have gone ahead if they had believed it possible to make a weapon? It is not easy to answer this hypothetical question, and Cassidy does not give a definite answer, but he implies that they probably would have done so, and I believe this is right.⁵ Several people report that Heisenberg made the strange statement that on finding out about the death camps and other atrocities, he decided that he did not want Germany to be defeated, because the hate generated by these events would result in the complete destruction of Germany. He therefore felt he should donate his efforts to his country. It is not clear what he meant by this, since at that stage there was no way in which his work on atomic energy could have assisted the war effort.

Heisenberg said after the war, “It was from September 1941 that we saw an open road ahead of us, leading to the atom bomb.” This was no doubt based on the knowledge that a reactor would produce plutonium, which was suitable material for making weapons. But he must have been aware that this open road was still extremely long. The Germans had not yet succeeded in making an experimental chain reaction (indeed they never did so), and if they succeeded in that, it was still a long way to a production reactor, which would have required more heavy water and uranium metal, both in short supply, as well as plutonium extraction facilities and bomb design. When in 1942 Heisenberg indicated to the authorities that there was a possibility of a bomb, he was more concerned with maintaining support for the work of the German scientists than with a real expectation of such an outcome.

The opinion of Heisenberg and other German scientists about the feasibility of making a weapon during the war is made clear in the “Farm Hall transcripts,” the recently released record of the conversations between German scientists, including Heisenberg, during their internment in England after VE Day, in a house that was bugged by British intelligence. When the first news came of the atom bomb dropped on Hiroshima, most of them refused to believe this, claiming that the Allies were bluffing. Even when more detailed statements convinced them that this was an atom bomb, Heisenberg kept saying that he could not understand how the Americans had been able to make a weapon in the time available to them. The transcripts also dispose of the idea that the Germans did not make a bomb for moral reasons: they discussed at great length the reasons for their failure, but they did not claim that moral scruples stopped them from working on the bomb. When Weizsäcker tentatively suggested that such scruples had prevented success, Otto Hahn firmly contradicted him.

The question of Heisenberg’s visit to Bohr in 1941 is another matter for controversy, and here we are not likely ever to get a clear answer. Bohr’s and Heisenberg’s accounts of their conversation differ completely, and we cannot believe either. Heisenberg’s recollections were very much influenced by his later thoughts, and Bohr, who was much better at talking than at listening, would often misunderstand what people said. Cassidy reviews various hypotheses based on Heisenberg’s accounts. Perhaps he wanted Bohr to know that an atom bomb was possible, but that the Germans were not working on it. Perhaps he wanted Bohr’s advice on whether one should work on it. In a postwar letter to B. L. van der Waerden, Heisenberg said he wanted to avert a crash program by the Allies. The last is most implausible, because he did not then know that Bohr was in touch with the British, and also because he believed that a bomb could not be made in wartime. Bohr said later that Heisenberg came to threaten him with the bomb; and Bohr’s wife, Margrethe, said that Heisenberg wanted to sound out Bohr on what the Allies were doing. If, as seems the case, he did not know Bohr was in touch with them, this is not very plausible either.

There was never any chance of a dispassionate conversation between Bohr, a prominent citizen of an occupied country, and Heisenberg, who though an old friend, was now a representative of the hated occupying power. The inability of Heisenberg to see this was a typical example of his insensitivity, his lack of understanding of other people’s points of view. Cassidy quotes a number of cases in which, during his lecture tours in occupied or neutral countries during the war, his remarks were deeply offensive to his hosts.

Some sections of Cassidy’s book are difficult to read partly because the author tends to jump around in time. Some deviation from strict chronology is of course necessary. But here it is done much more than seems necessary, so that the reader has difficulty seeing what period is referred to at a given point. This can lead to substantial errors if the author himself gets confused about timing.⁶

Still, Cassidy supplies much interesting information, and he has collected some of it with meticulous care. For example, the chapters about Heisenberg’s youth contain not only summaries of many personal letters, but quotations from his school reports and the comments of his teachers. The only material missing was destroyed during the war.