137: Jung, Pauli, and the Pursuit of a Scientific Obsession Part 12

To date no violations of CPT symmetry have been found in the laboratory-that is, incorrect predictions of equations which can be traced to violating CPT, or what is the same, with violating relativity theory. It underlies every theory of elementary particles and is essential for studying the behavior of its three component symmetries-C, P, and T-in this increasingly bizarre world.

Pauli wrote up his conclusions in a milestone paper to be published in a volume to celebrate Niels Bohr's seventieth birthday the following year, 1955. It was the capstone to a subject he had studied with a pa.s.sion ever since he was a young man-relativity-and it finally set his greatest discovery, the exclusion principle, firmly in its embrace, along with another off shoot of the exclusion principle, spin. He began his paper on a historical note, recalling "a long and still continuing pilgrimage since the year 1922, in which so many stations are involved."

It was precisely as he was writing this paper that he dreamed that curious dream about the Chinese woman and the reflections that were not reflections. But at the time he thought no more about it.

The father of the neutrino.

In June 1956, the experimental physicists Frederick Reines and Clyde Cowan made an exciting discovery. They succeeded in finally verifying in the laboratory the neutrino, which Pauli had predicted twenty-six years earlier, actually existed. They immediately sent him a telegram. Pauli was at a symposium in CERN, the huge nuclear physics laboratory outside Geneva, at the time. Full of elation he read it out to the audience: "We are happy to inform you that we have definitely detected neutrinos from fission fragments from observing inverse beta-decay of protons. Observed cross-section agrees well with expected 6 1044 cm2."

Pauli was acclaimed worldwide as the "father of the neutrino" and was much called upon to give lectures on the subject. Legend has it that he commented, with quiet satisfaction, "Everything comes to him who knows how to wait."

The downfall of parity.

That same month-June 1956-two Chinese American physicists, T. D. Lee and C. N. Yang, sent Pauli an article they had written in which they argued that perhaps mirror symmetry-parity-might not always be conserved. They had studied the scientific literature and were convinced there was very little actual experimental evidence to support it, added to which certain puzzling phenomena in elementary particle physics could be clarified if it was considered to be not generally valid. They suggested specific experiments for testing their proposal. To suggest that the law of parity might not be inviolate was outrageous. Pauli chuckled and put the article aside.

Nevertheless the two presented such a powerful case that other physicists became curious and started carrying out experiments. On January 17, 1957, Pauli wrote to Weisskopf that he was "ready to bet a very high sum" that the experiments would fail. Little did he know that the previous day The New York Times had carried a front-page report on what it called the "Chinese Revolution" in physics. A group of physicists from Columbia University headed by a woman, Chien-s.h.i.+ung Wu, had carried out a very beautiful experiment proving beyond a doubt the overthrow of parity in the case of weak interactions.

Weak interactions are interactions between elementary particles-such as electrons, protons, and neutrinos-occurring with a force far weaker than the nuclear force, which binds the nucleus together, or the electromagnetic force between charged particles. On a scale of one to ten, the nuclear force is magnitude 1; the strength of the electromagnetic force, given by the fine structure constant, is 0.00729-which can also be expressed as 1/137;* while the weak force is a mere 0.00000000000001, very weak indeed.

In their experiments Wu and her co-workers monitored the number of electrons emerging from the nuclei of a radioactive isotope (an alternative form) of cobalt undergoing beta-decay. The beta-decay process involved the transformation of a neutron in the nucleus of the radio active sample of cobalt into a proton, electron, and neutrino. To define a direction-in this case up and down-they aligned the spins of the nuclei by placing them in a magnetic field. If parity really was a universal law, if nature really did not distinguish one direction from another, then one would expect precisely equal numbers of electrons to be emitted upward and downward. But this was not what happened. In fact, the electrons came out asymmetrically. In other words, Wu's experiment was not the same as its mirror image. The beauty of this experiment-which scientists found so impressive-was its precision. The apparatus had to be set at the lowest possible temperature, close to absolute zero. This was necessary to eliminate any movement of the nuclei due to heat agitation, which would have ruined the alignment of their spins. Thus Lee and Yang were proved to be right.

So parity had been overthrown in the weak interactions-an event which struck Pauli like a bolt of lightning. He was, he confessed "very upset and behaved irrationally for quite a while." He wrote to Weisskopf that he was glad that in the end he had not made any bet. "It would have resulted in a heavy loss of money (which I cannot afford); I did make a fool of myself, however (which I think I can afford to do)," he said.

He wrote humorously to Bohr about the event (a slip of the pen led him to use the wrong date for the overthrow of parity): It is our sad duty to make known that our dear female friend of many years.

PARITY..

had gently pa.s.sed away on January 19, 1957, following a brief suffering caused by experimental treatment. On behalf of the bereaved.

e,,.

(e, , -electron, muon, and neutrino-are three of the many particles that partic.i.p.ate in the weak interactions.).

In real life, of course, our bodies are not symmetrical; our heart is on the left, for a start. But up until then scientists had taken for granted that the laws of physics were mirror symmetrical. Equations had always been drawn up on that a.s.sumption. At the atomic level, at least, it had turned out that this was not invariably the case. Perhaps "nature is not mathematical and does not conform to our thinking," Pauli wrote to Fierz. It was as dramatic a revelation as the Pythagoreans realizing that the square root of two was not a rational number.

Pauli firmly believed that principles of symmetry had to prevail. The way to find them lay not only through logic, but in the more irrational dimensions of thought. "With me the mixture of mysticism and mathematics, which finds its main results in physics, is still very dominant," he wrote.

Two decades earlier Pauli had argued with Bohr when Bohr suggested that the law of the conservation of energy might not entirely hold in the case of beta-decay. It was to preserve this law that Pauli had proposed the existence of the neutrino. As we have seen, the neutrino had been discovered in the laboratory six months earlier and played a role in Wu's experiment. It is one of the most weakly interacting particles of all.

"[Bohr] was wrong with the energy law, but he was right that the weak interactions are a very particular field where strange things could happen, which don't happen otherwise," Pauli wrote. He added that physicists should bear in mind something else Bohr had said: "We have to be prepared for surprises." Pauli himself was willing to speculate that in interactions much weaker than the weak interactions, not just parity but energy too might not be conserved (that is, the amount of energy involved at the start of a process is not the same as at the end). "'Be prepared for surprises' not anywhere but specifically with the beta-decay," he wrote.

Pauli had met Chien-s.h.i.+ung Wu in 1941 when he visited the University of California at Berkeley and described her to Jung as impressive, "both as an experimental physicist and an intelligent and beautiful Chinese young lady." Born in Shanghai in 1912, she had come to America in 1936 and worked first at Berkeley before moving to Columbia. Photographs show her formidable intelligence as well as her beauty. She was a perfectionist-just the person needed to attempt the highly precise experiment to test parity.

Pauli wrote to her that "what had prevented me until now from accepting this formal possibility [of parity violation] is the question why this restriction of mirroring appears only in the 'weak' interactions, not the 'strong' ones." But what did the strength of an interaction have to do with a law of conservation? The question has still to be answered. "In any case, I congratulate you (to the contrary of myself)," he added. "This particle neutrino-on which I am not innocent-still persecutes me."

"G.o.d is a weak left-hander after all," he wrote exuberantly to Jung. A neutrino only spins in one direction. If one looked at it in a mirror, it would still spin in the same direction. Most screws are right-handed-you twist the screwdriver in the same direction as the curl of the fingers on your right hand and turn the screw toward your right thumb. Neutrinos are left-handed in that they spin in a direction opposite to their motion, the direction in which you would twist a screwdriver for a left-handed screw. So G.o.d is a left-hander, but a weak one, because he is only a left-hander in the weak interactions-featuring the neutrino-where parity is violated.

The Chinese woman.

Pauli could not fail to notice what a supreme example of synchronicity this was. A Chinese woman had played an important part in his dreams, particularly those involving mirrors and their reflections; and a Chinese woman had carried out the critical experiment that brought about the downfall of parity-that is, of mirror symmetry-in physics. He wrote to Jung of his "shock" at this "'Chinese revolution' in physics."

Fierz told him he had "a mirror complex." "I admitted as much," Pauli wrote to Jung. "But I was still left with the task of acknowledging the nature of my 'mirror complex.'"

Pauli's curious dream of 1954 had occurred right after he finished his work on mirror symmetry. He was convinced that "unconscious motives play a role" in creative thinking, especially in the case of symmetry. "'Mirroring' is an archetype [and] this has something to do with physics. Physics relies on a connection of an image reflected in a mirror and between mind and nature," he said in an interview in 1957. He recalled having "vivid, almost parapsychological dreams about mirroring, while I worked mathematically during the day." The mathematical work seemed to cause "some archetype [to be] constellated [that is, to emerge into consciousness] which subsequently made me think about mirroring." The connection, he concluded was "a kind of synchronicity, because there are unconscious motives when one is involved in something."

Other examples of synchronicity soon cropped up. Two months after the ground-breaking experiment that spelled the end of parity, in March 1957, Pauli's friend, Max Delbruck, an eminent biologist, sent him an article on a one-cell, light-sensitive mushroom known as a phycomyces.

A few weeks later Pauli was talking about psychophysics with Karl Kerenyi, an authority on Greek mythology and a close friend of Jung's. Pauli told him about some dreams he had had in which he was wandering about in the constellation of Perseus. Synchronisms started to spring up. For a start, Perseus contains a binary, or double star, known as Algol. Moreover, in Greek mythology, Perseus fought Medusa while looking at her reflection in a mirror. Shortly afterward Pauli came across an article by Kerenyi on Perseus. It concluded with an ancient Greek pun about Perseus's founding of the city of Mycenae. It had been so named after a mushroom called myces-the very mushroom that had been the subject of Delbruck's scientific paper.

Mirror images.

That same month-March 1957-Pauli had a dream in which a "youngish, dark-haired man, enveloped in a faint light" hands him a ma.n.u.script. Pauli shouts, "How dare you presume to ask me to read it? What do you think you are doing?" He wakes up feeling upset and irritated.

Writing about the dream to Jung, Pauli suggested it revealed his "conventional objections to certain ideas-and my fear of them," most notably his belief that parity could never be violated.

In another dream a couple of months later he is driving a car (though in real life he no longer had one). He parks it legally but the young man from the previous dream suddenly appears and jumps in on the pa.s.senger side. He is now a policeman. He drives Pauli to a police station and pushes him inside.

Pauli is afraid that he will be dragged from one office to the next. "Oh no," says the young man. An unfamiliar dark woman is sitting at the counter. In a brusque military voice the young man barks at her, "Director Spiegler [Reflector], please!" Taken aback by the word "Spiegler," Pauli wakes up. When he falls asleep again the dream continues.

Another man comes in who resembles Jung. Pauli a.s.sumes he is a psychologist and explains to him in great detail the significance of the downfall of parity on the world of physics.

For Pauli the dream reflects his long-held belief that the "relations.h.i.+p between physics and psychology is that of a mirror image." In the dream he appears first as his narrower Self who understands both physics and parity, then as his own mirror image-the psychologist who knows nothing about either. Spiegler-the reflector-is responsible for bringing out the psychologist and is attempting to bring the two together. But now that parity has been violated, there is no longer any mirror symmetry.

Looking at the question in terms of archetypes Pauli finds the loss of mirror symmetry not so shocking. Before the downfall of parity, he feels physicists and psychologists had not been looking deeply enough into matter and mind. They had considered only "partial mirror images." Full reflections and more profound symmetries can be obtained only by going deeper into the psyche. The CPT symmetry that Pauli himself discovered-exchange of particle and antiparticle, symmetry of right-left, and time reversal-is exactly that profound symmetry because it talks about mirror symmetry on the grandest of scales. It a.s.serts that our universe cannot be distinguished from a mirror universe in which all matter is replaced with antimatter, all positions are reflections, and time runs backward.

Thus Pauli worked out that parity could be restored in a new and profound way by taking into account a fuller symmetry-CPT, which reveals the full symmetry of phenomena.

Over the years scientists have discovered some of the stunning implications of Pauli's CPT symmetry. One is the following. In experiments on certain elementary particles it seemed that the combined symmetry of CP (matter/antimatter and parity) was violated. As one was violated and the other not, the two together-the product C P-is violated. (As in mathematics where +1 1 = 1.) This is therefore a loss of symmetry. For CPT to remain valid, time reversal (T) would have to be invalid too, which would make the combined symmetry of the three-CPT-valid. (As in 1 1 = +1.) In the late 1990s, scientists actually produced direct proof of the violation of time-reversal invariance on the subatomic level, that is, when time was made to run backward the laws of physics concerning this specie of weak interaction did not remain the same. From this they were able to show that the transformation of matter into antimatter is not symmetrical in time. The cosmic implications of this are enormous. It helps explain a question that intrigues physicists: why the universe is made up of matter rather than antimatter, even though equal amounts of both were created in the big bang.

After the fall of parity, as Pauli commented with quiet pride to Jung, "The 'CPT theorem' was on everybody's lips." "To many physicists CPT was a fixed point around which all else turned," T. D. Lee recalled of that turbulent era. It also seemed to be a way to bring together Pauli's interests in physics and psychology. He had "no doubt that the placing side by side of the points of view of a physicist and a psychologist will also prove a form of reflection." The startling "mirror" symmetry of CPT related elementary particles in a new and profound way. So why should the apparently dissimilar views of a physicist and a psychologist not mirror each other as well?

Pauli and T. D. Lee (whose theoretical work had brought about the downfall of parity) quickly developed a rapport. Pauli was intrigued by Lee's research on how elementary particles transform into one another. On one occasion Pauli visited Lee at the Brookhaven National Laboratory on Long Island. They planned to go out for dinner that evening with their wives. There was valuable scientific equipment on site and a guard was posted at the gate. As he was leaving in his car, Lee handed the guard his identification card. An uncomfortably long time went by. Lee inquired whether there was a problem. The guard apologized. He had somehow misplaced the card, he said. In all his years on duty it was the first time it had ever happened. Lee laughed. It was a first for him, too. The guard finally located the card; it had fallen through his fingers under a table. Pauli exclaimed gleefully from the back seat, "It's the Pauli effect!"

From mirror symmetry and archetypes to...UFOs.

The violation of parity-that it was, in fact, possible to distinguish between left and right in atomic physics-struck a chord in Jung's ongoing fascination with unidentified flying objects (UFOs), an interest which, as Jung admitted, "might strike some people as crazy." At the time-the 1950s-many people were fascinated by UFOs and a number of highly successful books had been written. During their long dinners at Jung's huge house on the lake, Pauli and Jung often discussed the subject. Jung begged Pauli to make inquiries about flying saucers among his scientific colleagues. Pauli's theory was that they were either hallucinations or secret experimental aircraft invented by the Americans. He had nothing but scathing comments on the many ma.n.u.scripts that were sent to Jung on the subject.

Taking up Pauli's quip on the violation of symmetry-that "G.o.d is a weak left-hander, after all," Jung declared that "the statements from the unconscious (represented by UFO legends, dreams, and images) point to...a statistical predominance of the left-i.e., to a prevalence of the unconscious, expressed through 'G.o.d's eyes,' 'creatures of a higher intelligence,' intentions of deliverance or redemption on the part of 'higher worlds' and the like."

Jung was convinced that at this moment in history the unconscious was in a stronger position in relation to the conscious-a dangerous situation. The way to resolve this imbalance was through the redeeming Third-an archetype of some sort or other, a latent symbol. The UFO legend was perhaps this latent symbol. It was lurking somewhere in the psyche where it was trying to elevate the collective unconscious to a higher level. This would ultimately resolve the conflict of the unconscious and the conscious by paving the way for a dialogue between them, finally permitting the Self to emerge in the process Jung called individuation. The Third provides asymmetry and tips the balance toward the conscious. Putting it in physics terms, Jung thought that certain key elementary particles in the weak interactions played the part of the Third, while the law of parity of an object and its reflection paralleled the opposition between conscious and unconscious and right-wing and left-wing in the political sense.

Jung saw "an almost comic parallel" in the tumult in physics caused by the weak interactions. It was precisely the same as when tiny psychological factors "shake the foundations of our world." "Your anima, the Chinese woman," he wrote to Pauli, "already had a scent of asymmetry."

For Jung the UFO legend indicated that the Self was ultimately Spiegler, "The Reflector," representing both a mathematical point and the circle, universality, "G.o.d and mankind, eternal and transient, being and nonbeing, disappearance and rising again, etc." "There is absolutely no doubt," he concluded, "that it is the individuation symbolism that is at the psychological base of the UFO phenomenon."

All the same, as far as Jung was concerned, UFOs were not merely symbols but very real, as evidenced by the many historical sightings recorded in the books, magazines, and newspapers piled high in his study.

After one of their lengthy late evening conversations on the subject of UFOs, Pauli had a sighting, though not of a UFO: As I was walking up the hill from Zollikon station after leaving your house, I did not actually see any "flying saucers," but I did see a particularly beautiful large meteor. It was moving relatively slowly (this can be explained by factors of perspective) from east to west and then finally exploded, producing an impressively fine firework display. I took it as a spiritual "omen" that our general att.i.tude toward the spiritual problems of our age is in the sense of , in other words is more a "meaningful" one.

(In ancient Greek, is the window of opportunity in which something meaningful can be achieved.).

Pauli went so far as to consult with his scientific colleagues as to whether UFOs really existed. Among others, he corresponded with the eminent German electrical engineer, Max Knoll, who was also an adept of Jungian psychology. Knoll was willing to believe that UFOs resulted from the individuation process but he was adamant that they did not physically exist. He replied at length to queries from Pauli on the nature of radar systems and dismissed every known sighting of UFOs, whether on radar or with the naked eye: "Jung must be made to understand that the UFOs seen on radar screens are no more 'real' than those sighted directly," he wrote tetchily. "[There] are no reliable sightings."

Pauli forwarded Knoll's letter to Jung. Jung's personal secretary, Aniela Jaffe, responded on his behalf: "Professor Jung was much interested in Knoll's letter. But that did not stop him from saying, in a tone of resignation: People think I am more stupid than I am!"

By this time Jung was a venerable figure, receiving scores of visitors at his mansion in Kusnacht, outside Zurich. More than his psychological work, most wanted to hear his views on UFOs. In 1958 he published Flying Saucers: A Modern Myth of Things Seen in the Skies. It was greeted with an acclaim that astonished even him.

Among the visitors to Kusnacht who tried to convince Jung that UFOs did not exist was Charles Lindbergh, the first man to fly across the Atlantic. The United States Air Force had investigated hundreds of sightings of UFOs, he told Jung, and found not the slightest evidence to support them. The author of one of Jung's favorite books on flying saucers, Donald Keyhoe, suffered from poor mental health, he added, and the Pentagon had disproved all his allegations.

The commander of the American Air Force, General Carl Spaatz, had told Lindbergh that if UFOs actually existed, surely both of them would have heard about it. Jung snapped, "There are a great many things going on around this earth that you and General Spaatz don't know anything about."

Pauli's last letter to Jung was in August 1957. He continued to send him off prints of his papers. Aniela Jaffe apologized for replying on Jung's behalf, saying that he was very tired. He was now eighty-two. She sent Pauli her "best wishes for 1958-many long journeys."

Carl Jung was to outlive Pauli. Jung died on June 6, 1961, at the age of eighty-five.

The Mysterious Number 137.

The fine structure constant.

PAULI once said that if the Lord allowed him to ask anything he wanted, his first question would be "Why 1/137?"

One of his colleagues mischievously filled in the rest of the story. He imagined that one day Pauli did get the chance to ask his question. In response the Lord picked up a piece of chalk, went to a blackboard and started explaining exactly why the fine structure constant had to be 1/137. Pauli listened for a while, then shook his head. "No," said the man who was famous for declaring of a theory, "Why, that's not even wrong!" He then pointed out to the Lord the mistake that He had made.

The fine structure constant is one of those numbers at the very root of the universe and of all matter. If it were different, nothing would be as it is. As Max Born put it, it "has the most fundamental consequences for the structure of matter in general." To recap: spectral lines are the lines that are the fingerprints of an atom, revealed when they are illuminated by light. The fine structure is the structure of individual spectral lines. The fine structure constant, in turn, is the immutable figure that defines the fine structure.

Pauli's mentor, Arnold Sommerfeld, calculated the fine structure constant as 0.00729. Later scientists, however, discovered that this could be written as the simpler, more meaningful number 1/137 (that is, 1 divided by 137). It soon became known more familiarly as 137.

This number was beyond discussion. It simply had to be 1/137 because this determines the s.p.a.cing between the fine structure of spectral lines, as had been discovered in the laboratory. But why this figure? Why 137? There was something about 137-both a prime and a primal number-that tickled everyone's imagination.*

To reiterate: The three fundamental constants that make up the fine structure constant are the charge of the electron, the speed of light, and Planck's constant, which determines the smallest possible measurement in the world. All these have dimensions. The charge of the electron is 1.61 1019 Coulombs, the speed of light is 3 108 meters per second, and Planck's constant is 6.63 1034 Joule-seconds. All three depend on the units in which they are measured. Thus the speed of light is 3 108 meters per second in the metric system but 186,000 miles per second in the imperial system. All three would certainly play an essential part in a relativity or quantum theory formulated by physicists on another planet in another galaxy, but these physicists might have a different system of measurements from ours and therefore the exact figure would almost certainly not be the same.

The fine structure constant is entirely different. Even though it is made up of these three fundamental constants, it is simply a number, because the dimensions of the charge of the electron, Planck's constant, and the speed of light cancel out. This means that in any number system it will always be the same, like pi which is always 3.141592.... So why is the fine structure constant 137? Physicists could only conclude that it cannot have this value by accident. It is "out there," independent of the structure of our minds.

Never before in the history of modern science had a pure number with no dimensions been found to play such a pivotal role. People began referring to it as a "mystical number." "The language of the spectra"-the spectral lines, where Sommerfeld had found it-"is a true music of the spheres within the atom," he wrote.

Arthur Eddington and his mania for 137.

In 1957, when Pauli was fifty-seven, he wrote to his sister Hertha: I do not believe in the possible future of mysticism in the old form. However, I do believe that the natural sciences will out of themselves bring forth a counter pole in their adherents, which connects with the old mystic elements.

Perhaps the clue lay in numbers-more specifically, the number 137.

Until 1929, the fine structure constant was always written 0.00729. That year the English astrophysicist Arthur Eddington had a bright idea. He tried dividing 1 by 0.00729. The result was 137.17, to two decimal place accuracy. The actual measurement of the fine structure constant as ascertained in the laboratory, Eddington pointed out, was close to that (it was somewhere between 1/137.1 and 1/137.3). There were two ways in which scientists determined the fine structure constant. When they calculated it from the measured values of the charge of the electron, Planck's constant, and the velocity of light, the result was 0.00729. Or they could measure the actual fine structure of spectral lines-that is, determine it in the laboratory; the most frequent value that resulted was 0.007295 .000005. However, the latter method required input from a particular theory and this presented a problem, for the theory of how electrons interacted with light-quantum electrodynamics-was still in flux, as indicated by the difficulties Heisenberg and Pauli experienced in their work on this very subject. With this in mind, Eddington felt justified in throwing numerical accuracy to the wind and writing the fine structure constant simply as 1/137.

Eddington had a strong mystical streak. To him, mysticism offered an escape from the closed logical system of physics. "It is reasonable to inquire whether in the mystical illusions of man there is not a reflection of an underlying reality," he mused. Like Pauli, he struggled with the dichotomy between the two worlds, both equally invisible, of science and the spirit. He was sure that mathematics was the key that would open the door between these two worlds and he set about an obsessive quest to derive 137 however he could.

The equation for the fine structure constant is.

and the charge of the electron, e, appears in this equation as e e, or e2. As a result, besides being a measure of the fine structure of spectral lines, the fine structure constant (1/137) also measures how strongly two electrons interact.

Eddington argued that according to relativity theory, particles cannot be considered in isolation but only in relation to each other and therefore any theory of the electron has to deal with at least two electrons. Applying a special mathematics that he had invented, Eddington found that each electron could be described using sixteen E-numbers (E stood for "Eddington"). Multiplying 16 by 16 gave a total of 256 different ways in which electrons could combine with each other. He then showed that, of these 256 ways, only 136 are actually possible; 120 are not. He wrote this mathematically as 256 = 136 + 120. Like pulling a rabbit out of a hat, he thus magically produced the number 136 from purely mathematical (if dubious) reasoning.

Of course 136 was not 137, but for Eddington it was close enough. He was convinced that the elusive "one" would "not be long in turning up." As the physicist Paul Dirac put it, "[Eddington] first proved for 136 and when experiment raised to 137, he gave proof of that!" The obsessive pursuit of 137 took over Eddington's life. American astrophysicist Henry Norris Russell remembered meeting him at a conference in Stockholm. They were in the cloakroom, about to hang up their coats. Eddington insisted on hanging his hat on peg 137.

Eddington added to the mystery by pointing out that 137 contained three of the seven fundamental constants of nature (the other four are the ma.s.ses of the electron and the proton, Newton's gravitational constant, and the cosmological constant of the general theory of relativity). Seven, of course, is a mysterious number in itself, encompa.s.sing the seven days of creation, seven orifices in the head, and seven planets in the pre-Copernican planetary system. Eddington's speculations were a catalyst in the search for numerical relations.h.i.+ps among the fundamental constants of nature.

In January 1929 Bohr wrote to Pauli, "What do you think of Eddington's latest article (136)?" Pauli hardly bothered to reply, commenting only that he might soon have something to say "on Eddington (??)." The two question marks are his. "I consider Eddington's '136-work' as complete nonsense: more exactly for romantic poets and not for physicists," he wrote to his colleague Oskar Klein a month later. He added in a letter to Sommerfeld that May, "Regarding Eddington's = 1/136, I believe it makes no sense." ( is the fine structure constant.) Pauli and 137.

It seemed that Pauli had not caught the 137 bug. In February 1934, however, he wrote to Heisenberg that the key problem was "fixing [1/137] and the 'Atomistik' of the electric charge." At the time he was trying to find a version of quantum electrodynamics in which the ma.s.s and charge of the electron were not infinite; but no matter which way he manipulated his equations, the concept of electric charge always entered-hence the mystical "'Atomistik'-atom plus mystic-of the electric charge."

The problem was that quantum electrodynamics did "not take the atomic nature of the electric charge into account" when the electric charge entered the theory of quantum electrodynamics as part of the fine structure constant (that is, 1/137). "A future theory," Pauli wrote, "must bring about a deep unification of foundations."

As Pauli saw it, the crux of the problem was that the concept of electric charge was foreign to both prequantum and quantum physics. In both theories the charge of the electron had to be introduced into equations-it did not emerge from them. (This was similar to Heisenberg and Schrodinger's quantum theories in which the spin of the electron had to be inserted, whereas it popped out of Dirac's theory.) Quantum theory exacerbated this situation in that it included the fine structure constant, 1/137 = 2e2/hc, that is, it linked the charge of the electron (e) with two other fundamental constants of nature-the miniscule Planck's constant, h (the smallest measurement possible in the universe and the signature of quantum theory which deals with nature at the atomic level), and the vast speed of light, c (the signature of relativity theory which deals with the universe).

Pauli continued to worry about the connection between the fine structure constant and the infinities occurring in quantum theory. It was a problem that would not go away. "Everything will become beautiful when [1/137] is fixed," he wrote to Heisenberg in April 1934. And on into June: "I have been musing over the great question, what is [1/137]?"

That year, in a lecture he gave in Zurich, he underlined the importance of eliminating the infinities that persisted in quantum electrodynamics and drew attention to the theory's relations.h.i.+p to our understanding of s.p.a.ce and time. The solution to this problem would require "an interpretation of the numerical value of the dimensionless number [137]."

So what had happened? Why did Pauli suddenly begin to discuss his thoughts on 137? Perhaps it was the effect of Jung's a.n.a.lysis opening his mind to mystical speculations.

In 1935, the senior scientist Max Born, Pauli's mentor at Gottingen who was then at Cambridge, published an article ent.i.tled, "The Mysterious Number 137." He looked into the reasons why 137 should have such mystical power for scientists. The main reason was that it seemed to be a way in which one could achieve the Holy Grail of scientific studies-linking relativity (the study of the very large-the universe) with quantum theory (the study of the very small-the atom).

In his article he looks at some of the qualities that make the number "mystical," prime among them being that even though it is made up of fundamental constants that possess dimensions, it is itself dimensionless. It is also enormously important in the development of the universe as we know it. He writes: "If [the fine structure constant] were bigger than it really is, we should not be able to distinguish matter from ether [the vacuum, nothingness], and our task to disentangle the natural laws would be hopelessly difficult. The fact however that has just its value 1/137 is certainly no chance but itself a law of nature. It is clear that the explanation of this number must be the central problem of natural philosophy."

In 1955, at the hundredth anniversary of the ETH, Pauli addressed a huge audience in the main lecture hall of the physics department at Gloriastra.s.se on the subject "Problems of Today's Physics." Contrary to his usual style Pauli spoke from a prepared ma.n.u.script. He obviously found this difficult. With a flourish he threw the paper aside and spoke off the cuff with great pa.s.sion and verve. The crux of his argument was the vital importance of the fine structure constant and also what an impenetrable problem it was. It did not merely designate how two electrons interact with each other, it was not merely a constant to be measured; what scientists had to do was "to accept it as one of the actual main problems of theoretical physics." There was thunderous applause.

Realizing its fundamental importance in understanding spectral lines in atomic physics and in the theory of how light and electrons interact, quantum electrodynamics, Pauli and Heisenberg were determined to derive it from quantum theory rather than introducing it from the start. They believed that if they could find a version of quantum electrodynamics capable of producing the fine structure constant, it would not contain the infinities that marred their theories. But nothing worked. The deeper problems that beset physics-not only how to derive the fine structure constant but how to find an explanation for the ma.s.ses of elementary particles-remain unsolved to this day.

In 1985 the brash, straight-talking, American physicist Richard Feynman, who had studied Eddington's philosophical and scientific papers on 137, wrote in his inimitable manner: It [1/137] has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Immediately you would like to know where this number comes from.... n.o.body knows. It's one of the greatest d.a.m.n mysteries of physics: a magic number that comes to us with no understanding by man.

The magic number 137.

So where did this magic number come from? How did Sommerfeld, who discovered it, alight on it? To get a glimpse of his thought processes, we need to take a short mathematical journey.

Mulling over the problem of the structure of spectral lines, Sommerfeld took another look at the key equation in Bohr's theory of the atom as a miniscule solar system. It is This is an equation for the energy level of the lone electron in an atom's outermost sh.e.l.l, such as the electron in a hydrogen atom or in alkali atoms-hydrogen-like in structure, in that they have one electron free for chemical reactions, while all the rest are in closed sh.e.l.ls (Pauli studied them in his work on the exclusion principle); ergs are the units in which energy is expressed. The equation shows the energy (E) of the electron in a particular orbit designated by the whole quantum number n. Z is the number of protons in the nucleus; and the minus sign indicates that the electron is bound within the atom. The quant.i.ty 2.7 10-11 ergs results from the way in which the charge of the electron (e), its ma.s.s (m), and Planck's constant (h) occur in this equation: It is also the energy of an electron in the lowest orbit (n = 1) of the hydrogen atom (Z = 1).

Sommerfeld decided that the mathematics in Bohr's original theory needed to be tidied up. His brilliant idea was to include relativity in the new mathematical formulation, making the ma.s.s of the electron behave according to E = mc2, in which ma.s.s and energy are equivalent. This was the result: In this new equation, the additional quantum number k indicated the additional possible orbits for the electron and allowed the possibility for an electron to make additional quantum jumps from orbit to orbit. It therefore also allowed the possibility of the atom having additional spectral lines-a fine structure.

The first term in the equation for En,k-outside the brackets-was the same as in Bohr's original equation. But a whole extra term had appeared inside the large brackets.

Multiplying this term was an extraordinary bundle of symbols that no one had ever seen before: . In this expression, e is the charge of the electron, h is Planck's constant, and c is the velocity of light. Sommerfeld deduced the number 0.00729 from this bundle of symbols. He realized that this was the number that set the scale of the splitting of spectral lines-that is, of the atom's fine structure-and called it the fine structure constant. It is there in the equation because it is there in the atom; it is part of the atom's existence, which includes the fine structure of a spectral line. Physicists knew the fine structure existed. They had measured the fine structure splitting, but they didn't have an equation for it that agreed with experiment. Now they did: This extraordinary equation, in which 2e2/hc is replaced by 1/137, perfectly described the fine structure of spectral lines as observed in experiments.

Not just scientists but many others have grappled with 137. For a start, 137 can be expressed in terms of pi. Some complicated ways of doing this, all of which end up with 137, are We can also write 137 as a series of Lucas numbers, which are connected with Fibonacci numbers and the Golden Ratio.

Fibonacci numbers is a sequence of whole numbers in which each number starting from the third is the sum of the two previous ones. The sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, and so on (0 + 1 = 1, 1 + 1 = 2, etc.).

If we take the ratio of successive numbers in the series-1/1 = 1.000000, 2/1 = 2.000000, 3/2 = 1.500000, 5/3 = 1.666666, and so on to 987/610 = 1.618033-we reach 1.6180339837, the Golden Ratio, which has been a guideline for architecture since the days of ancient Greece. It appears on the pyramids of ancient Egypt, the Parthenon in Athens, and the United Nations building in New York City.

Fibonacci numbers were discovered by the Italian mathematician Leonardo Fibonacci in the twelfth century. It was Kepler who discovered their relation to the Golden Ratio. Then Edouard Lucas, a French mathematician, used them to develop the Lucas numbers in the nineteenth century.