137: Jung, Pauli, and the Pursuit of a Scientific Obsession Part 11

The audience of strangers is eager to learn more, but Pauli leaves and finds himself back with the piano teacher. He tells her that while giving the lecture he has produced a "child" for her. The "child" is a product of his unconscious indicating that the woman is indeed his anima, and represents a new holistic att.i.tude-a fusion of psychology, physics, and biology. The problem is how to make it acceptable to everyone. The answer, Pauli realizes, lies in numbers. He suddenly notices that the teacher has Chinese eyes, like the Chinese woman who, in his earlier dream, had led him to the lecture hall.

A voice says, "Wait, transformation of the evolutionary center." Suddenly the teacher has a ring on her finger marked with the mathematical symbol i-the square root of 1. She tells him that it symbolizes the oneness of the rational and the irrational. But Pauli sees another oneness: i is a key element in Schrodinger's wave function in quantum physics. It describes the wave and the particle properties of matter and symbolizes the unity of wave and particle.

Pauli puts on his coat and hat. He is about to leave when he hears the teacher play a four-note chord. The three-note chord he played at the beginning of the fantasy has mutated into four. A wholeness has been achieved, a child has been produced, and Pauli's thoughts are now focused on the archetype of number, particularly on three and four and how the shift from one to the other brings about a unity.

The two-thousand-year-old problem.

Nevertheless, the great problem remained unresolved. As Jung put it, "Oddly enough, the problem is still the same 2,000-year-old one: How does one get from Three to Four?" Pauli's own thoughts on this date back to his discovery of the exclusion principle and the "difficult transition from three to four." That was really the main work," he added. Now it began to lead him into other aspects of numerology.

Writing to von Franz, Pauli continued the introspective and numerical mode of The Piano Lesson: "One can not at all proceed from three to four." As far as the 2,000-year-old question was concerned, he was stymied. But perhaps he could try a different approach. "However, one can proceed in various ways to three and four," he went on. Then he had a brain wave. Four times three equals twelve; but twelve can also be expressed as two times six. He played with this conundrum at the start of his letter: A. To the sign of 6.

B. 2 6 = 12.

The professor who shall calculate numerically.

Twelve, he remembered was the number of constellations in the zodiac. "My path proceeds via 2 6 to the zodiac, since what is still older is always the newer," he concluded.

In the zodiac, the twelve signs were divided into four triangles of three signs. So perhaps the zodiac contained the solution as to how to get from three to four. Perhaps its symbolism, focusing on the quaternity, was more in touch with irrationality than was Christianity, which emphasized the Trinity. Followers of Christianity, he wrote, were "cosmic babies, 'greenhorns,'" their religion akin to the physics of people who "believe that the full moon and the new moon" are not the same moon.

Then he received a letter from his friend and one-time a.s.sistant, the physicist and Jungian disciple Markus Fierz. Fierz told him about a dream described by the sixteenth-century Cambridge Platonist Thomas More. In his dream, More glimpsed twelve sentences written in gold but he could recall only the first six. He was aroused from his dream by the braying of two donkeys.

Pauli set to work to a.n.a.lyze the dream. He reasoned that the splitting of the twelve sentences in More's dream into two sixes, along with the two donkeys, rendered "the quaternity" impossible.... The natural splitting of 12 would be realized in 3 4, which also corresponds to the splitting in the zodiac (of which Fludd always spoke). But the time was not ripe for a quaternary world-picture, and the dark half relapsed into the unconscious." In More's time, the zodiac must have been seen as two sixes-6 2. The world was not ready for the number four to emerge in Western thought.

It was a case of synchronicity. Pauli had homed in on 2 6, not realizing at first that he was reimagining the dreams of a man of the Renaissance, when these topics were hotly debated.

The division into two-symbolized by the two donkeys-reflected an era in which there was a split between matter and mind, soon to be manifested in the emergence of modern science in the work of Kepler and Descartes. Early scientists focused on matter because it could be described by mathematics in three-dimensional s.p.a.ce, another case, like the Trinity, of three.

Or perhaps the two donkeys in More's dream had something to do with Pauli's own "two life phases." "A Zen Buddhist would understand this, as G.o.d speaks to us always in riddles," he added.

To ill.u.s.trate the letter to von Franz, Pauli drew two six-sided stars of David, which he labeled as the two stages of his life: "the youth phase (until 1928) [and] the phase after World War II until the summer of 1953." The two stars sprang from Pauli's "active imagination"-two six-sided stars: 2 6.

In the years between these two life phases-1928 and 1945-Pauli lived through many turbulent events: two marriages, divorce, flight from Europe, rejection by colleagues at the ETH, the lonely war years in the United States, and his a.n.a.lysis by Jung, which had led to a deeper understanding of himself and the world about him. He depicts these two contrasting periods in three pairs of opposing archetypes.

The "youth phase" of Pauli's life, to 1928. (Based on Pauli's drawing in his letter to von Franz.).

In the youth phase of his life the archetypes are the "Light Anima" (superior; Pauli's intellectual side which was dominant in that "at the time I was completely absorbed in physics") versus the "Shadow, projected entirely on the father along with repressed negative emotions about Judaism" the "intellectual side of the 'Self' projected onto the teacher" versus the "Dark Anima [whom Pauli saw as] ("inferior," a "prost.i.tute"); and the "Ego" versus a "Real woman (mother) with whom I had a positive relationship."

The period of Pauli's life from 1946 to 1953. (Based on Pauli's drawing in his letter to von Franz.).

The transforming event in Pauli's life, as he remembered, was his marriage to Franca. This brought about the adult phase. Here the archetypes appear in new forms. The Light Anima, now inferior and projected onto the "wicked stepmother," is set against the Shadow. But the Shadow is no longer projected onto the father even though Pauli still regards him as "controversial, intellectual, divested of feeling." The "Ego" is set against the "real woman" with whom Pauli now has the "positive feeling of being at home" this woman is no longer his mother. The third pair includes the "Master Figure" whom Pauli a.s.sociated with Merlin. In an earlier letter to Emma Jung he described him as seeking a way to move from three to four solely by rational reasoning, using physics. But Pauli now knows this cannot be accomplished by logic alone and so places him in opposition to the Dark Anima who is now superior, appearing as the "Chinese woman."

Pauli then laid out the pattern of this, the second half of his life.

The connection with physics cools off. A positive connection with Kabbalah (and Cha.s.sidism) arises.

Then: the Kepler work.

Good and evil appear relativized and coincide with light (spiritual) and dark (chthonic).

Religion: is sought for.

Values of the youth phase threaten to be lost. At the high point of this phase a compensatory stagnation kicks in with anima-projections upon actual women.

Pauli continued to mull over three times four, six times two, and the zodiac. An "inner storm" raged. Finally his "'active imagination' or perhaps 'synchronicity'" led him to realize something he had missed: "the dilemma regarding the patriarchalistic versus the matriarchalistic sphere [and the] dilemma concerning 3 versus 4-these seem to me to be merely two aspects of the same problem." In other words, the contrast between the patriarchalistic view (that is, the male-dominated view of the world in which the number three or Trinity predominates) and the matriarchalistic view (that is, female-dominated view of the world in which the quaternity predominates). According to ancient creation myths, the matriarchalistic world was overthrown and the patriarchalistic one took over.

Because "every 'correct' solution (i.e., meeting the demands of nature) must contain 4 as well as 3," Pauli tried different approaches including 16 (4 4) which can be mathematically tied to 12 (the number of signs in the zodiac). He explained why 12 and 16 were related: "The professor further calculates numbers. In the sign of the 12. 12:16 = 3:4-a problem with thorns and horns." Dividing each term in the ratio 12:16 by four gives the ratio 3:4.

But there was still something missing in the number twelve and its relationship with three and four, something Pauli could not quite put his finger on. He became weary and set aside the problem.

That night he had a dream. In his dream three others are present. One is a Chinese woman-now elevated to a "Sophia," a seer or wise woman. She tells Pauli, "You must play every conceivable combination of chess." Chess involves the opposition of black and white and thus of dark and light, the two animas. Dark is compa.s.sion and feeling, light is rationalism. It is like the teacher's advice in The Piano Lesson, that every possible melody can be played on the black and white keys: "It is only a question of knowing how to play." In his dream Pauli works on the problem of how to make four emerge from two, three, and six, but still can't solve it. He suddenly wakes up.

Then, in a waking vision, he hit on the solution. "This I will never forget. The experience had a numinostic character (obviously of archetypal nature)," he wrote in wonder, caught up in the moment of enlightenment. "In my youth I often had such experiences with physics problems," he added.

In the vision, a voice-possibly the Chinese woman's-wakes him from his dream. The voice tells him the solution in clear tones: "In your drawings [the six-sided stars in Pauli's previous letter to von Franz] one element is perfectly correct and another transitory and false. It is correct that the lines number six, but it is false to draw six points. See here"-and I saw a square with clearly marked diagonals. "Can you now see finally the 4 and the 6? Namely, 4 points and 6 lines-or 6 pairs* out of 4 points. They are the same six lines that exist in the I Ching. There the 6, containing 3 as a latent factor, is correct. Now observe the square more closely: 4 of the lines are of equal length, the other two are longer-they are irrationally related, as you know from mathematics. There is no figure with 4 points and 6 equal lines. For this reason symmetry cannot be statically produced and a dance results. The coniunctio refers to the exchange of places during this dance. One can also speak of a game of rhythms and rotations. Therefore the 3, already contained in a latent form in the square, must be dynamically expressed."

The square where the dance of diagonals occurred in Pauli's "waking vision."

Finally here was the solution to the problem that had been nagging at Pauli for so long. The four, or quaternity, emerged intact, while the three was also already contained "as a latent factor" in the square. This is the way it is in the I Ching, in which each hexagram used for divination is made up of six lines subdivided into two three-line segments (trigrams).

In mathematics the diagonals of a square cannot be expressed as whole numbers. Mathematicians refer to the relationship of the diagonals to the sides of a square as "irrational." Pauli extended the meaning of this term to psychology. In the dance of the diagonals, three and four are both present in a coniunctio resulting from "a game of rhythms and rotations" in which diagonals and sides transform into one another. Pauli recognized the influence of the I Ching-with its "6 lines and play of transformations"-on this solution.

Perhaps what catalyzed this line of thought for Pauli was that the tetraktys plus its mirror image make up the holy quaternity. Two equilateral triangles fused along one of their sides form not a square but a parallelogram, while laying two equilateral triangles one on top of the other produces the star of David. Pauli's friend and former a.s.sistant, Markus Fierz-who was, we should remember, an acolyte of Jung's-had argued along these lines in a letter he wrote to Pauli a month earlier where he represented the opposition of light and dark each with its own tetraktys.

Fierz's geometric figure formed from two triangles, each a tetraktys.

The four-sided figure formed from the two triangles-one white, the other black-represents a state of the unconscious in which, Fierz wrote, light and dark "must either fly apart or flow one into the other," as the unconscious (represented by the dark lower triangle) flows into the conscious.

The other case in which three and four occurred simultaneously had been in Pauli's dream image of the world clock in which "three rhythms are contained." However, since the "image of the zodiac is not yet correct, then also is the 12 'incomplete,'" Pauli wrote to von Franz. The zodiac is "not yet correct"-he felt, but didn't know why. Perhaps the error lay in something Jung had missed in examining why the patriarchal view arose in Christianity: he had limited his clues to those within Christianity. It occurred to Pauli that the Zodiac had pre-Christian roots. He decided to look into the cultural history of something that Jung and his circle "too strongly neglected"-horoscopes. Even though Pauli had nothing but disdain for them, he saw their importance as a cultural artifact.

He discovered that the horoscope then in use was based on the zodiac of third-century-B.C. Babylonia. But this was a time when patriarchy had replaced matriarchy. So this zodiac is a.s.sociated with the all-male Trinity of Father, Son, and Holy Ghost which, being three, is incomplete. The use of this patriarchical horoscope had much to do with the masculine slant of Christianity and so, too, its preference for the number three over four. Jung had been wrong to focus his attention on the Christian era in his search for the emergence of four from three.

Thus Pauli resolved the 2,000-year-old problem of how to go from three to four-to his own satisfaction, at least. In fact, he realized that the problem was more than 2,000 years old, harking back to Babylonian times and the venerable I Ching. Pauli's liking for mathematical symmetry carried over to the I Ching, which, as he put it, exhibited "the exact symmetrical mental att.i.tude of the pairs Yin (feminine, chthonic, dark = moon) and Yang (masculine, intellectual, light = sun)." Horoscopes, however, exhibited no such symmetries.

In Pauli's opinion horoscopes "far exceed all rational thought" and so had no value at all. But the I Ching with its properties of synchronicity appealed to him "instinctively." And he now knew, thanks to Jung, that intuition was the psychological function best suited to take in the whole situation.

Pauli did however once have a horoscope drawn up and included it in a letter he wrote to Jung in December 1953. It was not published in the Jung/Pauli correspondence and the two never discussed it in their letters. It is not known who constructed the horoscope and it is unlikely that Pauli attached much significance to it. Yet it may or may not have had something to do with Pauli's statement to Jung that equinoxes were times of "relative psychic instability, which can manifest itself both negatively and positively (creatively)." In Pauli's horoscope the spring equinox (the boundary between Pisces and Aries) is on the cusp between the seventh house, the "house of conjunction," and the eighth, the "house of the unconscious" and the autumn equinox is on the cusp between the first house, the "house of the ego" and the second, the "house of material things." One interpretation of Pauli's instabilities might be that they reflected the instabilities of these boundaries between houses.

In working on the psychological side of the problem of how we go from three to four Pauli had gained a deeper understanding of himself and how the whole course of physics seemed to be guided by the "archetype of the quaternity." He saw this course as leading to an extension of archetypes out of the collective unconscious into a new form of physics. This would surely be a major result of his joint work with Jung. He wrote to him: In this way, the ancient alchemical idea that matter indicates a psychic state could, on a superior level, experience a new form of realization. I have the impression that this is what my physical dream symbolism is aiming at.

PAULI had definite ideas on how an appropriate form of mysticism would appear. He was adamant that "my real problem was and still is the relation between Mysticism and Science, what is different between them and what is in common. Both mystics and science have the same aim, to become aware of the unity of knowledge.... And who believes that our present form of science is the last word in this scale? Certainly not I."

In the summer of 1957 Pauli described his att.i.tude to mysticism in a letter to the Israeli physicist and historian of science, Shmuel Sambursky: "In opposition to the monotheist religions-but in unison with the mysticism of all peoples, including Jewish mysticism-I believe that the ultimate reality is not personal. Thus is it also in the Vedantic philosophy, and so it is in Chinese Taoism, the Nirvana of Buddhists...and the En-Sof of Jewish mysticism. It is the task of mankind, through personal a.s.sociation not to implement these forms themselves (Yoga-teaching).... In this sense only is Yahweh for me a local demon who displays his efficacy primarily in Israel. How has he behaved with me? He was relatively mild, he only beat me gently on the left ear." Why "left"? Perhaps Pauli was thinking of his unconscious. Or perhaps he meant that G.o.d gently chided him for suggesting the existence of the neutrino, the weak particle that ended up causing a revolution in physics because it spins only to the left.

As for von Franz, in 1955 Pauli was writing to her using the familiar "Du." But two years later their exchanges abruptly ended. Perhaps Pauli felt he opened up too much to her. As he once wrote to her, when it comes to feelings "there I am no celebrity, but underdeveloped, even infantile." Von Franz claimed that he had become unpleasant and wanted her to a.n.a.lyze his dreams for free. She was bitter about this and, in turn, became critical of him.

According to Carl A. Meier, who knew both of them, "she totally misunderstood Pauli, failing to appreciate his efforts to conduct an a.n.a.lytic dialogue with her and that their relationship was tragic."

A supreme example of synchronicity: The Pauli effects pile up.

On May 26, 1955, Pauli was due to give a lecture on Einstein at the Zurich Physical Society, to celebrate the fiftieth anniversary of the discovery of the special theory of relativity. Before the lecture, three of his friends and colleagues met up for a teetotal dinner. Then they all set off for the meeting.

David Speiser, a young Swiss physicist, was on his Lambretta. He discovered he was low on gas and went to a gas station. Then his scooter suddenly caught fire. He threw a jug of water over the flames and extinguished them but the scooter was totaled and he had to walk. Another young Swiss physicist, Arman Th.e.l.lung, discovered his bicycle had two flat tires so he also had to walk. Ralph Kronig, the original discoverer of electron spin, took the tram. It was a journey he had made many times in the past but for some reason he failed to notice the Gloriastra.s.se stop and forgot to get out. He only realized several stops later. It was a magnificent example of a multiple Pauli effect. Fortunately they all arrived on time for Pauli's talk and Pauli himself was most amused to hear about their mishaps. As Th.e.l.lung recalled, "a defining feature of the Pauli effect was that Pauli himself never experienced any harm."

Fierz wrote: "Pauli himself thoroughly believed in his effect. He has told me that he senses the mischief already before as a disagreeable tension, and when the antic.i.p.ated misfortune then actually hits-another one!-he feels strangely liberated and lightened. It is quite legitimate to understand the 'Pauli effect' as a synchronistic phenomenon as conceived by Jung."

Second Intermezzo-Road to Yesterday.

The dream.

ON NOVEMBER 4, 1955, Pauli's father died. By now the two had reconciled and Pauli was deeply affected. It felt like a defining episode in his life. As he put it, "the shadow with me was projected onto my father for a long time, and I had to learn gradually to distinguish between the dream figure of the shadow and my real father."

Despite the rift between them after the suicide of Pauli's mother, Wolfgang Sr. had been always immensely proud of his son's achievements. Eventually father and son managed to overcome their differences and were back on good terms. Perhaps their reconciliation was a combination of time healing emotional wounds and, of course, Jung's therapy.

When Germany invaded Austria, in 1938, it placed Pauli's father in great danger. For despite his conversion, he had been born a Jew. Pauli immediately arranged for him to move into Switzerland. Wolfgang Sr. had to leave all his possessions behind and arrived in Zurich with only a suitcase, accompanied by his wife, Maria (Pauli's "wicked stepmother"). Initially they stayed with Pauli and Franca. Franca did not get along with Maria. In the end Maria decided to return to Vienna and was not reunited with her husband until after the war. In Switzerland Wolfgang Sr. was welcomed at the chemistry department of the University of Zurich, where he continued his scientific research. After he died Maria had severe monetary problems, often turning to her stepson for help. She also had an alcohol problem.

Soon after Pauli's father's death, Jung's wife Emma also died, followed by the elegant mathematician Hermann Weyl. Weyl's cremation was set for December 12 at 17.00 hours.

A few weeks earlier, on October 24, Pauli had had a dream. In it he is on an express train, departing at 17.00 hours-the exact time of Weyl's cremation. The train encounters an obstacle and has to swerve around it. Then Pauli goes into a church with Franca and a Swiss friend whom he calls Mr. X. In the church "some strangers" are waiting-the strangers who occur again and again in Pauli's dreams. There is a blackboard in the church. Pauli goes up to it and writes some complicated equations to do with the quantum theory of magnetism.

Then a famous preacher appears, the "Master" or the "great stranger." He walks to the blackboard and says in French that the subject of that day's sermon "will be the formulas of Professor Pauli. There is here an expression with four quant.i.ties," taken from one of Pauli's equations on magnetic effects. The equation reads: HN/V. Mu () is the extent to which a material is magnetized, H the magnetic field produced by the number (N) of electrons in the magnet, and V is the magnet's volume.

In all, there are four symbols-the number four again. Later Pauli recalled that in Jung's books, particularly Aion, he had mentioned that magnets were often considered a source of magical power, in that they contain opposite poles, north and south, in a single object.

In Pauli's dream the strangers become excited and shout in French "parle, parle, parle"-"speak, speak, speak." As always they want him to speak about feelings (France being the country of feelings) and about physics and psychology. (In his account of this to Jung, Pauli comments humorously, "In my dreams, by the way, I often speak somewhat better French than I do when I am awake.") But he is reluctant to speak up, fearing for his reputation among fellow scientists. His heart begins to pound so hard that he wakes up.

Musing over his dream, Pauli interprets the church as a new house, free from any struggle between opposites. Franca is with him. He is at one with himself.

Through a.n.a.lysis, he tells Jung, his function schema has changed. In earlier years his thinking function was dominant, but now that role has shifted to his intuition. Things are going better with his feeling side-represented by France-while extraverted sensation has become the inferior function. In other words, Pauli has become a nicer person, though further removed from reality.

This self-a.s.sessment was corroborated by Marie-Louise von Franz, who said of him: "He was highly intelligent, very honest in his thinking, but otherwise a very immature big boy in his feelings.... He had a patriarchal outlook on women. Women were pleasant things to play with, but not something to take seriously."

Pauli described his dream to Fierz as well as to Jung. Fierz asked rhetorically, "To where is this journey?" He pointed out that the formula Pauli had written on the blackboard referred to optics as well as magnetism. The combined subject is called magneto-optics and concerns how light is transformed when it is pa.s.sed through a material immersed in a magnetic field. Pauli had made important advances in it, one of which was this formula. Fierz reminded Pauli that magnetism was to do with attraction-the attraction of the north and south poles-while optics refers to visualizations. "What is the connection for us of these magnetic visualizations?" he asked.

"The connection," he continued, answering his own question, "is an alchemical one which concerns a transformation leading to an unfolding of events. How so and why so, you know much better than others from personal experience. 'The magneto-optical transformation and the 4 quantum numbers,' this is the key to your biographical experience." But Fierz did not know the meaning of the journey in the dream or how it related to the alchemical notion of transformation as Jung reinterpreted it.

In fact Pauli was about to make a very significant train journey.

Brief encounter.

Pauli told the story of his journey in three different ways in three different letters: to his friend Paul Rosbaud, the Scientific Director of Pergamon Press; to Fierz; and to Jung. The events took place during a trip to Hamburg between November 29 (full moon night) and December 1. Pauli also described the trip to Bohr. He referred to it only as "this 'road to yesterday,'" with no details.

Pauli's trip to Hamburg on November 29 was to give a lecture at the university there on "Science and Western Thought." He spoke on how important it was to reconcile the rational-critical (that is, Western science) with the mystical-irrational (that is, Eastern thought) to try to create a single framework of the physical and the psychical. It was an important lecture for him because it was one of the very few times he ever spoke in public on this topic. "It is precisely by these means," he concluded, "that the scientist can more or less consciously tread a path of inner salvation. Slowly then develop inner images, fantasies or ideas, compensatory to the external situation, which indicate the possibility of a mutual approach of poles in the pairs of opposites."

Early that evening, at precisely 17.00 hours, the phone in his hotel room rang. Pauli picked up the receiver. He recognized the voice immediately. It was the beautiful, blonde girlfriend from his Sankt Pauli days whom he had abruptly dumped when she had become a morphine addict. In writing about this meeting to his friends, he kept the woman's name a secret.

Ten years earlier, she said, she had seen his name in a newspaper, announcing that he had won the n.o.bel Prize. But she couldn't track him down. She didn't know where he was living. Then she spotted an advertis.e.m.e.nt in a newspaper saying that he was to give a lecture in Hamburg. His hotel was also named.

Pauli was excited to hear from her and curious as to what had become of her. But he was also apprehensive. Even though so many years had pa.s.sed since then, he still felt the old dread of mixing his night and day selves. In the end he agreed to meet her on the day he was due to leave, in the lobby of his hotel, the Hotel Reichshof, one of the best in Hamburg.

She was two years younger than he, so she would have been fifty-three. Nevertheless, when she came through the revolving doors he saw that she was still beautiful, blonde, and alluring. "This young woman suddenly appears qua woman. (Regeneration motif! N.B. shortly before, on 4 November, my father died) and she was in good health," he wrote to Fierz.

For two hours they talked intensely. "A whole lifetime of 30 years pa.s.sed before me-her cure, a marriage, and a divorce, with war and National Socialism as a historical background."

Perhaps, he thought, the situation was archetypal, a fairytale "being played out." After all, November 29, the night that she contacted him, was the night of the full moon. The first time they met, he recalled, had been in his Jekyll and Hyde days in Hamburg: 30 years ago my neurosis was clearly indicated in the complete split between my day life and my night life in my relations with women, but now it was very human.

As for seeing her again-"erotic it was not." Rather it was a painful reminder of the very different person he had been thirty years earlier: I saw myself as in a dark mirror, in a time 30 years previous with its sharp cut between the worlds of night and day, which I worked strenuously to maintain-until the breakdown of 1930 came upon me (my great life crisis). In the day calming works, in the night s.e.xual entertainment in the underworld-without feeling, without love, indeed without humanity. "What price glory!"

Pauli told her that he regretted falling out of contact. He recalled how pretty she had been in those days and, he added, now too. A human life unrolled before him. He felt ashamed that he had no more to say. "But should I speak-'speak, speak'-what should I say," he thought, in French. As with the "strangers" in his dream who wanted him to speak about his feelings, he was tongue-tied in front of this woman.

"One should not give up hope," he wrote to Fierz. "I gave up on this young lady in 1925, too early. But, personally, even if she at the time would have been entirely healthy, the life rhythms were not so. (It is very probable, that at that time I kept away from her-I wanted at that time no external connection [no relationship])."

The woman walked Pauli to his train. When they arrived they were both aware that this was a moment that would not occur again. Pauli told her how pleased he was to have seen her again. He was married, he said, lived in Zurich, and was easily within reach. He thought of kissing her, then hesitated and decided not to. "Now it was as friends-at that time not."

He described their parting to Jung:.

But now it was very human, and as we parted on the platform, it seemed to me like a coniunctio. Alone in the express train to Zurich, my mind went back to 1928 as I took the same route toward my new professorship and my great neurosis. I may be a little less efficient than in those days, but I think the prospects are a bit brighter as regards my mental and spiritual well-being.

Afterward Pauli could not put the meeting out of his mind. In search of a deeper understanding of it he thought back to Fierz's comment on his dream about the blackboard. Fierz had pointed out the fourness it contained in the four symbols in Pauli's equation as well as the four quantum numbers. All of a sudden, Pauli realized that this research was part of his tumultuous past, his Hamburg days. The blackboard dream had occurred before the death of his father, a defining episode in his life. Meeting the woman in Hamburg made him realize that he had broken with that past. "There was a transformation in those 30 years, at the [station] platform [where they said goodbye] it had for me somewhat of a humanistic-conciliatoriness, a 'coniunctio.'...My individual life attained a sense of symmetry between past and present," he wrote to Fierz. Just as Fierz had suggested, the number four held the key to his "biographical experience." Pauli's train ride was not to meet his neurosis but to return home.

"May sometime the preacher of dreams make it possible for you to make a journey as I have made to Hamburg," Pauli finished his story.

Through the Looking Gla.s.s.

Dreams of reflections.

IN NOVEMBER 1954 Pauli had a dream so curious that three years later he was still thinking about it. He sent a description of it to Jung. In his waking life Pauli was very preoccupied with issues of symmetry, both in physics and in psychology-the conscious and unconscious as mirror images of each other. It was not surprising that this preoccupation should seep into his dreams as well.

In the dream he is with a dark woman-his anima-in a room in which experiments are being carried out involving reflections. The "others" in the room think that the reflections are real objects, but Pauli and the dark woman know they are just mirror images. They keep this secret. "This secret fills us with apprehension." From time to time the dark woman changes into the Chinese woman of Pauli's earlier dreams, who had paraded Pauli before the "strangers." The Chinese woman, according to Jung, represents the dark woman's holistic side, in that Chinese philosophy seeks to reconcile opposites.

Pauli guessed that the "others" represented the collective opinion which he took to be his "own conventional objections...to certain ideas-and [his] fear of them." The problem with which he is struggling is that "there is no symmetry of 'objects' and 'reflections' in this dream, since the whole point is about distinguishing between the two." Even though he can see that what appear to be objects are simply reflections, the "others" cannot. In this dream there is no mirror symmetry. But this is impossible.

In the very first set of dreams he had presented to Jung in 1932, he had spoken of the conscious and the unconscious as mirror images of each other. When he was sure that the "left is the mirror image of the right," he felt at one with himself because it meant his conscious and unconscious were in balance.

Charge, parity, and time reversal (CPT)-Pauli's third great breakthrough.

Pauli never worked out quite why it was that he started working on the mathematics of mirror images. The year was 1952. As he wrote, "between 1952 and 1956 there was not actually anything going on in the world of physics to justify focusing on that particular subject." It was two years later that he dreamed about the Chinese woman and began to suspect that "there must have been psychological factors involved."

Pauli began his investigation into mirror symmetry by looking at time reversal. Representing time with the symbol T, he placed a minus sign in front of it. In mathematical terms, he made time run backward. (Hard though it is to imagine, this can actually be done in the laboratory at a subatomic level.) When time is run backward, we look into a world in which a particle that was originally moving to the right is now moving to the left; the particle's speed is also reversed. The law of time reversal a.s.serts that the laws of physics remain the same when time is reversed-time-reversal invariance-which means that there is no difference between the state of a collection of moving elementary particles (or billiard b.a.l.l.s or cannonb.a.l.l.s) and the same collection in which time has been reversed. Time-reversal invariance is not a property of a specific state of a collection of objects, but of two different states. In other words, it is not intrinsic to any particular particle, like the spin of an electron is.

Pauli's lectures on this inspired other physicists to look into the connection of time reversal (T) with two other symmetries, parity (P) and charge conjugation (C). Parity is the mirror-image effect, the interchange of left and right. In both prequantum and quantum physics, the law of parity conservation states that every physical system (that is, atoms, electrons, billiard b.a.l.l.s, etc.) should be independent of any difference between right and left. Physicists believe that atomic systems have a particular parity independent of the system's location in s.p.a.ce and time and which must be maintained throughout all interactions. If an experiment is performed it should turn out exactly the same when observed in a mirror; it should be a perfect mirror reflection. This is called parity invariance (P-invariance) or mirror symmetry.

In mathematics, the law of parity conservation means that a physics equation must remain the same when right and left are exchanged. Parity invariance explains many properties of atomic systems and, at the time that Pauli began working on it, was taken as axiomatic; it had never been questioned.

By the mid-1930s physicists agreed that every charged particle must have a matching antiparticle. Charge conjugation (C) describes the mathematical process used to convert every particle into its antiparticle, and so matter into antimatter. In quantum mechanics it is considered to be an intrinsic property of every elementary particle (for example, an electron) along with parity.

In 1954, two years after he began working on mirror images, Pauli decided to look deeper into the whole subject. Instead of exploring charge conjugation (C), parity (P), and time reversal (T) separately, he looked at all three together-the whole combined operation of CPT. This entails the exchange of particle and antiparticle (C), right-left symmetry (P), and time reversal (T)-(particle antiparticle) x (left right) (future past). CPT makes the astonishing a.s.sertion that a mirror universe-in which all matter is replaced with antimatter, all positions are their own reflections, and even time runs backward so that all speeds are reversed-would actually be indistinguishable from our own.

Explaining this complex concept to Jung, Pauli wrote, "The combination of CPT of all three parity operations...is correct under much more general a.s.sumptions (that is, deducible, demonstrable) than the operations C, P, and T taken individually." The exclusion principle played a central role in his calculations because it required that collections of particles and antiparticles with half a unit of spin and those with a whole number of spin be treated differently. He proved that if the equations describing an atom remain unchanged under CPT, this was the same as requiring any of those equations to agree with relativity theory.