“A man who knows everything”. This, reportedly, was my reply to a school teacher asking me what I’d like to become when I grow up. I was eight years old, or thereabouts, and what I wanted to say was “professor”, but, still not knowing everything, I had forgotten that word. And what I really meant was “scientist”, someone who unravels the secrets of the fundamental Laws of Nature.
This perhaps was not such a strange wish. Science, after all, was in my family. Just about at that time, 1953, my grand-uncle, Frits Zernike had earned his Nobel Prize for work that had led him to the invention of the phase contrast microscope. He had worked out the theory and singlehandedly constructed his microscope, with which he had stunned biologists by showing them moving images of a living cell. My grandmother, Zernike’s sister, used to tell us anecdotes about her brother when they were young. One day, for instance, he had purchased a telescope at a local market. That night, the police came at their door to warn her parents that there were “zinc thieves on their roof”; it was Frits however, trying out his new telescope and studying the heavens. She herself had married her professor, a well known zoologist, Pieter Nicolaas van Kampen at the University of Leyden. I never knew him, he passed away, after a long illness, when my mother was eighteen years old.
My uncle, Nicolaas Godfried van Kampen was appointed Professor of Theoretical Physics at the State University of Utrecht. My mother did not opt for a scientific career. “It never came up”, she now says, adding that actually math and science were not particularly difficult for her at school, but being a girl, you wouldn’t admit that you actually liked such subjects. She went to art school but later achieved a degree in French, and now she teaches that language in a private class.
Was it the environment or was it in my genes to choose to become a physicist? My grandmother adored scientists and by that she may have further determined my choice, but I think that my mind was made up long before I could talk. A picture was taken of me, at the age of two, studying a wheel. I do not remember the event, of course, but I do remember being fascinated by wheels when other kids were just running around, playing. My very earliest recollections are about being obsessed with phenomena I observed. I watched the ants crawling in the sand, and wondered what life would be like if you were an ant. You would be able to go into the tiniest spaces between the pebbles, and those would be as big as houses for you. But, I realized, an ant’s life must be totally different from ours. Still being a toddler I saw one day how the wheels of two children’s bikes, which were upside down, touched each other. If you turn one wheel, the other one would start rotating as well. You can make one wheel turn by rotating the other. The principle of transmission. How fascinating Nature is. I was well over two years old before I started to speak. Was it because there were so much more interesting things I wanted to understand than to communicate with people? I was also late in reading and writing. This, I remember, was because I thought reading meant being able to decipher my mother’s handwriting.
Though born in Den Helder, I spent my childhood in The Hague, with my parents, my older sister who had changed her official name Elise into Ita as soon as she could talk, and my younger sister Agnes. My father had obtained a degree at Delft in naval engineering. He made his career at the dockyards of the big ocean cruisers of the Holland-America Line. He used to talk of the giants “Maasdam” and “Rijndam” as his ships. Then for a long time he worked at an oil company until he had enough of that. Like his father, he loved ships and all high-tech industry having to do with the sea. Noticing my interest in natural phenomena, he thought that it would be easy to get me interested in engineering as well. He bought me books about ships and car engines, which I never touched. “Those things have already been invented by someone else”, I objected. “I want to investigate Nature and discover new things.”
When I was eight, my family moved for a ten month’s period to London, England, where for the first time I was forced to master a foreign language, English. Too late, my parents discovered that sending their children to a private school would have required registration three years or more ahead. We went to a public school. School uniforms were not required, but there were strict regulations on clothing. One cold day I entered the school in long trousers. I was allowed in because I was a foreigner, and they always were very kind to me, but shorts, reaching until the knee, were the norm for the school. In summer time, during the week-ends, we would make long trips in the beautiful country-side. It seemed that all rain in England fell during the week-ends. I saw my first mountains, that is, hills taller than 100 meters, which hardly exist in the Netherlands. I was thrilled to notice that the tree trunks grow along the lines of gravity and ignore the direction of the slope. I also noticed some fundamental differences in English and Dutch architecture, so that, if you show me some houses, old or new, I can immediately tell the Dutch and English ones apart.
My father made more money than usual, and this afforded him to buy me some expensive boxes of Meccano. It was one of the great things he did for me. However, I had to make a deal with my father. Alternatingly, I would construct a model described in the book, and then construct something out of my own imagination. He thought the models in the book were more instructive, but I preferred my own imagination. The most fantastic things I constructed were robots, that I could persuade to pick up something, although infinite diligence was needed for that.
After primary school I went to the Dalton Lyceum, also in The Hague. It is a school system where students are given extra hours for studying homework material in the presence of teachers, and it worked well for me. After one year the choice was to be made between a non-classical and a classical continuation, the classical one including ancient Greek and Latin, which would take one year more, and it would be more demanding. My uncle said the choice would be immaterial. “You don’t need Latin and Greek for physics”, he said, “but it doesn’t do any harm either.” I chose to take the challenge. Why? I think I couldn’t stand the idea that some kids would learn things I didn’t know. I never regretted the choice.
My father bought me a book about radios, and that did interest me. “You know, Gerard”, a schoolmate had once said to me, “nobody in the world understands how a radio works”. This I found difficult to believe. “Look at all those things inside”, I said, “the guy who designed that must have had some idea.” But if there were any not understood secrets, I was going to find out about them, that I promised myself. The radio in the book had lamps in it, diodes, triodes, pentodes. Later I learned that transistors work the same way, and you could buy sets with complete instructions how to assemble a radio. I would never build a radio before I understood why it had to be assembled precisely this way. Why, for instance, would the designer always suppress the amplification power of a transistor by back coupling? I tried to make an amplifier with fewer transistors and no suppression. Can you make a radio with just one transistor for both the high frequency and the low frequency signal? I learned the answers to all these questions.
Of the modern languages, English, French and German, besides Dutch, were obligatory. I had difficulties with the logic of linguistic arguments and besides, the texts we had to translate were such that even in my own language I could hardly understand what they were about. But I managed, and now I am happy that I can communicate with the inhabitants of a major fraction of Europe.
So much easier were math (of which there was surprisingly much: algebra, analysis, trigonometry, stereometry), physics and chemistry. My physics teacher was a friendly, middle aged man with a small beard and a soft voice. He taught physics using a book that he and another teacher at our school had written, and which was being used throughout the country. It was sound and pedagogical, but not always equally accurate. Where fluids were discussed, it explained that the cross section of an airplane wing has “a droplet form” because “droplets take a shape of least resistance”. Elsewhere, the rainbow is derived, and there droplets were spherical.
Being pedagogical was high on my teacher’s priority list. But he also inspired us and made us think. “If there were any real geniuses in this class”, he would say, “then they could have argued as follows, … “. But then, he assured us, there were of course no real geniuses in this class. Then, there was an interesting page in his book about photons. “A light bulb emits about 109 photons per second,” it said. The argument was simple. “A single photon has a wave packet of about 10-9 seconds long. If there were much more than 109 photons, then for each photon vibrating in this way, you could find another photon vibrating in the opposite direction. You’d have destructive interference, and so there would not be any light.” I had long arguments with him about this. Finally, with the help of my uncle, we could sort things out. This page does not appear in the later editions of the book.
Biology was taught by an elderly lady, too kind for this world. She would never give anyone failing marks, unless someone really asked for it, but high marks were also rare. My marks quickly dropped when the lessons became boring, such as the discussion of symmetry patterns in flowers (I thought the symmetry was never perfect anyway), or incomprehensible, when the human body was discussed (some parts were hardly mentioned, except outside hours among the pupils, and there were things that no-one could explain to me, and I didn’t dare to ask).
Then, one of the teacher consultation days, my father noticed that none of the parents wished to talk to our biology teacher, since she never made anyone fail. He stepped towards her and said: “Did you know Professor P.N. van Kampen?” Of course she did, surely she did, she had attended all his lectures. He was such a scholar, he was so bright! Is Gerard really his grandson? If only had she known! The next day she started with zoology. I was given special attention. Van Kampen’s grandson! My grades skyrocketed. She gave me the assignment to write a thesis. I chose to write about bacteria. Our local library had nothing about bacteria. One pre-war book was there, written in German in Gothic letters. I still don’t know how I managed to produce a thesis using that. But it did not matter. My grade for it was superb.
I had the good fortune of having an enthusiastic art teacher. I suspect it was only because of my good geometric insight that I could make quite realistic drawings. But my mother spotted the weak points in my art. If you want to draw a human face or body, you have to know exactly how the bones and the muscles go, she said, otherwise you do it all wrong, and it doesn’t look good. I was too shy to make a careful study of human bodies, and so I specialized in animals and landscapes. This will never make me a very good artist, I decided.
When I was ten I encountered my first piano. We were on a vacation in the hills in the south-east of Belgium. It was continuously raining during the entire two weeks. The cottage we had rented had an old piano in it. There were a few books with some songs in them. My father explained how the notes relate to the keys on the instrument. “The rest you can figure out by counting”. Both my parents had suffered from compulsory piano lessons when they were young, and had intended not to subject any of their children to such a torment. But now that I wanted them, I could get my piano lessons. I had a private teacher. She was tough. She herself had had lessons from the wellknown Dutch pianist Cor de Groot, and she wanted me to reach similar heights. I had to practice scales. It amazed her that the first time I tried to play a scale simultaneously with left and right hand, I nevertheless had the right idea to switch fingers left and right at different moments. “Most people first do this wrong”, she said. She taught me Beethoven, Chopin, Debussy, Mendelssohn and many others. Much of it was too difficult for me, but I still play many of the pieces, and piano has become part of my life.
At age 16, the opportunity was offered to participate at the Dutch National Math Olympiad. It was the second time the olympiad was held. I passed easily the first round; only by being nervous I had misread the first exercise, which had been done correctly by most other participants. But I had done well with the others, and so I went with some 100 schoolkids to Utrecht for the next round. It was a tough one, and I had missed several questions. On hindsight, the questions had been very good ones, and I had only missed them because of lack of rigorous mathematical training. Today, math questions are phrased in such awkward ways, supersaturated with pedagogical nonsense, that I’d probably have missed them all.
Anyway, it came as a surprise when during a school break my younger sister came rushing towards me. “We searched for you everywhere,” she said, “you’re among the first ten!” The exact order was still kept secret. We came to Utrecht to learn that I had obtained the second prize. It consisted of two volumes of a book by Georg Pólya, “Mathematik und Plausibles Schliessen”, and I devoured them. This was math of a kind that I liked very much. They must have seen by the way I had answered the questions that this was math to my liking. It contained, among other things, Euler’s theorems for polygons in three-dimensional space, and this knowledge would turn out to be quite handy later in my career. I could have been number one in this Olympiad, if I hadn’t flunked the first exercise in the first round, but then, probably, the others too had made avoidable mistakes.
The final examinations at high school, 1964, were tough. My only real problem was the languages, but what about biology? The high grades given by my teacher were ridiculous. Biology would be examined orally, and this time there would be a biology university professor who would independently judge the answers. When I entered the room, the first thing my teacher said to the university professor was: “Now this is Professor van Kampen’s grandson! ” His face brightened, ‘Really?”, he said, he had followed all of Van Kampen’s lectures. Such a brilliant zoologist. And here is his grandson. He must be very bright. They asked something about some obscure sponge. I vaguely remembered the text in the book, and tried to reproduce it. “Yes, yes!”, they cried, “and sometimes it is said that…” and then came the real text, which I had practically forgotten. They gave me a 10 out of 10. I gladly dedicate this result to the memory of my grandfather.
I passed the examination and went to the State University of Utrecht. Leyden was closer to The Hague, but my uncle was teaching at Utrecht, and his lectures I desired to follow. My father insisted that I become a member of the most elite student organization, the Utrecht Studenten Corps. Freshmen were shaven bold. This was actually one of the lesser humiliating things they did; the elderly students had developed a special skill at humiliating their freshmen. Some of the new students had already been in military service; for them, it was all only too familiar, and they had no problem. But I was easy to crack, and they could ridicule my lack of interest in anything but science. “So you wrote a thesis about bacteria? What kinds of bacteria are there?” It was an elderly medicine student who asked the question. When I mentioned the spirochetes, he asked: “and which disease is caused by them?” I knew what he wanted to hear. “Syphilis”, I said. His opinion was that I should go into medicine, not physics.
But now I was near the Theoretical Physics Institute. I had rented a room just around the corner. Theoretical Physics occupied three adjacent houses opposite to a canal. One of the houses was owned by a lady who had introduced herself as a countess. There was some dispute as to whether she really was one. In summertime, when you opened the windows, chicken would hop in from the garden, and walk over the desks. Staff members would have coffee, lunch and discussions in a cellar. Through a narrow window you saw the legs of the pedestrians passing by. In earlier days the cellar had probably been in use by prostitutes. Of course, I was only a first year student, and I was not supposed to come in here. But more often than not, my uncle invited me in, and I adored the discussions, and the laughter.
The student organization forced me to spend time also on other things besides physics, which was exactly why my father had wanted me to become a member. I was coxswain in their celebrated Rowing Club, Triton, where I was appreciated because I could keep their boats coasting in straight lines. There was a student science discussion club, “Christiaan Huygens” where I have many fond memories, and together with some other students I organized a national congress for science students. But it was also at the student clubs where I learned to hate interminable meetings and pointless discussions. Especially the student revolts of the 60’s I found silly and I kept at the greatest possible distance.
I wanted to go into what I saw as the heart of physics, the elementary particles. Unfortunately, my uncle had developed a dislike of the subject. People in that field are very aggressive, he warned. He had also investigated elementary particles, deriving what the mathematical consequences are of the fact that no information can go faster than light. You find equations, he explained, called dispersion relations, but they don’t tell you everything about the particles. He had written a few articles, meticulously deriving these consequences. “And what happened? Others wrote dozens of papers, full of unwarranted assumptions, sloppy arguments and incredible results. But there were so many of those papers, that only they got all the citations. ” He thought that statistical physics was more to his liking.
There was a newly appointed Professor of Theoretical Physics who did specialize in subatomic particles, Martinus Veltman, or Tini, as he was normally called. When time came that I had to write an undergraduate thesis, somewhere in 1968, he was the person to advise me and judge me for it. Veltman naturally thought that those high grades of mine were just because of my family background, and if I were any good, he would first need some convincing. This never even bothered me, all I wanted was learn about elementary particles, and if he didn’t think much of me, so be it. First things first, he said. Here is a paper by C.N. Yang and R.L. Mills. This stuff you must know.
Now this was a brilliant paper. It was beautiful, elegant and unique. But it was also considered to be useless. “It describes particles which do not exist in Nature”, Veltman explained, “but in some modified form, they might”. What modified form? To a fellow student, Veltman gave the assignment to study spontaneous symmetry breaking. There was a lot of confusion concerning the so-called Goldstone theorem. Jeffrey Goldstone had derived that spontaneous symmetry breaking implies the existence of massless particles. Spontaneous symmetry breaking could not be the resolution of the Yang-Mills problem because such massless particles do not exist. Later, this would be recognized as just one more example of too much adoration for abstract mathematical theorems; people did not bother to read the small-print, where Goldstone clearly said when his theorem does not apply. I am glad I ignored the problem; I did not understand why people thought there were massless particles if I could not see any in the equations.
My assignment was to study the so-called Adler-Bell-Jackiw anomaly. This was a subject in which Veltman was involved. He had a formal theorem saying that neutral pions cannot decay into photons. But when you actually calculate the decay, you find that it should occur. And the experimental data agree with that: neutral pions decay predominantly into photons. Something is wrong with the formal theorem. It was based upon flawed mathematics. The flaw was something highly interesting, and it would continue to play an interesting role later in particle physics. There were related problems with the eta particle. It decays into three pions while it shouldn’t. The resolution to this problem was still entirely unknown.
They say that organizing a student congress causes one year delay in your studies. But I had never stopped thinking about physics, and I could begin my PhD studies in 1969. In Holland, the PhD is a very serious matter. I remembered my physics teacher being so proud of his thesis. My history teacher obtained his PhD late in his life, and he too had been telling us all about his defense of his lifetime work. Veltman was to be my advisor. He gave me the choice between various topics, but none could catch my imagination more than the subject he himself was working on: the renormalization of Yang-Mills fields. He explained to me that vector fields must be playing an elementary role in the weak interactions, but also in the strong interactions there were vector fields. All these fields were associated to spinning particles with mass. The mass was where the problem started. “These mass terms in the equations look quite innocent”, he explained, “but in the end they impede all my attempts to obtain a finite, meaningful theory.”
But he knew something else. He had studied the experimental data concerning the weak interactions. There, he had found very strong indications that the weak interactions have something to do with the theory of Yang and Mills. “But the matter becomes so complicated that you cannot do it by hand anymore”, he said, and he had started designing a computer program to handle the complicated algebraic expressions. Computers were still in their infancy those days. Today’s simplest hand-held calculators contain more electronic switches and are much faster than the bulky constructions that were called computers then. The monsters had to be fed with paper cards in which you had to punch your programs. His effort was an heroic one.
What I began thinking about was my own version of the Goldstone theorem, but I could not read those pompous mathematical theories. What I reconstructed in my own way was something that actually did exist already: it is now known as the Higgs mechanism, but important elements of it had also been derived by François Englert and Robert Brout. Unfortunately, these ideas were not along Veltman’s line of thought. He wanted to derive everything just by looking at the experimental data, and by performing field transformations for which he could use his computer program. In his opinion, I clearly lacked insight in experimental subjects. Something had to be done about that. We sent my application to various summer schools in theoretical physics. My first choice was a school at Les-Houches, a ski resort high in the French Alps, near Chamonix. Famous French physicists would be teaching there. Presumably because my application was late, I was not admitted.
The next choice was Cargèse, and here I was admitted. Near this small town on the French island Corsica, right at the sea, the French physicist Maurice Lévy had established an Advanced Science Institute, ten years earlier. The story goes that Lévy had looked up in the atlas which French town has the maximal amount of sunshine during summer, and then he found this location. Now, Lévy had developed a model for the strongly interacting particles together with Murray Gell-Mann. Formally, the model could be renormalized, but in practice there were numerous problems, and they were going to be discussed. It was summer 1970. Lecturers were, besides Lévy and many others: the Korean Benjamin W. Lee, the German of Polish descent Kurt Symanzik, and many Frenchmen such as Jean-Loup Gervais.
The Gell-Mann-Lévy model is a model with spontaneous symmetry breaking. The pions are here interpreted as Goldstone particles. These lecturers were talking about renormalization in the presence of spontaneous symmetry breaking, and they were telling us that the mass terms that are generated (the mass of the proton) cause no problems whatsoever. As far as I remember, I only asked one question, both to Benjamin Lee and to Kurt Symanzik: “why can we not do the same for Yang-Mills theories?”. They both gave the same answer: “if you are a student of Veltman’s, ask him, we are no experts on Yang-Mills.”
A general picture of how to deal with massive vector particles was forming in my mind, but I could not understand the negative attitude of all the experts towards such theories. Later, I would find out that they all had different reasons for rejecting such approaches: some people thought that there would be Goldstone bosons with physically unacceptable properties. Some thought that introducing fundamental scalar particles would not serve any fundamental physical principle such as local gauge invariance. To many people, a renormalization programme would seem to be so complicated that mathematical clashes would be unavoidable. Finally, there was the scaling problem. It was thought that scaling towards asymptotic freedom in the ultraviolet region would never happen in a field theory; this would imply that any relativistic quantum system with strongly interacting particles would explode nonperturbatively in the near ultraviolet, and therefore no perturbative quantum field theory would ever apply to such systems. Because of this universal agreement among the experts, no-one realized that all these arguments were wrong. Why had this faulty counter evidence not deterred me? Probably, Veltman’s determination that there had to be something right about quantum field theory influenced me. But as a student I had also learned only to believe those arguments that I could truly understand.
What I did understand from the Cargèse lectures is that renormalization is complicated and delicate. At least at this point I could agree with my advisor, Veltman. When I returned to Utrecht, his assignment to me was that I should first study the pure Yang-Mills system, without anything resembling a Higgs mechanism for generating masses. There was not much literature on the subject, except some very elegant papers by Richard Feynman, Bryce DeWitt and by Ludwig D. Faddeev and his coworker Victor N. Popov at Leningrad. But some of the papers seemed to contradict one another, and so I began to collect the pieces of information that I could understand.
I learned how to formulate the Feynman rules for these Yang-Mills particles, and I learned that the discrepancy between the different papers was only an apparent one: you could perform gauge transformations to relate one to the other. I thought I was making tremendous progress towards formulating the exact renormalization procedure for this case, but Veltman had various objections. After long discussions, which again gave me many more insights, my first publication appeared. I had derived identities among amplitudes which were subsequently used by A.A. Slavnov and J.C. Taylor to derive more general identities, and their first references to my work made me feel very proud. The generally accepted name for these identities would be the “Slavnov-Taylor identities”.
After having learned so much about renormalizing massless Yang-Mills fields, doing the same thing for theories with Higgs mechanism was relatively easy. But it was this second paper with which I caught world-wide attention. Veltman realized that now the problem that he had been working on for years had been solved, and he was enthusiastic. As he was one of the organizers of an international conference on particle physics at Amsterdam in 1971, he decided to use his new pawn (me) in his battle for the recognition of Yang-Mills theories, and gave me 10 minutes (but no place in the Proceedings) to explain our new results. A period of intensive cooperation followed. Together, we worked out the so-called dimensional renormalization technique. Certainly, the work I had done was considered to be good enough for a PhD degree, and I graduated in 1972.
This, by the way, was also the year of my marriage. While I was making my great discoveries in physics I had also discovered whom I wanted to marry: Mrs Albertha A. Schik (Betteke). She had grown up in the town of Wageningen, and had studied medicine at Utrecht University.
We went to CERN, Geneva, where I had a fellowship, and Betteke could begin her work to obtain her certificate as a specialist in anesthesia, at the Hôpital Cantonal of the town of Geneva. The day before she was to meet her new superiors and colleagues there, we had made a trip to the Mont Blanc; on the way back we were in a minor car accident, and she fractured a bone in her foot. Her entry at the hospital will be remembered.
Veltman also came to CERN, and together we refined our methods for Yang-Mills theories. We were delighted with the great impact that our theories had. From 1971 onwards, all theories for the weak interactions that were proposed were Yang-Mills theories. Experiments were set up aimed at selecting out which of these Yang-Mills theories were correct. One of the simplest models continued to be successful; every now and then some particles were added to it, but its basic structure remained the same.
At CERN, I became interested in the quark confinement problem. I could not understand why none of the expert theoreticians would embrace quantum field theories for quarks. When I asked them, why not just a pure Yang-Mills theory?, they said that field theories were inconsistent with what J.D. Bjorken had found out about scaling in the strong interactions. This puzzled me, because when I computed the scaling properties of Yang-Mills fields, they seemed to be just what one needs. I simply could not believe that no-one besides me knew how Yang-Mills theories scale. I mentioned my result verbally at a small conference at Marseille, in 1972. The only person who listened to what I said was Kurt Symanzik. He urged me to publish my result about scaling. 1f you don’t, someone else will”, he warned. I ignored his sensible advice. I had also made a remark about scaling in my 1971 paper on massive Yang-Mills fields. No-one had taken notice.
Veltman told me that my theory would be worthless if I could not explain why quarks cannot be isolated. He attached more importance to another project we had embarked upon: we had started a lengthy calculation concerning the renormalizability of quantum gravity models. Although complete renormalization would never be possible, it was still worth-while to study these theories at the one-loop level, and there were some important things to be learned. Our work would be continued by Stanley Deser and a fellow PhD student of Veltman’s, Peter van Nieuwenhuizen, who discovered patterns in the renormalization counter terms that would lead to the discovery of supergravity theories.
But I also continued to think of gauge theories for the strong interaction. Quark confinement was indeed a problem, and I started to work on it. It was this question that led me to discover the magnetic monopole solutions in Higgs theories, the large N behaviour for theories with N colours (instead of 3, the physical number), and later the very important effects due to instantons. In the mean time, the scaling properties were rediscovered by H. David Politzer and by David Gross and Frank Wilczek in 1973, who now realized that this invalidated the age-old objections against simple, pure Yang-Mills theories for the strong interactions. The pure Yang-Mills theory with gauge group SU (3) was finally being accepted as the most likely explanation for the strong interactions, and it received the beautiful name “Quantum Chromodynamics” (QCD).
In 1974 we returned to Utrecht. I had been given an assistant professorship there. I was making progress understanding confinement as an effect due to Bose condensation of colour-magnetic monopoles. An important observation by Kenneth Wilson was that permanent quark confinement appears naturally if one performs the 1/g expansion instead of the g expansion in gauge theories, provided that a lattice cut-off is used. We were just beginning to see the extremely rich topological structure of gauge theories, and its consequences for the quantized system.
In 1976, 1 was invited for guest positions at Harvard (Morris Loeb lecturer) and Stanford. I worked on the question whether the delicate effects due to instantons – topologically twisted field configurations that should play a role in quantum chromodynamics – would survive when a renormalized perturbation expansion was applied. This led to one of the most complicated calculations I ever did: the one-loop corrections to instantons. It turned out that instantons in QCD give finite and well-defined contributions to the amplitudes. They give the symmetry structure a twist in such a way that many riddles in the experimental data concerning chiral symmetry were finally resolved, the most notable one being the problems with the eta particle, mentioned earlier. Several of my friends and colleagues at Harvard, MIT and Princeton such as Roman Jackiw, Sidney Coleman and David Gross but also physicists elsewhere (Moscow), students and postdocs joined the game of unraveling the secrets of instantons and monopoles. In the mean time my first daughter, Saskia Anne, was born, at Boston. When I returned to Utrecht I was appointed Full professor there. My second daughter, Ellen Marga, was born at Utrecht in 1978.
The years that followed I spent much energy and inventiveness to shed more light on the quark confinement problem. The neat and clean treatment of QCD that I hoped to find did not exactly materialize, but by the beginning of the 1980s the elementary mechanism for this phenomenon had become clear. QCD can be treated numerically when lattice cut-offs are used, and nowadays increasing accuracies are being reached by investigators using ever improving hardware and software. The problems remaining seem to be rather mathematical ones and not physical ones. QCD had become an integral ingredient of the Standard Model. I decided to turn towards the many open questions concerning the physics of this model.
I felt pain and sadness when for personal reasons Veltman left Utrecht in 1981. What about the deep, open problems in the Standard Model? Many of my colleagues agree that supersymmetry, a symmetry relation between particles with different spins, should play an essential role. I had seen how supersymmetry was born, back at CERN during the early 1970s. Bruno Zumino and Julius Wess were producing highly intriguing papers, while Van Nieuwenhuizen and Sergio Ferrara, and many others were making progress in supergravity. But what should a supersymmetric “parent theory” be like? How and why should supersymmetry be broken to explain the world as we observe it today? Do we really have to believe that there are dozens of particle types called “super partners”, none of which have ever been seen? Such questions make me feel uncomfortable with supersymmetric theories.
The true answers must undoubtedly come from the incorporation of the gravitational force. At first sight it may seem difficult to believe that such an extremely weak force could cause so much havoc in a theoretical construction such as the Standard Model. The point is, however, that if gravity really corresponds to the curvature of space and time, as we must conclude from the successes of Einstein’s theory of General Relativity, then Quantum Mechanics predicts quantum fluctuations in this curvature that, at the tiniest distance scales, grow out of control. This means that either gravity theory, or Quantum Mechanics, or both, must be replaced by some superior paradigm when we wish to describe physics at distance scales smaller than 10-33 CM. Whatever paradigm this would be, it is likely to entirely reform our understanding of the fundamental interactions, answering all our present questions at one stroke.
In 1984, the superstring revolution took place. Many of my colleagucs were enchanted by the coherence of the mathematical structures they saw in this theory. Would this not be exactly what we are looking for, a new paradigm that naturally generates the gravitational force and an apparent complete unification of all interactions?
But to me, superstring theories presented as many new problems as they may solve; I still cannot quite fathom the fundamental logical coherence of these ideas. The short distance structure is as mysterious as it was before and the predictive power of these theories was disappointing, to put it mildly. I decided to try a different route. When Stephen Hawking discovered that black holes will radiate due to quantum field theoretical effects, this to me appeared to be a more solid starting point. Are black holes elementary particles? Are elementary particles black holes? I was stunned to learn that Hawking’s result would put black holes in a category fundamentally different from any ordinary form of matter. If that were so, then what exactly are the laws of physics for black holes? The answer is that present theories are inconclusive. They clash. They lead to a paradox that may be as elementary as the paradox that, one century ago, led Max Planck to revise the black body radiation law, and which ultimately gave us Quantum Mechanics. By studying this paradox, I hoped to stumble upon something equally great. Needless to say, I was asking for more luck than in the average lottery system. The problem is a sturdy one, and it still has not been solved. To illustrate the paradoxical nature of our problem I formulated a feature of the quantum gravitational degrees of freedom which, in discussions with Leonard Susskind, was called the “Holographic Principle”.
For a long time, I was among a small selected group of extravagants who studied quantum black holes. But superstring theory was catching on. As I had expected, superstring theory was not within a stone’s throw of “the final theory”, which had been what its addicts had prophesied, but it underwent fundamental changes. Membranes of various dimensionalities (“p-branes”) were added, and now a door was opened for studying black holes in string theory. Suddenly, I found myself to be nearly back in the “mainstream” of physics: string theoreticians are now seeing the “holographic principle” everywhere. But the solution to our problems, bringing the gravitational force fully in agreement with Quantum Mechanics, has not yet been achieved. As long as this is the case, we will not be able to produce verifiable predictions concerning the enigmatic details of the Standard Model.
This autobiography/biography was written at the time of the award and later published in the book series Les Prix Nobel/ Nobel Lectures/The Nobel Prizes. The information is sometimes updated with an addendum submitted by the Laureate.