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Interview of Gerard 't Hooft by David Zierler on April 8, 2021,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
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Interview with Gerard 't Hooft, University Professor of Physics (Emeritus) at Utrecht University in the Netherlands. 't Hooft considers the possibility that the g-2 muon anomaly experiment at Fermilab is suggestive of new physics, and he reflects broadly on the current shortcomings in our understanding of quantum mechanics and general relativity. 't Hooft recounts his childhood in postwar Holland and the influence of his great uncle, the Nobel Prize winner Frits Zernike and his uncle, the theoretical physicist Nico van Kampen. He describes his undergraduate education at Utrecht University where he got to know Martinus Veltman, with whom he would pursue a graduate degree and ultimately share the Nobel Prize. 't Hooft explains the origins of what would become the Standard Model and the significance of Yang-Mills fields and Ken Wilson’s theory of renormalization. He describes Veltman’s pioneering use of computers to calculate algebraic manipulations and why questions of scaling were able to be raised for the first time. 't Hooft discusses his postdoctoral appointment at CERN, his ideas about grouping Feynman diagrams together, and how he became involved in quantum gravity research and Bose condensation. He explains the value in studying instantons for broader questions in QCD, the significance of Hawking’s work on the black hole information paradox, the holographic principle, and why he has diverged with string theorists. 't Hooft describes being present at the start of supersymmetry, and the growing “buzz” that culminated in winning the Nobel Prize. He describes his overall interest in the past twenty years in thinking more deeply about quantum mechanics and he places the foundational disagreement between Einstein and Bohr in historical context. At the end of the interview, 't Hooft surveys the limitations that prevent us from understanding how to merge quantum mechanics and general relativity and why this will require an understanding of how to relate the set of all integer numbers to phenomena of the universe.
OK, this is David Zierler, oral historian for the American Institute of Physics. It is April 8th, 2021. It is my great pleasure to be here with Dr. Gerard 't Hooft. Gerard, it’s great to see you. Thank you for joining me today.
My pleasure too. Thank you for inviting me.
Gerard, to start, would you please tell me your title and institutional affiliation?
I am professor of theoretical physics at Utrecht University in the Netherlands. I am formally retired, but I still have an unpaid position as University Professor, which means that I can use all facilities I need to continue my research. It is very convenient.
As an emeritus professor, do you still supervise graduate students? Do you still sit on thesis committees?
I just took a new graduate student to supervise. One of our more active staff members is going to be involved as direct advisor. I am the official advisor. Perhaps a second student will come later, we don’t know yet. I have been without graduate students for some time before now.
Gerard, I’d like to ask a question that is very much at the top of the news in the world of physics right now. What is your reaction to all of the excitement at Fermilab with the muon g-2 anomaly experiment? Do you think that this is finally physics beyond the Standard Model?
It is too early to tell. There were reports of several interesting measurements hinting at deviations from the standard picture. The muon g-2 measurement, and calculation, is one of them. But you know, this has happened before. Today the deviations are three standard deviations. In my experience, such deviations, three times the assumed margins of error, are often unreliable. These are tremendously complicated measurements and calculations. They often push the limits of what can be done. It is easy to overestimate the accuracies of the results. I find it amazing that deviations at this level do not occur much more often. Considering the potential importance of these measurements, I am sure they will be repeated and checked as long as it is needed to decide whether the effects are real or not. The official rule is: if, after careful analysis, the deviations are equal to or more than 5 times the estimated uncertainty, then one can announce something like this as a new discovery.
We do expect new physics; deviations from the known theory were expected. For decades now, the real surprise has been that the existing theory works much better than we thought. Whenever deviations are detected, we naturally first ask whether they are real. There is no indication that any error was made, but we want to be sure.
Best-case scenario, if all of the excitement proves to be true, what would that look like, and what might that help us do in terms of understanding some of the ongoing mysteries in physics and cosmology?
In this particular case, the behavior of electrons was compared with the muons. Today’s theory makes no distinction except for the electron and muon mass values. But it was expected that new theories will explain this mass difference in terms of other interactions. This is why it is important to do this kind of experiments. And we want to know whether the observed effects will prevail.
We have a bunch of fundamental data about the standard interactions of which we do not understand what they originate from. Consider all fundamental particles that form the basis of the Standard Model. The problem is that the masses of these particles are all associated to freely adjustable parameters. These masses can all be measured, and we can compare them with other interaction parameters. But most of these mass parameters we cannot compute. The answers are not in the theory itself. Within certain ranges, the masses of the particles can be anything. For the principles on which the theory is based, it makes no differences which values these mass parameters have.
However, also the magnetic moments of particles can often very accurately be measured as well as calculated. These magnetic moments depend primarily on the various interactions that a particle can have with other particles, and these interactions are fixed consequences of the principles of the theory. So, if you see a deviation there, you are looking at what is going on deep inside the theory. Deviations there, could help us rephrase the theory better.
The Standard Model here gives very precise prescriptions if there are no hidden, unknown particles. These are very tough calculations, because also the experiments reach very high precision, and it is possible to compare these results. And if there’s a deviation there, it could be due to a new force; it could be a new particle; or a combination of things. But one always has to be aware that there could be glitches in the experimental setup, and there could be glitches in the theoretical calculation.
Comparing high accuracy theoretical calculations with accurate experiments has become a special sub-doctrine in physics called phenomenology. It’s not my field, I leave it to the phenomenologists to sort these questions out. But I’m usually rather skeptical, and I don’t react as quickly as some of my colleagues.
Gerard, another question, a more recent question, and that is, generally, over the past year plus, how have you fared during the pandemic? How has your science improved or set back as a result of remote work and physical isolation?
My wife and I are very much tied to our home these days. I found I have now more time to do my own thinking and research, and also take things a little bit easier. I am officially retired, so I don’t have to do anything anymore, and we do other things. Our country is officially in a curfew, we call it an evening clock, forbidding us to be outside during a certain time. The curfew is now after 10 o’clock pm until 6 in the morning, that we are obliged to stay indoors.
For me, it means that I have some extra time because when there are conferences and meetings, and one wastes a lot of time traveling around from one place to the other. And, also, our social activities have reduced quite a bit, so that I have now much more time in my hands to think about physics.
With that extra time, Gerard, in theory, are there any particular problems that you’ve been working on that you might not otherwise have had the chance to do?
I am thinking about the fundamental questions that we are facing in our field. These days, the progress in my field of science is less rapid than it was 100 years ago. It’s very interesting to compare the present status of science with what happened in our science 100 years ago, because at that time, there were numerous major discoveries. Elementary discoveries were made 100 years ago. I am thinking of relativity theory, of quantum mechanics, general relativity, so many discoveries, inventions, explanations following each other in a rapid pace. We don’t see science developing so quickly now, in spite of the fact that we are confronting several fundamental questions that may well require different ways of thinking. And when I say we need a different way of thinking, I receive tons of letters by people who respond with “Yes, we said it all the time, and we are thinking differently.” But when they explain their revolutionary new thoughts, I have to explain that, yes, but no, that is not what I meant.
We have to think very carefully about the fundamental questions that we are still puzzled by, and to which we don’t have answers of the kind we want. But it looks as if many people today are running behind the same rabbit, and not always doing original thinking at all, but just following the crowd. Many of our problems are in the field of gravity. We all agree that there has been some marvelous progress in gravity. One shouldn’t belittle that very important advances have been made in the detection of gravitational waves, an essentially new technology for detecting signals from far away in the cosmos. However, what came out of that was not really new physics, most of it had all been anticipated for several decades. Most of the signals that were detected had been predicted long ago; the fine details have been of enormous importance for those investigators, but our primary theories were not touched upon at all.
What I am worried about is that those magnificent theoretical insights that came to us some 100 years ago, in a rapid succession, are still presenting us essential problems today. We did improve our basic understanding a lot. The entire 20th century, new edifices were constructed to expand what was learned at the beginning of that century. Starting from special relativity, general relativity and quantum mechanics, what was added was the theories of the atoms, and the various kinds of materials one can form out of that, enormous advances in electronic devices, our knowledge and understanding of the universe, the life sciences, and so on. My own field of science expanded rapidly during the second half of the 20th century when the Standard Model of the subatomic particles was developed. That happened due to the successes of Quantum Field Theory, which can be regarded as a unification of special relativity with quantum mechanics.
But now, what are the trophies of the 21st century? What is badly needed is a fusion of General Relativity with quantum mechanics. I see more clearly now that the approaches advocated by almost all the experts, encouraged by the purported successes of Superstring Theory and “M-theory,” may not be as promising as they think. What has to be done first is a much more careful analysis of the deeper interpretations of quantum mechanics itself. Quantum mechanics is usually regarded as an advanced way to combine statistical mechanics with the dynamical laws of the nano world, the world of atoms and molecules. But I found that it is not that. I have tried to explain my new viewpoints in several papers, discovering that there is an ocean of misunderstanding between us. If we would understand better what quantum mechanics really is, we might well discover new alleys to confront the century-old questions. There is also an ocean separating today’s elementary particle physics from the super-microscopic world in which the laws of gravity and quantum mechanics come together. We should think of novel ways to cross these oceans. We should rephrase more precisely what we know; the attitude I’m having today in science is that we should take everything we know very carefully, in particular, in quantum mechanics, special relativity theory, and general relativity. We know all these theories. We know what they say, and we know to what extent they have been checked experimentally. But that is only the starting point.
I’m not trying to overthrow theories that have been very successful. But, in the past, if you look at the past, you see that there are several instances where successful theories were replaced by even more successful all-embracing theories.
Gerard, what would be a good example of that?
Well, think of Newton’s theory of dynamics and mechanics, which today is still very much valid under ordinary circumstances. But when Einstein came, and quantum mechanics was discovered, people realized that a better language should be developed to actually express the old theories without any change, but to add in some special circumstances the results of the new language, which is—are more precise, and which can sometimes give you a lot more insight. Special relativity is a very important example. Newtonian mechanics was not wrong, but Newton assumed that masses of objects were fundamentally constant.
Now, we can say that Newton’s theory is still very precise if you consider masses to be somewhat more dependent on the way you look at particles. For instance, particles that move very fast, in a sense, are a little bit heavier because with the E=mc2 equation, heavy particles contain some extra energy in their motion. That energy adds to the weight, in a sense. General and special relativity are much more precise engines, machines, that tell us exactly how to formulate this correctly. The result was that the old theories were true, but now, they could be made more precise.
The same is true for today’s theories. For instance, the Standard Model is a very important example because the Standard Model has been extremely successful, and it contains a lot of truth about the particles that we know to be flying around our ears. But we also know that that theory should be a part of a bigger—a grand scheme. And the big, grand scheme, is not well understood. Many people have formulated what, to their minds, the grand scheme should be, and they call it Grand Unification. In a sense, the Standard Model that we have today, came about by unifying the general concept of a particle, and the forces acting on a particle. Not literally, because we still see different kinds of forces active in the Standard Model, but conceptually, in the sense that all particle forces, all the dynamical properties of the particles, are now caught in one universal language. The primary response defended by the smartest investigators is, that this invites us to repair the Standard Model, so that it will be a true unification of all forces.
Then, if you speak the language of the Standard Model, you will have practically everything. We are assuming then that we have the proper language, while only some details are missing. Indeed, the theory works very well this way. But there are problems. I’m convinced that our present language is good, but it could be better. I am not the only one saying this. There is a quite spectacular new idea called Superstring Theory. This theory replaces the particles by strands of some types of strings. And indeed, this forces us to accept a different kind of mathematics, even a different type of logic. But does it cure our problems?
Amazingly, it may; it seems that the mathematics used suggests interactions that do mimic the gravitational force suspiciously well. “See,” the superstring theorists tell us, “We knew it. String theory will be the answer to all our present difficulties.” The problem here is that they did not know it. Gravity emerged as a surprise. Consequently, we do not really understand how this system works. And here I repeat, this is an interesting theory, but in order to understand it better, we should revise our language again. Saying this, I should brace myself for enthusiastic support from amateur scientists, for whom string theory was too difficult anyway. But no, I don’t say the theory should be discarded; we should learn how exactly to phrase the theory in such a way that general coordinate transformations emerge as a natural symmetry. All we know today is that the gravity perturbation series comes out of string theory, but the theory becomes quite cryptic when it comes to describe black holes for instance. Great intuitive responses have been phrased, but this is not the kind of logic I would consider acceptable.
There are similar concerns when the theory is applied to study cosmology, the science of the early cosmos. Conditions were very different, and there’s a lot of information in the findings of astronomers about the universe. We want to put all that together, but you have to find a better language to put it all together in. And the shortcomings I see in today’s general picture is that the language is too coarse, too imprecise. We should find a better language for everything. But that requires a lot of re-thinking, and if the past is anything to go by, it seems to tell us that what’s missing is precision in what we say.
Am I suggesting a paradigm shift? When they talk about paradigm shifts, most people immediately fill in all the details where they think the present paradigm is falling short, where everybody else is wrong, and how it has to be replaced by something better. In practice, that’s often not what happens when a paradigm is shifting. As I said, it’s the language.
I do not propose to replace bad things by good things. No, we should just improve the quality of our formulation; I’m not rejecting the old views. We should just add further details about how to do our work more precisely, and those are the things I’m thinking about today. There is enough room for such a paradigm shift. And what I am talking of now it the theory of quantum mechanics itself. The real question here is: what is it that quantum mechanics describes?
Are these questions that you’re thinking about now, are they essentially the same that you may have been thinking about 20 or 30 years ago? In other words, how static are these ideas, or how dynamic are they, based on advances during these past few decades in your career?
Yes, maybe I’m a little bit too static because many of the ideas I’m having now, I’ve already had more than 20 years ago also. But I’ve found, for myself, in my way of thinking and talking about things, many improvements. In particular, I’ve found improvements in the way I’ve been thinking about quantum mechanics, so that I, myself, have the idea that I understand quantum mechanics much better today than I did 20 years ago, even 10 years ago; and the same holds for general relativity.
The great big question hanging in front of all theoretical physicists today is how to reconcile general relativity with quantum mechanics. And to my own experience, I’ve sharpened my views a lot—not sharp enough to make a revolution, but I think there has been a lot of improvement.
Perhaps we can say you’re in good company because no one yet has achieved that revolution.
Indeed, and I shouldn’t lift myself much higher than where I’m wrong.
I’m not perfect. I also see that in what I’ve been thinking in the past, there were shortcomings. I wouldn’t call them errors, but I was—well—I was imprecise. It’s better now. But to really make a difference, you have to define this other language, a difference like what Einstein did in the very beginning of the 20th century with his relativity theory.
So, the question is how to go from one paradigm to another paradigm, going from one way of thinking to another way of thinking, but without losing out of sight the things you already know. And that last part is very important. I don’t want to overthrow valuable insights. I just want to get a better overall picture. The most important theme that I am trying to understand, is that quantum mechanics is not about statistics, not about uncertainties, not about the limitations of measurements, but about a special way to describe reality, using the mathematics of vector spaces.
Well, Gerard, let’s go much further back into the past. Let’s start with your parents. Tell me about them and where they’re from.
Yes, let me start with my mother’s family because my mother’s family included some very strong personalities in general. I had uncles and aunts who all had their specialties, and tried to make something out of their lives, tried to be different persons. For instance, we had a famous woman author, writer, novelist. And we had the first woman minister, preacher. In my mother’s side of our family, there were various teachers and professors. My grandfather, from Mother’s side, died at a young age, I never knew him, my grandfather was a very much respected zoologist. He made many journeys to tropical countries where you see the most species of little animals and plants. I think he was interested in insects, and small or larger animals, and plants.
My grand uncle, at my mother’s side, was also a Nobel laureate. He was Frits Zernike, laureated in 1953 for his contribution to optics. He realized that one should be able to use interferometry to get sharper images in optical microscopes. If you can generate contrasts when signals undergo phase shifts, then you can see much more, without the use of any chemicals for coloring. So, he made a microscope in which you can see live cells. That was not possible before. The method is called phase contrast, and he was the inventor of the phase-contrast principle in microscopes. At the same time, he was also a good experimentalist. He could actually make his machines work. He built his own phase microscope, working with the ZEISS Company of optics, optical instruments, and—
Gerard, did you know him? Did you get to learn from him?
I only met him once or twice, when I was a young boy. He was visiting our family. He was very old at that time. But still, he was naturally an important person in our family. My uncle, who stands right between my grand-uncle and myself, as a knight’s jump on a chessboard, my uncle was also a theoretical physicist, Nico van Kampen, and he was also very well-known and respected, also for his precision of formulation. I had great admiration for his way of doing science, and his way of asking questions. He was still in his full strength when I knew him, and when I bombarded him with my questions about physics.
Quite often, he would answer, “Well, this question is too hard for me to answer. I know the answer, but you should first finish high school, then come to the university, and follow my lectures on this subject when you’re a university student.” So, I had to wait, but of course, I followed his advice: attended his lectures, and asked my questions again. For me, he was a great example of how scientists should be. But he was sort of eccentric in his own ways. His way of life was to be completely devoted to science and knowledge. He didn’t think that his own well-being was of any importance. He spent all his life reading and doing scientific research.
As for my father’s side, my father was a naval engineer. He tried to get me interested in technology, in mechanics. He expected me to become interested in cars or ships. My father knew everything about ships. But I objected. I said, “I am only interested in things that do not yet exist, like spaceships.” I wanted to go to outer space. To understand how spaceships should be made, you must understand physics. To understand physics, one also has to learn mathematics. That’s what I wanted.
But spaceships did not yet exist at that time.
So, I said, “I want to invent something totally new.” My grandfather from father’s side had something to do with submarines. I don’t know exactly; my father mentions in his notes that he joined a test journey on the Submarine O11 when he was 13. I couldn’t find any further details of that. A submarine was indeed still something original at his time. It is something special, something that needs very special design, and does things that nobody else can—well, that was a novelty in those days.
So, my grandfather from my father’s side was also a naval engineer and, naturally, I was supposed to proceed in that tradition. But, when I said I wanted to study physics, my father said, “OK, fine, you study physics.” Then later, like himself, he expected me to make my career in a company, subsequently become director of a company, and so on. But that was not at all what I had in mind about studying physics. I wanted to do research and discover new things.
Gerard, what was your family’s experience during World War II? Did they suffer?
Yes, almost everybody suffered because our country was occupied. My father, with his knowledge of ships, had a job in a seaport, at a town called Den Helder. It’s in the far northwest of our country. There is a military bases there, and during the wartime, he had to work for the German occupiers, which he didn’t like al all. When he had to be a guard, he usually looked the other way when people, possibly members of resistance forces, were trying to do something, for instance, escaping from the country or so.
He wasn’t liked by the occupiers, but I don’t remember any of the details. Remarkably, there is still an account about the submarine O11 in Wikipedia. It was in Den Helder at that time, but the article says, Dutch personnel that was supposed to repair the ship managed to delay this so much that it never was of any use for the occupiers. I only have a few notes that he left. My father doesn’t say in his notes why he was expelled out of town, with his wife, my mother, whom he just had married. But that was actually a fortunate thing because he found refuge with a family in a sort of farmhouse in a small rural village called Anna Paulowna. It was fortunate because it meant that they didn’t suffer so much from the winter that was following; the last winter under the occupation of the northern part of our country was a very severe winter, and for many people there was no food; just no food. But in a farmhouse, there’s always food. I wasn’t born yet, but my older sister was. They had to live under very difficult circumstances. It was difficult to get things to eat, but they didn’t starve from hunger, and—
Gerard, in talking to your parents or people of that generation in the Netherlands, is your sense that people were aware during the war what was happening to the Jews of the Netherlands?
Yes, I remember my uncle remarked that, “Yes, we knew what was going on there. We knew what atrocities were being committed.” But I suspect that there were people who simply couldn’t imagine. My grandmother on my mother’s side, had a Jewish hideout in her house, a Jewish girl, nobody was supposed to know that she was there. My youngest uncle would falsify food cards, you know, during most of the war, you needed food tickets to get food. But because they had an extra mouth to fill, they needed to forge some of these food tickets. That’s what he was doing. And just to be safe, both my uncles together built a cave underneath the floor. They dug out a big hole in the floor, and they covered that with a lid. And on the lid, there was a carpet, to make the place was totally invisible from the outside. It was a hideout just in case.
Then one day, someone rang the doorbell, it turned out to be someone from the Dutch resistance. They were not very powerful, but they were organized. And this person said, “Your house is going to be searched in a few minutes”—and ran off. My grandmother quickly called the Jewish girl. And to be sure also my uncle who had been forging these food tickets, they both went in this hole.” She covered the thing with the lid, and she put the carpet on it. And then the doorbell rang again, and there was a German or a, well, a German-oriented policeman who said, “You’re suspected of hiding a Jewish person in your house. We need to search your house.” So, they searched the whole house, but they never found the hideout. So, they went away empty-handed. There was no refugee there, no hidden person.
I think if they didn’t have this hole in the ground, I wouldn’t be sitting here because I’m sure my grandmother would’ve been arrested, and life would have made a totally different turn. Many people in Holland did things like this. My wife’s parents had similar experiences during the war too, and they tried to help the people who were really in a desperate situation.
And, Gerard, where were you born, and where did you grow up?
I was born in this seaport town, Den Helder, but, after a year, my parents moved to The Hague, and I grew up in The Hague. We moved once or twice there, but otherwise I lived in The Hague. I went to an elementary school and then at high school in The Hague, after which I went to Utrecht to study, since my uncle was teaching as a professor in theoretical physics in Utrecht. I had asked him for advice, and of course his advice was, “You better come to Utrecht. The only alternative would’ve been Leiden, and they have good people there, but I think in Utrecht, we have better professors.” And that’s what I did: I went to Utrecht to study.
My father had studied in Delft, my uncles both in Leiden, and all three of them had been members of the so-called Student Corps, the student fraternity, you could call it. Both in Delft and in Leiden, these were the most elitist student organizations. My father insisted that I would also become a member of such an organization, the Utrecht Studenten Corps, warning that one can study at the university without joining any student organization, but if you weren’t a Corps member, you would be looked down upon. Of course, I did not want to disappoint my father or the others of my family.
So, I became a member of that organization, and I liked it, in a way. I didn’t really stay very active there, but for a while, yes, they had very interesting, well, nice and wild parties but also discussion clubs. The science club was called “Christiaan Huygens.” Getting drunk every night was practically standard. I joined them, and also joined their rowing club, where I was coxswain. Only after a few years, I found my research more interesting and more important than going every evening to the student society house. But I made many friends there, and it was a very special time.
Gerard, being born one year after the war, in 1946—is your memory, looking back, was the Netherlands mostly recovered during your childhood, or did you feel like it was still in a time of repair and rebuilding?
At the time, I was a young kid, and I wasn’t aware of anything. I do remember, also at an early age, that I joined my farther who had an office in Rotterdam. In my recollection, I thought Rotterdam was a horrible place because they had many terrible looking scars from the German bombardments in 1940, big empty spots filled with rubbish. The Dutch government had capitulated immediately after that bombardment, so that The Hague and Leiden had been spared.
The center of Rotterdam was practically obliterated, and that was the start of the war, the beginning of five years of German occupation of our country. As a little boy I thought that I would never want to go to Rotterdam again because of all these sinkholes. But later, when I was eight, nine, we got to live in London for a while. London also was littered with scars from the numerous V-1 and V-2 rochet attacks that it had had to endure during the war. When you’re as young as I was at that time, time goes very slowly, so I thought that these frightening war scars some towns have, would be eternal. The Hague wasn’t like that. So, I thought I wanted to stay in The Hague, but Utrecht also had stayed quite clean.
Holland was very determined to overcome the damage the war had made. Actually, Dutch people were very strong, united in rebuilding the country, and, in hindsight, it happened amazingly quickly. In 1953 there was a major flooding of a south-western part of the country during a storm at high tide, and that made it clear that the entire coastline needed reinforcements, and the most innovative construction methods were invented and employed. In hindsight, I think, it was in a time span of 10 years or less that enormous developments took place, without me sensing it directly because I was too young for that. But the country recovered quite quickly, and we were quite united in a sense.
There was very little crime. Housewives connected their front door handles with a string through the letter box. So that the children could get in without ringing the doorbell. This was safe almost anywhere in the country. There was very little violent crime. The worst thing that could happen was that your bicycle got stolen – if you forgot to lock it; that was a serious crime. Police would be called, and it was the worst kind of thing that could happen. But the kind of heavy crime that you see today did not exist. These things did not happen in our country. Today, it’s another story.
And, Gerard, what about the Cold War that divided Europe? Was that a big part of your reality, the Soviet threat, things like that?
Oh, yes, that was a new situation that was gradually building up. When I was a kid, I thought that the Cold War was a thing taking place far away. The USSR, the United States, they were all far, far away. The first time I was made aware that the world was divided into camps was in 1956, when the Soviets occupied Hungary, as a response to an uprising there. I was 10. The enemy camp now consisted in the ‘communists’ who were threatening world peace. But in those days, distances were much greater, it was not considered likely that things like this could happen in our country. Although, the elderly people warned us that occupations do occur, and they are terrible to endure.
But, when I was a young kid, the Cold War didn’t mean anything to me. That was sort of non-existent. But my primary school teacher said, “You know, the Americans have said, ‘We can come to intervene, but only 10 years from now.” For me, 10 years for me was an eternity, so I thought, OK, Hungary is lost. Then came the Vietnam crisis, and in general the Middle Eastern and Far Eastern wars, Korea, Vietnam, and other places. And, well, we got informed in a rather one-sided way, which generated a back reaction among the young people. I’m talking of the 1960s now, and young people started to unite in their conviction that the Vietnam War was a wrong thing to be involved with, and the United States should be taught a lesson, that they should have stayed out of Vietnam, ignoring the danger that communism would spread.
I decided not to go along with such arguments. I couldn’t understand what was going on, and why, so I focused on the one thing I could understand: theoretical physics. I listened to those revolting guys with disbelief. How do they know what is best here? I did not like what I heard about communism, I also did not like what was happening in Vietnam, but how can I know whom to blame? Which side should I choose? Stay out, is all I could think of.
And beyond the, Gerard, beyond the unique influence that you got in your own family, the window into science at a very high level that you had… even among your own family members, what were some of the larger global issues in science that may have captivated your imagination as a young boy, for example, the arms race or Sputnik or the moon landing, things like that?
Yes, of course, there were lots of fascinating things happening. I think science was indeed developing very fast, and in particular, also technology was developing very fast. So, it was sort of a shock to the world when the Sputnik was launched; I still remember that startling news that the Soviets had put, what they called, an artificial satellite in an orbit around the Earth for the first time, and the Americans were supposed to be much better in that technology, but they were beaten...
It took them quite some time before they put the first satellite in outer space, and that was a major event. And there were so many other captivating developments in science and technology. The most awesome thing was the nuclear bomb, the atomic bomb. This was really something that sparked our imagination, the fact that there is so much energy in the nuclei of the atoms, and that these were branches of physics where you needed to be someone like an Einstein to figure out what’s going on.
It was very, very influential, in my life that these developments were taking place. And I was quite determined that I wanted to become part of this. I was strongly motivated to become a physicist to figure out what exactly happens inside an atom. There were so many other surprises still waiting for us in these tiny atoms. I still remember the first television set when television had just been developed. They were originally very expensive and very clumsy machines with big, bulky screens that gave you a small black and white image. I was in London, in a hotel, where they had in a special room in the basement a television set. I saw my first Walt Disney animation, and I thought it was fantastic. Later, in the Palais de la Découverte, I saw the first demonstration of a color TV. The colors were so bad, I thought this was never going to work. All faces were either orange or green, this was just a mistake.
Color is out of the question. We are not going to have colored TV…
They quickly recovered, improved. Although, the first time I visited America, still many of these television screens had either yellow faces or green faces instead of the proper color of a human face. People didn’t seem to care about it. But even as a scientist in spe[?], I hadn’t imagined how quickly these initial shortcomings would be cured. So, there were still things developing. And the computer was coming, the idea that you could use electronics having many switches, eventually mimicking the human brain. I remember that I bought a lot of little relays, and I thought if I put all these little relays in a big chain, I’ll get what’s now called a computer chip. And I thought that would be the way to make a logical machine, a machine that eventually would become intelligent.
But my ideas about building intelligent computers were not yet very sophisticated, I’m afraid. Yes, these things were catching my imagination in a big way. And what were the other things? Of course, in the medical branch, discoveries about bacteria and viruses and so on, all these pieces of knowledge were fairly new, and they were developing fast, it was obvious that science is going to be a major factor in our lives. And, so, I, for sure, I wanted to become a scientist. This I knew this from a very early age on.
In the Dutch system, in the Dutch educational system, how early in your education do you declare a field of study of specialization? Does that happen in high school or college?
No, high schools, in principle, are still quite general. Well, elementary schools are completely general, except that some are based on religion or other convictions that the parents have. We have the religious schools, and we have the public schools. In general, in Holland, the public schools were of better quality than those schools that are based on principles, religious or educational.
There were also some good ideas about education, there was for instance the Montessori system. Maria Montessori had a special idea about how to set up education. Actually, I think indirectly, I profited from that. I was not in a Montessori school, but my nursery schoolteacher had some books about addition, subtraction and multiplication, and I was very excited about those books, but I was not supposed to read them. I was too young, but I devoured those books anyway. I wanted to learn how to do math. I had learned somehow that to understand the physical world, you have to understand mathematics. You have to understand how numbers work. So, I was always very excited about those books. But, apart from that, those are just minor details. Apart from those, the school systems are all very similar. So, there’s not yet so much variation in primary school.
Our secondary school system had significantly benefited from the insights of a politician in the 19th century, Johan Rudolph Thorbecke, who realized that the schools at that time mainly focused on intellectual abilities, to be fluent in Latin and Greek, in rhetoric and religion. In contrast, he introduced a school system for middle class pupils, where they were taught in mathematics, physics, chemistry, biology and modern languages such as English, French and German. This school system was called HBS, hogere burger school, Dutch for Higher Civilian School. Many successful scientists in the Netherlands had followed this new school system, Lorentz, Zeeman, Kamerlingh Onnes, and others. In particular, Lorentz could communicate with Maxwell in English, with Poincaré in French, with Einstein in German, and he published his papers in all these languages. No wonder that he later was chosen to preside the Solvay Meetings in science.
The HBS had a 5-year curriculum. But there was also a school system that lasted six years where they also teach you the classical languages, Latin and Greek, and more emphasis was put on the other languages as well. It is called Gymnasium. So, I asked my uncle, “What do you advise me? I want to become a physicist.” So, he said, “Don’t go to the Gymnasium because, for physics, you don’t need to know Latin and Greek at all. And the other languages—the only language you really need is English.” Why waste that extra year… However, he himself, had gone to the gymnasium. And, as you know, as a kid, you don’t listen to the advice you get, but you look at the examples you see. My uncle was doing physics, and he had gone to the gymnasium, so I also chose that.
There was a school system where they mix these things a little bit. I would learn Latin and Greek, but there would be plenty of focus on physics and mathematics, also taking 6 years. In their system, the pupils get more homework, and more extra time to work on that independently. So, one would be 18 years, normally speaking, when leaving that school. Otherwise, the HBS kids would leave the school already at 17. I never regretted that. Latin and Greek, they are at the basis of the modern languages, explaining how these are structured. I always found this information very useful. On hindsight, perhaps, I could have gained a year by not taking Latin and Greek, and go directly to the university at 17, rather than 18. But then, I couldn’t stand the idea that some kids would learn basic things that I wouldn’t know about.
There was also the option to take Spanish in addition. But that would have been too much. Six languages, that would be it for me.
Gerard, did you have a good idea of what your uncle was lecturing about? In other words, your motivations to go to Utrecht, were they specifically about the kinds of topics that your uncle was following at that time, or you just wanted to learn from him generally?
I wanted to learn from him generally because those topics he was interested in were shifting. Originally, he also was studying relativistic collisions between atoms and other particles, and he had done some marvelous work on dispersion relations. But then he found that he was getting annoyed by the aggressiveness of some people who do that kind of physics, whereas he wanted to put more emphasis on accuracy, and less on being revolutionary or on discovering new solutions for the world, and so on.
He was not so much interested in what else can go on in the elementary particles. That had been why he had shifted towards statistical physics. Statistical physics is about all sorts of stochastic processes, about liquids and gasses and plasmas. The plasma state is the most interesting and least trivial state of matter. He specialized in plasmas for a while. But then he continued to do statistical physics. I found that interesting but not very challenging. Statistical physics is not going to tell me where nature’s secrets really are. It just tells us what we already know, which is that atoms and molecules move in a chaotic way through each other, and that gives statistical mechanics, so why is that so special? No, I didn’t follow him that far. Eventually, I wanted to know the real secrets of nature, which were in the elementary particles, certainly in those days.
When I grew up, and entered the university, in the ’60s, most of the elementary particles were still sort of black boxes. You didn’t know what’s inside. You only knew what happens if two of these black boxes collide, and other black boxes come out. What happens inside the black boxes was still very, very difficult, and not at all understood. I was much more attracted to that field. I wanted to investigate those difficulties. On hindsight, it’s amazing how quickly the developments actually took place, and I was just lucky that I could be part of that, of all the new developments that went into what later would be called the Standard Model.
Gerard, as an undergraduate, what were some of the big mysteries and exciting promises in theoretical elementary particle physics?
Well, the fascinating thing is that we didn’t know. If we had known, then it would’ve been much easier for us. We knew that there were mysteries, but we also knew that these particles were constrained by fundamental principles. The fundamental principles were special relativity and quantum mechanics. What we needed to understand was how to set up equations for particles that obey simultaneously the laws of both quantum mechanics and special relativity. There were people who claimed that quantum mechanics is in contradiction with special relativity. Some people still say this today.
But what they really mean is that quantum mechanics becomes even more mysterious if you combine it with special relativity, but it does not become contradictory. It does become more mysterious if you ask what quantum mechanics really means when you switch on special relativity. This was not understood. What is amazing in quantum mechanics is that you don’t need to know what is going on. You need to know what results to expect when an experiment is performed, and the equations for that could be identified and checked. Only philosophers would ask what it is that ‘really goes on’. But asking such questions is like stepping in a trap. The precise answers were not understood, you can get paranoid when you try to understand that. Only now, more than 50 years later, I think I am homing in to answers that I can believe, but it is still a tricky question, the question “What is happening there?”
Anyway, the wise thing to ask was what the equations are. At that point, many smart discoveries had been made in those days; one was the rich symmetry patterns that the elementary particles have. It had become kind of an art to discover new symmetries among particles. Particles can spin, that is, rotate around their axis, and these spinning particles have properties that are complicated compared to particles that do not spin. Think of playing soccer or billiard balls, and think of all these balls spinning. They’re behaving in a much more complicated way than when they just move in straight lines without spin. Same thing for elementary particles, the spinning particles are more complicated. But then what was discovered was that particles have other properties that look like spin, as if they are rotating in some hidden, internal space, not just spin in ordinary spacetime.
In mathematics, we call this ‘isospin’, where ‘iso’ comes from Greek eisos, meaning ‘looks like’. These particles rotate in some internal space, displaying symmetries similar to spin but also different in an elementary sense. These symmetries were well understood. But then it was agreed that the interaction among particles should obey all sorts of symmetry requirements. Now this doesn’t really say everything about the way particles interact. At this point, a very ingenious discovery had been made in 1954, so that was long before I had actually gone to university, by C.N. Yang and R.L. Mills. These investigators had found that you can make symmetries local. And that means that you can make a twist here, another little twist here, and then the forces should still remain the same, or at least it should be possible to subject the forces to such modification of your coordinates in some internal space. All this was very ingenious. The only thing was people did not understand was how to use it.
This theory predicted particles that obviously do not exist. So, the theory was considered to be interesting, it’s very imaginative, but it’s also wrong because it doesn’t agree with experiments. And even Einstein had said, “If your theory doesn’t agree with experiments, throw it away.” But several people, notably also my advisor Martinus Veltman in those days, said, “No, I’m not going to throw away that theory because the theory might be useful nevertheless.” He saw some similarities between the particles that we do see and the properties they do have, and this Yang-Mills theory.
And that was going on at the time when I started to join forces, particularly with my advisor then, Veltman, where I just came in the right time, say, to assist him in solving some riddles there, and we managed to get some very nasty difficulties cleared up. And then, suddenly, that paved the way to what is now called the Standard Model. All interactions could be derived from this fundamental notion that particle properties can be spacetime-dependent the way dictated by Yang-Mills theory. Think of a particle that spins, but in a way different here than how it spins there. These things were fully in development, but not yet understood when I started, and—
Gerard, as an undergraduate, is your sense that your education was largely parochial? In other words, your exposure to theoretical physics was mostly Dutch, or were you aware of what was going on at places like Cambridge and Harvard and Stanford?
Well, theoretical physics was already, almost completely, international. One good thing about the Utrecht Institute, but it was also in other places in the country, was that young people were sent out. We would normally not employ people who had graduated at our same university. The first thing we tell people when they graduate—and we still do that—when they graduate in our university, in our institute, is: “And now go away, go to America, go to Egypt, to China, go no matter where, but find out for yourself what physics is like in those other countries. And when you’re more matured, there might be a possibility that you can come back to find a job in Holland.”
Many people just left, and they became professors in other places. And our professors often were also from other countries, so we had many foreigners as professors at our university. And I think also that was a good thing. And of course, these professors took with them the knowledge they had gained in, you name it, Harvard, Cambridge, Princeton, and so on—and also, of course, many other towns and places in the United States and elsewhere where physics is done. We had guest lecturers, also people coming from CERN at Geneva. CERN was doing very well already in those days, and so we had people who commuted regularly between Holland and Geneva.
Gerard, did you have interaction with Veltman as an undergraduate, or only in graduate school?
Mostly in graduate school but also as an undergraduate. In those days, the institutes were much smaller than they are today. And our Institute of Theoretical Physics was so small that everybody knew everybody else. We were having joint coffee and joint discussions, joint seminars. The separation between the different subfields was not at all like it is now. Now, we have people doing only superstring theory, or only statistical physics or only spintronics or only other branches of theoretical physics, and it’s diversified so much today that people often don’t meet each other so frequently anymore, and collaborations are more difficult to get.
But Veltman, yes, I saw him already as an undergraduate. I knew who he was and had followed his lectures. But when I became a graduate student, he explained to me what his problem really was. I thought the problem, as he explained it, was highly exciting. The question was, what should I do now? What topic should I choose for my graduate study?
But, Gerard, if I may interject, even before we get to what you’ll do for your graduate study, was Veltman the reason that you decided to stay put, and not go elsewhere for graduate school?
Yes, Veltman, and my Uncle Nico, they were both in the same institute, and it was a great institute. So, I saw no reason to go away, and they offered me immediately positions, first, as a staff member, then as professor. They did their best to keep me there, and, to a large part, they succeeded.
What was your interest in Yang-Mills as an undergraduate, even before you became a graduate student?
Well, that was Veltman, who said, “You know, this Yang-Mills paper?”—he didn’t insist that you read many papers. He said, “I’m not going to tell you what you have to read. You have to find it out for yourself. But this Yang-Mills paper’s the one exception. This, you have to read.” And I still remember I asked why. “What is so special about it?” And he said, “I don’t know. The details don’t make any sense. It doesn’t describe the particles we see. But it looks to be something so elementary that you have to know about it.”
I read the paper, and I agreed immediately, this was a brilliant paper. It was very well written. And it was telling something that sounded like saying, “This cannot be wrong. There must be something in there to make it apply to the real world.” This was the one thing that was very much on our mind. Find ways to generalize the notion of electromagnetism, the interplay between electric and magnetic fields. Now we have Yang-Mills fields, which are a generalization of that concept. It seemed fairly obvious that you have to generalize the notion of electromagnetism to get all the other particles accounted for. But how it had to be done was a big mystery.
And in terms of your intellectual partnership with Veltman, did he assign you to a problem to work on, or did you develop these issues together, more or less?
Well, to the contrary, he warned me that he had been busy with the subject for nearly ten years—maybe eight years or so he had been active—so that I would have to catch up with eight years of time difference. And since the time given for a graduate study is only four years or so, he said, “You know, maybe you want to do something else.” So, he gave me some other topics to look at, but I realized quickly that I didn’t like those so much because the only interesting fundamental questions were asked in this Yang-Mills paper. We had the so-called weak interactions, we had the electromagnetic interactions, and we had the strong interactions. It was understood that these forces are somehow tied into each other in a specific way. It looked like a gigantic jigsaw puzzle, you see all the pieces, you see that, somehow, they must hang together, but it’s very hard to find which piece goes where.
So, he hands me this gigantic jigsaw puzzle, and then some other baby toys which seemed to be not doing very much. They seemed to be at the outskirts of particle physics. So, I just said, “No, those other questions are probably wrong.” That later turned out indeed to be the case. Experimenters had thought that a new effect had been discovered, but they found it later to be an artifact of their measuring procedures.
And at the time, Gerard, what was understood about what could and could not be renormalized?
This topic was assumed to be extremely difficult, hopeless to find out. Electro-magnetism was one of the simplest forces among particles and there, discovering how to renormalize it had taken several decades. Many prejudices had to be overcome. Together with some other theoreticians, each in their own ways, Veltman had uncovered a crazy feature in the interaction of pions and nucleons with electromagnetism, something that seemed to ruin a particular type of isospin symmetry. They called it an anomaly, the Bell-Jackiw anomaly. Anomalies could affect renormalizability in a bad way. This had been the topic of my undergraduate work.
At that time, like it is still today, there were summer schools organized by different universities. Veltman managed to have me admitted at a school organized by people at Paris and Nice, in a resort at Cargèse, on the island of Corsica, in the Mediterranean Sea. In those days, such schools could last for three weeks. There, I learned from the experts that a modest amount of progress had been made in renormalization. But not for particles with spin. Those were the experts in the field. There was the Korean physicist Benjamin W. Lee, the Frenchman Jean-Loup Gervais, the German highly respected Professor Kurt Symanzik and others.
But when I asked them how their methods would work for Yang-Mills fields, their answer was unanimous: “If you are Veltman’s student, ask him, he’s the expert on Yang-Mills”. The only things they could handle were electrons, photons, and particles without spin. Forces between particles, such as electric and magnetic forces, come about when particles such as photons are exchanged between other particles or objects. But particles can be exchanged several times and bounce to anywhere. Whenever particles come too close to one another, the forces become too strong to handle, we have to re-arrange the motion of these particles such that infinitely strong forces are avoided, or somehow included or absorbed in the other particle properties like mass, charge, or field strengths. That’s what renormalization is about. In the Yang-Mills case we have to keep an eye on all the symmetry properties of the system, to ensure that these cancellations always work.
The particles bouncing to and fro can be represented by diagrams called Feynman diagrams. They are a bit like the networks in underground railway timetables in some busy town. You want to control that every train goes as planned. Particularly where these trains cross each other you should expect difficulties. For Yang-Mills particles it was not understood how to do this. A problem was then also that the Yang-Mills theory wasn’t quite right, as it would feature particles spinning like photons but carrying no mass, while the particles Veltman needed, to understand the weak force, would have to be photons with lots of mass.
Actually, the way out of this mess had already been suggested a couple of years earlier by the Belgian scientist François Englert and the American Robert Brout, and independently by Peter Higgs from Edinburgh: the equations should be as Yang and Mills had suggested, but the fields of the particles take an asymmetric shape. This would rearrange all particles in such a way that they all became different but most importantly, the photons obtained mass. But the equations wouldn’t change. I convinced myself that this should work, but I had not convinced Veltman. And Lee and Symanzik hadn’t studied the Yang-Mills system at all. This meant that I was walking around in Cargèse as the only person in the world with a possible solution as to how to renormalize Yang-Mills particles with mass. That was in 1970. But then, why did people think that this was so complicated?
Gerard, when did you have enough to publish your first paper, and how was that received broadly in the field at the time?
Well, that’s a very interesting question. I came back from Cargèse, more convinced than ever that not only could I understand how the weak force hangs together with Yang-Mills fields, I had some ideas how to do it right. There had been a beautiful paper by a Russian scientist in Leningrad (now St. Petersburg), Ludwig Faddeev and collaborator V. Popov, about renormalizing pure Yang-Mills theory without mass terms. That was the seed for a complete solution.
By that time, I thought, now, I know how to do it. But Veltman had been following a different path. He had modified the Yang-Mills equations to get a mass term for the photons. He wasn’t doing Yang-Mills theory itself. The modification he added was a good first try, but it spoiled renormalizability. I figured out that it could be done in a better way, completely following up the fundamental principle on which this theory is based. The way Yang and Mills had formulated the theory was in a sense easier because they had captured the main principle without doing anything to it to make it agree better with experimental observations. That had made that way of writing things simpler than what eventually came in the Standard Model. They had written the equations where the theory looked much more like a generalization of electromagnetism than the modern versions.
Consequently, the renormalization program should be doable in the original theory in the same way as it had been done successfully in the case of electromagnetism. Veltman’s original idea had been to modify the equations to make the theory agree with experimental observations. Then the only question left was how to renormalize that. But now I thought I knew how to add masses to the particles without modifying the equations, and if you did that right you would get another bonus: now you could also account for the fact that weak interactions act on charged particles in a way that differs from the neutral particles. So, this way, one could get even better agreement with the experiments.
Veltman had a superb way to find out who was right. The calculation of the various Feynman diagrams was enormously complex, impossible to do without mistakes. But he had pioneered in programming a computer to take over the complicated algebraic manipulations. His program was named “Schoonschip”, a name only Dutch speaking people can pronounce, just to remind the users that they would be using a Dutch invention. So, I had sorted out how to compute the interaction terms in the new Yang-Mills theory, and he was able to check the equations by feeding them to the computer. He was perplexed, because all unwanted infinite terms nearly cancelled out, but not quite. When we discovered that he had left out some irrelevant looking details in the equations as they were dictated by the theory, everything fell in its place, and we found that the renormalization procedure worked just perfectly.
But we also agreed that this conclusion was perhaps somewhat premature. We had assumed that the original Yang-Mills system could be renormalized just as the theory for electro-magnetism, but this was not so obvious. The situation with the pure Yang-Mills system was much more complex. We did succeed in one important sense: if the exchanged particles did not form more than just one closed loop in the Feynman diagrams, then the renormalization program works. For that, I used a trick involving an extra space coordinate.
My first paper was to report on this result. I knew how to do it when the solution to the field equations would be asymmetric as described by Brout, Englert and Higgs, but that would have to be left for my next publication. Having the one-loop diagrams also under control had not been an easy job. The problem was that there could be anomalies, I think I mentioned that earlier, the symmetry properties of a theory can get spoiled by renormalization, and in that case a theory might run into contradictions. The anomalies would occur primarily in the one-loop diagrams, but my analysis had showed that for pure Yang-Mills fields the one-loop anomalies are absent. But should we expect new difficulties in diagrams where particles twist into forming more closed loops? I tried the obvious thing: add even more extra coordinates, but I quickly convinced myself that that would never work. The one-loop renormalization procedure worked excellently also when the Brout-Englert-Higgs mechanism was invoked, and that was the subject of my second publication.
That’s the publication that, 28 years later would be remembered by Cecilia Jarlskog, at that time president of the Swedish Nobel Committee, as causing a “little bang” in the community, because people became instantly aware of how things were hanging together. But it took a while before I understood how to handle a problem. The problem came in higher diagrams, where more than one particle is being exchanged, or more than two particles. Then the situation became really nasty, and I figured that I couldn’t do it, unless I did something very wild. And a very wild thing was to consider the theory in different numbers of dimensions.
You know, normally you have three space dimensions and one time dimension. But you can replace this number three by any other number. In the time direction you always keep only one coordinate, the time coordinate, but in the space-direction the number of coordinates needed can be anything. Instead of three, you can imagine them to be four, or five, or six. But when you compute what this does to the Feynman diagrams, you find that their effects can be computed just for any number n of spacetime dimensions (the time coordinate works almost the same way as the space coordinates). So, in the ordinary world, n equals four, but now we could allow n to take any value you like. This gave us an extra handle to adjust the calculations. Normally, n is an integer number, n=1 or n=2, while in the real world it is n=4. The situation would become complicated, and renormalization would be in danger as soon as n is greater than 4.
Now is this of any use? You might think not, but something special occurs. What if, in the final answers of the calculations, we substitute = 3.9, or 3.999, or 4.001? Then, you get the theory of the real world almost exactly right, while the infinite expressions would be replaced by calculable numbers. This implied that we had obtained a new way to control our calculations. The number of spacetime dimensions became a useful administrative tool. In particular, this tool showed that no new anomalies would turn up. In fact, the old anomaly turned out to be related to an exceptional bug, a feature that can not be extended to different numbers of dimensions, but now we saw why it would not spoil renormalizability in our case. At a later stage in the Standard Model, the anomaly would become important again, dictating how quarks and leptons keep each other in balance.
I had expected that the idea to step out of the world of understandable systems, where the number of dimensions of space-time should be integer, would be met with much resistance and hostility, but the opposite was true. It was accepted by many researchers almost immediately. Where were the science philosophers? I still had to learn some practical rules about having new ideas: the further they go into strange, incomprehensible terrains, the easier it is to get them accepted. Today, almost 50 years later, I find much more resistance when I try to argue that quantum mechanics is not about strange, incomprehensible universes, but simply describing very normal kinds of interactions. This is not what people want to hear. Same as in science fiction: if you say that transportation of humans by means of laser beams, or travelling faster than light through wormholes, will never be possible, and telepathy will never be reliable, you aren’t a good science fiction writer. Nobody will read your stories.
My third publication, which I did together with Veltman, was on dimensional renormalization, as we would call it. It could be applied immediately to the Brout-Englert-Higgs mechanism. I do not remember well what I had read about Brout, Englert and Higgs and what I had reinvented myself, but anyway, re-invention does not count as a discovery in science. Our discovery was that it is an essential element needed to construct renormalizable theories with massive spin-one particles, and that anomalies would only pose dangers in very limited cases.
So, these insights all came together, and I was happy that Veltman was immediately enthusiastic about the progress that we had been making. And it so happened that he was one of the organizers of a big European conference in particle physics, which was to be held in Amsterdam. He sent me to Amsterdam but, unfortunately, the program was already written when Veltman realized that I should be there as well to explain how we are going to renormalize the weak force. And, so, he said, “If you manage to tell it in 10 minutes, then you’re in for 10 minutes to explain how it works.” I had my 10 minutes, and, immediately, I got many people enthusiastic about it. It’s amazing how quickly it was accepted that here’s a young student knowing basically nothing yet about the field, who found a way to renormalize the theory, and they realized they couldn’t punch a hole in my arguments. I said, “This is how you have to do it.” And I managed to say that in 10 minutes. And it was remarkably well received from the beginning—particularly also some of the people I had met before in Cargèse were there: Benjamin Lee, Kurt Symanzik, and several others were also in Amsterdam. The new ideas were grabbed immediately. I got very positive responses.
Gerard, I’d like to ask a question that I posed to David Gross and to Frank Wilczek because the historical parallels I think are quite significant. Obviously, at the time, you can’t know that this will contribute ultimately to your recognition with your advisor to the Nobel Prize. But the two questions there are: did you have a sense immediately of just how significant this research was? And, secondarily, why such a long gestation period between the finding and the Nobel Prize, which came decades later?
Well, that last question is difficult to answer. Veltman realized — he told me right away — that, if you really solve this problem in such a way that all the loose ends come together, then this is going to be a Nobel Prize. He was quite convinced of that, and he was just annoyed that the Nobel Prize first went to people who like Weinberg and Glashow, who had only parts of the true theory. But I never saw anything wrong with that. Weinberg and Glashow had made their observations long before us. Weinberg had written a paper about a model of the weak force based on this very same Higgs mechanism. He didn’t know how to renormalize it, but he did know how to formulate the theory. Glashow had made a theory along the same lines as Veltman has done originally. Both expressed their assumption that you could leave the renormalization to some, you know, some clerks who will figure out how all the mathematics goes.
But Veltman got annoyed because then they ran away with the Nobel Prize, and he thought, “Now, they’re going to not see what we have been doing.” But, actually, our contribution was very well received, very well recognized, and soon became part of the folklore. So, it seemed to be a natural thing to be recognized by the Nobel Committee. But there were so many other discoveries in those days. Science was going very rapidly. Today, I think it’s more difficult to imagine who should be given a Nobel Prize, particularly for theoretical physics. I think it’s hard because there’s no such fundamental pieces of progress anymore that I’m aware of. So, it goes—things are going slower these days than at that time. At that time, there were many discoveries of new particles, which all are parts now of the Standard Model. Most of them had been predicted, and then, much to everybody’s surprise, also found. The neutrinos formed a whole special lot of particles. They were all described in the Standard Model, but the Standard Model had also many question marks about neutrinos…
And, Gerard, on that point, when you were involved in this research with the second paper, did you feel that you were contributing to a Standard Model that was being built, or were you confirming what the Standard Model had already shown up until that point?
No, it’s the other way around. There was no Standard Model, the whole concept of the Standard Model came later, two years later or so. Before that, there were just particles, and these particles interact, and in the beginning, it wasn’t clear that the strong interaction had anything to do with a Yang-Mills system. It looked like something totally different. The strongly interacting particles were basically like black boxes doing something when they hit each other, and then they fly off again. The black boxes that come out are often different from what went in. And whether that had anything to do with the Yang-Mills principle was difficult to determine because Yang-Mills was merely a generalization of electricity and mechanism. Can that make particles behave like black boxes? This would be unbelievable.
So, people didn’t think of a complete Standard Model, but they did find this remarkable fact, the Yang-Mills theory can be applied to the weak force. But that brings the weak force and the electromagnetic force together, because now they’re almost the same. They were not quite the same. They’re still separate forces being active here. But these separate forces are mixed in a beautiful way. Due to the weak interactions, particles interact, and they can decay in many different ways. They carry electromagnetic charges, but also other kinds of charges, and there’s a big interplay of all these charge concepts. It all smelled like a unification taking place, and people were not shy to use the word “unification” there right from the beginning.
And, of course, they thought of also unifying the strong force there. The strong force did not look like a Yang-Mills system at all, in the beginning. But we had the quark theory. Notably, Murray Gell-Mann, Harald Fritzsch and Heinrich Leutwyler were thinking along these lines. Quarks could be held together with force lines showing an SU(3) structure. This could also be a Yang-Mills force! The question that would then arise was, how can it be that those quarks are never seen outside the hadronic particles? They would have fractional electric charges and such particles would have been observed experimentally, indeed observing them should have been easy. Where are they?
But you were aware of what Gross, Wilczek and Politzer were doing at this point?
Not really. I thought David Gross was on the wrong track. He was convinced that you can’t use quantum field theory at all to describe quarks. He thought that all quantum field theories must have Landau ghosts since they couldn’t be asymptotically free. He had ‘almost proven that’. I later asked David whether he remembers a conversation we had had in December 1971, when I visited him briefly. I told him that I had found the non-Abelian Yang-Mills theory to scale in a way opposite to the other theories. What is now called asymptotic freedom. He was so convinced that that shouldn’t be so that he probably hadn’t registered what I said.
Then, in 1972—there was a nice meeting in Marseille where Kurt Symanzik was present—Kurt Symanzik realized that what was needed was a theory with asymptotic freedom. You can have asymptotic freedom in a theory of ordinary scalar fields if you give the coupling constant the wrong sign. That doesn’t seem to be physically allowed, the theory should then become unstable, but he tried anyway. We had had a discussion before his talk, and he knew what I had to say. So he gave me the opportunity to say it. At the end of his presentation, I stood up and wrote the result of my calculation on the blackboard. Symanzik couldn’t believe it. “If that’s true you should publish it quickly, before someone else does it!”, he warned. And I should have listened, but to explain my calculations would require time that I did not have at that moment. Shortly after that, Gross, Wilczek and Politzer came with the correct result. Symanzik realized that I had been there earlier, and he also maintained that a remark at a meeting counts if priorities are in question.
One reason why I wasn’t in a hurry was that I could hardly imagine that such a calculation hadn’t been done long before. The fact that nobody really realized that these theories are asymptotic free was, for me, very mysterious because it was a relatively easy calculation. In fact, I had also made a remark in my second paper about massive Yang-Mills, but that was not picked up by anyone. So, I thought that many important people, like those teachers in Cargèse, they must’ve known about asymptotic freedom. Why not? But, well, they didn’t think in those terms. That’s what I said in the beginning of this interview, about asking questions the right way. I always insisted that you have to ask questions very carefully. So, the question, what happens when you scale a theory to smaller or larger sizes, to me, was a very important obvious question, and I asked it, and immediately found that I could calculate this, and I found the answer. But it was difficult for me to imagine that so few people had asked the question in that particular way. There was Kenneth Wilson.
I was going to ask if you were aware of Ken Wilson’s work on renormalization.
We knew Ken Wilson, and we knew he has also strong ideas about renormalization, but in statistical systems. There are interesting statistical models that are very complicated, where one can use renormalization, to calculate the scaling properties. He had written a paper about statistical physics in 3.99 dimensions. He went in the other direction because statistical physics is in three dimensions, not four.
So, he didn’t want to go to a very high dimension, but he went to nearly four, just a little bit lower, where one can calculate a lot more. So, he had the same idea, but applied it to statistical systems. After Gross and Wilczek published their results, Wilson also got interested in Yang-Mills theories, and approached these in his own way, using lattice theories. What was beautiful in his approach was that one could immediately see how a phase transition would occur that keeps the quarks confined inside the nucleons.
Later, we became aware of the fact that several people in the Soviet Union had also done calculations that indicated the occurrence of asymptotic freedom, longer ago, but they hadn’t quite interpreted their results that way, and their words were not heard. The Cold War was still strong, separating east from west, so what was happening in the Soviet Union, people didn’t know. And there were people who were doing calculations very similar to what Gross and Wilczek did, but more in connection with renormalization than in connection with scaling. To me, it seems that they also didn’t ask exactly the right questions—
Gerard, on that point—given the tremendous and rapid advances that are happening during these years, and the fact that you’re right in the middle of it, as a result of these advances, from your vantage point, what new questions are now able to be raised that weren’t before?
Oh, the question of scaling is very important because you can scale a long way. You can scale to one-millionth of the sizes you had before, one-billionth, one-billionth of one-billionth. You can go to very small distances. So, it’s a very large domain of science, actually, that is covered by scaling. So, now, when we understood that the strong force can be subjected to scaling, and that we should look what happens, this opened up the possibility to scale all our understanding of physics to a very different size-, distance-, and timescales than what we are used to. In particular, now, we can ask what happens at very short distances for the first time. And that was an important advance, this enabled us to ask questions which were impossible just a few years earlier.
And one of the discoveries made is, that if you apply scale transformations to all the forces, they continue to behave very similarly. If you look, with a microscope, at the particles in the Standard Model, the microscope will again show you the same particles with slightly different properties, only marginally different properties. This is not true for the gravitational force. Gravity is something totally different. Gravity will become much more significant if you scale to shorter distances. That’s a bit surprising because gravity acts as a strong force at very large distances, causing suns and planets and stars and galaxies all to be held together by gravity. Whereas at the scale of elementary particles, atoms and molecules, gravity is totally insignificant. My two fingers attract each other gravitationally but the force is so weak, even compared to weak forces, that people didn’t pay any attention to gravity for a long time. But now, for the first time, we can scale to short distances, knowing that gravity effectively becomes stronger there.
When will gravity take over? And that was a very important question that people started to ask already in the early ’70s. What about gravity? How does it take over at the small-distance scales? Gravity cannot be renormalizable exactly because it becomes very strong at short distance scales. So be it. Gravity will have to be replaced by something else, but then again, you have to ask the right questions. We would like to see how gravity can be replaced by a smarter theory that embraces all we have in one grand scenario. The electric and the weak and the strong forces, and the gravitational force should all be joined in one scheme. Now, that would be called Unification with a capital “U”, and it obviously looks important.
But people are still not asking the right questions, I believe. And because of this, progress is now going very slow. I think our problems in general are becoming harder, and because of that, our field of science has arrived at a more difficult position; we have been so successful in this field in the near past, we now have dozens of times more scientists doing this work then there were in the ’70s, let alone in the beginning of the 20th century. There were only a handful of scientists doing these kinds of things, and they were all discovering important things.
Nowadays, I think, to discover something important, you have to be much smarter than people were before. I think the problems are growing more difficult, and, as a consequence, a larger number of people are working on them, while only a smaller fraction of those are actually getting the new great ideas. It seems, that in spite of the larger numbers, the more expensive experiments, the new great ideas are further apart, and too much obscured by the bad new ideas of which you see very many.
Gerard, of course, what became your dissertation was the first and the second paper. Did you look at your thesis altogether as two separate concepts, two papers stapled together, or was there a unifying theme between the papers intellectually for you?
No, it was just one single subject to me. The fact that you needed the Higgs mechanism to generate mass was just one important observation, which changed the administration that you need to do the calculations. But the principle, the physical principle is exactly the same, unchanged. The Higgs theory, or the Brout-Englert-Higgs theory, to be precise, is the pure Yang-Mills theory in disguise, just some secondary features are added. There is the technical requirement of fixing the gauge condition, which can be done elegantly in the BEH scheme, so as to keep the calculations as simple as possible. Renormalizing the system goes exactly the same way as in the symmetric, massless, case. The whole scheme appears to be fully capable of reproducing all we know from experimental observations quite well. The Higgs mechanism really takes place.
All this became clear in the early 1970s, but it was only in, well, 2012, when the Higgs particles were really detected at CERN that people said, “You see, it all works. It all works as we anticipated, and there we are.” The strong force was successfully added to the system, although the strong force has other features to it, which are fairly unique for the strong force that you don’t see in the other forces. But, apart from that, the strong force also is a Yang-Mills theory, so you would just take all forces together, and unify them. All this could be understood in terms of straightforward calculations, and already in 1973 people started to talk about the “Standard Model”. It’s one almost unified picture of the forces at the most elementary level. The Standard Model’s a kind of minimalist model. Take the simplest of all possibilities, don’t add anything you’re not sure of, then you get the model that looks quite well like reality as we see it.
Let’s take that as our standard, that’s what the word “standard model” comes from, take that as a standard, and then see where to go from there by asking questions. Where does the model still fail? And — from the 1980s until now —, you’ll see many, many papers in the literature with titles like, The End of the Standard Model. Why should we improve the Standard Model? What’s wrong with the Standard Model? Why does it not give us everything? What do we have to do?
Well, the Standard Model isn’t better than what its name suggests. It is a sort of minimalist description of what we know. It is not expected to be universally valid in all circumstances. In particular, if you scale to very short distances, then, you know, other particles could be living there that could not have been detected today. We don’t know whether they’re there and why. We don’t understand what they are.
But, if they are there, then the behavior of the system at very short distance scales will change a lot. And that’s where new different physics comes in, and that’s, of course, all totally outside my dissertation. But I think the electromagnetic and the weak and the strong and the Higgs mechanism, all that fits nicely together in one unit.
Gerard, besides Veltman, who else sat on your thesis committee?
Who else? I have to look this up. Here’s what I have: G.A.W. Rutgers (pres), J.A. Tjon, P.J.Brussaard, Th.W.Ruijgrok, N.G. van Kampen, P.M.Endt, B.R.A.Nijboer, and some visiting scientists (the others were physics professors).
That was Nico van Kampen. Theoretical physics was still considered one subject; so, we had some visitors from abroad, who also attended the ceremony. It was all very formal.
Gerard, after you defended, what opportunities were available to you? What was most exciting for a postdoc?
I kept my (unpaid) appointment at Utrecht, and then went to CERN as a fellow. That was a great time. Then came back to Utrecht for an assistant professorship (called ‘lector’ according to the system then). Then I had a sabbatical in the USA (Harvard and SLAC, Stanford, Calif).
How long did you do that for?
Those two years at CERN, near Geneva, were great because of the nice atmosphere of discovery that we were having there, and people were making progress every day in theory. I witnessed up close how the theories on supersymmetry developed. And gravity and supergravity, the first ideas about string theory, and all the other new discoveries—that was in 1972-1974.
And I made several more secondary discoveries also in those days, the so-called magnetic monopole, which is a particle-like solution with a unit of magnetic charge, generated by the Brout–Englert–Higgs mechanism being so fundamental in generalizing electromagnetism. It also generalizes the concept of charge, so now the magnetic charge was, under some very special circumstances, possible. This so-called magnetic monopole would normally be considered not to exist, but now magnetic monopoles came in sight as real possible particles, and other similar features.
I was trying very much to understand the strong force in those days. So, I had ideas about grouping Feynman diagrams together. They had been ideas I’d had before but I had a more precise way of counting Feynman diagrams, and telling the important ones from the unimportant ones, and that gave me again some insight about what happens to those quarks. You know, the strong force particles are called quarks, and these quarks are displaying very strange behavior because of this asymptotic freedom business.
Did you continue to work as closely with Veltman at CERN as back in the Netherlands?
I didn’t work so closely with him there anymore, but we did still write some papers together, and we discussed a lot about our field. But, eventually, yeah, our interests became different.
And then when did you more completely get involved in quantum gravity?
It happened very gradually. The first paper I wrote on quantum gravity was together with Veltman on the question of renormalization. Why is it that gravity’s not renormalizable? Well, that was relatively easy to answer. But the question—the next question we asked was, how bad is that? What can we do instead? We can still do something that looks like renormalization. Let’s try it. So, that’s what we did, and the paper’s still being cited, so people realized that, yes, you can ask these questions. But these questions are not going to lead you to an answer as to how gravity fits in with the other forces. And that’s what we realized, of course.
But then for a long time, I thought, well, gravity is for idiots who don’t realize that gravity is such a weak force that you can never do any experiment on it, so forget it. Let’s do more important things like trying to figure out how quarks behave in a nucleus, and so on. That was for the next 10 years or so very much my attitude and interests. But every now and then, I was thinking about gravity, how to improve it, and then came another development, which was unexpected to me. Stephen Hawking came to CERN, talking about new ideas on black holes. We knew about black holes, but we didn’t really think that they have anything to do with elementary particles. But then when Stephen Hawking came with his observations about black holes emitting particles, I realized that he had made a fundamental new discovery, which could have important implications for particle physics.
Why, Gerard? What was so new about this at that point?
Oh, two things, one, the effect was a genuine quantum effect in a setting that could only exist due to general relativity. So here we had an example of quantum mechanics and general relativity acting together, giving rise to something indeed very strange: particles that were fundamentally invisible to one observer, managed to devour a black hole entirely, including the other observer who couldn’t see those particles. And then two, the distant observer would think something very familiar was happening, the black hole was very slowly evaporating, something a bucket of water in outer space would also do. A mundane phenomenon described in two entirely different ways.
It makes black holes almost look like complicated atoms, which are held together not by electromagnetic forces but by gravity, and eventually not only gravity but also topology, the special shape of space and time surrounding a very heavy object. There would be a horizon, and this horizon has separate peculiar properties. And then I learned -- I very quickly realized there’s something basically wrong in our present understanding of this situation, in particular when particles are being absorbed by a black hole, they go through to a horizon, and disappear forever. This looks very strange from the point of view of a particle physicist who just would insist that particles should go out as easy as they go in. But how can they get out?
Now, Stephen Hawking gave a beautiful analytic answer. He could calculate that black holes emit particles. He would exactly calculate how many particles a black hole emits per unit of time, and how to fit this into a neat theory. So, this was absolutely marvelous. It immediately made me realize there’s something very important missing in our understanding of gravity. If you scale to very short distances, the behavior of black holes would become more important because gravity becomes stronger and thus more important.
So, the very tiniest particles and very tiniest black holes are going to look more and more similar. I realized that in the present unified theories something is missing today, which is the role played by particles that look like black holes when they’re really large, while they look like elementary particles, when they’re very small. We would like to put these on one denominator. When we try to make a unified theory of elementary particles, the Standard Model particles, the quarks, the leptons, all that, it should also describe black holes, and the gravitons, they should all be part of it. They should all be on top of one denominator. And that turned my attention abruptly back to black holes and gravity, but it was very hard to make fundamental progress. I was learning what kind of questions to ask.
On the question of black holes, did you see this as an early interest in cosmology for you, or were you approaching these questions very much from the perspective of fundamental theoretical particle physics?
No, I have not been involved much with cosmology. I know cosmology is there, and people are making very important discoveries. In particular, cosmology tells us how the universe got started, the universe was very hot and, therefore, energetic particles that are normally not seen, played a decisive role in the formation of the universe in its very early beginning. According to findings of cosmology, the universe has gone through a stage of very rapid expansion and cooling. When the temperature was still very high, heavy particle types could have played a role, but it seems that there were only a few fields, and therefore not many different particle types. There must be important information there for particle physics, which we could not obtain any other way than by studying the universe, but I wait for more understanding.
The universe is a highly intriguing object for study but too many people are doing this already, and it has become a highly specialized domain of science; I haven’t been much occupied with cosmology at all. Maybe I should have, because cosmology is part of the equation where we should be able to find some further information. But it’s very indirect because we can’t really observe the Big Bang directly. We can only observe it very, very indirectly from all the remnants that are flying around our ears right now, the remnants of the Big Bang.
Yes, they are there, but they are too complicated for me to be understood. Eventually, yes, we should take cosmology as a factor in our attempts to understand the world, but I think I have enough indications already about how to continue without yet looking at an expanding universe. I agree with my friends who do study the universe that it is a very important topic. Here also, the question is how to ask the right questions. And I’m worried that, even in cosmology, people are not asking exactly the right questions. I am not going to do it, but someone should learn how to ask the right questions in cosmology and insist on being super rational about what we know and what we still have to learn.
Gerard, do you have a specific memory of when you first came across the term “quantum chromodynamics”?
No, it was fairly early on. I think I saw the word first used in the paper by Gell-Mann, Fritzsch and Leutwyler in 1972, but I am not sure. Harald Fritzsch told me once that they had had some discussion as to how to name the theory. Whoever invented the word, I think that ‘quantum chromodynamics’ is well chosen. I liked it, chroma is a Greek word, for color. In this theory, ‘color’ stands for a property quarks can have: their charges come in three types, rather than just + and - . It is tempting to say that quarks are either red, green, or blue, or they may be a blend of these basic colors. The anti-quarks have ‘anti-colors’ or a blend of them, the conjugate colors cyan, magenta, and yellow. And so the word “color” stuck, and rightfully so. I like it a lot. I did not invent it myself. But people came with the word “color” quite naturally, and the word “quantum chromodynamics” very well describes what the situation is with these charges.
During your time at CERN, did you take visits elsewhere? Did you visit the United States at all during this time?
Yes. Also, from CERN itself, I made several visits. I travelled to Harvard, Princeton, and later to Caltech.
In the United States, who were some of the people that you really wanted to meet and work with during your visits?
Well, the people I liked most to talk with were Sidney Coleman and Shelly Glashow, Roman Jackiw, and many younger people. Coleman was thinking much like I did. He was very mathematical, but he also liked to ask deep questions, and he had a great fantasy. He was very much interested in science fiction, and he loved to read science fiction stories. He was a complete walking library. He knew every science fiction book that had ever been written, I think. He was very strong. Like him, I also liked the idea of manned space flight to distant planets. Coleman had a great fantasy about how science could look in the future, and how civilizations could visit us, and so on. And it was a joy to discuss with him about such matters. I met Roman Jackiw many times. I knew him from his work on the Bell-Jackiw anomaly, and Jackiw was also thinking very much in terms of topologies. And Weinberg I met occasionally; not very often. Ken Wilson, I recall. In 1976 I spent more time, a whole year, in the US, most visits and discussions I remember from that time.
When did you start working on Bose condensation?
I only did a few things related to Bose condensation. The Higgs mechanism could be in a sense called Bose condensation, but the term’s a little bit too general. It can cover many things. Usually, in statistical physics, there are atoms of all sorts, that can go into Bose condensation. In particle physics, I would prefer the word Brout-Englert-Higgs mechanism as describing basically the same phenomenon, notably in perturbative theories. But, also beyond perturbation expansions you can think of composite particles undergoing Bose condensation. One important result was the idea that the phenomenon of complete and permanent quark confinement inside hadrons can be brought in connection with Bose condensation, where the condensing particles are color-magnetic monopoles.
But some people got much further with this. Mikhail Shifman used supersymmetry to understand Bose condensation under many different circumstances. There’s Frank Wilczek, who thought of neutron stars and quark stars; a star can collapse under its own weight, generating higher and higher densities. At some point, density and temperature can become so high, that particles will undergo various sorts of phase transitions. It was suspected that there might be phenomena where objects with color charge, or flavor charges, may Bose-condense. Now, color condensation has become somewhat like the Higgs mechanism in the color sector. But the problem I have with those ideas is that they often require calculations for strongly interacting kinds of matter, which are also somewhat dubious to me. You might be trapped into believing that you got it right, but you don’t know for sure whether you are doing the correct calculation.
Gerard, on the question of asking the right questions, how—what were—what was going on that allowed you to come up with a formula for calculating the masses of mesons?
There are two aspects of the mesons that I was interested in. One approach towards understanding the meson mass spectrum is string theory, that is to say, hadronic string theory, the theory that describes the color-field lines in QCD as elementary strings. The procedure is not extremely accurate, but qualitatively, it worked very well. The starting point here is color-magnetic monopole condensation as I just mentioned. You find that the color field lines obey the equations for relativistic strings. These equations tell us that there are sequences of meson mass states where mass-squared is proportional to their angular momentum, or spin. This works very well qualitatively, but there is a problem: it is difficult to figure out how these calculations should be corrected, so that the expressions become more precise. There exists no systematic perturbation expansion. I had hoped that one should be able to replace the color group SO(3) by SO(N), after which one can consider the 1/N expansion. Things simplify then, but still there is no precise expansion method.
But this approach does give us a very good intuitive picture of what is going on: the world is a color-magnetic superconductor. In ordinary super conductors, electron pairs Bose condense, allowing these pairs to move without resistance, so that we have super conductivity. A consequence of superconductivity is that magnetic fields can't penetrate a superconductor unless superconductivity is locally switched off, a process that costs energy. The new equations one then gets is that the magnetic field lines form strings. In super conductors, this phenomenon generates the so-called Meissner effect. Replace electron pairs by color-magnetic monopoles and you obtain a picture of what happens in QCD. There, the magnetic lines are replaced by color-field lines, keeping the quarks hooked together.
Gerard, when did you realize that studying instantons would be significant for QCD?
Well, this would be the second point I wanted to make, it's again a question of asking the right questions. Consider these string-like color-vortex lines that cause the Meissner effect inside a superconductor, and keep the quarks together in QCD, they can be called "solitons". A soliton is a particle-like structure that is obtained as a topologically stable solution of some field equations, like a steep wave propagating over a smooth surface of water. The wave displaces water along a line. Think of the buttons on your shirt: if you connect the buttons incorrectly at one spot, you can move the spot about, but the "anomaly" is only removed if you reached the end of the line. The one loose button is like a particle that can move but not disappear.
Vortex lines are something else than a particle. If I would remove one dimension, keeping two space coordinates rather than three, then you are describing the vortex crossecting a plane. That is a particle-like solution on the plane. The wave over the water requires only one space-coordinate in the direction of its motion. It is called a ‘soliton’. Roman Jackiw and Sidney Coleman talked about that kind of soliton. The magnetic monopole is a perfect example of a solution requiring three coordinates, so that acts as a particle in three dimensions. The number of dimensions just depends on the system you have, and on the field equations that it obeys.
So, my next question was: can we have something like this in four dimensions? Such a thing would not act as an ordinary particle, but rather as an event, a particle popping up momentarily and disappearing again. A name was easily found, this we called an instanton. Question was: when does that occur, and what are its implications? You see, all these solutions seemed to be doing something that ordinary particles can't. For instance, the Meissner effect is the only way to obtain magnetic flux inside a super conductor, the QCD vortex necessarily connects the quarks to make them stay inside a hadron, and a magnetic monopole is the only kind of particle that can carry an isolated chunk of pure magnetic North charge or South charge. An instanton should generate the violation of some conservation law at the spot where it occurs.
And we found an instanton. It can be constructed inside the QCD vacuum or the vacuum of any other non-Abelian Yang-Mills system. The Higgs mechanism played no significant role here. The equations (pure Yang-Mills), and the solution, had been described by four Russians, Belavin, Polyakov, Schwartz, and Tyupkin, just a year earlier. And they had noticed something: there is a conservation law, they said, that is normally valid, except here. And what they wrote down was exactly the conservation law that was broken by the Bell-Jackiw anomaly, the one I had been puzzled about. And so, we learned that the BPST instanton was the cause of the anomalous interactions that threatened to spoil a symmetry that one might need to renormalize the theory.
So, we had the equations, we had the solution, we had the violated conservation law, but what was the symmetry that we were looking at? This was what the Bell-Jackiw anomaly had been about: there is a symmetry between left-rotating and right rotating quarks. If a quark would spin to the left, as defined with respect to the direction of its motion, then it would spin to the left forever. If it spins to the right, it will spin to the right forever.
But the Standard Model, as we knew it then, was a bit more complicated than that. Direction of the spins got entangled with the distinction between particles and antiparticles, between baryons and antibaryons, due to the BEH mechanism. This implied that, in the Standard model, not only the spin of a quark would flip when it meets an instanton, but something more drastic would happen: a quark would transmute into an antiquark. The same instanton would also replace a lepton such as the electron, by its antiparticle, the positron.
One instanton would flip three quarks and one lepton in all three generations of quarks and leptons. This looked like a crazy interaction involving nine quarks and three leptons. And now you could see something else: in each generation the three quarks that are involved, would represent one unit of electric charge, as in a proton, and the electron would carry a negative unit of charge. All these twelve particles together, as the instanton acts on them, would have total charge conserved. So the charges cancelled out. Ouff, it would have been incomprehensible if this weren’t the case, but it looked very strange: a baryon turns into a lepton with the same charge? This was not supposed to happen, but it didn't violate any basic principle. This feature just ensured that the anomalies due to the quarks cancel against the anomalies induced by the leptons. This actually was known already, it was an important feature that rescued the renormalization procedure we had found from an imminent threat, but only now we began to understand the logic behind this.
But I almost forgot your question about the meson mass spectrum. There was an unresolved problem in quantum chromodynamics. This concerned the masses of the pions and the eta meson. Pions are very light compared to all other mesons. Why? Was this due to some accident? No, this was related to the symmetry between left rotating quarks and right rotating quarks. Thus, we understood why the pions are so light. The symmetry was only broken by the fact that quarks are not entirely massless. The mass terms for the quarks, due to the Higgs mechanism, break the symmetry of left against right rotation. Right, so this was the reason why pions have some mass, albeit not much.
But now came the problem: this symmetry was described by the symmetry group SU(2). It has four fundamental axes for symmetry rotations. All four were involved in this mass-protection mechanism. But wait, we have three types of pions, pi-plus, pi-minus and pi-zero. They are indeed light. Where is the fourth? A particle with the required quantum numbers was easily found. It is the eta meson. But the eta meson is nearly as heavy as a proton. Something was wrong. This was actually being held as an objection against our beautiful theory of quantum chromodynamics. And now we realized what the explanation of this anomaly is: the eta particle is attacked by instantons. In its path, instantons flip the spins of the quarks inside the eta. The instanton has exactly the right quantum numbers to do this. The pions are insensitive. The eta mass problem was solved. QCD came out with flying colors.
The instanton that generates the eta mass is the QCD instanton. It clearly has a measurable effect. In contrast, the instanton that acts on twelve particles at once, violating the conservation laws of baryons and leptons, is the same solution but in the electro-weak sector. It is now known that this instanton will cause an interaction that modifies the baryon number and the lepton number by three units at once, but its effect is extraordinary weak. It may have played an important role however in generating baryons and leptons during the early phases of the universe, when the temperatures were sufficiently high.
This was again a nice moment in our understanding —or further understanding— of the fundamental interactions. We saw that nature cares about mathematics. If there’s an anomaly in laws of nature, nature knows about it, and the particles react to it. It was interesting to see how taking the instanton onto account gave us more accurate values for the masses of other particles as well, the kaons, rho, omega, phi, all to be distinguished by their respective quantum numbers.
Gerard, when did you first become aware of Alexander Polyakov’s work, and did you ever work with him directly?
I did not work with him directly. I discussed with him a lot. He is a very nice fellow. And I could understand that he had this idea about monopoles also. He tried to see whether monopoles could be held responsible for quark confinement. We were much on one line on the subject of monopoles and instantons. But he continued getting more and more involved with string theory, and you may know that I have not been very active in string theory at all. So, we lost contact because of that.
He was asking the same questions in string theory as what I would like to ask. So, in that sense, I sympathized a lot with him, as he was asking important questions. I agreed with that. Some of his answers are not being used much in string theory, but Polyakov is an important player in our field. Others, well, they put emphasis on other things, as happens often. You know, you can ask the right question, get the right answer, but then discover that the question doesn’t help so much in understanding what goes on. And I think he also realized this, although the so-called Polyakov action does explain a lot in string theory as well.
When did you become involved in the color confinement puzzle, and what compelled you to introduce what came to be known as 't Hooft operators?
Yes indeed, I was interested in confinement very much. When I arrived at CERN in 1972, I was fully aware that the theory now called Quantum Chromodynamics would be the correct theory. Veltman wasn't much interested here. He thought that strong interactions are messy and unintelligible. He said that I would have nothing if I didn't understand the confinement mechanism. I should have objected by saying that yes, I do understand it, but instead, I started to search for a simpler explanation. I hoped that a theory somewhat like string theory today, but more precise, would do the job. But it should come with a good perturbation expansion and there, I failed. There seemed to be no easy way to relate the QCD Lambda parameter with the string constant rho.
In fact, the magnetic monopole was discovered during one of my attempts to understand quark confinement. I thought there’s some topological mechanism here. So, when I searched for a topological mechanism, I found one. But it didn't work well to explain confinement. Only in 1975, when I was asked to present a rapporteur's talk on progress in gauge theories in general, in the EPS meeting in Palermo, I gave a detailed account on how I understood quark confinement to work. That paper is now cited a lot; it is agreed upon that this mechanism was discovered independently by me and Stanley Mandelstam.
But I tried to do this better, by finding how the dual superconductivity story could be linked to string theory. There is the so-called Wilson operator, an operator that not only creates and annihilates quarks and antiquarks, but also the vortices connecting them, so that the entire operator is gauge-invariant. It was clear to me that a similar operator should exist in the same theory, that would be the dual opposite of a Wilson operator. It would primarily work for closed loops. The 't Hooft loop should wind around the Wilson loop, and one nice thing would be that you have clear and precise, non-trivial commutation relations for these intertwining loops. Whenever a Wilson loop would cross over an 't Hooft loop, the amplitude of the state would pick up a phase factor exp(2 pi i /N), where N is the dimensionality of the gauge group SU(N).
Kenneth Wilson had the good idea to consider gauge theories, of any kind, formulated on a discretized lattice rather than a strict continuum. In that case, one can indeed apply another perturbation expansion with respect to the gauge interaction constant g. He considered the expansion you get if g is very large instead of very small. In the 1/g expansion, you get right-away the physical states where all quarks are confined. That was a brilliant result but unfortunately very complex. It did not enable us to compute the meson spectrum very precisely, but yes, it was a perturbation expansion and it worked, it did give confinement directly.
I remember that shock that I experienced when I first heard him talk about this. I think that was in 1974 in London. What he had discovered was that, if you perform the 1/g expansion, all terms of the expansion can be computed but you should not try to apply gauge fixing, which is necessary in the small g expansion. If you don't fix the gauge then all terms in the 1/g expansion are still well-defined, but you don't get any gauge-dependent effects anymore, and this was the main reason why gauge non-invariant objects such as isolated quarks and gluons, are completely suppressed. Right he was.
There was yet another expansion that I tried, with a bit more success: take SU(N) as your gauge group and let N approach infinity. The gauge parameter is sent to zero in such a way that g2 N is kept constant. Then you can perform the 1/N expansion. 1/N acts like an interaction constant between hadrons, and it is small, 1/3. Often you only need 1/N2 which is 1/9. What is also nice about this expansion is that it simplifies the Feynman diagrams. They look very much like the string diagrams people use in string theory, and indeed this expansion could also explain confinement. My discovery was that, at large N, all Feynman diagrams can be drawn on a sheet of paper without crossings. The sheet of paper is the string world sheet. This was completely missed by some colleagues who had also tried to consider 1/N expansions, but they found nothing conspicuous happening. 1/N expansions are now used a lot in string theory.
Gerard, to return to Stephen Hawking for a moment, when did you first become aware of what has become known as the black hole information paradox, and what about it was problematic for you?
Well, the paradox has been around from nearly the beginning. At first, there was no paradox because the investigators involved, who did general relativity, like Stephen Hawking, didn’t think there was anything wrong with the idea that black holes absorb particles but don’t emit them. So, when Hawking found that black holes emit particles, he was one of the people most surprised by this answer. He did not expect it at all.
But even with the particles coming out, while we agreed that black holes emit particles, he was still completely fixed by the idea that a black hole is the mouth of a wormhole, and that this wormhole has another mouth in some other universe, or maybe in the same universe somewhere else, nobody knows where. There’s a wormhole in many science fiction stories, including movies like Interstellar. I’m sure Sidney Coleman loved wormholes because you can imagine great science fiction stories about them …
—you can do science fiction with them—but only bad science fiction because the problem in the real world would be that the forces are far too great to be manageable from ordinary spaceships, let alone people. No, everything will immediately evaporate when you come close to the mouth of a wormhole. But, anyway, a black hole was a mouth to a wormhole, and Hawking imagined, like in the science fiction stories, you should be able to travel through a wormhole, get in here, and get out somewhere else. And Hawking was also dreaming of manned spaceflight, he really hoped one day people can go through wormholes in one part of the universe to travel in no time to another part of the universe. That is extremely unlikely, unfortunately, because wormholes are far too violent to allow such fluffy things as human beings to get through in one piece. I don’t think that can ever happen. But, anyway, with such fantasies in his mind Hawking had no reason to be worried about information while going through a wormhole.
It would be unnatural for him to say that a wormhole only emits things that are controlled by quantum equations. So, he didn’t care much about that. But then came the particle physicists such as Lenny Susskind, me and a few others, who said, “Wait a minute, there is an important question to consider.” To me, a black hole is just like a particle, a composite particle perhaps. And it absorbs things. It emits things. But it does the same thing as a bucket of water does. You can throw a cup of tea in it, you can watch what comes out, but whatever you do, must obey laws of nature.
And it should be possible to derive the laws of nature by understanding general relativity sufficiently precisely. It should be possible to split up such a problem into many small problems, considering only many small regions of space and time, and ask that the behavior of all particles should be regular in these small pieces of spacetime. After all, if you have a small section of spacetime, and even if you have a black hole nearby, small regions of spacetime are relatively flat, and so relatively mundane physics should apply to them.
So the question is, if you apply these mundane laws of physics, can you understand why the black hole behaves the way it is? Well, the original answer was, no, the black hole behaves in a bizarre way. It’s like a thermal object, like a lightbulb that emits light, and continues to do so until it has lost all its energy. But then particle physicists like myself said, “Wait a minute, a lightbulb emits light according to the laws of thermodynamics, even though we can’t say where all the atoms in the lightbulb actually are. That’s why we have to do statistics to understand how the lightbulb behaves.” Now, statistics is useful if you want to know approximately what happens, but the true laws of nature are much more precise than that. I am somewhat annoyed that people in general do not realize this.
In principle, you could take a canonical ensemble to describe how a heated object emits light, and you don’t need to say that quantum mechanics is invalid or whatever. No, all the objects like a bucket of water, like a pot of tea, or any other atom or molecule, they all behave according to the laws of nature, even if you could also apply laws of thermodynamics to these same subjects. So, there’s no contradiction, in all physical systems what you get out will be related to what you threw in earlier. From the very beginning, I saw Hawking radiation this way. The Hawking radiation really tells you that a black hole has a finite temperature, and a finite entropy. It just behaves like things you have in statistical physics with energy, entropy, and other properties. So, you should be able to use ordinary physics to describe even something as complicated as black holes.
But it seems that this comes at a price, and the price is: think again about those microscopic laws, and how to handle—how to put these small pieces of spacetime together to make a black hole, what are the laws under the most extreme conditions? Do you have to make any changes in these laws? String theorists are aware that their theories should provide “all the answers,” so they publish loads of papers explaining how they think, or how they “know” that black holes have to be handled. But their answers are confused: the quantum microstates are “chaotic”, and only statistical statements can be provided. I would say that op to the point where Hawking particles carry energies not exceeding a couple of TeV, you should be able to use the Standard Model to find out what happens.
At the same time the behavior of particles in the very narrow region left, very close to the horizon, should be such that we might learn important things about how the Standard Model may have to be extended beyond those TeVs. I think this is a fantastically interesting question. But to my mind, string theory should only apply in the region for which it is designed, near the Planck scale. I don’t understand well what the string theorists are doing, but it does not sound like what I said just now.
It turns out that, if you make no significant changes anywhere in the Standard Model, then there is a problem. It’s not only me who says that; many people said that there is a problem; particles fall into the black hole, but there seems to be no opportunity for these particles on their way in, to transmit the information that’s in them to the outgoing particles. Because of that, the outgoing particles cannot be the result of an information transfer process from in to out. But phrasing the problem this way, I find it easy to punch holes in the claim that ingoing particles would not be able to pass information onto the out-going ones. I don’t believe this is correct. Just before they enter the horizon of a black hole, the ingoing particles will meet the outgoing particles predicted by Hawking. But they meet each other at a tremendously high center-of-mass energy.
In fact, if you take the time difference between in- and outgoing particles long enough, that center of mass energy could be bigger than the total energy of the universe. So, you can’t just apply ordinary physics there. Something has to give. There’s some additive constraint in your equations if you want them to describe the black holes correctly. And then I got more and more excited about this idea. There’s something basically wrong in the way people thought they could talk about this.
Unfortunately, most of my colleagues do not argue the way I argue now, that we should first consider a black hole where ingoing particles are in equilibrium with the outgoing ones. In that case we should have information in equals information out, and that’s all. Why not? What is wrong with that picture? But people argued from the other end. They are convinced that the information that went in cannot be carried away with all the out particles. But all you need is postulate a unitary quantum evolution operator. The only problem with that is that this operator will be non-trivial. So naïve calculations give the wrong answers, which make people believe that only string theory can cure that.
And because of that, there must be something else in the black hole that is responsible for the information transfer in to out. I have continuous discussions with people who say these things, but I don’t agree with them. I think if you look more carefully, there is no information problem anywhere provided that the evolution operator is unitary. I found a way to construct such an operator. To me it seems to be the only way, and a beautiful theory for black holes emerges. If you do it right, you see that the outgoing particles immediately start carrying away the information that you threw in when you made a black hole. Information sitting on a black hole horizon, plus information outside = preserved.
I had that conviction right from the beginning, but I couldn’t convince people that this is the way to look at things. This is the answer you should get. And the real problem that I’m having with this situation now, is I didn’t have the right equations, so I didn’t have equations that show that I’m right. And for a long time, it seemed to be hopeless. There was no way to get the right equations to show that the information in is transferred to the particles going out, via the horizon.
But then a decade or so ago, there was a meeting in Stockholm, and Stephen Hawking was there. He gave a talk that made us—me but also other people—realize that this is much more, closer to the way I had been looking at things all along. He had a very complicated way of formulating this, which I could not follow. But he eventually said that, yes, the information going in is represented in the particles going out. I now have the mechanism for it. I know how to calculate this. But I have to make one assumption that most people will not accept, and that is that if you go into the black hole, you’re entering a wormhole, but don’t even dream that the mouth of the wormhole brings you to another universe. No, it just brings you to the other side of the black hole, so you can get—you get out as quickly as you went in.
The picture works amazingly well for me, but many people don’t quite understand how this can be, and why you have to say this, why it should be inevitable. The problem is much like in the beginning of the 20th century, you have to answer—you have to react on different problems at the same time. There’s now two or three or four different questions. They can only be answered all by one theory, which is that the ingoing particles affect the outgoing particles. I can calculate how the outgoing particles are shaped by the ingoing ones, and there’s no mistake there at all. But people don’t believe my calculation. Some features are counterintuitive. And if you don’t do everything right, nothing seems to work. My theory fails if you don’t make some necessary assumptions. And then people say, “Of course, OK, so your theory fails.” It seems they don’t want to learn all about it. And that’s my fate.
And, Gerard, where is the holographic principle in all of this? Where does that enter the picture?
Well, the first thing you notice when you look at black holes is that most of the interesting physics and the dubious and disputable physics takes place at the horizon of a black hole. Now, string theorists also work on black holes, but they think it’s all strings, and they believe that strings don’t need the same kind of horizons. I fail to see the logic of that. Consequently, I have some fight now with the string theorists. Even Lenny Susskind, who had been on my side for a long time. They use something called ‘holography’ in a way somewhat different from string theory; let me first explain what I use this word for.
Originally, holography was defined to be a phenomenon in optics. Consider some three-dimensional object(s), and you shine a laser beam on them. The laser beam first goes through a semitransparent mirror, splitting it in two. One of the two beams is reflected by the objects, the other goes directly to a photographic plate. The first beam eventually also reaches the photographic plate, and now the beams together form an interference pattern. The objects were three dimensional, but the interference pattern is only two-dimensional. You develop the photographic plate, which gives you a picture of the interference pattern. If now you shine another laser beam directly on the interference pattern, a picture emerges of the original objects, but you can see these from different angles, and then it is really a three-dimensional picture that results. This picture is called a hologram.
What is particularly relevant for us is the quantity of information that is being processed. The three-dimensional picture cannot contain more information than what is in the interference pattern. In the interference pattern the lines typically have a resolution of about a micron. So, we have one bit of information at each square micron. The original three-dimensional object could have contained one bit per cubic micron, so by projecting that on a photographic plate, parts of the information must have gotten lost; the image of the 3D object must have got blurred somewhat. In describing black holes and such, we also use different numbers of dimensions, and holography is the concept we now use to go from one picture to another, changing the dimensionality.
For me, holography follows from an elementary observation. If you consider space and time in regions sufficiently far away from a black hole horizon (still close to the entire black hole), you’ll have to assume space and time to be reasonably flat there. This means that you can’t have a high density of particles there, and the particles you do have must be at sufficiently low temperatures. This in turn means that the number of allowed quantum states is quite limited (when counted as an orthonormal set). Only at the horizon itself, the density of quantum states seems to diverge. Therefore, the majority of all allowed quantum states are very close to the horizon.
Now according to the rules of thermodynamics, you can also count the states close to the horizon, and the result of that is that there will be approximately just one bit of information on one squared Planck length on the horizon, not much more or much less. This is as if a holographic photo can be made of all states, a picture that just fits on the horizon but represents all of space and time in the neighborhood. And it means that nature seems to be two dimensional rather than three dimensional as in ordinary physics. So, holography tells you that, basically, the horizon can be considered as an active, living membrane.
This is what Kip Thorne also emphasized in his book. It is not just a featureless region of space. In fact, no, it’s more like a membrane. It carries quantum states, and those quantum states will sit at the horizon without moving, the reason for that is that time stands still on the horizon. All these degrees of freedom, which would normally take enormous amounts of energy, now cost no energy at all by living on the horizon. You can count how many of these states will be sitting on the horizon if you assume that the whole picture, whatever comes out, should make sense. We must assume that whatever comes out of these marvelous calculations should amount to predicting that a black hole just behaves as a collection of particles. But, for that, you must say that the information that goes in and out of the horizon is the same information that went in from far away, and it goes out to far away. From far away, you can throw anything you like into a black hole.
But, as a response, anything that you might fear might eventually one day come out of the black hole. So, you consider all possible things going in and all possible things coming out. But those things coming in and coming out live in three space dimensions, whereas at the horizons of the black hole, there’s only two space dimensions and no time dimension at all because time stands still on the horizon. So, you are losing two dimensions. Well actually, there is also a way of saying that space-time has two dimensions on the horizon, but the outside observer does have a clock, a very slow one. Then you say that you have 2+1 spacetime dimensions.
Either way, you lose one dimension or two. This is how I see holography. String theory handles the situation a bit differently. They look at the spacetime transformations that leave the equations invariant, and then ask how many dimensions space and time have, in accordance with these symmetries. One then uses the fact that conformal symmetries in a field theory act as if there exists an extra dimension. These things typically happen in extreme black holes.
Again, this looks as if you need to store the three-dimensional world of information onto a two-dimensional surface. This is also holography. It was in a discussion with Leonard Susskind, we used the notion of holography to describe the mapping of particles outside the black hole onto the black hole horizon. But I was also thinking of the whole thing in a more generic sense where it doesn’t have to be exactly a black hole. I could just take any completely closed surface and say that whatever fits in the surface must not have so much energy that it creates a black hole, or at least not so much energy that the black hole it creates will be bigger than the surface itself. The surface itself would be the limit. Now you can ask, what is the maximal amount of energy one can squeeze inside this surface? How many quantum states would that have? How much information (in terms of bits) fits in there?
Again, you get one fundamental physical degree of freedom per Planckian surface element. Therefore, the surface of the horizon of the black hole behaves like that, but actually any other surface as well. Even if you don’t have a black hole inside, then the surface again acts as storing a maximum amount of information. You can’t put more information than a certain amount on that surface. But now, this includes all information you can put inside the surface. And this, at that time, was playing in the back of my mind when I was thinking of alternative theories of quantum gravity. Even before you try to imagine what the equations will be, you have to ask how much information the variables must be allowed to carry along, depending on where they are and whether or not they are parts of a black hole. This is the way I like to ask questions.
Should we say that the whole universe is a hologram?
I can say these things, but that’s not an answer to many of my questions. The question is how to quantify this, how to explain why the whole universe sometimes looks three-dimensional, sometimes only looks two-dimensional, and how do I go from one picture to the other picture, and how can all this make sense? Is this the way to describe the universe as we see it in our telescopes, in our microscopes, in our particle accelerators?
That should be the ultimate question, but it’s a very hard question. What we do in practice is we chop the question into very small parts, and we try to solve the small parts first. That has been the philosophy behind my latest investigations of black holes. Let’s see what the black hole horizon does to in- and outgoing particles and try to understand how the black hole returns back out the information thrown in, and why a black hole can, because of this, behave like a very ordinary object.
Gerard, to go back to a question from your earliest exposure to supersymmetry at CERN in the early 1970s, what was your perspective on supersymmetry in the 1980s, and particularly the 1990s when there was probably the most excitement around supersymmetry?
Yes, I saw supersymmetry when it was being born. That was at CERN, early 1970s. Bruno Zumino joined us in the lazy chairs in the CERN canteen. Talking about his newest supermultiplets, obtained together with Julius Wess. At the same time, there was Peter van Nieuwenhuizen, at Brandeis, in Massachusetts. Peter had been a fellow student in Utrecht. It had taken him long to graduate, on a tedious but dull subject given to him by Tini Veltman. But when he finally graduated, he went off like a rocket. He had learned how to do long calculations, and when Veltman and I had published our work on renormalizing gravity, he immediately started to investigate what could be added to that. He first checked what Veltman and I had done. It had taken us quite some time, but he reproduced that very quickly.
Then, he asked some very good questions. What about putting extra particles in? Veltman and I had considered a single scalar particle. That would not improve renormalizability at all. What about electromagnetism? What about fermions? Peter was a sharp observer. Something odd was happening, both with electro-magnetism and when you put fermions in. And then it quickly came to his mind that there was a symmetry that relates fermionic particles with bosonic particles. Unexpected, ununderstood. So, he started to work on that idea, and there were various people in different places who got attracted to very similar ideas, so they became competitors. I remember Peter, all excited. With Ferrara and Freedman, he had discovered supergravity. The hope was that symmetries such as these would lead towards a renormalizable theory.
It had been thought that mathematicians had proven that symmetries connecting particles with different spins can’t exist. And, of course, later people asked how come they’re proven so wrong? This thing happens often in our field: someone proves with mathematical precision that something cannot be done. And only a few years later it is done anyway. How could that have happened? Well, the guys who claimed to have the no-go proof had made a very reasonable looking assumption, it was written in small print that people never read. And then it was realized that the new important result just didn’t obey the assumption. I have several other examples of just such a thing happening. In the case of supersymmetry, the guys who had proved this to be impossible had made a very natural assumption, they excluded symmetry relations connecting bosons with fermions. Well, that’s what supersymmetry does, it connects bosons with fermions. But people don’t read the small print.
So, yes, there are symmetries between fermions and bosons. And I was at CERN at the time. Bruno Zumino would come in every day to tell us what he had found, what kind of new things he and Julius Wess had found together about this new symmetry. First, they did it in 2 dimensions, saying that they were sure it could also be done in four. At the same time, Peter van Nieuwenhuizen whom I saw regularly because he often came to Europe, gave talks about what he had found with Ferrara, Freedman, Stanley Deser and others.
But the theory became more and more complicated. I had a problem with supersymmetry, which was that I didn’t see the real necessity for supersymmetry anywhere in my understanding of the particles. So, yes, this would be a new symmetry of nature, but would the new symmetry be so powerful that it would explain the properties of the particles the way they interact, and particularly would they help us to renormalize gravity? It didn’t seem so. I hesitate to believe that the universe we live in has deep symmetries like supersymmetry built in, but this symmetry is manifestly present in our mathematical frameworks. The entire renormalization framework that we had pioneered, is clearly invariant under supersymmetry transformations. This is important to know, because this enables one to check complicated calculations.
Supersymmetry can also be used to study theories that resemble QCD but are just a bit different, for instance in the number of light fermionic matter particles, theories containing particle spectra different from QCD. After all, we don’t know what kinds of theories will be considered in the energy domains that cannot be reached experimentally today. Misha Schifman is the expert in this. There is only one argument that was used a lot to argue that there will be supersymmetry in our universe, and that is that unified theories with supersymmetry built in, have a more beautiful super-high energy behavior. The super unified theories appeared to be in an excellent shape. It was predicted that supersymmetry would show up soon in the LHC.
I was one of a minority who did not make such predictions. I only predicted the Higgs particle while I was very uncertain about the rest. I shouldn’t boast too much here, I always said that it was likely that some sets of particles might be found at higher energies, but I have no idea when and how, or what kinds of particles they are. In the meantime, there was one other very important development taking place: string theory. Originally, string theory was designed to describe the stringlike structures of the hadrons, where quarks were assumed to be tied together by strings. That theory was beaten by QCD. For a long time, I hoped that this kind of string theory could serve as an alternative to QCD in the sense that both theories could work at the same time, being exchangeable. But this did not happen. String theory failed for technical reasons. Only in a rough, approximative sense, string theory can be used in QCD.
Then, string theory was replaced by superstring theory, and it was suspected to serve as the perfect description of quantum gravity. Even renormalization would work out, because the theory, in a sense, is finite. You had to add supersymmetry in it, so this became yet another reason for many to believe in supersymmetry. The idea received a big boost in 1984 when some technical difficulties were resolved by Michael Green, John Schwarz and Edward Witten. Because their version of the theory required a lot of extra dimensions, the theory did become a lot more complicated. This was good, in a way, because it should eventually provide an explanation as to why the Standard Model is as it is, and that also contains a quite complex spectrum of elementary particles.
Here again, in 1984, I was the only one who didn’t cheer very loudly. I did not quite understand why I had to believe in this set of ideas. Yes, it’s interesting, I confessed, but we have very little by way of solid proof. Zero experimental evidence in favor, and it doesn’t really explain to me how gravity works. “The theory is so beautiful, it has to be true” – I’ve heard that before. Today, I have a more powerful argument against string theory: it should explain how quantum mechanics works, but the way it is being formulated, quantum mechanics is used as input; it is not explained.
Consequently, no explanation is to be expected on why the parameters of the Standard Model are what they are. When even more predictions of superstring theory had to be thrown overboard, the reactions from the string theorists themselves were deadly: the ‘Swampland’. You know, string theorists had a wide landscape of models that could solve the string theory equations and looked a bit like our universe. But when it was found that nowhere in this landscape a Standard Model, with positive cosmological constant, could be found, it was proposed that we shouldn’t search the landscape but go into the ‘Swampland’. This provides the theory with more and more characteristics of a religion. I’m not going for it.
And, Gerard, I assume that your concern about this would’ve been the same even if the SSC would’ve been built. At the energies of the SSC, you wouldn’t be convinced that supersymmetry would be seen there either?
No, it’s not clear whether the SSC would have seen supersymmetry. As you know, the SSC would have higher energies than the LHC now has been able to reach, so it could be possible that they would open up regimes that we cannot yet see with the LHC. But the LHC is looking very hard for supersymmetry, and they didn’t find any trace of the possible candidates that supersymmetry advocates came up with. There were other theories such as the existence of extra dimensions, which would be recognized in the form of chains of particles with bosonic properties, and things like this.
The proponents of supersymmetry did one very sensible thing: they tried to revise the Standard Model in some minimal way, such that it would contain a minimal amount of supersymmetry as an internal symmetry. It looked exciting but, to me, it was a little too far-fetched. I was worried whether people were asking the right questions.
This is a theme for you, Gerard. You always come back to this: are people asking the right questions at the right time?
Yes, indeed, I find this very important: what is the most appropriate question to ask? People often read the most recent history books, where the historians think they could reproduce the question that a researcher may have asked, and that may have led to a successful new pathway. Those questions might have worked well in the past, but success in the future is not guaranteed at all. Asking questions that have already been asked in the past in fact is not very likely to work again. In particle physics, people continue to ask: “What novel kinds of symmetry may I have missed?” In the early days there were lots of symmetries that people had missed, but not anymore, so you should ask different questions.
Gerard, as we get into the mid-1990s and the late 1990s, when do you start to detect a buzz that the Nobel Prize Committee is going to recognize your work and Veltman’s work?
Well, there had been a buzz like this for a long time, and it became stronger just a few years before 1999. I didn’t pay too much attention. I saw it was really getting the best out of Veltman, who got very irritated by these noises, he was getting angry that he still didn’t have this prize. I didn’t want to be like that, so I just ignored the whole thing, and that gave rise to a peculiar story. It was the summer of 1998, that people were convinced that I was going to get the Nobel Prize, and I received an invitation from my friend Antonino Zichichi. Zichichi is the organizer of summer schools in Erice, Sicily, and he does it very, very well. He is also a very good scientist, having performed excellent experiments, but also being quite at home in particle theory. And he was convinced I was going to get the Nobel Prize. And I’m sure he was also writing letters to the Nobel Committee, but whether that made a difference, I don’t know. He invited me to come to Bologna, his university, to receive an honorary doctorate, and I was quite happy and honored, so I said yes, I will come. He had a special date for that visit, and the date was—I always forget the exact date when the Nobel Prizes are being announced, but that was the moment I was planned to receive my honorary doctorate.
Only later I realized he wanted it to coincide with the announcement of the Nobel Committee, which he was convinced would come that year. But it didn’t come, and Antonino complained that that year, the Committee was very late with its announcement. He didn’t understand what was going on. But then he said, “Next year, you should come again.” So, next year, well, there was no longer an honorary doctorate, but I was still invited to come to Bologna, to give a talk at noon on this particular day. And I talked about the things I usually talk about, gravity and quantum physics, and so on. I had used the slide projector, in those days slides were transparences, put on top of a projector to have their contents, hand-written or printed, projected onto the screen.
When my talk was over, I received an applause, but the applause was longer and louder than I had expected. I thought by myself, I gave a good talk but not that good, so why this kind of applause? As it turned out, students had left the room, looked up on the internet, and found the announcement of the Nobel Committee 1999, which they had printed and projected on the screen, for everybody in the audience to see, except for me, as I had my back to the screen. They said, look at your screen, and only then I realized, that this would be a special moment in my life, that this prize is going to change it, and of course that’s what it did. Normally, the Nobel Committee gives a call to the new laureates an hour before the official announcement, but the problem was that I was in Italy, and even my secretary had not been able to locate me, I had not thought of leaving her a telephone number to reach me. It was also then that I realized the plot that Zichichi had planned for me.
I should advise anyone who expects a phone call from Stockholm that you better prepare yourself. I wasn’t prepared at all. They had tried to reach me, but they couldn’t find me. They didn’t know where I was. And even my secretary knew I was somewhere in Italy, but I hadn’t left any addresses. Even my wife, who wasn’t joining me at that moment, she was working, she couldn’t tell where I was.
Eventually, the first from home who could reach me was my sister, because my sister is a great fan of everything Italian, she also speaks Italian, and having heard that I was in Bologna, she called the University of Bologna, and asked to speak to Gerard 't Hooft. They said, “No, no, there are very important things that have to go first”, and this and that. But then she said in fluent Italian, “Yes, but I am his sister.”
And then the call was connected through, where even my wife couldn’t reach me that fast. My wife was still working around that time, and so she also didn’t know. She was doing her work as an occupational health officer. She has a medical degree, and was consulted by patients in companies, and so she was having a session with a patient. Before that session, she had had our daughter on the telephone, but then, during the session, her secretary intervened, saying “There’s an important call for you on the telephone. It’s your daughter.” My wife said, “What? But my daughter—I just had her on the phone?” But she said, “It’s very urgent.” And then my daughter explained to her mother, that some friends of her had looked up the internet and found that Daddy has a Nobel Prize.”
So, she got a shock. It caught her completely by surprise. Later, the patient said, “You know, your face changed from white to red to purple.”
The patient asked, “What’s going on with my doctor?”
Gerard, you’re un…you’re an understated and humble person. What might have been difficult for you in receiving all of this attention so quickly?
In the beginning, it was just something great happening to me. I only saw all the positive sides. Now, I see also some jealousy and some lack of appreciation around me, that happens to some extent. But it still doesn’t concern me a lot.
Yes, the most positive thing about it is what Shelly Glashow also explained. He also is a Nobel Laureate now. Shelly once gave a little speech, as you’re often asked to as a Nobel Prizewinner. He explained, you know, “You get all this money, but the American tax collectors take half of it. The most pleasant aspect of this prize is the peripherals, which is just the extras that come with it. You receive all sorts of honors and invitations. The peripherals of the prize are great, all this press interest, and your opinion is asked for everything, even on political issues.”
Well, Nobel Laureates come with as many different political views as one can find in the human population. And so, not very surprisingly, some have good political opinions; some have rather outspoken crazy ideas. People with crazy ideas are everywhere, including among laureates. Nevertheless, the laureates get much more attention, and when they say something crazy, they get much more credence than if any other crazy person said something crazy.
Gerard, on that point, have you ever used the platform offered to you by the recognition of the Nobel Prize to discuss political issues or other topics that might be important to you but have nothing to do with physics?
Well, a little bit of that is inevitable. I have one story. There was a group of enthusiastic young people who wanted to see what they can do to realize a manned spaceflight to Mars. And you know my affinity to science fiction issues is very high, so I thought it was a great idea. Let’s try to see if we can have them, well, propagate good ideas about how to send humans to Mars. Have them establish a genuine colony there. They wanted to have an ambassador, and I was happy to be their ambassador for a while.
Unfortunately, I realized only later that they didn’t do it quite right, when you want to send humans to Mars, there are many, many questions that you’ll have to be concerned about. There are many important issues and impediments that you have to confront before even dreaming to send people to Mars. One, of course, is money; this mission will be out of any proportion in its costs. They had ideas about that, but I couldn’t understand their figures, how this would approximately be enough. I said “OK, but I don’t understand your numbers.” After some time, they were ridiculed by the press. I don’t know whether they eventually could talk to Elon Musk or other people like him, but their idea didn’t go, they had underestimated the problems tremendously. I was happy to contribute to ask people’s attention for the idea that a manned flight to Mars might be a great adventure in the not so far future. Will cosmonauts go to Mars? I still like the idea, and we should see about how it can be realized.
At the same time, people like Elon Musk are being more pragmatic about this, and he’s able to generate so much money that he could even do the things that my friends wanted to realize but, of course, were unable to do. They made some initial steps, which I found interesting; they had enough money to have a space tech company investigate what technology you need to create the right atmosphere for a lasting human presence on Mars. What kind of machines do you need to create the oxygen and the other materials, and to get the temperature at the right value in a Mars dwelling? They investigated it, and found that it’s all doable, but the costs, and the weight of that spaceship will be very large, so they had to rethink again how to meet with all these obstacles. Eventually, it was way beyond their heads, but I thought it was a nice idea. It has to be left to people like Elon Musk, who’s considered by many people as a sort of eccentric. But, still, he is trying to see if he can realize some people’s dreams to go to Mars.
Gerard, in the 2000s, you started to think more deeply about some of the underlying issues in quantum mechanics.
What were those issues? What were the things that you were thinking of? And I’ll particularly come back to an earlier comment you made right at the beginning of our discussion that even 10 years ago, you don’t un…you didn’t understand quantum mechanics as well as you do now. So, I wonder if you could explain some of those deep mysteries for even you at this stage in your career?
Well, it’s a very interesting question. I never liked very much the way people talk about quantum mechanics. They talked either in terms of some pilot waves, which are around everywhere, telling particles where to go, so to speak. And the equations—again, it’s very important to have the corresponding mathematical equations. They seem to work, so there was nothing really wrong there. But the idea didn’t make sense to me, and I felt like I couldn’t imagine our universe being built like this. That cannot be right. Then, there was the idea of the many-worlds interpretation, that the wave function really generates lists of all possible ways a particle can evolve, and everything else in the universe. They come up with infinitely many ‘parallel universes’, which all are realized, forming a ‘multiverse’. Some people like such ideas. I’m sure that people like Sidney Coleman would’ve liked it because it gives a lovely source of strange science fiction plots.
But I said, “No, I don’t believe the world can be like this. In fact, I don’t even believe that quantum mechanics forces us to change our sense of logic.” This is, however, what the people of the generation before me, and even after me, had been thinking all the time, that quantum mechanics is a different way of thinking about reality than classical mechanics, and they keep repeating it time and time again. I think that’s incorrect. “But we proved that there exists no ‘realist’ interpretation,” it’s a no-go theorem. Well, you know how I think about no-go theorems. Here, I can exactly point to the assumptions that went in. They do not hold. I found out for myself that quantum mechanics is exactly the same as deterministic mechanics, but for discretized systems.
So, there are degrees of freedom, which are not forming a continuum, but they form a discrete subset of states. And then you need quantum mechanics to describe how this evolves. But many people say, “No, not only it doesn’t sound right, it is dead wrong. We proved it.” The no-go theorem was first phrased by John Bell. Using assumptions that ‘must be true’, he can ‘prove’ that there is no deterministic logic that generates quantum mechanical phenomena, because then you get contradictions. But I didn’t care much about his contradictions, particularly because I think I found equations, and those equations would actually tell us that a quantum world and a classical world are not fundamentally different.
Gerard, to put these ideas in historical context, what is your reaction to the fundamental disagreement going all the way back to Einstein and Bohr? What aspects of that disagreement are provisional, and what aspects are settled, in your mind?
I’m personally very much in favor of Einstein’s view that, actually, there ought to be a down-to-earth explanation as to why things seem to behave in this crazy way. So, Einstein was trying to convince Niels Bohr of his opinion. He failed, and Niels Bohr was given all the credit for formulating quantum mechanics, in a way people now think is correct. This became what came to be known as the Copenhagen agreement, the conviction that people arrived at in these discussions in Denmark. People found out how to think about quantum mechanics, and how to use it.
What came out was the equations. We know the equations. We’re sure the situation is very solid. If you solve the equations, you can predict as precisely as possible exactly not only with one particle; you can take many particles, you can take heavy or light particles, you can take any other kind of object. As soon as you know even approximately what kind of thing it is, you can construct a Schrödinger equation for it, and the Schrödinger equation will tell you all its quantum properties, and this works.
But then there was a question that Einstein immediately asked, and Bohr sort of denied. Einstein insisted: “There should be a reality. There should be something real going on, and whatever that is, [it] must then be handled statistically because we humans are not smart enough to find the right equations immediately. All you have to assume is that, today, we only have equations that yield statistical answers. They must be approximate equations. There are uncertainties. These are also fixed by equations. Of course, this must mean that we haven’t yet understood what really goes on. Why are you opposed to that?”
Indeed, our physics is not perfect. What else would you have expected? We are not perfect people anyway. Even Einstein is not perfect. Einstein also doesn’t know exactly what the equations are. But Einstein said, “I don’t know exactly what they are, but I can’t accept your views that quantum mechanics doesn’t say anything about what’s really going on. That it just only tells you how to calculate.” History has sided with Bohr in this issue only because Einstein couldn’t explain all his ideas in rigorous equations. And then John Bell much later came with his so-called no-go theorem that there is no way to describe quantum mechanics as if there are actually particles going from here to there, since it would force you to believe that particles can force observers what to measure and what not. Electrons in an atom seem to behave like clouds. If you try to construct a so-called hidden variable theory, forget it. It doesn’t work.
Many investigators now claim that Bohr had it right, and Einstein had it wrong. But I actually disagree. I think that Einstein basically was correct, but he didn’t have the right equations. Now I think I have the equations, at least most of them. I think it would have been easy for me to explain this to Einstein, not because Einstein would be a saint—far from it. Einstein made many mistakes, so he wasn’t a perfect person, but I think he had the right attitude towards mathematics and the right intuition about the laws of nature.
Anyway, I think, here I happen to side with him, and in this issue. And I first started to do what many people are still doing now, which is find some approximative version of Schrödinger equation where it doesn’t have to be completely exact, as long as it’s approximately exact. But then there are some cracks in the equation where you can hide all your difficulties. And that doesn’t sound right to me. Quantum mechanics is such a beautiful theory that there should be a beautiful explanation as to why it behaves in this strange way. And, well, 10 years ago, I had most of the equations I needed, but not all of them.
But then there were various technical observations that intrigued me a lot. You put them together, you get a very powerful general picture of what quantum mechanics supposed to be if you do everything right, except that you need bits of information that you don’t know. For instance, with the elementary particles, you need to know all the particles, all the particle types that exist. If you don’t, then you cannot write an exact equation, and then you are likely to make big mistakes. But of course, we don’t know all the particles that exist, because the energies we can put in a single particle are quite limited. Therefore, I cannot write down exact equations, and, for that reason, there are still big gaps in my understanding.
Now, these gaps are a little bit smaller than 10 years ago, but already 10 years ago, I wrote papers. I am still saying the same things but [I am] emphasizing more precisely what the reasons are why quantum mechanics seems to fool us. There are degrees of freedom, particles at very high energies, that we don’t know about, we don’t see them, but they do something very fundamental. These unknown particles are moving at energy scales that are far higher than we can reach with our machines today. At the energy scales where these particles are moving, the particles familiar to us are moving at zero energy. Consequently, my ‘hidden fast variables’ are also in their lowest energy states.
I’m only summarizing now my newer ideas, probably too brief to be understandable, so it’s better if I say, only in words, what’s happening: by assuming the existence of very massive particle fields that themselves behave classically, I find that these go into modes that cause the particles that we do see to behave exactly as in our quantum mechanics textbooks. This way, I obtain models that, at a super-microscopic scale, only obey classical laws, but the effects of these laws at the scale of atoms, molecules and ordinary elementary particles, look as if quantum mechanics dictates their behavior. It is this feature that I can now explain very precisely in mathematical terms. What is nice about this is that we may now return to our much better intuitive understanding of these classical laws of motion.
There always used to be a wide gap between on the one hand the theory of gravity and its quantum mechanical description, as far as we think we can go, and the Standard Model of the elementary particles on the other. Up to today, people have only extremely vague ideas on what quantum gravity should mean physically, and they make the wildest, most mystic assumptions as to what their theories really mean.
I have equations that hang together quite solidly now, telling me that this is a valid way to think, except that there is still this so-called no-go theorem by Bell. And most of my opponents—let’s call them that—agree with Bell that, no matter what I say, his no-go theorem tells them that what I say is incorrect. I can shout and jump up and down saying it’s all very simple, but I am only discovering that physics is a bit like religion. The more vagueness your theories need to hang together, the more attention and respect they seem to receive.
I now studied Bell’s work carefully, but mainly also through discussions with colleagues who studied Bell very meticulously; they could explain Bell much better what Bell had ever done himself. Before, I hadn’t for a long time paid much notion to Bell, but my opponents insisted that Bell had disproved me. My response was “No, I think he made assumptions. He assumed that no matter what state the photons are in, an observer can choose what he or she observes. I claim that that cannot be so.” Problem is that this is perceived as ‘conspiracy’ among the photons, which appear to foresee what the observers will try to observe. “This wouldn’t be science”, is what they say in their reaction.
But it is science. Only after you turn to the simplifying quantum mechanical formulation, which I call a mathematical trick, it seems as if photons are conspiring and foreseeing things. But at the level of the ultimate laws of nature that I start from, there is no conspiracy or clairvoyance at all, and that’s the only thing that counts. The point at which I do not agree with Bell, where I think it all amounts to, is that he thinks the states the photons are in, which at the very end should be described as a probabilistic distribution, must be independent of the decisions made by observers later. The observers must have ‘free will’. Otherwise, you would have ‘retro-causality’, something that he finds absurd. My point is that ‘retro-causality’ is not a well-defined concept. If you do observations, the well-defined concept should be the statistical correlations that you observe.
Now, claiming that the statistical distributions of photons in the past may depend on the settings chosen by observers later, is not so strange, particularly if you take into account that, in turn, photons themselves aren’t strictly well-defined, realistic objects, they in turn also consist of statistical distributions of the fields they represent. And the real laws of nature do not depend on statistics at all: the fields have one value, or another value, and they evolve realistically. Even 10 years ago, I didn’t have all this quite right—there were still some missing ingredients that I could fill in later. And what I filled in just only a few years ago is that the notion of energy is very important, but energy in a quantum mechanical sense, which means that when things evolve, you might generate solutions that oscillate in time. And the faster they oscillate, the higher the energy. In our machines, even in the LHC, the energy of the particles that can be observed is limited. That means that the LHC cannot follow oscillations faster than a certain beat of oscillating features of particles.
Gerard, for the last part of our talk, let’s focus these ideas on what for you and so many eminent physicists in the field regard as the holy grail that remains in theoretical physics. Of course, that is figuring out how to integrate the gravitational force so that it’s fully in agreement with quantum mechanics. And so on that point, let’s return to this theme of asking the right questions at the right time.
Because this remains such an intractable problem, because we remain trapped, so to speak, in the Standard Model, what are the questions that we’re not asking, or what are the questions that we’re asking in the wrong way? And do you see a greater misunderstanding in the way we approach gravity, or in quantum mechanics—
Yes, I see a lot of misunderstanding.
—that might allow us to understand how these things are eluding a better concept of how they should fit together?
Well, of course, I don’t have a satisfactory answer to your question. If I had, I would be doing my calculation right now. But what I’m worried about is that many people ask questions the same way, while one of my starting points is there’s no question that is forbidden. People should ask as many different questions as they can. But make sure that your question makes sense, and it doesn’t help to ask questions to which nobody can ever give an answer right from the beginning.
So, we must ask our questions in such a way that it is conceivable that some good calculator can actually calculate the answer to the question, or a good experimenter can measure it, and then hopefully the question is so good that the answer to that question makes a difference in how we are looking at things. And, of course, how to ask such questions, nobody knows. So, the best solution is to ask as many questions as possible, but don’t shy away from any kind of question. In particular, the questions people are not asking enough are the simple questions, the very basic starting points.
It’s a bit dangerous to say these things because I receive letters every day from amateur physicists who exactly say the same thing, but who have not understood what science is telling us about elementary particles. This must be understood first of all. Only then you are in a position to ask meaningful questions, I believe.
So, one thing that you can do wrong is ask the same questions as thousands of people have done before you. Then the odds that you find something special is going to be very small. So, you have to see if you can ask questions different from what other people are asking. And I think there are enough such questions. Unfortunately, many amateurs who send me mails, come with metaphysical or mystical questions that I cannot handle at all.
One important notion is the discretization of physics. Some variables will take the form of dice, allowing for just 6 different states to emerge (or something like that). Quantum mechanics, as its name may imply, is about the mechanical laws obeyed by discretized variables. This is a much deeper insight than saying that quantum mechanics appears to generate uncertainties, these uncertainties just originate from imprecise formalisms, badly defined variables.
Indeed, I suspect that quantum mechanics is about data that are not only deterministic but also discretized. There is discrete data everywhere, in particular these very high energy objects. They go around so fast that they find it more difficult to go into a different state. So, there’s going to be limitations on fast oscillating things, and that is what quantum mechanics said from the very beginning. If you have a wave at high frequency, then the energy of the wave is constrained in terms of big units of energy.
Discretized physics is much harder than when all data are beautiful, smooth, continuous fields, and this makes our subject difficult. I suspect that space and time should not be described by real numbers because you need an infinite amount of memory space to describe any real number. You need to describe all decimal places of all real numbers that you encounter. That’s an infinity to a high degree. The ultimate theory of nature cannot be like that. But it’s very difficult to write down one whole set of equations to describe properly a discretized world.
A notable example that has been studied a lot is theories where the physical variables are not defined on a space-time continuum but on a lattice. Such systems are very suitable for studies on a computer. Then a question you can ask is, what happens if we rotate a lattice by 47 degrees or 53 degrees? How does the theory look in these rotated coordinates? Well, if I rotate it, it looks different. In the real world, the equations seem to stay exactly the same no matter how you rotate the coordinates. Nature’s laws are said to be rotationally invariant. But how can this be if you have a space-time lattice? That question is easy to ask but very difficult to answer. This is a very difficult obstacle that we have to deal with. There are many such obstacles that tell you that perhaps you should give up. This is not going to work.
So, then the next question is, how can we ask questions that we can answer? Asking questions that nobody can answer, is easy. Asking questions that anybody can answer is also easy. We want to ask questions that look very easy but are not so easy to answer, while also not impossible to answer. How to find such questions, that’s a big problem. So, we have to sit down and think very carefully about getting the right kind of questions.
Gerard, for my last question, perhaps it’s the most difficult because we’ll look to the future, and by definition, it will have to be speculative. But assuming that we get there, that we ask the right questions, that observation and experiment do lead us in these directions, when gravity and quantum mechanics are integrated, what will that look like, and how will we even know when we get there?
I don’t think we’ll get there any way soon, and there are many obstacles in the way. But ultimately, we hope to find more answers, trivial ones, expected ones, but also surprising ones. The one question that’s very, very far away for us now is how did the universe get started? Could it have started with just one single state? What kind of state is that? And how could we ever guess the laws of nature correctly?
The answer to such questions might ultimately be like the one written in an old science fiction story—I forgot who wrote the story. A computer had been working day and night to answer a complicated question, and after many years, finally it came with the answer: 47. The answer was 47, but nobody could understand it, they all had forgotten what the question was. I like that story because it’s a little bit like the way I think about asking questions. A possible answer to the question how the universe got started, and what laws does it obey, could be that the universe is a set of numbers. So, think of numbers one, two, three, and begin with number zero. The number zero describes the Big Bang. What else can it do?
Take the integer numbers, one, number two, number three, and notice that the number six is the product of the numbers two and three. Say that the numbers two and three interact to get to the number six. And on it goes until you get very complicated numbers with special properties, large prime numbers, special numbers, and so on, after which some of them will eventually look like the particles in some universe. Some particles have different properties than others. Some stars have different properties than others. All these are just comprised in one gigantic big basketful of numbers.
So, now, you can say, “I’m religious. Who was the creator of these numbers?” Well, the answer to that would be, “No, you don’t have to be religious because the numbers have always been there. The numbers are just numbers. So, the world of all the numbers is there, and all we have to do is figure out how they behave.” No need for any God. And that could be the universe that we live in. As I said, this is a possible answer to your question. It is a bad question because nobody can check this answer, and it will take quite a while for anybody to answer—to make sense of such an answer. For that reason, my question is a wrong question. But it’s just something to keep in your mind.
It’s a kind of view on reality that could be the ultimate view. There can’t be anything beyond that. Once we realize that the universe is just a set of numbers, we’re there. There’s nothing else you can ask. What you can ask, and indeed you should ask next, is: “how do these numbers generate the world that we know today, and what are the intermediate steps?” Why is the proton 1,836 times as heavy as an electron? You can still ask such questions in my number-universe. I have no idea what the answer to that question would be, but that eventually would be the new set of questions that people would have to answer. But the whole thing makes sense only if you know how to relate the set of all integer numbers with phenomena that we see in our universe around us, and that will be a tough problem for a long time.
Gerard, it has been absolutely captivating listening to all of your insights and explanation of your science over the course of your career. I’m so happy we were able to do this, and I want to thank you so much for so generously sharing your time with me.
Thank you, David, for your questions and listening to my replies.