In collaboration with American John Schwarz, the British theoretical physicist Michael Green—a professor emeritus at the University of Cambridge and a professor at Queen Mary University of London—published two papers in 1984 that led to the so-called first superstring revolution. The studies fixed mathematical inconsistencies in string theory, which hypothesizes that the universe is made up of microscopic filaments—called strings—that vibrate in up to 26 dimensions of space-time. The papers simplified the introduction of fermions, one of the two major types of elementary particles (the other is bosons), to string theory and revived interest in a field of study that was in decline.
Originally formulated in the late 1960s, in its early versions string theory included only bosons. This category covers particles that transmit electromagnetic, strong nuclear, and weak nuclear forces, such as photons, gluons, and Z and W bosons. These forces are absorbed or emitted by fermions, the matter particles (electron, muon, tau, three types of neutrino, and six types of quark). “What John and I did was reformulate string theory to include both fermions and bosons and thus include supersymmetry,” explains 73-year-old Green. “Fermions behave very differently from bosons.” Supersymmetry predicts that each known fermion has a hypothetical boson as a supersymmetric partner, sharing its mass and other features—and vice versa.
Green first visited Brazil in early February. He was in the city of São Paulo for events at the International Center for Theoretical Physics of the South American Institute for Fundamental Research (ICTP-SAIFR), based at the Institute for Theoretical Physics at São Paulo State University (IFT-UNESP), where Green has recently assumed the presidency of its scientific council. In this interview, he talks about the importance of his work and string theory.
String theory is not a theory in and of itself, but a mathematical framework for discussing many different theories
What are your duties and plans as president of the scientific council of ICTP-SAIFR?
I am still learning about the institute, which is new and quite ambitious. I have known Nathan Berkovits [director of ICTP-SAIFR] for many years and it is amazing how he managed to set up a research center with such broad interests. The focus of mathematical sciences is shifting. There is a lot of potential to work on topics related to biology. Other areas of theoretical physics, which were already interesting before, are now even more interesting. I am still learning about the financial limitations of the institute. With more money, we can expand the areas of research.
Did you have any formal relationship with ICTP-SAIFR before being appointed to this position?
No. I have been on similar committees at other institutes. There is a similar institute in Bangalore, India, where I am still on the committee. It is structured differently from the ICTP; it is larger as are its scope of activities. The central issue is how to secure revenue for the future. If there are uncertainties about future funding, that makes it difficult to attract people to the institute.
Could you expand on why your work with John Schwarz in 1984 was so significant in the field of string theory?
Those articles were the zenith of our collaboration. At that time, John [of the California Institute of Technology, Caltech] and I had been working together for five years. Every year, we spent three to four months together, either in the United States or in the United Kingdom. String theory has been around since the late 1960s, but interest in the area had dwindled in the mid-1970s. This was because of a series of developments in an area we call quantum field theory, a basic tool for building theories with elementary particles. In the early 1970s, for example, the Standard Model emerged, explaining most of the observations made in particle physics experiments. Soon after, there were theoretical developments in the area we call supersymmetry. These advances attracted to those areas people who had worked on early versions of string theory. But John and I—alongside a few other colleagues—remained interested in string theory. At the same time, those working with supersymmetry faced great difficulties. Then, in 1984, we discovered that string theory prevented the occurrence of problems that were also affecting studies on supersymmetry and other areas.
What were the problems, exactly?
They were violations that we call anomalies. There are certain properties of classical physics, formulated before quantum theory, that are considered sacred and cannot be destroyed. This is the case, for example, with the laws of conservation of energy and electrical charges. In quantum systems, these laws can be violated—but not in classical systems. Some anomalies are acceptable. Others, such as the violation of energy conservation, mean trouble. These are serious inconsistencies for a theory. The Standard Model is a beautiful theory; it has no anomalies. But when attempts were made to take it further and create a theory that explained all the forces of nature, the attempts presented anomalies. We were always told that we would find anomalies in string theory as well. But in 1984, we did some calculations and saw that string theory avoided this kind of problem in a very smart manner.
At that time, was it still difficult to put together a string theory that contained fermions and connected them to bosons through supersymmetry?
What John and I did was reformulate string theory to include both fermions and bosons, thus including supersymmetry. Fermions behave very differently from bosons. The claim that they are linked by supersymmetry is not obvious, and it is even less obvious from an experimental point of view. To this day, there is no direct experimental evidence that supersymmetry exists in nature. The reason people were so excited about our work was quite theoretical. A theory that includes supersymmetry has mathematical properties that make it possible to understand things in a deeper way than using a theory without supersymmetry. That is why the connection between string theory and mathematicians has become so strong. The problem is that supersymmetry is always broken in physics experiments.
Could you explain this further?
This is a difficult concept. There are known symmetries in physics that we do not see. Let me give you an easy example. Imagine a ball placed on top of a symmetrical mountain. The ball may roll down in either direction. While the ball is at the top, there is complete symmetry between the equations that describe this situation. But we know that the ball will roll down one of the two sides, where there are valleys. Once it rolls down, the symmetry will be broken. What we see in nature with the experiments is like the ball in the valley. At the top of the mountain, the ball is very unstable. The idea of breaking symmetry is quite common in nature. If supersymmetry [of bosons and fermions] does exist in nature, it must also be that way. For each boson-type particle, in theory there should be a fermion-type particle with the same mass. But we know that this is not true; there isn’t a double for every single particle. Therefore, if supersymmetry does exist, it must present itself in a broken manner. The question then is: can we understand it?
If we can only observe supersymmetry once it has been broken, how can we know that it was intact before?
This is precisely one of the criticisms of supersymmetry. People defend this idea for various emotional reasons, such as the belief that, in some fundamental way, all particles are interrelated. Today, supersymmetry is the only way to establish this relationship between bosons and fermions. In addition, the mathematical properties of supersymmetry theories are so beautiful. Mathematicians consider them beautiful—which is not to say the physics behind them is solid.
Is the equipment available to physicists today powerful enough to find valid experimental evidence of string theory?
The issue is that we do not know what the predictions of string theory really are. When Einstein thought about general relativity, there were several assumptions. As soon as he formulated his famous equation, he immediately recognized that it would explain the anomalous precession of Mercury’s orbit and the deviation of light during a solar eclipse.
The idea that space is a static backdrop is a good approximation. Space vibrates much like the particles moving in it
Would it be correct to say that string theory is the search for a theory of everything, an attempt to move beyond the Standard Model and unify relativity with quantum field theory, something that has not yet been done?
I don’t think so. It is not a theory in and of itself. In general terms, it is a structure, a mathematical framework, for discussing many different theories. Let me give you an example. People talk about quantum field theory. It was developed after quantum mechanics was proposed. Paul Dirac [British theoretical physicist who won the 1933 Nobel Prize in Physics] was one of the first to talk about quantum field theory. It does not define a theory, but an approach to theories. I believe string theory is similar. It contains a quantum field theory, such as Einstein’s gravity, or electromagnetism. It represents an interesting way to talk about portions of theoretical physics. Furthermore, I ask myself: what is everything? Everything is what we believe to be important today, but it does not include what we may still discover. It is not a particularly useful concept.
The image relating strings vibrating in different dimensions to different particles is very elegant. But will this idea prevail?
I sincerely hope that string theory will lead somewhere, but I suspect we are not likely to see any strings. We need a new language. In order to think of a string vibrating in space, there needs to be space first. The idea that space is a static backdrop where particles vibrate is a good approximation. We know from quantum gravity that space is dynamic, in the sense that its geometry vibrates like the particles moving in it. I will draw a rough analogy. Imagine a microscopic string on a sheet of paper. Seen through a powerful microscope, the paper has a fine structure that is neither homogeneous nor continuous. There are variations in its mesh. Therefore, if we place a minuscule string on the paper, it will also not be a continuous object. After all, there are fluctuations in the paper itself. The idea that it is possible to separate the string from the space it moves in is an approximation used in perturbative string theory. In it, the assumption is that the background is smooth and has no structure. This approximation allows the creation of the quantum vibrations of the strings, but not the quantum vibrations of space, whatever that means. This is the problem of quantum gravity. Although its meaning is not known, quantum mechanics requires, in its most general sense, that the idea of continuous space be undone at very, very small distances.
From 2009 to 2015, you held one of the most internationally recognized academic positions: the Lucasian Chair of Mathematics at Cambridge University, previously occupied by Stephen Hawking and Isaac Newton between the end of the 17th century and the beginning of the 18th. What were your responsibilities in that role?
If Hawking [1942–2018] had not existed, no one would have heard of the Lucasian Chair, even though it has been filled by icons such as Isaac Newton [1642–1727] and Paul Dirac [1902–1984]. Hawking was a great physicist who lived with a serious health issue, which is unbelievable. That is one of the reasons why he is well-known. Many people know nothing about the physics he created. There are no responsibilities in particular; it is just a title. And you must retire at 67. In Britain, no universities except for Oxford and Cambridge impose a retirement age. They work much like in the United States, where you can remain for as long as you want. In exceptional situations, the institutions may impose retirement. Oxford and Cambridge argued that they are exceptions and that their faculty structure would be greatly affected without the imposition of a retirement age. People tend to go to Cambridge or Oxford and never leave. I believe that the retirement of professors is a good thing for universities, because there are few jobs available for younger researchers.
When it was created, the Lucasian Chair functioned as a sort of fellowship, right?
As I said, nowadays it is simply a title. Funding for the Lucasian Chair was donated by a man named Henry Lucas [1610–1663], a member of parliament, in the 17th century. Newton was the second person to occupy the position. The money was invested to pay for salaries, but that funding has not been around for a long time. The resources to pay the Lucasian professor no longer come from that fund. Historically, some who occupied the Lucasian Chair retired quickly in order to take on better-paying chairs. And people don’t care much about titles, they care about money. Although it is a mathematics chair, many of its occupants over the last century have been theoretical physicists.
Moving on to a more general topic: How will Brexit impact science in the UK?
No one knows for sure what is going to happen. For those who work with basic physics, like myself, the need for funding is modest. We need money to travel and to have PhD students and postdoctoral interns. Our budget is small when compared to that necessary for experimental physics. Right now, a large portion of that funding comes from the European Union, through the European Research Council (ERC) and the Marie Curie Fund. It seems that Britain will not be part of these entities, although there are rumors that, like Israel and Switzerland, we could become associate members. The British government has promised to dramatically increase funding for science. A few weeks ago, Dominic Cummings, Prime Minister Boris Johnson’s chief advisor, said he wants to put more money into math. Whether that will really happen… Times are very unpredictable. In terms of funding for science, Brexit may even be good, after all, but it will be terrible from a social point of view. It will separate us from Europe. I hope not all ties are cut. Academic collaborations are very important.