“String theory is a religion”, says Nobel Prizewinner Martinus Veltman. Theoretical physicist Robbert Dijkgraaf however thinks string theory inevitably follows from the historical development of theoretical physics. “I feel that the mathematical framework of string theory is too solid to eventually crumble. We are able to ask questions within it about space, time, black holes and the big bang that we can’t ask in any other theory.”
This article has originally appeared in the Dutch science monthly Natuurwetenschap & Techniek (september 2003)
Martinus Veltman: “If we do away with the experiments, science becomes religion. From that moment on it won’t be the facts that count when we’re trying to determine what’s true, but the opinions of someone who’s been elected pope.”
‘Public relations’. That’s what the theoretical physicist Peter Woit identifies as string theory’s biggest success in String Theory: An evaluation. A robust judgement of a fundamental theory of physics that has been the focus of international research for more than twenty years. But he is far from alone in his criticism. The Dutch Nobel Prizewinner Gerard ‘t Hooft writes the following about string theory in his book In search of the Ultimate Building Blocks: “What we have now is a kind of conjurer’s book and you have to be a magician to use it to make oracular pronouncements. That isn’t what nature is really like.” His co-Nobel Prizewinner, Martinus Veltman, explains that he disapproves of the fact that string theorists “have been fiddling about for decades with a theory that makes no connection whatsoever with the real world.”
Of course the critics meet with rebuttal from the string theorists themselves. According to Edward Witten, winner of the Fields medal (a kind of Nobel Prize for mathematics), it’s a fact that gravity follows logically from string theory “one of the biggest theoretical discoveries ever made”. And Cumrun Vafa of Harvard University thinks string theory offers “the best insight into the universe we’ve ever had”.
String theory began to make headway as the new theory in physics in the 1980s. The fundamental assumption was that pointlike particles such as quarks and electrons should be perceived as minuscule, one-dimensional vibrating strings. A string is approximately as long as the Planck length, the smallest scale of space. The way in which a string vibrates produces the mass and the charge of a real particle. Also the special particles for mediating fundamental forces – gravitons for gravity, gluons for the strong force, photons for the electromagnetic force and vector bosons for the weak nuclear force – are connected with the strings’ distinctive patterns of vibration.
Every force of nature and all matter should arise from the characteristics of vibrating strings. This assumption of string theory proves quantum mechanics and the general theory of relativity (the theory of gravity). Such an idea appeals to every physicist. For the ultimate challenge in theoretical physics is to unite the theory for the very small, quantum mechanics, with the theory for the very large, gravity. According to many, string theory is at the moment the only realistic theory capable of giving a quantum-mechanical description of gravity.
Initially it seemed there were five different string theories in existence, but in 1995 theorists discovered that the five theories were components of one larger theory. This so-called M-theory also contains, besides the one-dimensional strings, the two-dimensional frisbees (two-branes) and three-dimensional clots (three-branes). M-theory is an eleven-dimensional string theory that contains ten space dimensions and a single time dimension. But the theory is still incomplete. No one knows as yet how the ten space dimensions roll up into our familiar three dimensions. No one can even write down the exact equations of the theory. Only approximate equations exist, and these are so difficult that they have only been partially solved. Dutch researchers like Robbert Dijkgraaf, Jan de Boer and the twin brothers Erik and Herman Verlinde play a seminal role in the development of string theory.
Expansion without improvement
Sitting in the garden of his home in Bilthoven in the Netherlands, Emeritus Professor Veltman explains his objections to string theory. “How does one know if something’s good or not? When something’s good it keeps improving. That’s not the case with string theory. In forty years I’ve often seen theories that in time only got worse. Mathematical antics are constantly required to save the theory. That’s also the case with string theory.”
The most important objection opponents raise to string theory is that it has not yet made a single experimental prediction. Besides which, the energies necessary for a serious test would have to be so high that with the present technology we would need a particle accelerator as large as the Galaxy.
Professor of Mathematical Physics Robbert Dijkgraaf of the University of Amsterdam has been working since the 1980s on string theory and is prepared to counter the criticism. At the university’s temporary accommodation in the Wibautstraat in Amsterdam he comments: “Predictions for effects at low energy do exist. Supersymmetry for example. The next round of experiments could discover this feature. String theory further predicts the existence of extra space dimensions. The past few years it has become clear that these extra dimensions could be much larger than the Planck length. This means that quantum-gravitational effects, like the production of microscopic black holes in particle accelerators, could take place at much lower energies. We only need the huge energies in the remote corners of string theory, where it behaves most simply.” Dijkgraaf did his doctoral research in Utrecht with Gerard ‘t Hooft, who in turn did his doctoral research with Martinus Veltman. A difference of two generations of research therefore, a mere thirty years in age.
The difference is very evident in their ways of thinking about physics. “Mathematics has historically proven to be a good guideline, in my view, to formulating physical theories”, Dijkgraaf says. “It is true that it should not be the starting point, but it certainly is an extra ingredient. Therefore we find symmetries and symmetry breakings in solid-state physics, astrophysics and elementary particle physics. Symmetries are such excellent principles because they are general structures. Mathematics typically describes these kinds of structures. I think that the most fascinating fact about the world we live in is that we have such a strong hint that mathematical structures form the basis of nature.”
“The difference between string theorists such as Dijkgraaf and me”, Veltman says, “is that I couldn’t care less about mathematics. I don’t have faith in it. We need mathematics as an instrument, but it does not provide us with real insight into nature. There is only one criterion for a good physical theory and that’s solid experimental facts. I’ll be the first to congratulate string theorists if they come up with an experimental prediction that is later corroborated. But they don’t have one and I haven’t seen them make any progress for twenty years. On the contrary: they have a negative record because they are unable to calculate a single experimentally known parameter of the present theory, such as the mass of an electron.”
Due to the work of Veltman and ‘t Hooft the mass of the top quark was predicted and later experimentally measured. A big success for the Standard Model, which is at present the best description of fundamental forces and elementary particles in nature. String theory has not produced a similar prediction. The framework of the Standard Model does by definition form part of string theory.
Veltman describes the developments in the 1960s and 1970s, when all kinds of unexplained data resulted from experiments. “These generated new ideas about nature. With the exception of the existence of neutrino masses there hasn’t been any more new experimental data to help further theory development. That’s an enormous impediment and it is an important difference with a great deal of the time when I was working.”
Theoretical physics and experimental physics need each other, Veltman says. “Experimental physics is the laboratory of theoretical physics. Theoretical physics is not worth anything until the laboratory has shown that it’s correct. I think that the amount of information we have about nature just isn’t large enough. Something’s missing. We don’t understand why all the known elementary particles belong to three families that have the same structure. What theorists are attempting at the moment is probably just like imagining Max Planck trying to discover quarks around 1900 with what he knew then. It’s not possible. He didn’t even know that protons and neutrons existed.”
Dijkgraaf thinks it’s still much too early to pass judgement on string theory. “Just like with a jigsaw puzzle we started by working on the edges of the string puzzle. That’s where most of the pieces of the puzzle are already in place. On the inside we still see many gaps. String theory must describe everything, all forces, all particles, black holes, the big bang. That’s quite a lot. We can’t switch on the big string machine to make very specific predictions, because it just isn’t complete yet. Sorry. On the other hand it is an important fact that at the moment it is the only functional theory of quantum gravity. Many important questions in physics, especially in cosmology, and all related to directly observed phenomena – for example vacuum energy and black holes – require such a theory.”
What the critics insufficiently appreciate according to the Amsterdam mathematical physicist is that the theory allows questions to be asked that can’t be posed in any other framework. “A number of the facts we take for granted aren’t obvious at all. Why do we live in an expanding universe? Why do we have three space dimensions? Why does time have a beginning? Why was there a big bang? Why does dark matter exist? It’s a great achievement to be able to we ask these fundamental questions within string theory and to be making so much progress in answering them.”
“You can indeed write down as a positive point that string theory can ask certain questions”, Veltman says. “But I could easily invent a theory in which I could also ask all kinds of new questions. As yet string theory is a heap of mathematics. As a physical theory it must simply make predictions, and if it doesn’t, then it’s irrelevant.”
The emeritus professor and Nobel Prizewinner goes back a few centuries in time. “Galileo came into conflict with the church when he said that the Earth orbits around the sun. In those days one was limited by morality and religion. The natural sciences only got off the ground when people started to take hard facts seriously instead of the opinions of the church. Start from known facts, construct a theory and then try to predict new facts, that’s the essence of physics.”
Veltman: “Do string theorists want to take us back to the age of religion in which a person’s opinion that a theory is very beautiful and elegant is more important than the experimental facts? Should we dispose of the principle that scientists should predict numbers? If we do away with the experiments, science becomes religion. From that moment on it won’t be the facts that count when we’re trying to determine what’s true, but the opinions of someone who’s been elected pope. Something’s only all right if he gives his blessing. People will start to play the role that should be reserved for nature. That’s exactly what string theorists are doing now. Who decides whether string theory is elegant? It’s only an opinion. All those arguments about elegance, beauty, how natural it is, etcetera are illegitimate arguments that don’t belong in the profession. Unfortunately Einstein introduced them himself.”
“According to physicist and Einstein biographer Abraham Pais, Einstein didn’t achieve any more new results after 1920 because he started believing more in mathematics than in physics. I think that should serve as a warning to string theorists.”
“The suggestion that string theorists don’t any longer want to make predictions is simply absurd”, Dijkgraaf says. “But in order to make a prediction based on your theory you have to understand how the theory works. To discover how quantum field theory works has taken us about fifty years. It’s just not realistic in the case of a much more complicated theory like string theory to suddenly become impatient and to start saying that it’s not leading anywhere.”
Theoretical physicist David Gross, who works both in conventional physics as well as in string physics has described the present situation as follows: “It used to be that as we were climbing the mountain of nature the experimentalists would lead the way. We lazy theorists would lag behind…We all long for the return of those days. But now we theorists might have to take the lead. This is a much more lonely enterprise.”
The big bang in reverse
One of string theory’s successes according to Dijkgraaf is that within its framework a microscopic black hole is indistinguishable from an unstable particle. “The fact that string theory can handle black holes proves that it is a mature theory of quantum gravity. With string theory we can give a perfectly consistent quantum-mechanical description of a black hole. A black hole is a kind of big bang in reverse and this makes us hopeful about eventually also tackling the question of what happened at the time of the big bang.”
If he had ten fundamental theories about nature, Dijkgraaf would treat all ten of them with the same consideration. “But we don’t have ten. I consider string theory to be the only serious candidate at the moment. Every physicist wants to deflate a theory straight away but that hasn’t happened to string theory yet. Our understanding of the theory has only improved spectacularly. We have avoided all of the many internal inconsistencies that can plague theories. It is an enormous challenge to establish whether string theory, which incorporates all the ingredients of modern physics, does or does not actually describe our world.”
In the middle of the 1980s Nobel Prizewinner Sheldon Glashow wrote about string theory: “The theory depends for its existence upon magical coincidences, miraculous cancellations and relations among seemingly unrelated (and possibly undiscovered) fields of mathematics. Are these properties reasons to accept the reality of superstrings? Do mathematics and aesthetics supplant and transcend mere experiment?…Superstring theory is so ambitious that it can only be totally right, or totally wrong. The only problem is that the mathematics is so new and difficult that we won’t know which for decades to come.”
A decade later Glashow was milder because non-string theorists had made no progress whatsoever in ten years’ time. He saw string theory then as ‘the only game in town’. Veltman confirms this, but he does get worked up about it. “Why is it ‘the only game in town’? Just because so many smart people work on it internationally doesn’t prove a thing. The majority of researchers are simply hangers-on. Incapable of finding their own way they simply tag along with Witten (one of the driving forces behind string theory) and his associates. If I were young today, I would attempt to find a different way from string theory. It is of course a hellish job but too few young researchers try to do it.”
Veltman gives an example based on his own research history. In the late 1960s everyone thought the field theory didn’t have a leg to stand on. All sorts of other wild ideas were gaining ground and one theory in particular got many supporters. “Then I too sometimes thought: if so many people are working on that theory, then perhaps there must be something in it. But when I started calculating I encountered one unsolvable problem after the other. Finally I said to myself: ‘let the others trudge on, I’m going my own way’” And that did get results. The Nobel Prize-winning work by Veltman and ‘t Hooft from the early 1970s brought field theories back to the fore and they still form the basis of the Standard Model.
Dijkgraaf thinks Veltman’s sneer at young researchers is unfair. “My impression is that it is precisely the youngest generation who are working on various aspects of the high-energy physics, some of them are inspired by string theory, such as extra dimensions, but others aren’t. Some researchers only take parts of string theory and puzzle on with that.”
The initial conditions of the universe
String theory has an exceptionally rigid mathematical structure. There is no room for fine-tuning the whole on the basis of the experimental results by adjusting all kinds of nuts and bolts. A theory of everything or nothing. “In general in physics we are used to theories that have room for manoeuvre”, says Dijkgraaf. “You adjust the model therefore as long as is necessary for it to describe reality. I’m not really satisfied with this. I think that the fact that string theory requires so little experimental input and that it attempts to be as unique as possible is exactly why it’s such an attractive idea.”
Choices can slip into string theory through the back door however, for example the initial conditions of the universe, or the way ten dimensions roll into one. “Most probably string theory has many non-equivalent basic states, so it’s not clear that the theory predicts unique initial conditions of the universe”, the mathematical physicist explains. To predict the mass of the electron string theorists might need the initial conditions of the universe.
Veltman: “They say that with the particle accelerator Large Hadron Collider (LHC) that’s being built in Geneva they might be able to prove supersymmetry. That’s an essential part of string theory. But I’m cynical enough to say that if the LHC doesn’t find evidence of supersymmetry, the string theorists will fit that into their theory again. It’s the same every time. Moreover it’s not even clear that the principle of supersymmetry holds up. It’s also already been adjusted twice.”
The answer is just around the corner
Popular scientific literature, but also string theorists themselves have often been guilty of proclaiming string theory the potential Theory of Everything. “Yes, that seems to sell well”, is Veltman’s reaction. “Some claim that they are looking for one equation that describes the whole of nature. But we don’t even know whether there is a single equation for everything! The only thing we are looking for is a description that fits well. We’re free of all religions!”
The late physicist Richard Feynman who died in 1988, and with whom Veltman sometimes discussed these matters in the 1960s, also had strong doubts about string theory, whose early years he experienced. Sometimes he said that perhaps he was too old for it. But the theory was too distant from experiment for him. He also disapproved of the rhetorical language of a Theory of Everything. The Feynman biography Genius quotes some of the interviews with the flamboyant, extremely creative American theorist, who was one of the most influential physicists of the 20th century: “People say to me, “Are you looking for the ultimate laws of physics?” No, I’m not...I’m just looking to find out more about the world and if it turns out there is a simple ultimate law which explains everything, so be it, that would be very nice to discover. If it turns out it’s like an onion with millions of layers and we’re just sick and tired of looking at the layers, then that’s the way it is...Whether or not nature has an ultimate, simple, unified, beautiful form is an open question, and I don’t want to say either way...I’ve had a lifetime of people who believe that the answer is just around the corner.”
James Gleick. Genius – Richard Feynman and modern physics. Abacus, 1992
Brian Greene. The Elegant Universe – Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. Vintage Books, 2003
Gerard ‘t Hooft. De bouwstenen van de schepping – Een zoektocht naar het allerkleinste. Amsterdam: Prometheus, 2002. (English title: In search of the Ultimate Building Blocks.)
Martinus Veltman. Facts and Mysteries in elementary particle physics. World Scientific Publishing, 2003