# Focus on research: theoretical physicist Jan de Boer

Photo: Bob Bronshoff

Armed only with pen and paper, theoretical physicist Professor Jan de Boer addresses the largest unsolved issues in science. In the course of his quest for a theory of everything, he rolls up dimensions and dreams of worlds in which no gravity exists!

Working with oscilloscopes in a laboratory isn’t quite Jan de Boer’s thing. ‘I can’t relate to experiments at all; I used to hate practicals during my studies. I’m just not skilful at that type of thing, I don’t like doing odd jobs about the house either’, he laughs. De Boer prefers theoretical problems. ‘I heard about string theory for the first time when I was a student. It was just becoming a popular theory then. I worked my way through a book on string theory together with my supervisor, and that’s how I ended up in this field.’

### Infinite gravity

There are two successful theories in physics, one describing the world on a large scale, and one on a small scale. Everyone is familiar with physics on a large scale: gravity. The theory of gravitation as developed by Newton and Einstein works just fine in daily life. It describes neatly that if you let go of something, it will fall down, and that we ourselves don’t fall off the earth. It also works outside the earth: the theory of gravitation describes with great precision the earth’s orbit around the sun and even the movement of the star systems.

However, when you zoom in on particles, even further than molecules and atoms, the theory of gravitation no longer works so well. The particles that atoms are built up of are considered to be point particles, or miniscule points with an extremely small mass. Since the particle is so small, you could argue that it has no volume, but because it does have mass, its density (the mass per volume) is a figure divided by zero, and that is infinite. Point particles therefore have infinite density. And infinite density means infinite gravity, which is where the problem arises, because at small distances the force of gravity hardly plays any role at all, let alone being infinite. Other forces (the strong nuclear force, the electromagnetic force and the weak nuclear force) predominate at small distances. These forces and the corresponding elementary particles are described well by the so-called Standard Model. ‘At small distances this theory works excellently, describing, for example, why your hand doesn’t drop through a table’, according to De Boer.

So there are two successful theories which work on different scales: the theory of gravitation and the Standard Model. ‘On earth, you never need both theories simultaneously’, explains De Boer. ‘There are conceivable situations where this might be so, but they are very extreme. For example, when the universe was formed, and in black holes. It is conceivable that events occur on earth for which both theories are required simultaneously, but this is still unclear and depends on how the world is actually made up.’

### Elastic bands

Separately, both theories are very successful but no one has yet succeeded in combining them. ‘The big challenge to theoretical physics is to combine them to make one consistent theory.’ The problem is that gravity doesn’t fit into the Standard Model if you consider elementary particles to be point particles. One way to avoid infinite gravity is to consider the particles as vibrating elastic bands, or strings, and not as points. This is exactly what string theory does. The faster a string vibrates, the higher its energy. And since energy is proportional to mass, quickly vibrating strings make it possible to describe particles with a higher mass.

In string theory, a string has various forms and can vibrate in all dimensions in all directions – and there are lots of those! ‘The standard string theory is only consistent in ten dimensions instead of four.’ Physicists describe the world with four dimensions, three for direction and one for time. These four dimensions make it possible to describe any point in space at any moment. ‘We cannot see the other six dimensions because we fold them up so that they become awfully small, so small that we are unable to measure them. There are very many ways to fold six dimensions up into a small ball like that.’

### 'Krakeling'

A coffee cup and a donut both have the same topology, which depends only on the number of holes.

If you wanted to roll up two dimensions, you could do so in various ways. You could make a ball out of a two-dimensional piece of paper, but you could also make a donut shape, or a shape with three holes, like those Dutch ‘krakeling’ biscuits. These are all two-dimensional surfaces with a different topology: they each have a different number of holes: zero, one and three.

These are two-dimensional surfaces, but you can also do something similar with six-dimensional surfaces. Just like a two-dimensional sheet of paper, you can fold them up to something finite. In two dimensions, the ways in which you can fold are limited. In fact, the number of holes (the topology) in the various surfaces is the only distinguishing factor. A coffee cup has the same topology as a donut. The more dimensions you have, the greater the number of possibilities. ‘Drawing them is no longer an option!’, says De Boer, laughing.

‘It is difficult to explain why exactly ten dimensions are necessary for string theory. If you calculate using a model with less than ten dimensions, you get inconsistencies. For example, the result of a calculation is that the chance for a certain event is greater than one, which is obviously nonsense.’

‘According to some people, string theory fits together so neatly that it must be true’, says De Boer. However, the theory hasn’t yet been verified experimentally, and it doesn’t look as if that will be possible in the near future either. Nevertheless, a few practical experiments are being carried out, the outcome of which could be very important to Jan de Boer. At Geneva, a large accelerator is being built in which particles can be fired at each other at the speed of light. ‘This accelerator, the LHC, will be the most powerful microscope in the world, attaining perhaps 10 to the power of minus 20 metres. That is still many orders of magnitude away from the expected size of the strings: they are 10 to the power of minus 35 metres. We probably won’t be able to see strings directly.’

So what’s so exciting about this experiment? ‘Of course, it depends on how the world fits together, but they may find a new particle, perhaps even a super-symmetrical particle’, says De Boer enthusiastically. ‘This wouldn’t prove that string theory is correct, but would certainly be a strong suggestion that we’re on the right track. It is also possible that they find signs in the accelerator indicating that there are indeed more than four dimensions in the world. If they are actually able to see such phenomena in the accelerator, we really will need string theory.’

### Restricted

‘String theory didn’t originate as a ‘theory of everything’, it started out as a phenomenological theory to describe certain experiments. Quarks, which protons and neutrons are built up of, don’t exist individually in nature. They are restricted and can only exist in pairs or threes. The way they are kept together is described by means of a sort of string. String theory was, thus, developed with a different view in mind.’

At a certain moment a better theory was developed for quarks, Quantum Chromodynamics (QCD). This theory is now part of the Standard Model. ‘String theory became somewhat deadlocked, with only a small group of scientists working on it worldwide, who were seen as being somewhat eccentric. They discovered that strings can only exist in ten dimensions, and that strings could also provide a theory for gravitation. It was only at the start of the ‘80s that they succeeded in thinking up a really good string theory. Since then the subject has been booming.’

De Boer becomes enthusiastic as soon as he starts to explain the possibilities of string theory. ‘An interesting possible scenario with string theory is the Brane World Scenario. A surface can also be called a membrane, and a surface with an arbitrary number of dimensions is called a brane, hence the scenario’s name. It’s not really such an exotic idea and it is, in fact, generally accepted in string theory. According to this scenario, we are captured in a kind of four-dimensional world from which only gravity can escape in those six extra dimensions. If we place an ant on a sheet of paper, and it can only look ahead and sideways, it has no idea that another direction exists. We experience our four-dimensional world in the same way, whereas it actually has many more dimensions.’

‘We are, thus, captured in a four-dimensional world and it could just happen that, when we carry out an experiment in the accelerator, particles escape into those extra dimensions; according to the theory, only gravitational particles are able to do so. If this should happen, they energy really disappears from our 4D world. This doesn’t mean that the laws of energy are transgressed, but only that that energy disappears into those other dimensions. Perhaps we will be able to observe this in the accelerator. In some scenarios, small black holes could be formed when particles collide, which then immediately evaporate. It would be truly spectacular if they made discoveries like this. Personally, I think it’s rather improbable, but you never know!’

### Holography

‘One of the neatest things in string theory so far is that a special duality has been found: an exact equivalence between a theory with gravity and one without gravity. I worked a lot on that, my best results can perhaps be found in that area.’

‘A world with gravity can be exactly the same as a world without gravity. In a theory without gravity, you’re not bothered by all those problems caused by gravity, so in principle they are solved. That being done, you have solved the theory with gravity, because they are equivalent. The theories with and without gravity look totally different. The one with gravity always has one dimension more than the theory without gravity. This is known as holographic equivalence; a hologram is two-dimensional, but you can project a three-dimensional image onto it. All information describing the three-dimensional world is contained in the two-dimensional hologram. Holography is a very important concept in string theory. Our best understanding of what gravity is follows from this principle.’

### Cafe

Photo: Bob Bronshoff

It doesn’t worry De Boer that his field of research is difficult to explain to others. ‘There are about two thousand people working on string theory worldwide with whom you can have in-depth discussions on the subject. Even here at our institute, there are more than twenty people working on string theory with whom you can have frequent discussions. But if I’ve found something interesting and announce enthusiastically at the café : I have found the new product formula for modular invariant expressions of the entropy of black holes in certain dimensions, the general reaction is: “Yeah, sure, I guess…..”.’