Theories of everything
Professor John Barrow
The idea of a theory of everything, a way of predicting and understanding everything that we see in the world, is a tantalising idea for the human mind, but it is by no means a new idea. We don’t only find it in the realms of modern particle physics and science. If you look back in your history books to the early myths and legends about the beginnings of the world, what characterises those stories about the nature of everything around us is their desire to be totally complete, to leave absolutely nothing out of the story. Everything that could be seen in the world had a meaning and there was a place for everything and everything had its place in the created order. Nothing was left unexplained. So you can see this idea of complete explanation is a sort of hallmark of a certain type of fantastic description of the world, that often has ourselves located at the centre.
In modern times, physicists have attempted to produce the so-called theory of everything, and in this talk I want to tell you about some of the ways in which they have progressed towards doing that and what the current state of play looks like.
The first conception of the theory of everything in the modern sense goes back about 250 years to a Croatian physicist called Roger Boskovich, who spent much of his life in Venice as the scientific advisor to the Pope. He was a great admirer of Newton’s work, 300 years ago, and he set about extending it to include descriptions of certain things that Newton could not provide an explanation for. In his famous book of 1758, Boskovich announces that he has a single force law, a rule which would enable people to deduce everything from a single law of forces.
There is a picture of that unusual theory of everything of Boskovich’s. It is just a picture of how a law of force varies with the distance between two objects that are being acted upon by the force. The force, on this rather messy 18 th Century drawing, is an asymmetry curve. Where the curve is above the axis, the force is repulsive, and where the curve is below it, it is attracted. So at very large distances, it just looks like Newton’s law of gravitation, but at short distances, it is occasionally repulsive and occasional attractive. What he has in mind is that the places where the curve crosses the zero line are places where there is no overall force on things; there are equilibria there. So if you have objects in the world, whether they are people, atoms, rocks, planets, they will be located at those equilibrium points. What Boskovich realised was that in order to explain why there are stable objects in the universe, it is not enough just to have forces of attraction. You have to have countering forces of repulsion so the two can come into balance and we can have the equilibrium states that we see in the world.
After Boskovich, there were not many successful forays into the business of finding a theory of everything. In the 20 th Century, there were two heroic failures by very great scientists.
The first was Arthur Stanley Eddington, the person who taught us how the stars work, who was responsible for the first test of Einstein’s Theory of General Relativity and much else besides. Eddington was fixated with the idea of what he called a fundamental theory. This he did largely by numerological tricks. He wanted to try and explain all the constants of nature in terms of other constants of nature, and just coincidences between mathematical formulae. This really came to nothing. He died in 1944, with the work unfinished, and often undergoes, I think, quite a lot of criticism and even ridicule for the whole programme.
Albert Einstein himself took up the quest for a fundamental theory, which he called a Unified Field Theory, in the latter part of his career. He was anxious to extend his Theory of Gravity to include other forces, like electromagnetism. But at the time of his death, this work was still unfinished, and little understood by anyone else. Looking back, there is little of it really that has been of any interest and consequence.
One of the problems for both of these great scientists was that they were premature in their search for a unified theory. You see, they did not really even have straight what it was that needed to be unified. Einstein was trying to join together electricity, magnetism and the force of gravity. He ignored completely the strong nuclear forces and the forces of radioactivity. So the moral of the story is that if you want to unify forces of nature, it is very important to understand what it is that needs unifying and what are the truly fundamental ingredients that you need to include in the story.
Today, we think that we understand what are the bits that need unifying. We know there are four very different fundamental forces of nature in the world around us, at relatively low temperatures and low energies. We call those forces gravitation, which keeps our feet firmly on the ground; electricity and magnetism, that keeps the light shining; the strong nuclear force which holds the nuclei of all our atoms together; and then an almost innocuous force of radioactivity, which we call the weak interaction, that plays a key role in powering the stars and also is the source of radioactive decays. If you are in the business of trying to produce a theory of everything, of uniting these different forces, you have two immediate problems on being confronted with these four forces. One is a quantitative problem, and the other is a qualitative problem.
The quantitative problem is that the forces are enormously different in strength. Gravity is incredibly weak – one part in ten to the 39 – compared with a strong interaction, which would have a strength of one on the same scale; whereas electromagnetism is a thousand times weaker, and the weak interaction a hundred thousand times weaker. The forces also act on different sorts of particles. Gravity acts on everything, but electromagnetism just acts on particles that carry electric charge, and the strong and the weak interactions have a different collection of subjects in turn. So it is very odd to think that these forces are really one and the same in disguise, because they look so different, and their strengths and characteristics are so different in the world around us.
However, our modern conception of the world has given us a way in which we can make those forces look much more similar than they might otherwise appear. The place you look is perhaps a rather unexpected place. It is a place where you would not expect to find anything at all, and that place is the vacuum. In the classical world, and perhaps even the world of school science, the vacuum is extremely simple: it is nothing at all. It is just a completely empty box. But the quantum vacuum is something which is much more complicated and much more interesting.
Quantum mechanics teaches us that if we take a volume of space, it is not possible for there to be nothing in it. What we mean by the vacuum in quantum theory is simply all that remains when everything that can be removed from the box is removed. It is a sort of lowest energy state, a ground state, for the system. In that state, there is a particular type of process going on, which physicists call a virtual process.
Before you can understand what a virtual process is, you have to know what a real process is. Heisenberg taught us, in the 1920s, that there is an Uncertainty Principle governing what we can see in nature. If a process involves a certain amount of energy, change delta E, and we want to observe it for a brief interval of time, delta T, then the product of the energy and the time has to be bigger than some number which is defined by Planck’s Fundamental Constant of Nature. This Uncertainty Principle tells us that if a process with an energy E existed for a time of T, where the inequality went the other way, we would not be able to observe it. It would be what we would call a virtual process. If we perturb it in some way, so the inequality is turned around, it lives a bit longer say, then it becomes real and we can see it.
The vacuum is seething with virtual processes all the time. Electrons and positrons are appearing and annihilating back into light and then re-appearing out of light, all in this unobservably short interval of time governed by this inequality. So if you take an electron and you put it down in the quantum vacuum, you should imagine it to be surrounded by all sorts of virtual processes, appearing and disappearing. But once you introduce the electron, something very strange happens to the vacuum. It becomes, as we say, polarised.
So if I represent an electron, sitting in a vacuum, and throw in another electron of the same charge, which is going to be deflected by it, two electrons of the same charge repel one another, just like two identical magnetic poles do. By measuring the strength of the repulsion, you could determine and judge how strong the force of electricity and magnetism really is. But once we introduce an electron with a negative charge in a quantum vacuum, all sorts of positively charged, anti-electrons and ordinary electrons, virtual particles are appearing all around it, and what happens is that the positively charged virtual particles get attracted to the negative electron at the centre, and so the negative charge gets shielded by a halo of virtual positive charges. So when the other electron comes in to be deflected by it, it does not see the full electric charge of the electron, it sees a partially shielded charge, which is much less negative, and so the electron deflects more weakly from the central charge. You can then realise that the deflection starts to depend on how energetic the incoming electron is. If it comes in with very high energy, then it penetrates right through the shielding cloud and gets a good look at the full negative charge in the centre, and deflects strongly, but if it comes in at low energy, it does not get very far through the cloud, it sees an awful lot of shielded cloud, and it deflects rather weakly. So at high energies, the electromagnetic energy interaction looks stronger than it looks at lower energy.
If you start to think about the strong interaction, which in ordinary energies around us is much stronger than the electromagnetic interaction, something else happens. Look at the interaction between two quarks. Quarks have a quality which is called colour. It is nothing to do with the everyday hue of things. It is another form of charge, and it comes in different varieties. If a quark comes in, and it is going to interact and be deflected by another quark, the same sort of thing happens. The vacuum produces lots and lots of quark, anti-quark pairs, which form a shield of opposite colour around a charge – exactly the same as with the electron. But something else is going on here as well. In the case of the two electrons, the other particles that are around are photons, but they do not have an electric charge, so you can just forget about them. They do not alter the charge distribution. The particles that play the role of photons when quarks interact are called gluons, and they are unusual because they do also carry the colour charge. So the appearance of the virtual gluons produces a counter balancing effect. It tends to surround the quark with gluon colour charge of the same colour as itself. The question is, what wins out? The opposite colour or the same colour? This depends on how many varieties of quark and colour and gluon there are in the world, and in our world, the number is small enough that the winner is the gluon effect, which tends to smear out the quark charge. As a result, when a particle comes in, as the energies get higher, it tends to deflect more weakly than it would have at low energy. So the strong interaction gets weaker when you go to higher energies; the electromagnetic interaction gets stronger.
This effect for the strong interaction in fact was awarded the Nobel Prize this year. The three predictors of this effect, called asymptotic freedom, Wilczek, Politzer and Gross, received the Nobel Prize this year for their prediction. The experimental evidence, fairly recently, enables you can see this really does happen. You can see the strength of the strong interaction, in some measure, getting bigger as you go upwards. You can also see the energy increasing, and which should interact the quarks. You can see, as the energy goes up, the strength of the interaction goes down, exactly as predicted by this theory of asymptotic freedom.
So the first lesson that we learn from modern physics and the properties of the vacuum is that the effective strength of the forces of nature change as the energy of the world in which interactions changes. At high energies, the strong interaction is weaker, electron weak interactions are stronger, and the consequence of this is something which has become known as grand unification: if you extrapolate the way the forces change, as you go to higher and higher temperature and energy, not only do they change in different senses, but they are predicted approximately to cross over at one very high energy, when the temperature is about ten to the 27 degrees Calvin. This cross over has become known as grand unification. It is very suggestive to physicists that when you look at extremely high energies, the different forces of nature do not look different in the way that they look at low energy. So there is great suggestion, great encouragement, that there really is the possibility of unifying these three forces of nature at very high energy.
You will remember there was a qualitative problem as well, that the particles acted on by one force, say the strong force, were not necessarily acted upon by the other force. So it was like having two populations subject to different types of legislation. If you really have this unification, you need to somehow bind them together. To do that, what you require are new types of particle which mediate and talk to the two populations which would otherwise be disjoined. This is something that we have seen before. In the case of the weak and the electromagnetic interactions, it was predicted that these should come together and be joined at a temperature corresponding to about ten to the power 13 degrees Calvin. Back in the 1970s, it was predicted that such a unification should take place and, if it did, there must exist in nature two new types of particle that became known, rather prosaically, as the W and the Z particles. These enabled the electromagnetic and the weakly interacting particles to transmute and interact with one another.
In 1983, at CERN, the new particle accelerator there which was built for this purpose discovered those two particles, with exactly the masses that are predicted they must have if this unification takes place, masses of about 90 and 100 gv, billion electron volts. So we know this type of unification pattern exists, first for the electromagnetic and the weak interactions, and we have observed it in some detail.
If the grand unification takes place, and the strong interaction can be joined to the electron weak, there has to be another type of new particle in nature, that we call the X particle. What the X particle has to be able to do is to transmute and mediate interactions between quarks, which carry this colour charge, and leptons or particles like electrons and neutrinos, which do not. So a typical interaction, mediated by the X particle, would change two quarks into a positron and another quark or anti-quark.
This interaction sounds rather innocuous, perhaps even rather unexciting, but it has a catastrophic consequence. It means that all matter is unstable. Protons are not for ever, because a proton is made of quarks. Each has an electric charge of a third, and if this type of interaction could occur in nature, two of the quarks in the proton could turn into a positron and the other quark would turn into an anti-quark, where it would pair up with the other quark, which produces pyon, which quickly decays into light. So all protons would eventually decay away, all neutrons as well, all ordinary matter, of which we are made, would be unstable. Fortunately, the lifetime is expected to be extraordinarily long. The half life of protons and atoms is certainly longer than about ten to the 35 years. That is not as outrageously long as you might think. We could directly detect the consequences if the decay was as short as ten to the 30 years, which would correspond to a few atoms in your body decaying in your lifetime. So it is a challenge for the future to find a way perhaps of seeing this observational consequence of grand unification taking place.
I have a schematic that illustrates the trend, the development in physics, a sort of unification story if you like. This is the type of history of physics that physicists like. Everything is very successful, moves forward in time, showing only successes. If we start about 300 years ago, the picture shows we have more, and as time goes forward, we have less. So at the time of Newton, 300 years ago, people thought there might be two sorts of forces in nature responsible for gravitation: something that keeps our feet firmly on the ground and makes apples fall from the trees; and something that Kepler understood as being responsible for the laws of planetary motion, that we might call celestial gravity. Newton showed they were really one and the same, and a single law could explain them both.
Similarly, with static and dynamic electricity: one makes balloons stick to the wall when you rub them on your sweater; the other makes currents flow. They are really one and the same. In the 19 th and 18 th Century, physicists show that magnetism and electricity are just different aspects of the same so-called electromagnetic force that we have been talking about so far.
In the 20 th Century, radioactivity was shown to be due to the weak force and nuclear reactions to the so-called strong force. We have just seen that relatively recently, in the last 40 years, we have unified the weak and the electromagnetic forces into a single electro weak force, and there is good experimental evidence for that.
Where we are lacking experimental confirmation is the next step in the game. How do we join the electro weak to the strong force in the way that I have just mapped out? There are many theoretical deductions of what such a unified theory should be like, but we have got no decisive experimental evidence that tells us exactly which unification pattern nature has decided to pursue.
What about the last part of the story? We have said nothing much about gravity so far, and you will see why in a moment. Einstein superseded Newton’s description of gravity. We would like to find a way to add gravity to that grand unified theory. It is that final four-fold unification that people generally refer to as the theory of everything. There are some candidates that we are going to look at in the moment, the most famous of which is the so-called super-string theory.
Until rather recently, gravity was a very serious fly in the ointment. Adding gravity to the unification story was not just doing one same old thing over and over again. Gravity is completely different to the other forces of nature. It is the only force that acts on everything. In Einstein’s picture of things, gravity alters the structure of space and time; it makes the geometry of space alter according to the amount of mass and energy that are in different places. If you want to join the theory of gravity of that sort to a quantum theory, you therefore have a very big problem.
We talked a little while ago about Heisenberg’s Uncertainty Principle. One way to phrase that in simple language is that we cannot know where a particle is and how it is moving, with perfect precision, at the same moment. Well, if that were the case, and you were following Einstein’s picture of gravity, where the shape and geometry of space is determined by the locations and movements of all the particles that move in the universe, you see you have a real dilemma. If you cannot know with perfect accuracy the location and the motion of every point in the universe, you cannot know the geometry of space and the flow of time into which you are introducing them in the first place, so you have a nasty vicious circle, with these two theories being in conflict with one another. So you suspect that any theory that joins quantum theory and general relativity together is going to be very unusual, is going to be radical in many respects.
For a long time, when people looked at theories of elementary particles, and in particular theories that attempted to introduce gravity, they had one very nasty consequence. The consequence was that they always predicted that there would be measurements that you could make in the universe of processes and interactions which would have infinite values. This seems completely unphysical, that you should be able to make a local measurement which would give an infinite energy or an infinite velocity, infinite momentum, and so this problem of infinities, as it was called, was regarded very much as a disease, as a problem of the theory itself, that we were trying to structure it in the wrong way. What the structure of these theories was, it regarded the most elementary things in nature as little point particles that could be made as small as you like – in fact their size could be completely neglected – and they interacted with one another rather like billiard balls rebounding or deflecting one another and perhaps exchanging energy in that way. All those theories had this awkward problem - divergences, infinities.
In 1982, this theory was replaced by a new type of theory, known as string theory, which was invented by George Schwarz, from Caltech in America, and Michael Green, here in Cambridge, who, by a strange coincidence, was standing in this very spot half an hour ago giving a teaching lecture before I began my talk. What Green and Schwarz did in 1982, which caused something of a revolution in physics and changed the direction of research of almost everyone working in high energy physics, is that they gave up the idea that the fundamental ingredients in nature should be thought of as points of energy. Instead, they proposed that they should be regarded as little lines or little loops of energy, one dimensional things, rather than simply points, and those lines could either be never-ending lines of energy or they could be little closed finite loops of energy that could do all sorts of things: they could oscillate, they could interact with one another, they could change their shape. When a point moves in space, it traces out a line, a trajectory. When a loop moves, it is going to trace out a cylindrical tube and, we will see in a moment, this has all sorts of interesting consequences.
The reason everyone got so excited about this idea and why it was much more than just trying the next thing, if you like, is that they discovered that theories like this did not possess all the infinities and divergences of point-like theories. So this problem was solved at one stroke. The other remarkable thing about these theories was, whereas the point-like theories people had tried before were allergic to including gravity – gravity messed everything up – these theories liked the inclusion of gravity. In fact, they only worked if gravity was included. So they appeared a natural and complete description of the four basic forces of nature. They went one step further than simple grand unification.
However, there was one awkward feature of these theories. They did indeed remove the infinities, but they removed the infinities only if space and time had a total of ten dimensions. Dimensions of just four, one time and three space, like we are familiar with, all have infinities, whether they are string theories or not. So this is a very strange prediction. Only in worlds of this very special sort, say with one time and nine dimensions of space, is everything well defined and finite and works beautifully.
There is a simple way to see, almost at a cartoon level, why the infinities disappear. I have a picture of what is going on in time and in space. We are suppressing all but one dimension of space. Think of two particles. They come in and interact with one another. The way they do that is to exchange, say, a photon, if they are two electrons, and then they go out again as two electrons on slightly different trajectories with different energies. So this is just like the situation we looked at in the vacuum earlier on. Diagrammatically, the infinities arise because of the sharp corners in the diagram, the history in space and time. The sharp corner in the interaction is where the infinite values for an observable develop.
What happens if you move to strings? Well, instead of thinking of the electron as a moving point, tracing out a straight line, you now think of the electron as a little loop. As it moves, it traces out a tube. But when the two tubes come to interact with one another, the shape of the interaction is quite different. There is no longer a sharp corner. There has to be a tube going out. The only way to sew it together can be seen in a type of trouser-type diagram, which I call the right trousers. So the right trousers gives you a seamless link between the two trousers coming in and the two going out, and you notice that the interaction is completely smooth. There is no sharp corner here. The two trousers are joined to one another without those infinities arising.
Well, what are these things? What sort of properties do they have? You should think of them perhaps as little loops of energy, but like rubber bands that we are familiar with, they also have a tension. They can be stretched, there is some resistance to them being stretched, and just as with the properties of the vacuum, the tension that the strings possess change as the energy of the environment around them changes. The way it changes is that, as the temperature falls, so we move to a lower and lower temperature world, the tension increases, and the loops collapse down and become more and more like points. That’s nice, because it means if we go down to the low energy, low temperature world which we have around us today, these stringy theories look more and more like point-like theories, and they make all the successful predictions that the point-like theories make. But if we go to very high energies, up where that grand unification should occur and above, the loops will have low tension and they will behave in an intrinsically stringy and new way, and will predict all sorts of new types of physics.
Extracting those predictions about that new physics is the biggest challenge for people that work on string theory. It requires all sorts of very fancy new mathematical methods, which so far have, to a great extent, defeated physicists to unravel and extract the predictions. The sort of thing that they are expecting to do you can imagine as follows.
A super-string is like any other type of string. If you fix two ends, you can make it vibrate, like a guitar string, and it has certain fundamental basic modes of vibration, just like the guitar string. Engineers would call these normal modes of vibration. Each of those normal modes will have a certain energy associated with it, and via Einstein’s famous E=MC 2 formula (the only formula of physics I can rely on members of the audience actually knowing!) you can see each energy of vibration corresponds to some mass. The expectation in these theories is, if you could find the whole spectrum of possible vibrational energies of the super-string, it would predict for you all the possible masses of the things that we call elementary particles today. So you can think of them almost like knots or excitation energy modes of the string. So the challenge is to make those predictions: we believe they are all hidden somewhere in the mathematics of the theory. The only simple prediction that has been extracted is that there is one type of particle which actually has a zero mass, and it has a particular spin which indicates that its role is to make things attract one another, and if you follow through the theory and you say, well, what are the equations at low energy which govern this particular excitation of the string, the excitation is the particle that we call the graviton, and the equations that govern it turn out miraculously to be Einstein’s Theory of General Relativity. So out of this theory of strings and loops of energy, that seems to have nothing to say about gravity, pops the whole of Einstein’s Theory of General Relativity, gravitational radiation, and this is why people take the theory so seriously. There is something rather magical, something rather smarter than we are, about this mathematical structure, and perhaps there is much more that we can extract in the future.
When the investigations of these theories began, people at first hoped there might just be one of these theories. After all, if there is a theory of everything, you might expect it to be a unique, one and only thing. But pretty soon, people found there were five of these theories. They gave got rather exotic names. What the names correspond to is that they are based on different patterns, so there is a different type of pattern which determines the form of the unification that takes place. For about ten years, people, thought perhaps there are just five theories of everything, and our world, our universe, has for some reason or other to adopt one of them, but which one?
There was something of an impasse until 1995, when the foremost theorist in this area, Ed Witten in Princeton, gave a remarkable talk at the International Strings Theory Conference, where he showed that these five theories are not different at all. They are all just different limiting cases of some as yet unknown slightly bigger theory that he dubbed M Theory. This new 11 dimensional theory is, at it were, being projected on to the walls of the room, you could imagine, in shadow, and these five theories are just the shadows of this bigger theory that has yet to be mapped out. More interesting still, at low energy, this theory also resembled another theory that we already knew about called Super-Gravity Theory. Each of these supposedly different string theories could then be turned into the other by a particular transformation, by a particular viewpoint.
So there is some unknown ultimate theory, called M Theory. There is a dispute as to whether M stands for mystery or matrix or millennium. If you look at it in different ways, at low temperature or high temperature, in other particular limiting situations, it will look like one of the other string theories. The challenge in this business is to try to discover what is this theory that we only see dimly in projection, and that is where the centre of activity in fundamental physics now resides.
Let’s go back to the rather awkward property of this theory. It has got to have lots of extra dimensions of space, either six, or in the M theory case, seven extra dimensions of space, although I should add there is no reason why there should only be one dimension of time in these theories, but it is usually supposed that only one of the dimensions is a time. If you try to have more than one dimension of time, very bad things happen, things decay very rapidly, and huge instabilities develop. So the position that we are in is that we have a prediction that there might be nine or ten dimensions of space in the universe in total. We know that three of those dimensions are large, and we walk around in them all the time. So where are the others?
The interpretation that is adopted in these theories is that the other dimensions, six or seven of them, are incredibly small, fantastically small, perhaps as small as ten to the minus three of a centimetre. Some variants of the theory allow these dimensions to be rather larger. In some variants of the theory, only gravity extends its influence into these other dimensions, the other forces do not, and in those theories, these dimensions could be as large as about a hundredth or a twentieth of a millimetre. They really could be almost visible to the naked eye. The way you would test to find those large extra dimensional examples is by looking for quite large changes in Newton’s law of gravity at those sub-millimetre scales. This is very hard to do experimentally, but there are experimental groups in Seattle, Washington in the US actively searching for these rather dramatic changes in the form of Newton’s law of gravity, from an inverse square law to an inverse fourth power law down sub-millimetre scales. The reason those experiments are so hard to do is because gravity is such a weak force and, as you can see by looking at a fly walking on the ceiling, ordinary adhesive and frictional forces are much, much stronger than the force of gravity. So if you want to test the form of gravity on very, very small scales, you have got to isolate things from all the other forces of nature, and that is extraordinarily difficult and, in some cases, impossible to do.
Let’s step back and look at this notion of the theory of everything. Perhaps it is a string theory; perhaps it will turn out to be something yet more exotic. What can we say about such theories? If you stop the ordinary person on the street and mention the idea of a theory of everything, they think everything really means everything: the works of Shakespeare; the structure of you and me; what is on at the cinema tonight. Do these theories really predict everything? Well, of course they do not. A theory of everything in this sense is just a unified theory of the four fundamental forces of nature: gravity, electromagnetism, weak radioactivity and strong nuclear forces. Such a theory is necessary to understand everything that we see in the world, but it is far from being sufficient. If you have such a theory, it will not help you understand the structure of the human brain, the workings of economies or complex human societies in any way at all. So what we have to appreciate about the laws of nature that theories of everything are trying to unify is that they are not the whole story. When we look around the world, we do not see laws of nature at all. What we see are the outcomes of the laws of nature, and they are much more complicated and much more unusual than the laws.
If I hold this pointer up vertically, it is going to be subject to the law of gravitation if I let it go. Gravity is totally democratic, it does not make the pointer fall in one particular direction all the time, but if I let the pointer go, it will always fall in some direction; it may be different each time. So the symmetry of the law of gravity, democracy with respect to all directions, is broken in this particular outcome, and that is why the world is complicated, because the symmetries which underlie the theory of everything, the individual forces of natures, are broken in the outcomes of those laws. When we look around the world and we see complicated structures, like brains, animals, cats and dogs, computers, telephone systems, speedboats, cars and so forth, they are the consequence of things which are allowed by the laws of nature, but all sorts of other organisational linkages take place. What makes the computer and the human brain what it is is the wiring diagram, the organisation of the components, and that is not something that is dictated by the theory of everything.
If you want to understand the world completely, you certainly need a theory of everything, but you need to know lots of other things as well: you need to know how those symmetries break when the pointers fall; you need to know if there are principles about how things can be organised and joined together. If there are conditions which set out how things start - if we drop a glass on the floor, it will smash. The laws of nature allow the pieces of glass to come together to make a glass, but you never see the second sequence of events, because the starting conditions for it to occur, pieces of glass coming together in just the right way to make a tumbler, are so improbable that they are never seen. But dropping the glass on the floor so it smashes has a very simple and easily arranged initial condition. So there is much more to the world than just a theory of everything.
If we try and measure the extent to which we know a theory of everything or the basic laws of nature against the complexity of the outcomes or the phenomena which issue from those laws, then there are certain situations that we are familiar with – simple chemistry, simple engineering – where we have essentially no uncertainty about the equations and the laws and the complexity is very low – making an artificial arm joint or throwing a ball against the wall. If you are a particle physicist on the search for a theory of everything, looking at particle decays at CERN in Geneva, then you will be greatly worried about uncertainties in the laws of nature and the theory of everything, but you will be studying very simple phenomena: the decay of a neutron, say, into a proton, and positron and a neutrino. But if you are interested in the dynamics of solar system, emotions, or trying to predict the weather or turbulent fluids, you will have pretty much no uncertainty about the laws and the equations that govern those things, but the complexity of the phenomena is extraordinarily high, and so we do not have a good understanding of turbulent fluids - what happens when you turn the bath tap full on.
So there is a trade-off between uncertainty about the laws of nature, knowing the theory of everything and its components, and uncertainty about the complexity of the outcomes of those laws. Very simple laws can have highly complex outcomes. Very sophisticated laws can have very simple outcomes. Where we have a very awkward regime, we have some uncertainty about the laws themselves, and the complexity of the phenomena is also very great. In, for example, social science and economics, we enter a very different situation, where things are unpredictable in principle, because if you go on the television and predict the future of the economy, you will actually alter the course of the economy in ways which are intrinsically unpredictable. I cannot predict your future action in a way that will be binding upon you if I make it known. I can keep it secret and understand everything you do in the future, but it would not be binding on you. But if I announce my prediction to you, you can always choose to falsify it. So there are things in nature we need to know about, in addition to the theory of everything, if we are going to predict its behaviour in full.
So the moral of our talk today is that the world does indeed appear to be governed by a small number of simple laws, as we call them, which look very different and unusual at low energy, but when we look at the world at high energy, these laws come together. There does indeed appear to be a unification structure in nature, a theory of everything, and at the moment, physicists are actively trying to discover whether super-string theory or its variant M Theory is that theory of everything. But remember, the theory of everything, while it may be necessary to understand the world, is far from sufficient; we need many other ingredients in order to complete our understanding even of the physical world around us. Once we have a theory of everything, there will still be an unlimited amount of the world to try to understand, to predict, to explain and to enjoy.
© Professor John Barrow, Gresham College, 16 February 2006