The Theory of Everything: The Origin and Fate of the Universe - Stephen Hawking (2002)
Chapter 7. SEVENTH LECTURE - THE THEORY OF EVERYTHING
It would be very difficult to construct a complete unified theory of everythingall at one go. So instead we have made progress by finding partial theories.These describe a limited range of happenings and neglect other effects, orapproximate them by certain numbers. In chemistry, for example, we can cal-culate the interactions of atoms without knowing the internal structure of thenucleus of an atom. Ultimately, however, one would hope to find a complete,consistent, unified theory that would include all these partial theories asapproximations. The quest for such a theory is known as “the unification ofphysics.”
Einstein spent most of his later years unsuccessfully searching for a unified the-ory, but the time was not ripe: Very little was known about the nuclear forces.Moreover, Einstein refused to believe in the reality of quantum mechanics,despite the important role he had played in its development. Yet it seems thatthe uncertainty principle is a fundamental feature of the universe we live in. Asuccessful unified theory must therefore necessarily incorporate this principle.The prospects for finding such a theory seem to be much better now becausewe know so much more about the universe. But we must beware of overconfi-dence. We have had false dawns before. At the beginning of this century, forexample, it was thought that everything could be explained in terms of theproperties of continuous matter, such as elasticity and heat conduction. Thediscovery of atomic structure and the uncertainty principle put an end to that.Then again, in 1928, Max Born told a group of visitors to GöttingenUniversity, “Physics, as we know it, will be over in six months.” His confidencewas based on the recent discovery by Dirac of the equation that governed theelectron. It was thought that a similar equation would govern the proton,which was the only other particle known at the time, and that would be theend of theoretical physics. However, the discovery of the neutron and ofnuclear forces knocked that one on the head, too.
Having said this, I still believe there are grounds for cautious optimism that wemay now be near the end of the search for the ultimate laws of nature. At themoment, we have a number of partial theories. We have general relativity, thepartial theory of gravity, and the partial theories that govern the weak, thestrong, and the electromagnetic forces. The last three may be combined inso-called grand unified theories. These are not very satisfactory because theydo not include gravity. The main difficulty in finding a theory that unifiesgravity with the other forces is that general relativity is a classical theory. Thatis, it does not incorporate the uncertainty principle of quantum mechanics. Onthe other hand, the other partial theories depend on quantum mechanics in anessential way. A necessary first step, therefore, is to combine general relativitywith the uncertainty principle. As we have seen, this can produce someremarkable consequences, such as black holes not being black, and the uni-verse being completely self-contained and without boundary. The trouble is,the uncertainty principle means that even empty space is filled with pairs ofvirtual particles and antiparticles. These pairs would have an infinite amountof energy. This means that their gravitational attraction would curve up theuniverse to an infinitely small size.
Rather similar, seemingly absurd infinities occur in the other quantum theories.However, in these other theories, the infinities can be canceled out by a processcalled renormalization. This involves adjusting the masses of the particles andthe strengths of the forces in the theory by an infinite amount. Although thistechnique is rather dubious mathematically, it does seem to work in practice. Ithas been used to make predictions that agree with observations to an extraor-dinary degree of accuracy. Renormalization, however, has a serious drawbackfrom the point of view of trying to find a complete theory. When you subtractinfinity from infinity, the answer can be anything you want. This means thatthe actual values of the masses and the strengths of the forces cannot bepredicted from the theory. Instead, they have to be chosen to fit the observa-tions. In the case of general relativity, there are only two quantities that can beadjusted: the strength of gravity and the value of the cosmological constant. Butadjusting these is not sufficient to remove all the infinities. One therefore hasa theory that seems to predict that certain quantities, such as the curvature ofspace-time, are really infinite, yet these quantities can be observed andmeasured to be perfectly finite. In an attempt to overcome this problem, a the-ory called “supergravity” was suggested in 1976. This theory was really just gen-eral relativity with some additional particles.
In general relativity, the gravitational force can be thought of as being carriedby a particle of spin 2 called the graviton. The idea was to add certain othernew particles of spin 3/2, 1, 1/2, and 0. In a sense, all these particles could thenbe regarded as different aspects of the same “superparticle.” The virtual parti-cle/antiparticle pairs of spin 1/2 and 3/2 would have negative energy. Thiswould tend to cancel out the positive energy of the virtual pairs of particles ofspin 0, 1, and 2. In this way, many of the possible infinities would cancel out,but it was suspected that some infinities might still remain. However, the cal-culations required to find out whether there were any infinities left uncanceledwere so long and difficult that no one was prepared to undertake them. Evenwith a computer it was reckoned it would take at least four years. The chanceswere very high that one would make at least one mistake, and probably more.So one would know one had the right answer only if someone else repeated thecalculation and got the same answer, and that did not seem very likely.Because of this problem, there was a change of opinion in favor of what arecalled string theories. In these theories the basic objects are not particles thatoccupy a single point of space. Rather, they are things that have a length butno other dimension, like an infinitely thin loop of string. A particle occupiesone point of space at each instant of time. Thus, its history can be representedby a line in space-time called the “world-line.” A string, on the other hand,occupies a line in space at each moment of time. So its history in space-timeis a two-dimensional surface called the “world-sheet.” Any point on such aworld-sheet can be described by two numbers, one specifying the time and theother the position of the point on the string. The world-sheet of a string is acylinder or tube. A slice through the tube is a circle, which represents the posi-tion of the string at one particular time.
Two pieces of string can join together to form a single string. It is like the twolegs joining on a pair of trousers. Similarly, a single piece of string can divideinto two strings. In string theories, what were previously thought of as particlesare now pictured as waves traveling down the string, like waves on a washingline. The emission or absorption of one particle by another corresponds to thedividing or joining together of strings. For example, the gravitational force ofthe sun on the Earth corresponds to an H-shaped tube or pipe. String theory israther like plumbing, in a way. Waves on the two vertical sides of the H corre-spond to the particles in the sun and the Earth, and waves on the horizontalcrossbar correspond to the gravitational force that travels between them.String theory has a curious history. It was originally invented in the late 1960sin an attempt to find a theory to describe the strong force. The idea was thatparticles like the proton and the neutron could be regarded as waves on astring. The strong forces between the particles would correspond to pieces ofstring that went between other bits of string, like in a spider’s web. For this the-ory to give the observed value of the strong force between particles, the stringshad to be like rubber bands with a pull of about ten tons.
In 1974 Joël Scherk and John Schwarz published a paper in which they showedthat string theory could describe the gravitational force, but only if the tensionin the string were very much higher-about 1039tons. The predictions of thestring theory would be just the same as those of general relativity on normallength scales, but they would differ at very small distances-less than 10-33centimeters. Their work did not receive much attention, however, because atjust about that time, most people abandoned the original string theory of thestrong force. Scherk died in tragic circumstances. He suffered from diabetesand went into a coma when no one was around to give him an injection ofinsulin. So Schwarz was left alone as almost the only supporter of stringtheory, but now with a much higher proposed value of the string tension.There seemed to have been two reasons for the sudden revival of interest instrings in 1984. One was that people were not really making much progresstoward showing that supergravity was finite or that it could explain the kindsof particles that we observe. The other was the publication of a paper by JohnSchwarz and Mike Green which showed that string theory might be able toexplain the existence of particles that have a built-in left-handedness, likesome of the particles that we observe. Whatever the reasons, a large numberof people soon began to work on string theory. A new version was developed,the so-called heterotic string. This seemed as if it might be able to explain thetypes of particle that we observe.
String theories also lead to infinities, but it is thought they will all cancel outin versions like the heterotic string. String theories, however, have a biggerproblem. They seem to be consistent only if space-time has either ten ortwenty-six dimensions, instead of the usual four. Of course, extra space-timedimensions are a commonplace of science fiction; indeed, they are almost anecessity. Otherwise, the fact that relativity implies that one cannot travelfaster than light means that it would take far too long to get across our owngalaxy, let alone to travel to other galaxies. The science fiction idea is that onecan take a shortcut through a higher dimension. One can picture this in thefollowing way. Imagine that the space we live in had only two dimensions andwas curved like the surface of a doughnut or a torus. If you were on one side ofthe ring and you wanted to get to a point on the other side, you would have togo around the ring. However, if you were able to travel in the third dimension,you could cut straight across.
Why don’t we notice all these extra dimensions if they are really there? Whydo we see only three space and one time dimension? The suggestion is that theother dimensions are curved up into a space of very small size, something likea million million million million millionth of an inch. This is so small that wejust don’t notice it. We see only the three space and one time dimension inwhich space-time is thoroughly flat. It is like the surface of an orange: if youlook at it close up, it is all curved and wrinkled, but if you look at it from adistance, you don’t see the bumps and it appears to be smooth. So it is withspace-time. On a very small scale, it is ten-dimensional and highly curved.But on bigger scales, you don’t see the curvature or the extra dimensions.If this picture is correct, it spells bad news for would-be space travelers. Theextra dimensions would be far too small to allow a spaceship through.However, it raises another major problem. Why should some, but not all, ofthe dimensions be curled up into a small ball? Presumably, in the very earlyuniverse, all the dimensions would have been very curved. Why did threespace and one time dimension flatten out, while the other dimensionsremained tightly curled up?
One possible answer is the anthropic principle. Two space dimensions do notseem to be enough to allow for the development of complicated beings like us.For example, two-dimensional people living on a one-dimensional Earthwould have to climb over each other in order to get past each other. If a two-dimensional creature ate something it could not digest completely, it wouldhave to bring up the remains the same way it swallowed them, because if therewere a passage through its body, it would divide the creature into two separateparts. Our two-dimensional being would fall apart. Similarly, it is difficult tosee how there could be any circulation of the blood in a two-dimensional crea-ture. There would also be problems with more than three space dimensions.The gravitational force between two bodies would decrease more rapidly withdistance than it does in three dimensions. The significance of this is that theorbits of planets, like the Earth, around the sun would be unstable. The leastdisturbance from a circular orbit, such as would be caused by the gravitationalattraction of other planets, would cause the Earth to spiral away from or intothe sun. We would either freeze or be burned up. In fact, the same behavior ofgravity with distance would mean that the sun would also be unstable. It wouldeither fall apart or it would collapse to form a black hole. In either case, itwould not be much use as a source of heat and light for life on Earth. On asmaller scale, the electrical forces that cause the electrons to orbit around thenucleus in an atom would behave in the same way as the gravitational forces.Thus, the electrons would either escape from the atom altogether or it would spi-ral into the nucleus. In either case, one could not have atoms as we know them.It seems clear that life, at least as we know it, can exist only in regions ofspace-time in which three space and one time dimension are not curled upsmall. This would mean that one could appeal to the anthropic principle, pro-vided one could show that string theory does at least allow there to be suchregions of the universe. And it seems that indeed each string theory doesallow such regions. There may well be other regions of the universe, or otheruniverses (whatever that may mean) in which all the dimensions are curledup small, or in which more than four dimensions are nearly flat. But therewould be no intelligent beings in such regions to observe the different num-ber of effective dimensions.
Apart from the question of the number of dimensions that space-time appearsto have, string theory still has several other problems that must be solvedbefore it can be acclaimed as the ultimate unified theory of physics. We do notyet know whether all the infinities cancel each other out, or exactly how torelate the waves on the string to the particular types of particle that weobserve. Nevertheless, it is likely that answers to these questions will be foundover the next few years, and that by the end of the century we shall knowwhether string theory is indeed the long sought-after unified theory of physics.Can there really be a unified theory of everything? Or are we just chasing amirage? There seem to be three possibilities:
✵ There really is a complete unified theory, which we will somedaydiscover if we are smart enough.
✵ There is no ultimate theory of the universe, just an infinitesequence of theories that describe the universe more and moreaccurately.
✵ There is no theory of the universe. Events cannot be predictedbeyond a certain extent but occur in a random and arbitrary manner.Some would argue for the third possibility on the grounds that if there were acomplete set of laws, that would infringe on God’s freedom to change His mindand to intervene in the world. It’s a bit like the old paradox: Can God make astone so heavy that He can’t lift it? But the idea that God might want tochange His mind is an example of the fallacy, pointed out by St. Augustine, ofimagining God as a being existing in time. Time is a property only of theuniverse that God created. Presumably, He knew what He intended when Heset it up.
With the advent of quantum mechanics, we have come to realize that eventscannot be predicted with complete accuracy but that there is always a degreeof uncertainty. If one liked, one could ascribe this randomness to the interven-tion of God. But it would be a very strange kind of intervention. There is noevidence that it is directed toward any purpose. Indeed, if it were, it wouldn’tbe random. In modern times, we have effectively removed the third possibilityby redefining the goal of science. Our aim is to formulate a set of laws that willenable us to predict events up to the limit set by the uncertainty principle.The second possibility, that there is an infinite sequence of more and morerefined theories, is in agreement with all our experience so far. On many occa-sions, we have increased the sensitivity of our measurements or made a newclass of observations only to discover new phenomena that were not predictedby the existing theory. To account for these, we have had to develop a moreadvanced theory. It would therefore not be very surprising if we find that ourpresent grand unified theories break down when we test them on bigger andmore powerful particle accelerators. Indeed, if we didn’t expect them to breakdown, there wouldn’t be much point in spending all that money on buildingmore powerful machines.
However, it seems that gravity may provide a limit to this sequence of “boxeswithin boxes.” If one had a particle with an energy above what is called thePlanck energy, 1019 GeV, its mass would be so concentrated that it would cutitself off from the rest of the universe and form a little black hole. Thus, it doesseem that the sequence of more and more refined theories should have somelimit as we go to higher and higher energies. There should be some ultimatetheory of the universe. Of course, the Planck energy is a very long way fromthe energies of around a GeV, which are the most that we can produce in thelaboratory at the present time. To bridge that gap would require a particleaccelerator that was bigger than the solar system. Such an accelerator wouldbe unlikely to be funded in the present economic climate.However, the very early stages of the universe are an arena where such ener-gies must have occurred. I think that there is a good chance that the study ofthe early universe and the requirements of mathematical consistency will leadus to a complete unified theory by the end of the century-always presumingwe don’t blow ourselves up first.
What would it mean if we actually did discover the ultimate theory of the uni-verse? It would bring to an end a long and glorious chapter in the history ofour struggle to understand the universe. But it would also revolutionize theordinary person’s understanding of the laws that govern the universe. InNewton’s time it was possible for an educated person to have a grasp of thewhole of human knowledge, at least in outline. But ever since then, the paceof development of science has made this impossible. Theories were alwaysbeing changed to account for new observations. They were never properlydigested or simplified so that ordinary people could understand them.You hadto be a specialist, and even then you could only hope to have a proper grasp ofa small proportion of the scientific theories.Further, the rate of progress was so rapid that what one learned at school oruniversity was always a bit out of date. Only a few people could keep upwith the rapidly advancing frontier of knowledge. And they had to devotetheir whole time to it and specialize in a small area. The rest of the popula-tion had little idea of the advances that were being made or the excitementthey were generating.
Seventy years ago, if Eddington is to be believed, only two people understoodthe general theory of relativity. Nowadays tens of thousands of university grad-uates understand it, and many millions of people are at least familiar with theidea. If a complete unified theory were discovered, it would be only a matterof time before it was digested and simplified in the same way. It could then betaught in schools, at least in outline. We would then all be able to have someunderstanding of the laws that govern the universe and which are responsiblefor our existence.
Einstein once asked a question: “How much choice did God have in construct-ing the universe?” If the no boundary proposal is correct, He had no freedomat all to choose initial conditions. He would, of course, still have had the free-dom to choose the laws that the universe obeyed. This, however, may notreally have been all that much of a choice. There may well be only one or asmall number of complete unified theories that are self-consistent and whichallow the existence of intelligent beings.
We can ask about the nature of God even if there is only one possible unifiedtheory that is just a set of rules and equations. What is it that breathes fire intothe equations and makes a universe for them to describe? The usual approachof science of constructing a mathematical model cannot answer the questionof why there should be a universe for the model to describe. Why does the uni-verse go to all the bother of existing? Is the unified theory so compelling thatit brings about its own existence? Or does it need a creator, and, if so, does Hehave any effect on the universe other than being responsible for its existence?And who created Him?
Up until now, most scientists have been too occupied with the developmentof new theories that describe what the universe is, to ask the question why. Onthe other hand, the people whose business it is to ask why-the philoso-phers-have not been able to keep up with the advance of scientific theories.In the eighteenth century, philosophers considered the whole of humanknowledge, including science, to be their field. They discussed questions suchas: Did the universe have a beginning? However, in the nineteenth and twen-tieth centuries, science became too technical and mathematical for thephilosophers or anyone else, except a few specialists. Philosophers reduced thescope of their inquiries so much that Wittgenstein, the most famous philoso-pher of this century, said, “The sole remaining task for philosophy is the analy-sis of language.” What a comedown from the great tradition of philosophyfrom Aristotle to Kant.
However, if we do discover a complete theory, it should in time be understand-able in broad principle by everyone, not just a few scientists. Then we shall allbe able to take part in the discussion of why the universe exists. If we find theanswer to that, it would be the ultimate triumph of human reason. For then wewould know the mind of God.