Illustrated Theory of Everything: The Origin and Fate of the Universe (8 page)

At first, I believed that disorder would decrease when the universe recollapsed.This was because I thought that the universe had to return to a smooth andordered state when it became small again. This would have meant that thecontracting phase was like the time reverse of the expanding phase. People inthe contracting phase would live their lives backward. They would die beforethey were born and would get younger as the universe contracted. This idea isattractive because it would mean a nice symmetry between the expanding andcontracting phases. However, one cannot adopt it on its own, independent ofother ideas about the universe. The question is: Is it implied by the no bound-ary condition or is it inconsistent with that condition?

As I mentioned, I thought at first that the no boundary condition did indeedimply that disorder would decrease in the contracting phase. This was basedon work on a simple model of the universe in which the collapsing phaselooked like the time reverse of the expanding phase. However, a colleague ofmine, Don Page, pointed out that the no boundary condition did not requirethe contracting phase necessarily to be the time reverse of the expandingphase. Further, one of my students, Raymond Laflamme, found that in a slightlymore complicated model, the collapse of the universe was very different fromthe expansion. I realized that I had made a mistake. In fact, the no boundarycondition implied that disorder would continue to increase during the con-traction. The thermodynamic and psychological arrows of time would notreverse when the universe begins to recontract or inside black holes.What should you do when you find you have made a mistake like that? Somepeople, like Eddington, never admit that they are wrong. They continue tofind new, and often mutually inconsistent, arguments to support their case.Others claim to have never really supported the incorrect view in the firstplace or, if they did, it was only to show that it was inconsistent. I could givea large number of examples of this, but I won’t because it would make me toounpopular. It seems to me much better and less confusing if you admit in printthat you were wrong. A good example of this was Einstein, who said that thecosmological constant, which he introduced when he was trying to make astatic model of the universe, was the biggest mistake of his life.

The Theory of Everything: The Origin and Fate of the Universe

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: