As was explained in the first chapter, it would be verydifficult to construct a complete unified theory of everything inthe universe all at one go. So instead we have made progressby finding partial theories that describe a limited range ofhappenings and by neglecting other effects or approximatingthem by certain numbers. (Chemistry, for example, allows us tocalculate the interactions of atoms, without knowing the internalstructure of an atom’s nucleus.) Ultimately, however, one wouldhope to find a complete, consistent, unified theory that wouldinclude all these partial theories as approximations, and that didnot need to be adjusted to fit the facts by picking the valuesof certain arbitrary numbers in the theory. The quest for sucha theory is known as “the unification of physics.” Einstein spentmost of his later years unsuccessfully searching for a unifiedtheory, but the time was not ripe: there were partial theoriesfor gravity and the electromagnetic force, but very little wasknown about the nuclear forces. Moreover, Einstein refused tobelieve in the reality of quantum mechanics, despite theimportant role he had played in its development. Yet it seemsthat the uncertainty principle is a fundamental feature of theuniverse we live in. A successful unified theory must, therefore,necessarily incorporate this principle.

As I shall describe, the prospects for finding such a theoryseem to be much better now because we know so much moreabout the universe. But we must beware of overconfidence -we have had false dawns before! At the beginning of thiscentury, for example, it was thought that everything could beexplained in terms of the properties of continuous matter, suchas elasticity and heat conduction. The discovery of atomicstructure and the uncertainty principle put an emphatic end tothat. Then again, in 1928, physicist and Nobel Prize winnerMax Born told a group of visitors to Gottingen University,“Physics, as we know it, will be over in six months.” Hisconfidence was based on the recent discovery by Dirac of theequation that governed the electron. It was thought that asimilar equation would govern the proton, which was the onlyother particle known at the time, and that would be the end oftheoretical physics. However, the discovery of the neutron andof nuclear forces knocked that one on the head too. Havingsaid this, I still believe there are grounds for cautious optimismthat we may now be near the end of the search for theultimate laws of nature.

In previous chapters I have described general relativity, thepartial theory of gravity, and the partial theories that governthe weak, the strong, and the electromagnetic forces. The lastthree may be combined in so-called grand unified theories, orGUTs, which are not very satisfactory because they do notinclude gravity and because they contain a number ofquantities, like the relative masses of different particles, thatcannot be predicted from the theory but have to be chosen tofit observations. The main difficulty in finding a theory thatunifies gravity with the other forces is that general relativity is a“classical” theory; that is, it does not incorporate the uncertaintyprinciple of quantum mechanics. On the other hand, the otherpartial theories depend on quantum mechanics in an essentialway. A necessary first step, therefore, is to combine generalrelativity with the uncertainty principle. As we have seen, thiscan produce some remark-able consequences, such as blackholes not being black, and the universe not having anysingularities but being completely self-contained and without aboundary. The trouble is, as explained in Chapter 7, that theuncertainty principle means that even “empty” space is filledwith pairs of virtual particles and antiparticles. These pairswould have an infinite amount of energy and, therefore, byEinstein’s famous equation E = mc2, they would have aninfinite amount of mass. Their gravitational attraction would thuscurve up the universe to infinitely small size.

Rather similar, seemingly absurd infinities occur in the otherpartial theories, but in all these cases the infinities can becanceled out by a process called renormalization. This involvescanceling the infinities by introducing other infinities. Althoughthis technique is rather dubious mathematically, it does seem towork in practice, and has been used with these theories tomake predictions that agree with observations to anextraordinary degree of accuracy. Renormalization, however,does have a serious drawback from the point of view of tryingto find a complete theory, because it means that the actualvalues of the masses and the strengths of the forces cannot bepredicted from the theory, but have to be chosen to fit theobservations.

In attempting to incorporate the uncertainty principle intogeneral relativity, one has only two quantities that can beadjusted: the strength of gravity and the value of thecosmological constant. But adjusting these is not sufficient toremove all the infinities. One therefore has a theory that seemsto predict that certain quantities, such as the curvature ofspace-time, are really infinite, yet these quantities can beobserved and measured to be perfectly finite! This problem incombining general relativity and the uncertainty principle hadbeen suspected for some time, but was finally confirmed bydetailed calculations in 1972. Four years later, a possiblesolution, called “supergravity,” was suggested. The idea was tocombine the spin-2 particle called the graviton, which carriesthe gravitational force, with certain other particles of spin 3/2,1, ?, and 0. In a sense, all these particles could then beregarded as different aspects of the same “superparticle,” thusunifying the matter particles with spin ? and 3/2 with theforce-carrying particles of spin 0, 1, and 2. The virtualparticle/antiparticle pairs of spin ? and 3/2 would havenegative energy, and so would tend to cancel out the positiveenergy of the spin 2, 1, and 0 virtual pairs. This would causemany of the possible infinities to cancel out, but it wassuspected that some infinities might still remain. However, thecalculations required to find out whether or not there were anyinfinities left uncanceled were so long and difficult that no onewas prepared to undertake them. Even with a computer it wasreckoned it would take at least four years, and the chanceswere very high that one would make at least one mistake,probably more. So one would know one had the right answeronly if someone else repeated the calculation and got the sameanswer, and that did not seem very likely!

Despite these problems, and the fact that the particles in thesuper-gravity theories did not seem to match the observedparticles, most scientists believed that supergravity was probablythe right answer to the problem of the unification of physics. Itseemed the best way of unifying gravity with the other forces.

However, in 1984 there was a remarkable change of opinion infavor of what are called string theories. In these theories thebasic objects are not particles, which occupy a single point ofspace, but things that have a length but no other dimension,like an infinitely thin piece of string. These strings may haveends (the so-called open strings) or they may be joined upwith themselves in closed loops (closed strings) (Fig. 11.1 andFig. 11.2). A particle occupies one point of space at each instantof time. Thus its history can be represented by a line inspace-time (the “world-line”). A string, on the other hand,occupies a line in space at each moment of time. So its historyin space-time is a two-dimensional surface called theworld-sheet. (Any point on such a world-sheet can bedescribed by two numbers, one specifying the time and theother the position of the point on the string.) The world-sheetof an open string is a strip: its edges represent the pathsthrough space-time of the ends of the string (Fig. 11.1). Theworld-sheet of a closed string is a cylinder or tube (Fig. 11.2):

a slice through the tube is a circle, which represents theposition of the string at one particular time.

Two pieces of string can join together to form a singlestring; in the case of open strings they simply join at the ends(Fig. 11.3), while in the case of closed strings it is like the twolegs joining on a pair of trousers (Fig. 11.4). Similarly, a singlepiece of string can divide into two strings. In string theories,what were previously thought of as particles are now picturedas waves traveling down the string, like waves on a vibratingkite string. The emission or absorption of one particle byanother corresponds to the dividing or joining together ofstrings. For example, the gravitational force of the sun on theearth was pictured in particle theories as being caused by theemission of a graviton by a particle in the sun and itsabsorption by a particle in the earth (Fig. 11.5). In stringtheory, this process corresponds to an H-shaped tube or pipe(Fig. 11.6) (string theory is rather like plumbing, in a way). Thetwo vertical sides of the H correspond to the particles in thesun and the earth, and the horizontal crossbar corresponds tothe graviton that travels between them.

String theory has a curious history. It was originally inventedin the late 1960s in an attempt to find a theory to describe thestrong force. The idea was that particles like the proton andthe neutron could be regarded as waves on a string. Thestrong forces between the particles would correspond to piecesof string that went between other bits of string, as in a spider’sweb. For this theory to give the observed value of the strongforce between particles, the strings had to be like rubber bandswith a pull of about ten tons.

In 1974 Joel Scherk from Paris and John Schwarz from theCalifornia Institute of Technology published a paper in whichthey showed that string theory could describe the gravitationalforce, but only if the tension in the string were very muchhigher, about a thousand million million million million millionmillion tons (1 with thirty-nine zeros after it). The predictions ofthe string theory would be just the same as those of generalrelativity on normal length scales, but they would differ at verysmall distances, less than a thousand million million millionmillion millionth of a centimeter (a centimeter divided by 1 withthirty-three zeros after it). Their work did not receive muchattention, however, because at just about that time most peopleabandoned the original string theory of the strong force infavor of the theory based on quarks and gluons, which seemedto fit much better with observations. Scherk died in tragiccircumstances (he suffered from diabetes and went into a comawhen no one was around to give him an injection of insulin).

So Schwarz was left alone as almost the only supporter ofstring theory, but now with the much higher pro-posed valueof the string tension.

In 1984 interest in strings suddenly revived, apparently fortwo reasons. One was that people were not really makingmuch progress toward showing that supergravity was finite orthat it could explain the kinds of particles that we observe. Theother was the publication of a paper by John Schwarz andMike Green of Queen Mary College, London, that showed thatstring theory might be able to explain the existence of particlesthat have a built-in left-handedness, like some of the particlesthat we observe. Whatever the reasons, a large number ofpeople soon began to work on string theory and a newversion was developed, the so-called heterotic string, whichseemed as if it might be able to explain the types of particlesthat we observe.

String theories also lead to infinities, but it is thought theywill all cancel out in versions like the heterotic string (thoughthis is not yet known for certain). String theories, however,have a bigger problem: they seem to be consistent only ifspace-time has either ten or twenty-six dimensions, instead ofthe usual four! Of course, extra space-time dimensions are acommonplace of science fiction indeed, they provide an idealway of overcoming the normal restriction of general relativitythat one cannot travel faster than light or back in time (seeChapter 10). The idea is to take a shortcut through the extradimensions. One can picture this in the following way. Imaginethat the space we live in has only two dimensions and iscurved like the surface of an anchor ring or torus (Fig. 11.7). Ifyou were on one side of the inside edge of the ring and youwanted to get to a point on the other side, you would have togo round the inner edge of the ring. However, if you wereable to travel in the third dimension, you could cut straightacross.

Why don’t we notice all these extra dimensions, if they arereally there? Why do we see only three space dimensions andone time dimension? The suggestion is that the otherdimensions are curved up into a space of very small size,something like a million million million million millionth of aninch. This is so small that we just don’t notice it: we see onlyone time dimension and three space dimensions, in whichspace-time is fairly flat. It is like the surface of a straw. If youlook at it closely, you see it is two-dimensional (the............