INTRODUCTION.
The search for the Grand Unified Theory (GUT) of physics may be thought of in terms of the two great theories of the twentieth century: the general theory of relativity and quantum mechanics. The first, the general theory of relativity, is a theory of gravity that relates gravity to the curvature of spacetime. It is essentially a theory of structure of space and time. The curvature of spacetime is responsible for the force of gravity. The second, quantum mechanics, describes the behavior of the atomic and subatomic world; there are quantum theories which describe each of the other three forces of nature, apart from gravity; the quantum electrodynamic theory (QED) describes electromagnetism at quantum level, the quantum chromodynamics theory (QCD) describes the strong force, and the electroweak theory of weak interactions. A fully unified description of the Universe and all that it contains (called a "theory of everything", TOE) would also have to describe gravity and spacetime at the quantum level. This implies that spacetime itself must be, on a very short-range scale, quantized into discrete lumps, not smoothly continuous. The extension of the string theory known as the SuperString Theory (SST), naturally produced a quantum description of gravity. But it took several years for gravity to fall out of the superstring theory.
The string theory took off in the middle of the 1980s, after a new variation on the theme was developed by John Schwarz and Michael Green. They started working together at the end of the 1970s, after they met at a conference of CERN, and discovered that, unlike everybody else studying particle physics at the time, they were both interested in strings. They began almost immediately to produce results. The first step that they took was to realize that what was needed was a theory of everything - not just of hadrons but of all particles and fields. Naturally, from the outset the new version of string theory had SUSY built in. In such a theory, the strings would have to be very small - much smaller than Nambu's strings, which were only designed to describe hadrons. Even without knowing how the theory would develop, Schwarz and Green could predict what scale the strings would operate on, because they wanted to include gravity in the theory. Gravity becomes seriously affected by quantum effects at a scale about 10-33 cm (about 10-35 m), the distance scale at which the very structure of spacetime is affected by quantum uncertainty. The scale at which quantum effects become significant for a particular force depends upon the strength of the force. Since gravity is the weakest of the four forces of nature, the quantum effects only become dominant for gravity on such a tiny scale. It is by measuring the strength of gravity (the value of the gravitational constant, G) that the physicists can work out what scale quantum gravity operates on.
The first string model that was developed by Schwarz and Green, in 1980, dealt with open-ended strings vibrating in ten dimensions, able to link up with one another and break apart. Superficially, this model looked like a shrunken version of the Nambu's string theory. But in fact it went far further, including in principle string states corresponding to almost all known particles and fields, and all known symmetries affecting fermions and bosons, plus supersymmetry. There was one exception - gravity. In spite of their intentions, gravity still could not be explained by the new string theory.
But in spite of this deficiency, this early version of the superstring theory set the scene for what was to follow. The central idea of all subsequent superstring theories is that the conventional picture of fundamental particles (leptons and quarks) as points with no extension in any direction is replaced by the concept of particles as objects which have extension in one dimension, like a line drawn on a piece of paper, or the thinnest of strings. The extension is very small, about 10-35 meters. It would take 1020 such strings, laid end to end, to stretch across the diameter of a proton.
The next step in development of a superstring theory of everything came in 1981, when Schwarz and Green introduced a new twist (literally) to the theory. The open string theory became known as the Type I theory, and the new Type II theory introduced a key variation on the theme - closed loops of string. The Type I theory only had open-ended strings; the Type II theory had only closed loops of string. In a particularly neat piece of packaging, in closed loops, fermionic states correspond to ripples running around the loop one way, while the bosonic states correspond to ripples running around the loop the other way, demonstrating the power and influence of supersymmetry. The closed loop version had some advantages over the open model; it proved easier to deal with those infinities that plagued particle physicists in the open string model. But the Type II theory also had its difficulties, and did not seem at the time capable of predicting, or encompassing, all varieties of the known particle world.
There was another cloud on the horizon. In 1982 Ed Witten and Luis Alvarez-Gaume discovered that the Kaluza-Klien compactification trick will only work to make the forces of nature in the way required if you start out with an odd number of dimensions before compactification. This made eleven-dimensional supergravity look more attractive than ever before, but gave the ten-dimensional string theories real problems. But this did not stop people from working on those theories; it just gave them something extra to think about.
The next step forward was actually a step backward. Dissatisfied with Type II theory, Schwarz and Green went back to the Type I theory, and tried to remove the infinities which plagued it. The problem was that there were many possible variations on their theme, and that all of them seemed to be beset by not just infinities, but by what were called anomalies - behavior that did not match the behavior of the everyday world, especially its conservation laws. For example, in more than one version of the theory, electric charge is not conserved, so charge can appear out of nothing at all, and disappear, as well.
But in 1984 Schwarz and Green found that there is one, and only one, form of symmetry [SO(32)] which, when applied to the Type I string theory, removed all the anomalities and all the infinities. They had a unique theory, free from all anomalities and infinities, that was a real candidate for the theory of everything. It was at this point that other physicists started to set up and take notice of strings once again.
One of the team that was fired up by the success achieved by Green and Schwarz in 1984 was based at Princeton University. David Gross and three colleagues (together they were known as the 'Princeton String Quartet') took a second look at the closed loop idea, writing it down using a different mathematical approach. There was plenty to write down, because the theory is a little more complicated. But bosonic vibrations described (at first, unintensionally) by Nambu's first version of the string theory actually take place in twenty-six dimensions. Gross and his colleagues found a way to incorporate both kinds of vibration into a single closed loop of string, with the ten-dimensional vibrations running one way round the loop and the twenty-six dimensional vibrations running the other way round the loop. This version of the idea is called the heterotic string theory. ("Heterotic" is from the Greek root as in "heterosexual", implying a combination of at least two different things.)
The heterotic strings neatly tidy up a loose end of the Type II theory. In theories involving open strings, some of the properties we associate with particles (the properties that physicists call "charges") are tied to the end points of the whirling strings (this may be electric charge, if we are dealing with electromagnetism, or "color charge" of quarks, or something else.). But closed loops do not have end points so where are these properties located? In heterotic strings, these properties are described, but have to be thought of as somehow smeared out around the strings. This is the main physical distinction between heterotic strings and the kind of closed strings that Green and Schwarz investigated at the beginning of the 1980s; you can picture heterotic string theory as a kind of hybrid combination of the oldest kind of string theory and the first superstring theory.
How can two different sets of dimensions apply to vibrations of the same string? Because for the bosonic vibrations, sixteen of the twenty-six dimensions have been compactified as a set, leaving ten more which are the same as for the ten-dimensional fermionic vibrations, with six of those ten dimensions being compactified in a different way to leave us with the familiar four dimensions of spacetime. It is the extra richness provided by the sixteen extra dimensions that makes for the richness in variety of bosons, from photons to W and Z particles and gluons, compared with the relative simplicity of the fermionic world, built up from a few quarks and leptons. The sixteen extra dimensions in the heteroic string theory are responsible for a pair of underlying symmetries, either of which can be used to investigate the physical implications of the theory (any other choice of symmetry groups leads to infinities). One of these is the SO(32) symmetry group, which had already turned up in the investigation of open strings (32, of course, being twice 16); the other is a symmetry group known as E8 × E8, which actually describes two complete worlds, living alongside each other (8 plus 8 also being 16). Each of the E8 symmerties can be naturally broken down into just the kind of symmetries used by particle physicists to describe our world. When six of the ten dimensions involved are curled up, they provide a symmetry group known as E6, which is itself broken down into SU(3) × SU(2) × U(1). But SU(3) is the symmetry group associated with the standard model of quarks and gluons, while SU(2) × U(1) is the symmetry group associated with the electroweak interaction. Everything in particle physics is included within one of E8 parts of the overall E8 × E8 symmetry group.
Since only one of the E8 components is needed to describe everything in our Universe, that leaves a complete duplicate set possibilities. The symmetry between the two halves of the group would have been broken at the birth of the Universe, when gravity split apart from the other forces of nature. The result would, some physicists believe, be the development of two universes, interpenetrating one another but interacting only through gravity - our world and a so-called "shadow" universe. There would be shadow photons, shadow atoms, perhaps even shadow stars and shadow planets, inhabited by shadow people co-existing in the same spacetime that we inhabit, but forever invisible. A shadow planet could pass right through the earth, and never affect us, except through its gravitational pull. It sounds like science fiction, but one reason that the idea is taken seriously is that there is astronomical and cosmological evidence that a lot of the Universe exists in the form of dark matter, detectable gravitationally but not seen. It is, though, at least as likely that in the shadow universe later symmetry breakings occurred differently from in our own world, so that there are no shadow stars, and so on, after all. All this is tangential to the story being told here. It has, though, brought us back to gravity, and gravity is the reason why interest in string theory and supersymmetry exploded in the middle of 1980s.
The excitement was largely to do with the way gravity appeared naturally out of the superstring theory. Gravity may be thought of in two ways. Starting from Einstein's description of curved spacetime, we are led to the image of gravity waves, ripples in the fabric of spacetime, with, of course, an associated particle, the spin-2 graviton. This is the way the concept appeared historically. But we could, in principle, start out with a quantum field theory based on a zero mass, spin-2 particle, the graviton, and see what the equation describe. Carry the calculations through, and you end up with Einstein's general theory of relativity. The problem with all theories prior to superstrings (except, just possibly, N = 8 supergravity) is that when you add in a massless, spin-2 particle, they are beset with infinities that are impossible to remove even by renormalization. The dramatic discovery that emerged in the mid-1980s is that whenever theorists set up a mathematical description of superstring loops, tailored to describe the behavior of the known particles, a description of a massless, spin-2 particle always falls out of the equation and the quarks and leptons and the rest. What's more, it does so without causing those uncomfortable infinities to rear their ugly heads. One of the founders of superstring theory, John Schwarz, refers to this as a "Deep Truth", that must be telling us something about the way the Universe works.
Gravity must be included in superstring theory, and arise naturally in a way that can be portrayed in simple physical terms. The simplest form of closed string that emerges automatically from the theory has the properties of a spin-2 vector boson, the quantum particle of gravity. Indeed, they are gravitons, the carriers of the gravitational force. Gravity, including Einstein's equations of the general theory of relativity, emerges naturally from string theory as a quantum phenomenon.
M-THEORY.
All this was exciting enough to encourage more theorists to begin to work on strings and superstrings after 1984. But, just as there had been a gap of about ten years between the first breakthrough in string theory (involving SUSY itself) in the mid-1970s and the combination of the discovery of heteroic strings and that gravitons are a part of string theory in the mid-1980s, so it was to be another ten years before the next breakthough occurred. It might have happened sooner - remember that puzzle about the need for an odd number of dimensions to make compactification work? And the joker in the pack, eleven-dimension supergravity? In the late 1980s, a few theorists, including Michael Duff, of Texas A & M University, raised the possibility that we ought not be dealing with strings at all, but ought to add another dimension, making them resemble two-dimensional sheets (membranes) rather than one-dimensional lines. The extra dimension brings the total number up to eleven, but one of these dimensions is immediately rolled up so that the membrane behaves like a ten-dimension string of string theory. This idea is more a speculation than a fully worked out theory, and it was laughed out of court at the end of 1980s. But it was revived, as a much more complete theory, in the 1990s, and today the membrane idea (often referred to as M-theory) is just about the hottest game in town.
The reason why M-theory is causing excitement at the end of 1990s is that it offers, at last, a unique mathematical package to describe all the forces and particles of nature. String theory itself comes in several different varieties, which each having their good points and their bad points. In fact, there are exactly five variations on the theme. These are the Type I theory of Schwarz and Green, two versions of the Type II theory (Type IIA theory and Type IIB theory), and two versions of the heterotic strings (Heterotic O(32) theory and Heterotic E8 × E8 theory). In addition, there is still that wild card, the eleven-dimensional supergravity. It can be shown mathematically that these are only viable variations on the theme; all other possibilities involving supersymmetry are plagued by infinities.
At first sight, six rival contenders for the title "theory of everything" seems like a lot. But, in fact, this is a remarkably short list. The old-fashioned particles physics approach to grand unified theories gives us a plethora of possibilities, any of which are just as good as any of the others. To have only a half a dozen theories to choose from seemed remarkable in the 1980s. The dramatic new discovery made in the mid-1990s was that all six theories are related to one another. Specifically, they are all different manifestations of a single M-theory. In a manner reminiscent of the way the electroweak is a single theory that describes what seemed to be two separate interactions at lower energies (electromagnetism and the weak interaction), M-theory is a single theory at even higher energies, and describes what seems to be six different models at lower energies. Specifically, the differences between the six models appear at the level of weak interaction, and the unity is clear at the level of the strong interaction.
We may not have to wait too long to find out how good a theory is M-theory, and whether it is indeed the long sought-after theory of everything. The kinds of energies needed to probe the predictions of M-theory should be achieve at the latest high energy particle accelerators, the Large Hadron Collider (LHC), which is expected to begin operation at CERN in Geneva, Switzerland, by the end of the first decade of the twenty-first century. The ultimate test of any physical theory is by comparing its perdictions with the results of experiment.