The Elegant Universe: Superstrings, Hidden Dimensions and the Quest for Ultimate Theory 
by Brian Greene.
Vintage, 448 pp., £7.99, February 2000, 9780099289920
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The great ambition of scientists is to grasp the far from obvious nature of the physical world at ever more fundamental levels, and in doing so, to unify our understanding of phenomena that had previously appeared to be disparate. We have been enormously successful in this, demonstrating that complex objects are made from simpler components, and they in turn are made of even simpler ones. Everything around us, ourselves included, is composed of molecules, which are composed of atoms – carbon, nitrogen, oxygen, phosphorus and so on – which are composed of negatively charged electrons, and a nucleus of positively charged protons and uncharged neutrons, which are composed of quarks. Thus underlying the immense complexity of life is a simplicity of microscopic composition.

The way in which these various particles combine and interact is controlled by just four fundamental forces: the electromagnetic force, which unifies electricity and magnetism and is the common basis of light, radio waves and X-rays (all now identified as electromagnetic waves); the gravitational force, which as well as causing things to fall onto the floor, causes the planets to move around the sun and galaxies round each other; the weak nuclear force, which is responsible for hard-to-detect effects such as the radioactive decay of neutrons into protons and electrons; and the strong nuclear force, which holds the protons and neutrons in the nucleus of an atom together, thus making it stable despite the electrical repulsion between the protons that tends to rip it apart.

It has taken centuries to arrive at the amazingly successful understanding of the structure of the physical world that we now have, whose basic feature is the law-like descriptions we can give of the behaviour of matter, testable in detail by experiments. These laws are formulated mathematically, enable us to make quantitative predictions, and are universal inasmuch as they are believed to apply to all matter at all times and in all places. If we discovered matter that didn’t obey them, that would signal that we needed to modify our understanding and look for more general relationships still.

Our understanding of both particles and the forces involved in their interactions has evolved in response to ever more refined data from experiments. In particular, the question of whether, at its most fundamental level, matter behaves in a ‘wave-like’ or ‘particle-like’ way has been a source of continuing puzzlement. Our present belief, based in quantum theory (the theory that describes the behaviour of matter at very small scales), is that, at sub-atomic levels, matter isn’t either wave-like or particle-like in nature but both, depending on the circumstances, and behaves unpredictably in a manner quite unlike anything we are familiar with in everyday life.

Our ideas about forces have also undergone a major evolution, from being thought of as simply constituting the direct action of one object on another, either through contact or at a distance, then as being mediated by the effects of various ‘fields’ pervading space and time – e.g. the electromagnetic field that currents and magnets generate, exerting forces on charged particles – and finally to being understood as involving the exchange of force-carrying particles, photons in the case of electromagnetism, gluons in the case of the strong nuclear force.

Forces and particles, then, are not as distinct from each other as was once thought. Additionally, it seems now that not even the four ‘fundamental’ forces are independent of each other, but that the electromagnetic and weak nuclear forces are in fact different aspects of a single, more fundamental force, which would have functioned as a single interaction in the very early days of the Universe but appears under present-day conditions to comprise separate forces. Attempts to include the strong nuclear force also in this unifying scheme are well advanced.

Even our understanding of space and time has evolved, these formerly distinct concepts now being understood as separate aspects of a single four-dimensional space-time continuum. This has two quite different sets of implications. On a large scale, gravity (which controls the evolution of the Universe) is now seen as being caused by the curvature of four-dimensional space-time, and as able to convey energy over vast distances by means of gravitational waves. On very small scales, when combined with quantum theory, it implies an equivalence between mass and energy (i.e. E = mc2), as evidenced in such nuclear reactions as those that power the radiance of the sun, and predicts the existence of anti-particles, which produce enormous amounts of energy when they annihilate with their corresponding particles – when an electron and its anti-particle, the positron, collide, for example, the result is pure radiation, emitted in the form of two high-energy photons; the particles then no longer exist. This in turn has led to a major revision of the concept of a ‘vacuum’ – understood nowadays not as an emptiness with nothing happening in it, but as a seething sea of particle and anti-particle pairs continually coming into existence and annihilating. All of this follows from the unification of relativity theory and quantum theory, two of the great intellectual achievements of this century.

Despite all these advances, however, there are still great gaps to be filled in. The quest now is for an even more fundamental theory that would unify gravitation and quantum theory – something that has so far eluded us. The hope is that such a theory would also include the other three fundamental forces in a single scheme, and show them to be simply different aspects of a single ‘super-force’, explaining into the bargain many properties of fundamental particles that at the moment appear somewhat arbitrary.

The most promising attempts made to date have given us the family of what are known as Superstring theories, in which our ideas of both particles and of space-time are revised in an astonishing way. According to Superstring theorists, our perceived four-dimensional space-time has to be seen as only an approximation to a ten or eleven-dimensional space-time, with the other six or seven spatial dimensions rolled up so small that they are indistinguishable from a point. On top of which, particles are no longer to be seen as point-like objects, but rather as patterns of vibrations of extended two-dimensional objects like strings or ribbons; thus electrons and quarks, for example, would be made up of vibrating Superstrings.

This whole structure is subject to so-called ‘Supersymmetry’, whereby kinds of particle with apparently quite different properties are found to be related to each other and indeed may be transformed into each other under certain circumstances. For this method of unification to work, we need to identify symmetries in the interactions represented by (often hidden) similarities in the laws of physics. A simple example: if a physical system’s interactions are constant in time, then its dynamical properties are the same at later times as they were at earlier times, and its energy is conserved; if the system’s interactions are constant in space, then its momentum is conserved. And just as it’s possible to represent mathematically the symmetries involved in the rotations of a solid object (a cube, say) that move it in such a way as to leave it exactly where it was but with the different faces rotated into each other, so we can represent the relation between families of fundamental particles in terms of abstract rotations that transform them into each other. Realising this has enabled physicists to predict the existence of previously unknown types of particle, which are required if we’re to complete the symmetry patterns. Experimental proof of their existence has been a major vindication of this form of analysis.

Up until quite recently, there were five alternative Superstring theories on offer, each with somewhat different symmetries, but this has now become an area of much excitement, as new unifications are achieved between models previously seen as distinct, suggesting that there may be only one theory that encompasses and unifies all of the others. The excitement came about with the discovery by the American theoretical physicist, Edward Witten, of previously undetected further sets of symmetries (or ‘dualities’), which link various parts of the theory, in particular its reasonably well-understood low-energy aspects to the rather ill-understood high-energy ones, where it’s not even clear how to formulate the theory. This should help us to understand ‘strong-coupling’ behaviour, which occurs when the interactions in a physical system are intense because the energies involved are high, and which has hitherto been inaccessible because we don’t know how to solve the immensely complex relevant equations. We can now do this by using one of the new symmetries to compare strong-coupling behaviour with the corresponding properties in a ‘weak-coupling’ regime, where the interactions are weak and thus easy to analyse. As the hype would have it, the discovery of these theoretical structures may mean we can one day complete the physicists’ ultimate dream – a Theory of Everything (TOE) that will explain the behaviour of all the fundamental particles and forces in a single framework.

In The Elegant Universe, Brian Greene guides us through these fundamental ideas and recent developments in as full and comprehensible a way as is possible without going into the exceedingly difficult mathematics involved. He aims to explain many of the central ideas of Superstring theories by means of analogy and explanatory diagrams rather than equations, and I can only say that his book is an explanatory tour de force.

He starts with the basic ideas of relativity and quantum theory, explaining why these need to be unified, and then moves on to Superstrings. Here he goes into detail about the notion of ‘quantum spin’ (a microscopic version of the spin that can be put on a tennis ball) that separates particles into two distinct families: matter particles, which spin at one speed, and force-carrying particles that either don’t spin or spin twice as much, but four times as much when the force is gravitational. He next shows how the theory of Supersymmetry connects these two families of particles and in so doing predicts the existence of many new particles which we’ve yet to detect. From there, Greene goes on to the strange idea that the Universe may have more dimensions than meet the eye, may have ‘both extended and curled-up dimensions’. The hope that we will be able to unify existing physical theories by means of these extra dimensions follows from ideas originally introduced by Theodor Kaluza and Oskar Klein, who suggested that space-time was really five rather than four-dimensional, the postulated fifth dimension carrying the electric and magnetic fields.

Superstring theory in fact requires the Universe to have no fewer than nine spatial dimensions. The question then arises of why the three of them we are familiar with should be large and the other six so small as to be unnoticeable. Another problem arises from the extraordinarily complex structure that these curled-up dimensions are required to have: they are connected together in a contorted topology that is extremely difficult to describe. Nevertheless, the theory holds that they ‘are an integral and ubiquitous part of the spatial fabric: they exist everywhere’.

Greene is now at the point where he can deliver the final, astonishing, unifying vision:

From one principle – that everything at its most microscopic level consists of combinations of vibrating strands – string theory provides a single explanatory framework capable of encompassing all forces and all matter ... The observed particle properties ... are a reflection of the various ways in which a string can vibrate ... Force particles are also associated with particular patterns of string vibration, and hence everything, all matter and all forces, is unified under the same rubric of microscopic string oscillations – the ‘notes’ that a string can play.

This result necessitates the existence of an infinite number of other particles in addition to those we’ve detected so far, but almost all of them will have to be so massive that we cannot now, nor indeed will be able ever, to achieve experimentally the energies that would be required to observe them.

Finally, Greene comes right up to date by describing the dualities that tie the various aspects of string theory into a unity (the so-called ‘M theory’), and discusses the way this can be used to calculate properties of black holes, before speculating about how it might all relate to cosmology. In particular, the theory has been used to calculate the number of physical states that are no longer accessible to an observer because they are hidden behind the ‘horizon’ of a black hole. This calculation serves to confirm in an interesting way the idea first discovered by Bekenstein and Hawking, that when they collapse, massive astrophysical objects create a black hole which has remarkable thermodynamic properties, similar to those of ordinary thermodynamics – thus linking quantum theory, gravitational theory and thermodynamics in a way never before achieved.

It would be hard to imagine anyone producing a clearer account than this of the difficult ideas involved, and Greene even brings out something of the actual excitement of scientific discovery when he recalls his own role in exploring some of the remarkable changes of structure that can occur in the topology of the new nine-dimensional space sections.

Having said this, a word or two of caution is in order. First, Superstring theory is still far from complete; it is in many ways as yet simply a set of suggestions of the way things might be, rather than a well-developed theory of how we know that they are. The form of the ‘central theory’ remains unknown, and the actual calculations that have been done to date have mainly to do with various weak-field versions of what is merely a hypothesis. Some features even of these are far from clear: for example, how the apparently extremely stable properties of the known families of identical particles can be reliably deduced from the proposed model as being vibrations of a string, and whether all the features of General Relativity theory are satisfactorily recovered. Secondly, the theory relies on massive extrapolation from selected aspects of our existing physics onto very different scales and into very different conditions and thus goes way beyond the point where we have any proof that what is suggested is remotely right. Not only are there at present no experimental data supporting this vastly complex structure, but there may never be any, because the scale and energies required by much of the theory are such that it may for ever be beyond experimental investigation. It is possible that some variant of Superstring theory will one day explain in a satisfactorily unified way the behaviour of precisely that spectrum of particles which we can detect in the world around us, including being able to predict their masses. If so, that will be one of the greatest feats of theoretical physics ever achieved. But we are a long way from that situation at present. Even the concept of Supersymmetry, which plays a central role in the theory and should be amenable to experimental test, may or may not be true; none of the predicted supersymmetrical partner particles to known particles have yet been detected. Superstring theory is the one truly comprehensive attempt to find such a fundamental physical theory that we currently have, and it is a magnificent one. This is not enough of course to guarantee that it’s right. It may have latched onto the correct intimations about the nature of the as yet unknown aspects of fundamental physics, but then again it may not. Greene doesn’t try to conceal this uncertainty, but he is himself an enthusiast for the theory, something it’s important not to lose sight of when reading this book.

There was only one place in The Elegant Universe where I felt uncomfortable about what Greene was saying. It comes when he gets on to discussing the possibility of an ultimate ‘Theory of Everything’, and touches briefly on the issue of reductionism. He does not examine this as carefully as he might have done. He writes, for example: ‘Almost everyone agrees that finding the TOE would in no way mean that psychology, biology, geology, chemistry or even physics had been solved or in some sense subsumed.’ But why would any sensible person suppose such a thing? Any serious suggestion that Superstring theory might have such ‘greedy’ reductionist implications is likely to bring the whole programme into disrepute. If its reductionist implications are to be considered, then this should be done in a much more nuanced fashion. The philosophical implications of a theory dealing as this one does with the nature of emergent order and meaning in complex, hierarchically structured systems, should either be passed over altogether or dwelt on for longer than they are here. Greene might also have drawn attention to the limitations inherent in all of our mathematical and physical models of reality, and the need not to confuse them with reality itself.

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