In pursuit of the ultimate theory

The biggest names in particle physics are meeting in Mumbai to take a close look at the 'String Theory', which is widely held to have opened up the path towards a Theory of Everything.

AS the new millennium sets in, some of today's greatest minds in particle physics - indeed all of theoretical physics, as these are the leading lights in the pursuit of the ultimate theory or the Theory of Everything (TOE), as it has come to be called - will be headed towards the Tata Institute of Fundamental Research (TIFR), Mumbai, where a major international conference, 'Strings 2001' is to get under way on January 5, 2001. The five-day conference is so named because its subject is 'String Theory', w hich is widely held to have opened the path leading up to the TOE, the Holy Grail of particle physics, that will unify and explain the existence of the myriad elementary particles, which are the constituents of all matter and the different forces of inte raction among them. The names that the conference has attracted include such luminaries as Stephen Hawking, Edward Witten, David Gross, John Schwarz and Michael Green and, of course, India's own Ashoke Sen.

The search for such a TOE may seem impossibly ambitious. At a philosophical level one may even ask why should there be a TOE at all? But most of the physicists who would be assembled in Mumbai would tend to disagree. Their argument: if one looks at the h istory of physics in recent times, the search for a unified explanation of physical phenomena has been the cornerstone of major revolutionary ideas which, in turn, have contributed immensely to the development of science and technology. Towards the end o f the 19th century, Maxwell's Electromagnetic Theory resulted from the attempt to explain electricity and magnetism in a unified framework. Hundred years ago, an attempt to understand thermodynamics or black body radiation in terms of Maxwell's ideas led Max Planck to make his revolutionary quantum hypothesis. The constancy of light predicted by Maxwell's theory led to Einstein's revolutionary concept of unifying space and time and the formulation of the Special Theory of Relativity. Quantum mechanics, which rules phenomena at very small distances (subatomic phenomena), resulted from the attempt to resolve the fundamental inconsistency of Maxwell's Theory with Newtonian mechanics. Einstein's General Theory of Relativity resulted from viewing Newton's t heory of gravitation from the perspective of a unified spacetime. Unifying quantum mechanics and Maxwell's Theory produced the spectacularly successful theory of Quantum Electrodynamics (QED), whose predictions have been verified to an astonishing degree of accuracy.

While electromagnetism and gravitation are two forces that act over large distances and are experienced at the macroscopic level, there are two other forces of nature that act at the quantum or microscopic level - the weak nuclear force responsible for r adioactive decay and the burning of stars and the strong nuclear force which binds together neutrons and protons to form stable nuclei. The bid to go one step further from QED, by unifying electromagnetism with the weak force, resulted in the discovery o f a basic symmetry principle called 'gauge symmetry', which governed the behaviour of forces. This principle forms the basis of the enormously successful and Nobel Prize-winning Weinberg-Salam-Glashow unified theory of the electroweak force. Developed in the mid-1970s, its various predictions have been borne out by experiments. Inclusion of the strong force in this framework, in the form of what is known as Quantum Chromodynamics (QCD), has also now been achieved in what is today called the Standard Mod el (SM). The SM has provided a reasonably good understanding of processes involving elementary particles over a large energy range. In the last couple of decades, the SM, in turn, has led to the formulation of somewhat more ambitious unification schemes such as Grand Unified Theories (GUTs) and Supersymmetric Grand Unified Theories (SUSY GUTs) which have had limited successes.

Despite its remarkable success, the SM is only three-fourths the way to complete unification because, as would be noticed, the SM does not include gravity in its unification scheme. One may ask, besides the aesthetic reason that a complete theory must in clude gravity as well, what is the compelling reason to include gravity, whose effects are extremely weak in any case? While the force is small at low energies, at higher energies the effect of gravitation will become strong. To appreciate this, consider the force of gravitation between two protons at rest. It is 10 -36 times weaker than the electrostatic force between them. Imagine that the protons are accelerated so that each of them carries an energy of 1018 giga electron volt (GeV) of energy. Given that the mass of a proton is equivalent (via th e relation mc2) to an energy of 1 GeV, this energy increases the effective mass of the proton 1018 fold. The gravitational force between them at such energies will become 1036 fold and comparable to the electrostatic forc e.

Also, in grand unification theories, unification of the three forces occurs around 1016 GeV. This is close to the energy scale of 1019 GeV, known as Planck Mass, when quantum effects are expected to become important in gravity. Ther efore, inclusion of gravity in a quantum theory of particles and forces becomes important. However, it turns out that trying to unify gravitation in this framework only leads to inconsistencies. This inconsistency can be traced to a fundamental difficult y in reconciling gravitation with quantum theory.

String Theory resolves this. Indeed, gravitation emerges naturally from String Theory, which led Witten, of the Institute of Advanced Study, Princeton, the world's leading string theorist, to this famous remark: "The fact that gravity is a consequence of String Theory to me is one of greatest theoretical insights ever." The rise of String Theory as a strong candidate for a TOE can be attributed chiefly to this one fact.

John Wheeler, the well-known physicist of yesteryear, is said to have remarked that when we come to the final laws of nature, we shall wonder why they were not obvious from the beginning. Whether String Theory will ultimately lead one to such a simplisti c view of all nature is a moot point because as it stands, it includes concepts that may seem bizarre, uses complex mathematics that most theoretical physicists find hard to comprehend, is yet to reproduce fully successful partial unification theories su ch as SM and, worst of all, is yet to predict something that can be tested by experiments. Indeed, the proposed unification occurs at energy scales that no experiment can conceivably attain even in the distant future. One is talking here of an energy sca le that is a million billion times the energies achievable in present-day particle accelerators.

And yet, many top-ranking theoretical physicists are excited about the manner in which String Theory seems to incorporate naturally, and in many ways uniquely, most features - if not in precise quantitative detail but at least qualitatively - of lower th eories such as SM, SUSY GUTs and the general theory of relativity in their domains of applicability. String Theory, according to them, is like what the final theory should indeed be, the requirement of a single unified scheme of all lower-level theories seems to lead almost uniquely to such a theoretical structure. The theory's fascinating concepts and mathematical structure have caught the imagination of aspiring young theorists all over the world. Young Indian theorists are not far behind in this, wit h significant contributions coming from Ashoke Sen of the Harish Chandra Institute of Mathematics in Allahabad and those at the TIFR.

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Notwithstanding these, the claim in the mid-1980s that a TOE was just round the corner with the advent of a consistent String Theory was perceived by sceptics as sheer arrogance of its proponents. A decade ago Paul Ginsparg and Sheldon Glashow remarked: "Contemplation of (super) strings may evolve into an activity as remote from conventional particle physics as particle physics is from chemistry, to be conducted at schools of divinity by future equivalents of medieval theologians... For the first time s ince the Dark Ages we can see how our noble search may end, with faith replacing science once again."

Indeed Hawking, whose discovery of the curious quantum properties of black holes, has found a satisfactory explanation only within the String Theory framework, belonged to this band of sceptics. He remarked in 1994 (before String Theory actually explaine d his finding): "I suspect... there may not be any observable predictions of String Theory that cannot be predicted from general relativity... If this is true, it raises the question of whether String Theory is a genuine scientific theory. Is mathematica l beauty and completeness enough in the absence of distinctive observationally tested predictions?" Witten, who is now credited with the new revolutionary concept in String Theory called M-theory, disregards such sentiments. "Good wrong ideas are extreme ly scarce and good wrong ideas that even remotely rival the majesty of String Theory have never been seen," he says.

So what is String Theory all about? Elementary particles are of two kinds. There are 'particles of matter' with which all matter is made of, like quarks (which make up neutrons and protons), electron, muon and neutrinos. Then there are 'particles of forc e', which mediate the four seemingly disparate forces of interaction, like photons, which transmit electromagnetism, W and Z bosons, which transmit the weak nuclear force, gluons, which transmit the strong nuclear force, and graviton which transmit gravi tation. These behave - at least as far as we know - as point objects. That is, particle probes with the highest energy accelerators, which accelerate particles to about 1,000 GeV, have not revealed any substructures in them though such theories - for exa mple, the picture of a quark as made up of 'preons' - have been around for some time. Low-energy phenomena involving these particles too have been successfully explained by models such as SM by treating them as fundamental and as point objects.

The picture of the world that String Theory, whose earliest version appeared in the 1970s, now gives us is that, unlike earlier descriptions of nature in terms of point particles, the fundamental entity is a string, a one-dimensional object, unlike the d imensionless point particles, and all the particles arise as its different vibrational modes, much like the overtones or harmonics of the strings of a veena or a violin. A highly imaginative and elegant idea. But the strings of a veena - or other strings - are made up of neutrons, protons (which themselves are made of quarks) and electrons. In String Theory it is the other way round. All the known (and unknown) elementary constituents of matter are made of strings. Thus, for example, an electron is a ti ny loop of string in a particular vibrational mode. The remarkable thing about the String Theory is that one of the modes of vibration turns out to be the graviton. That is, the particle of the gravitational force naturally arises in String Theory. The t heory puts 'particles of matter' and 'particles of force' in the same footing because both are different vibrational modes of the same string. Thus we, and everything around us, are made of strings!

To ask what a string is made of is as meaningless as asking what an elementary particle like quark or electron is made of. But these one-dimensional objects of String Theory are extremely tiny, about 10-33 cm long. They can be open strings wit h two free ends of closed strings like a rubber band as they move about in space oscillating and manifesting as different particles. The string size is much smaller than the length scale that can be probed by present-day accelerators, which is about 10 -15 cm. The energy required to probe a length scale of 10 -33 cm is a whopping 1019 GeV. Such energy scales were obtained for a split second during the bang. Therefore, to current particle accelerators which reach only 10 trillion times less energies, particles would still appear point-lik e even though String Theory endows them with structures of dimensions of the order of 10-33 cm, known as Planck Length. That is, fundamental particles are, from the String Theory perspective, "extended objects".

In String Theory, therefore, the description of interaction of say an electron with a photon is somewhat different. Since both the electron and the photon are different vibrational modes of the same string, emission of a photon by an electron is describe d as the splitting of a string into two strings and absorption of a photon by an electron is described as the joining of two strings into one. Because strings are extended objects, there are no point interactions, the cause of singularities in point part icle quantum theories which give rise to inconsistencies and infinities. While in most theories, like QED and SM, such infinities could be removed by absorbing them into definitions of parameters of the theory, such as mass and charge, this process (call ed renormalisation) could not be achieved in a quantum theory of gravity. The picture of string interaction provides a heuristic way of understanding why fundamentally a string theory is able to include gravity without the problem of infinities as in ear lier theories.

The fact that elementary particles we perceived as point-like are actually extended is not inconceivable. The more serious departure of String Theory from reality as we perceive arises from the fact that these strings are actually vibrating in a world of 10 dimensions, nine spatial and one time. This is six dimensions too many as the world we see has only three space and one time dimensions. Where are these extra dimensions? Actually these extra dimensions are supposed to be curled up - "compactified" i n mathematical parlance - as six-dimensional balls of sizes too small to be perceived by us. That is, each point in the observed space time is actually a very small closed six-dimensional space.

This can be illustrated by the following. From a very great distance a long hose appears as a one-dimensional line. If we come closer, the circular loop making the hollow of the tube becomes visible. In the case of strings, however, these extra dimension s may never reveal themselves if the curled spaces have sizes of 10-33 cm, distances that cannot be probed at all. (However, there are some recent models with much larger curl-up scales of 10-21 cm which are only 10,000 times smalle r than the size of the nucleus. Such scales can be probed by 1,000 GeV particles, achievable by upcoming accelerators.)

The idea of invoking extra dimensions to unify is, however, not new to physics. It dates back to the 1920s when physicists Theodor Kaluza and Oskar Klein introduced the fifth dimension - an extra spatial dimension - to unify the two forces of nature that were known then - electromagnetism and gravity. They showed that gravitation in four space dimensions was equivalent to gravitation and electromagnetism in three-dimensions. It also had an added bonus. The compactification of the fourth spatial dimensio n into a loop constrained the motion of an electron in a loop in the unseen dimension. This naturally explained why electric charge occurred quantised in units of 'e'. Similarly, in the context of String Theory, the expectation is that constraints arisin g from compactification of the extra six dimensions would uniquely fix the parameters for a lower dimensional theory such as SM.

Why10 dimensions? This number is actually forced on the theory by consistency requirements. A string-theorist way of looking at this number is that here is a theory where the number of dimensions of space time we live in emerges from the theory and is no t put in by hand. It describes the universe as it is and not as we perceive it. But in the early days of String Theory it appeared that one can potentially construct an infinite number of different 10-dimensional theories. How does one know which is the correct one that will lead to a TOE? A breakthrough occurred in 1984 - the First String Theory Revolution - when Joel Scherk and John Schwarz showed that of all the possible string theories only five were mathematically sturdy.

But this was still four theories too many. Worse still, it was found that the extra dimensions curled up in tens of thousands of ways. Each of these squeezed spaces yielded a different solution to the theory with its own version of the four-dimensional w orld, not always the one desired. String theorists had hit a wall and the theory began losing its attraction. However, there remained a band of die-hard string theorists led by Edward Witten who had described the situation as "a piece of 21st century phy sics that fell by chance into the 20th century." The Second String Theory Revolution came in the mid-1990s and string theorists were back in business again. The many ways to curl up the extra dimensions were all found to be closely related. And the five 10-dimensional theories turned out to be just different views of a single underlying 11-dimensional theory, called M-theory.

These five different theories are connected through "duality", a principle that reveals the bizarre nature of 'String Geometry' in which distances cease to have any absolute meaning. Large distances correspond to small energies and small distances corres pond to high energies and the principle of duality says that one theory at high energies is equivalent to another at low energies. In quantum theory of particles, short distances or high energies are extremely difficult to calculate. So, instead of worki ng in the high-energy regime of one theory, one can work in the low-energy regime of another theory, which is "dual". Duality in string theories implies that one can choose any of the five theories depending on the energy scale to be studied. The concept of duality becomes a calculational tool. This is also related to the fact that, as mentioned earlier, in string theories there are no point interactions.

Quantum gravity being a key success of String Theory, some outstanding problems of quantum gravity are now beginning to be solved using String Theory. An important problem that String Theory has addressed is the quantum properties of a black hole. Hawkin g had argued that when quantum effects are taken into account, a black hole is not really black because it emits a steady stream of particles, emitting heat and light. Black hole in quantum mechanics is a black hole with a glow. This glow is called Hawki ng Radiation. This finding has serious implications: a black hole has a temperature and corresponding entropy which Beckenstein and Hawking calculated.

Now entropy is a measure of the internal states of a system. There is a seeming contradiction in the notion that a black hole has internal states. In 1996, Andrew Strominger of Harvard University used M-Theory to resolve both these issues for a special c lass of black holes by providing a complete quantum description of the phenomenon. He showed that Beckenstein-Hawking entropy is because of a black hole's microscopic states, which are not evident in general relativity, and that Hawking Radiation is inde ed analogous to thermal radiation from an ordinary hot object like charcoal or a star. The resolution of this problem is regarded as a major triumph.

String theorists hope that many more such successes will come the theory's way. But there are many outstanding issues still. Even the full equations of the theory are not known yet, let alone how they will reduce in four dimensions to those of the SM. Th ere are fundamental questions that are yet to be addressed. How do masses of particles arise? There are no predictions of the theory that can be tested. The theory's proponents, however, believe that, sooner or later testable predictions will be discover ed. What M-Theory represents is not quite clear. In M-Theory, there is a proliferation of fundamental entities and strings constitute only a sub-class of these.

Sceptics maintain that for all the conceptual revolutions in String Theory there is little to show except a lot of beautiful mathematics. To an outsider, String Theory would seem to be getting more and more away from reality. But string theorists still f irmly believe that they are on the right track to a TOE. Strominger's remark sums up the state of things in this esoteric field: "We were once considered semi-crackpots working on some bizarre idea. While that may still be true, at least we are no longer perceived that way."