übertheory the theory formerly known as STRINGS By Michael J. Duff The Theory of Everything is emerging as one in which not only strings but also membranes and black holes play a role t a time when certain pundits claim that all the important discoveries have already been Amade, it is worth emphasizing that the two main pillars of 20th-century physics, cially on the idea of supersymmetry. quantum mechanics and Einstein’s gen- Physicists divide particles into two classes, eral theory of relativity, are mutually in- according to their inherent angular mo- compatible. General relativity fails to com- mentum, or “spin.” Supersymmetry re- ply with the quantum rules that govern quires that for each known particle having the behavior of elementary particles, while integer spin—0, 1, 2 and so on, measured supersymmetry implies gravity. In fact, black holes are challenging the very foun- in quantum units—there is a particle with supersymmetry predicts “supergravity,” dations of quantum mechanics. Something the same mass but half-integer spin (1/2, in which a particle with a spin of 2—the big has to give. 3/2, 5/2 and so on), and vice versa. graviton—transmits gravitational inter- Until recently, the best hope for a the- Unfortunately, no such superpartner actions and has as a partner a gravitino, ory that would unite gravity with quantum has yet been found. The symmetry, if it with a spin of 3/2. mechanics and describe all physical phe- exists at all, must be broken, so that the Conventional gravity does not place nomena was based on strings: one-dimen- postulated particles do not have the same any limits on the possible dimensions of sional objects whose modes of vibration mass as known ones but instead are too spacetime: its equations can, in principle, represent the elementary particles. In 1995, heavy to be seen in current accelerators. be formulated in any dimension. Not so however, strings were subsumed by M- Even so, theorists believe in supersymme- with supergravity, which places an upper theory. In the words of the guru of string try because it provides a framework with- limit of 11 on the dimensions of space- theory, Edward Witten of the Institute for in which the weak, electromagnetic and time. The familiar universe, of course, has Advanced Study in Princeton, N.J., “M strong forces may be united with the most three dimensions of space: height, length stands for magic, mystery or membrane, elusive force of all: gravity. and breadth; time is the fourth dimension according to taste.” New evidence in fa- Supersymmetry transforms the coor- of spacetime. But in the early 1920s Pol- vor of this theory is appearing daily, rep- dinates of space and time such that the ish physicist Theodore Kaluza and Swe- resenting the most exciting development laws of physics are the same for all ob- dish physicist Oskar Klein suggested that since strings first swept onto the scene. servers. Einstein’s general theory of rela- spacetime may have a hidden fifth dimen- M-theory, like string theory, relies cru- tivity derives from this condition, and so sion. This extra dimension would not be DUSAN PETRICIC 12 SCIENTIFIC AMERICAN Updated from the February 1998 issue COPYRIGHT 2003 SCIENTIFIC AMERICAN, INC. LIFE, THE UNIVERSE AND EVERYTHING may arise from the interplay of strings, bubbles and sheets in higher dimensions of spacetime. IIA and Type IIB strings. (The Type I is an “open” string con- sisting of just a segment; the oth- ers are “closed” strings that form loops.) The E8 × E8 seemed—at least in principle—capable of ex- plaining the elementary particles and forces, including their handed- ness. And strings seemed to provide a theory of gravity consistent with quan- tum effects. All these virtues enabled string theory to sweep physicists off their feet and supergravity into the doghouse. After the initial euphoria over strings, however, doubts began to creep in. First, important questions—especially how to confront the theory with experiment— seemed incapable of being answered by traditional methods of calculation. Sec- infinite, like the others; instead it would the theory ultimately predicts depends on ond, why were there five different string close in on itself, forming a circle. Around how the extra dimensions are rolled up, à theories? If one is looking for a unique that circle could reside quantum waves, la Kaluza and Klein. The several curled di- Theory of Everything, surely this is an em- fitting neatly into a loop. Only integer mensions could conceivably allow physi- barrassment of riches. Third, if super- numbers of waves could fit around the cir- cists to derive, in addition to electromag- symmetry permits 11 dimensions, why do cle; each of these would correspond to a netism, the strong and weak nuclear superstrings stop at 10? Finally, if we are particle with a different energy. So the en- forces. For these reasons, many physicists going to conceive of pointlike particles as ergies would be “quantized,” or discrete. began to look to supergravity in 11 di- strings, why not as membranes or more An observer living in the other four di- mensions for the unified theory. generally as p-dimensional objects, in- mensions, however, would see a set of In 1984, however, 11-dimensional su- evitably dubbed p-branes? particles with discrete charges, rather pergravity was rudely knocked off its Consequently, while most theorists than energies. The quantum, or unit, of pedestal. An important feature of the real were tucking into super-spaghetti, a small charge would depend on the circle’s ra- world is that nature distinguishes between group was developing an appetite for su- dius. In the real world as well, electrical right and left. Witten and others empha- per-ravioli. A particle, which has zero di- charge is quantized, in units of e, the sized that such “handedness” cannot mensions, sweeps out a one-dimensional charge on the electron. To get the right readily be derived by reducing spacetime trace, or “worldline,” as it evolves in space- value for e, the circle would have to be from 11 dimensions down to four. time [see top illustration on next page]. tiny, about 10 –33 centimeter in radius. Similarly a string—having one dimension: The unseen dimension’s small size ex- P-Branes length—sweeps out a two-dimensional plains why humans, or even atoms, are SUPERGRAVITY’S position was usurped “worldsheet,” and a membrane—having unaware of it. Even so, it would yield elec- by superstring theory in 10 dimensions. two dimensions: length and breadth— tromagnetism. And gravity, already pres- Five competing theories held sway, desig- sweeps out a three-dimensional “world- ent in the four-dimensional world, would nated by their mathematical characteris- volume.” In general, a p-brane sweeps be united with that force. tics as the E8 × E8 heterotic, the SO(32) out a worldvolume of p + 1 dimensions. In 1978 Eugene Cremmer, Bernard heterotic, the SO(32) Type I, and the Type As early as 1962, Paul A. M. Dirac Julia and Joel Scherk of the École Nor- male Supérieure in Paris realized that su- MICHAEL J. DUFF conducts research on unified theories of elementary particles, quantum pergravity not only permits up to seven gravity, supergravity, superstrings, supermembranes and M-theory. He earned his Ph.D. in extra dimensions but is most elegant theoretical physics in 1972 at Imperial College, London, and joined the faculty there in when existing in a spacetime of 11 di- 1980. He became a Distinguished Professor at Texas A&M University in 1992. Duff is now mensions (10 of space and one of time). Oskar Klein Professor of Physics at the University of Michigan and director of the Michigan The kind of real, four-dimensional world THE AUTHOR Center for Theoretical Physics. www.sciam.com THE EDGE OF PHYSICS 13 COPYRIGHT 2003 SCIENTIFIC AMERICAN, INC. TRAJECTORY of a particle in spacetime traces a worldline. Similarly, that of a string or a membrane sweeps out a worldsheet or worldvolume, respectively. cle with charge e would be equivalent to a solitonic particle with charge 1/e. Be- cause its charge is a measure of how strongly a particle interacts, a monopole would interact weakly when the original particle interacts strongly (that is, when e is large), and vice versa. had constructed an imaginative model of symmetries of the laws of physics. For The conjecture, if true, would lead to based on a membrane. He postulated instance, conservation of electrical charge a profound mathematical simplification. that the electron, instead of resembling a follows from a symmetry under a change In the theory of quarks, for instance, point, was in reality a minute bubble, a of a particle’s wave function. physicists can make hardly any calcula- membrane closed in on itself. Its oscilla- Sometimes, however, attributes may tions when the quarks interact strongly. tions, Dirac suggested, might generate be maintained because of deformations But any monopoles in the theory must particles such as the muon, a heavier ver- in fields. Such conservation laws are then interact weakly. One could imagine sion of the electron. Although his attempt called topological. Thus, it may happen doing calculations with a dual theory failed, the equations that he postulated that a knot in a set of field lines, called a based on monopoles and automatically for the membrane are essentially the ones soliton, cannot be smoothed out. As a re- getting all the answers for quarks, be- we use today. sult, the soliton is prevented from dissi- cause the dual theory would yield the Supersymmetry severely restricts the pating and behaves much like a particle. same final results.