7. ON RECENT DEVELOPMENTS IN SUPERSTRING THEORY Bose-Einstein statistics is the statistical mechanics of a system of indistinguishable particles for which there is no restriction on the number of particles that may simultaneously exist in the same quantum energy state. Bosons are particles that obey Bose- Einstein statistics, and they include photons, pi mesons, all nuclei having an even number of particles, and all particles with integer spin. Fermions (electrons, protons, neutrons) are particles that obey the Pauli exclusion principle: i.e., no two fermions of the same kind can occupy the same quantum state. In particle physics, string theory is a theory of elementary particles based on the idea that the fundamental entities are not point-like particles but finite lines (strings), or closed loops formed by strings, the strings one-dimensional curves with zero thickness and lengths (or loop diameters) of the order of the Planck length of 10^(-35) meters. The fundamental forces comprise the gravitational force, the electromagnetic force, the nuclear strong force, and the nuclear weak force, and the "grand unified theories" are theories that aim to provide a mathematical frame- work in which the electromagnetic forces, strong forces, and weak forces emerge as parts of a single unified force, with the three forces related by symmetry. Supersymmetry is an aspect of an extension of the grand unified theories, an attempt to unify all the four fundamental forces, i.e., linking gravitation to the electromagnetic force, the strong force, and the weak force through a supersymmetry scheme, and superstrings are strings in this scheme that obey supersymmetry. ... ... John H. Schwarz (California Institute of Technology, US) presents a brief overview of some of the advances in understanding super- string theory that have been achieved in the last few years. String theories that have a symmetry relating bosons and fermions, called "supersymmetry", are called "superstring" theories. Major advances in understanding of the physical world have been achieved during the past century by focusing on apparent contradictions between well-established theoretical structures. In each case the reconciliation required a better theory, often involving radical new concepts and striking exper- imental predictions. Four major advances of this type were the discoveries of special relativity, quantum mechanics, general relativity, and quantum field theory. This was quite an achieve- ment for one century, but there is one fundamental contradiction that still needs to be resolved, namely the clash between general relativity and quantum field theory. Many theoretical physicists are convinced that superstring theory will provide the answer. QY: John H. Schwarz, California Inst. of Technology 818-395-6811 (Proc. Natl. Acad. Sci. US 17 Mar 98) ------------------- Related Background: ON THE EVOLUTION OF STRING THEORY TO MEMBRANE THEORY ... Membrane theory (M-theory) is a recent extension of string theory in which the fundamental physical entities are considered as surfaces in a many-dimensional space (membranes) rather than as lines or loop elements (open or closed strings). Given all of the above, some caution is necessary: the translation of a highly abstract mathematical model of physical reality into non-mathem- atical language is often an exercise of limited usefulness, and in this case in particular, we are presenting only the ghost of the theoretical scheme. String theory was originally invented in the 1960s as a theory of the strong force, became overshadowed by the strong force theory of gluons and quarks, then had a revival in the 1980s -- but with the history more dependent on new work than on fashion. ... ... M. Duff (Texas A & M Univ., US), who is active in string theory and membrane theory, in a review of various aspects of the history and essentials of string theory and membrane theory, suggests that future historians may judge the 20th century as "a time when theorists were like children playing on the seashore, diverting themselves with the smoother pebbles or prettier shells of superstrings, while the great ocean of M-theory lay undiscovered before them." QY: Michael J. Duff, Texas A & M Univ., Dept. Physics 409-847-9451 (Scientific American February 1998)