The Birth of The Superstring Theory

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The superstring theory has perhaps the weirdest history in the annals of science. Nowhere else do we find a theory that was proposed as the solution to the wrong problem, abandoned for over a decade, and then resurrected as a theory of the universe.

The superstring theory began in the 1960s, before the flourishing of the Yang-Mills theory and gauge symmetries, when the renormalization theory was still floundering as a theory bedeviled by infinities.

A backlash had developed against the renormalization theory, which seemed contrived and artificial. The opposing school of thought was led by Geoffrey Chew of the University of California at Berkeley, who proposed a new theory that was independent of elementary particles, Feynman diagrams, and the renormalization theory.

Instead of postulating a series of intricate rules detailing how certain elementary particles interact with other particles through Feynman diagrams, Chew’s theory required only that the S-matrix (which mathematically describes the collisions of particles) be selfconsistent. Chew’s theory postulated that the S-matrix obeys a rigorous set of mathematical properties, and then assumed that these properties are so restrictive that only one solution was possible. Thisapproach is often called the bootstrap approach, because one is literally picking oneself up by one’s bootstraps (one begins with only a set of postulates, then theoretically derives the answer using only self-consistency).

Because Chew’s approach was based entirely on the S-matrix, rather than on elementary particles or Feynman diagrams, the theory was called the S-matrix theory (not to be confused with the S-matrix itself, which all physicists use).

These two theories, quantum field theory and S-matrix theory, are based on different assumptions about the meaning of an elementary particle. The quantum field theory is based on the assumption that all matter can be built from a small set of elementary particles, whereas the S-matrix theory is based on an infinite number of particles, with none of them elementary.

In retrospect, we see that the superstring theory combines the best features of the S-matrix theory and the quantum field theory, which in many ways are opposites.

The superstring theory resembles the quantum field theory because it is based on elementary units of matter. Instead of point particles, however, the superstring theory is based on strings that interact by breaking and reforming via Feynman-like diagrams. But the significant advantage that superstrings have over the quantum field theory is that renormalization is not required. All the loop diagrams at each level are probably finite by themselves, requiring no artificial sleights of hand to remove the infinities.

Similarly, the superstring theory resembles the S-matrix theory in that it can accommodate an infinite number of elementary particles. According to this theory, the infinite variety of particles found in nature are simply different resonances of the same string, with no particle any more fundamental than any other. The great advantage, however, that the superstring theory has over the S-matrix theory is that it is possible to calculate with the superstring theory and eventually get numbers for the S-matrix. (By contrast, the S-matrix theory is exceedingly difficult to calculate with and extract usable numbers.)

The superstring theory, then, incorporates the best features of both the S-matrix theory and the quantum field theory because it is based on a startlingly different physical picture.

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