Technically Speaking: Supersymmetry

The "Super" in superstrings refers to supersymmetry. Recall from our discussion of degenerate gases in Chapter 21 that elementary particles can be classified either as bosons or as fermions. This distinction is fundamental, because all matter appears to be made of fermions (for example, electrons and quarks), but all basic forces appear to be carried by bosons (for example, photons, which carry the electromagnetic interaction). Normal symmetries, such as rotations or parity, keep fermions and bosons distinct. However, there is a class of more sophisticated symmetries called supersymmetries in which the symmetry operations convert fermions to bosons or vice versa. All superstring theories are based on such supersymmetries.

Superstrings and m-Branes

Our ordinary description of the microscopic world, quantum mechanics, is based on the idea that elementary particles are point-like. That is, they have no internal structure and therefore exist at a point in spacetime.
Point-Like Particles
A point has zero dimension, since it has neither breadth, width, nor height. (Of course, if you symbolize a point by making a dot with a pencil, the dot has a small spatial size. But by a point we mean an idealized mathematical point having no spatial extension.) This feature of quantum mechanics leads to very serious technical mathematical problems (the earlier allusion to division by zero and the appearance of infinities). In our description of the strong, weak, and electromagnetic interactions, a complex mathematical prescription has been worked out that avoids these problems. The technical term for this prescription is renormalization. It systematically removes infinite quantities that would otherwise crop up in the theory and leaves us with a logically consistent description of these forces.

Gravity is Different
But gravity is different. Because of its fundamental microscopic properties, the renormalization procedure that works for the other three fundamental interactions fails for gravity. This means that if we try to apply ordinary quantum mechanics to gravity we end up with quantities that become infinite in the theory. Since we do not understand how to deal with these infinite quantities mathematically, quantum gravity based on point-particle quantum mechanics leads to a theory that is not logically consistent and cannot be used reliably to calculate observable quantities. This has two related implications. First, we do not have a way to describe gravity on the Planck scale. Second, we cannot join gravity with the other three forces into a unified description of all forces based on point-particle quantum mechanics.

One-Dimensional Building Blocks
The basic idea of superstring theory is to change the assumption that the elementary building blocks of the Universe are particles existing at a point. Instead, superstring theory assumes that the fundamental building blocks of the Universe are tiny (Planck length size) objects that are not points but instead have a length. That is, they are like strings. These strings are also assumed to possess a particular kind of symmetry called supersymmetry (see the top right box), so these elementary string-like building blocks are called superstrings. Because they have a length, they are 1-dimensional, rather than the 0-dimensional particles of ordinary quantum mechanics. The top portion of the adjacent figure illustrates (we shall describe the m-branes in the lower portion of the figure below). Although this may not seem to be a very large change, it is. In particular, it can be shown mathematically that the assumption that the basic building blocks are not 0-dimensional points permits the troublesome infinities to be avoided.
Testing Superstrings
The preceding discussion implies that a logically consistent quantum theory of gravity, and a logically consistent unification all all four fundamental forces, may be possible based on superstrings. We cannot yet be certain because the mathematics of superstring theory is very difficult and is still being developed. As a consequence, it has not yet been possible to use the theory to make a quantitative prediction that can be tested by currently feasible experiments. Recall that a hallmark of modern science is experimental verification of theories. No matter how beautiful mathematically a theory is (and superstring theory is very beautiful), it must pass the experimental test to be acceptable as a description of nature. It is hoped that superstring theory will be capable of a quantitatively testable prediction within the next decade.
m-Brane Theory
Since the basic idea of superstrings was introduced in the early 1980s, five different versions of string theory have been developed based on five different fundamental symmetries. In the 1990s, it was realized that these five versions of string theories were actually strongly related to each other. They appeared to be different because the discussion to that point had been based on approximate solutions of the five theories (recall the earlier comment that the mathematics of superstrings is very difficult, making exact solutions of the equations hard to obtain). When more exact solutions were obtained it was realized that the five existing versions of superstrings could be unified in a single more general theory. This more general theory is called m-brane theory, because it implies a generalization of the idea of fundamental particles having one dimension to having m dimensions. The resulting geometrical surfaces are called m-branes, with the integer m signifying the number of dimensions. The above left figure illustrates a 2-brane. That is, a two-dimensional object with dimensions comparable with the Planck length (superstrings may be called 1-branes in this terminology).
The Basic Stuff of the Universe
Superstring theory, and its generalization m-brane theory, imply that what we currently call "elementary particles" (things like electrons, photons, and quarks) are not really elementary. They have an internal structure that can be seen only on the Planck scale. This internal structure consists of a set of elementary building blocks for all mass and energy in the Universe that are not point particles but are instead 1-branes (strings), 2-branes, 3-branes, and so on (the theory suggests that branes up to 9-branes can exist). Since we have no hope in the forseeable future to be able to probe the Planck scale directly, the challenge to these new theories is whether they can make any testable scientific predictions at energies below the Planck scale that would allow their validity to be checked. As noted above, there is hope for such predictions within the next decade, but a large amount of mathematical development is required first.

How Many Dimensions?
Superstring theories indicate that even our ideas about the number of dimensions in spacetime may require revision. These theories suggest that spacetime has more dimensions than the four (three space and one time) that we are used to dealing with in our everyday lives. However, the extra dimensions are "rolled up" in such a way that we cannot see them until we get down to distances close to the Planck length. A simple analogy is a cylindrical pipe. A cylinder is a two-dimensional surface, but if we view the pipe from a distance it looks like a line, which is a one-dimensional surface. Only when we are close can we see the "hidden" extra dimension. The adjacent right animation illustrates this basic idea of how we can be fooled about the number of dimensions for a space.