String theory

A string theory is a physical model whose fundamental building blocks are extended objects (strings, membranes and higher-dimensional objects) rather than points. String theories are able to avoid problems, such as infinite energy density, associated with the presence of mathematical points in a physical theory.

The term 'string theory' properly refers to both the 26-dimensional bosonic string theories and to the 10-dimensional superstring theories discovered by adding supersymmetry to bosonic string theory.
Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name 'bosonic string theory'.
The different superstring theories were discovered to be different limits of an unknown 11-dimensional theory called M-theory proposed by Horava and Witten in the 1990s.

A central consequence of string theory is that the observed physics of the known universe can be stated as arising from two seemingly incompatible geometries: one being 'as large as we see', and the other being smaller by far than the Planck length. Since both geometries lead to the same observed physics, but the small scale phenomena are beyond human investigation, there has been considerable discussion of the impact of string theory on both the philosophy of science (is it 'science' if no experiment can be run to disprove it?) and the philosophy of mathematics (if two geometries lead to the same physics, should geometry itself not reflect the same universe its discoverers and codifiers live in, and prove that there is a single common phenomenom that the two geometries reflect?).
On a more practical level, string theory has led to advances in the mathematics of folding, knots and Calabi-Yau spaces. Because much of this mathematics is new, the uncertainty has been increased somewhat, as very few people can understand either the physics or the mathematics on which it depends.

Problems with string theory

String theory suffers from two major problems. The first problem is that, in the words of Wolfgang Pauli, it is not even wrong. In other words, it does not make any predictions that may be subject to experimental verification. It can be neither proven nor disproven. That is a serious problem for any theory of physics.
The second problem is that it assumes, as did Newtonian mechanics and special relativity, a fixed space-time background. Ultimately, a theory subsuming quantum mechanics is needed which is independent of any fixed space-time and thus consistent with general relativity. M-theory has been hypothesized to overcome the latter problem. Loop quantum gravity overcomes both.

bosonic string theory

to be written

See also: superstring theory, Calabi-Yau spaces, Compactifications