The deepest problem at present in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, planets, galaxies), with quantum mechanics which describes the other three fundamental forces acting on the microscopic scale.
The development of a quantum theory of a force invariably results in infinite (and therefore useless) answers. Physicists have developed techniques to eliminate these infinities that work on for the electromagnetic, strong nuclear and weak nuclear forces. But these techniques do not work when applied to general relativity; thus the development of a quantum theory of gravity must come about by different means than were used for the other fundamental forces.
There are five mathematically possible superstring theories. In order to be consistent, string theory requires space to have either 10 or 26 dimensions. This requirement can be reconciled with the observation that the universe seems to have only three spatial dimensions, by making the universe measured along these other dimensions subatomic in size.
By saying that a dimension is subatomic in size we really mean that this is the distance a particle would have to travel along its axis before it reaches its initial position again. This is rather like an ant travelling round the surface of a balloon. The ant sees a 2D plane, but the plane is curled round so that eventually it comes back to where it started. So it is more accurate to say that the dimension is subatomic when measured along its own axis.
Our minds have a hard time understanding extra dimensions because it is only the three spatial dimensions we have control over (time is also hard to picture as a dimension). Although these dimensions do affect our world, by the time they scale up to our size their direct influence seems to have been cancelled out. This is similar to many relativistic effects such as [time dilation]?; Travelling very fast has an effect on our time relative to other people, but at the speeds we travel these effects are miniscule.
Superstring theory is not the first theory to propose extra spatial dimensions; see Kaluza-Klein theory.
Theoretical physicists have been troubled by the existence of five separate superstring theories. This seems to be solved by the recent development of M-theory; the five superstring theories have been found to be simply different subsets of M-theory.
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