The characteristic linear dimension is given as a certain combination of the three most fundamental constants of nature: (1) Planck's constant h (named after the German physicist Max Planck, the founder of quantum physics), (2) the speed of light c, and (3) the universal gravitational constant G. The combination, called the Planck length (Gh/c3)1/2, equals roughly 10-33 cm, far smaller than the distances to which elementary particles can be probed in particle accelerators on the Earth.
The energies needed to smash particles to within a Planck length of each other were available to the universe at a time equal to the Planck length divided by the speed of light. This time, called the Planck time (Gh/c5)1/2, equals approximately 10-43 second. At the Planck time, the mass density of the universe is thought to approach the Planck density, c5/hG2, roughly 1093 g/cc . Contained within a Planck volume is a Planck mass (hc/G)1/2, roughly 10-5 g. An object of such mass would be a quantum black hole, with an event horizon close to both its own Compton length (distance over which a particle is quantum mechanically "fuzzy") and the size of the cosmic horizon at the Planck time. Under such extreme conditions, spacetime cannot be treated as a classical continuum and must be given a quantum interpretation.
The latter is the goal of the supergravity theory, which has as one of its features the curious notion that the four spacetime dimensions (three space dimensions plus one time dimension) of the familiar world may be an illusion. Real spacetime, in accordance with this picture, has 26 or 10 spacetime dimensions, but all of these dimensions except the usual four are somehow compacted or curled up to a size comparable to the Planck scale. Thus has the existence of these other dimensions escaped detection. It is presumably only during the Planck era, when the usual four spacetime dimensions acquire their natural Planck scales, that the existence of what is more fundamental than the usual ideas of mass-energy and spacetime becomes fully revealed. Unfortunately, attempts to deduce anything more quantitative or physically illuminating from the theory have bogged down in the intractable mathematics of this difficult subject. At the present time superstring theory remains more of an enigma than a solution.
Excerpt from the Encyclopedia Britannica without permission.