Our experience of space-time is that of a continuous object, without gaps or discontinuities, just as it is described by classical physics. For some quantum gravity models however, the texture of space-time is "granular" at tiny scales (below the so-called Planck scale, 10-33 cm), as if it were a variable mesh of solids and voids (or a complex foam). One of the great problems of physics today is to understand the passage from a continuous to a discrete description of spacetime: is there an abrupt change or is there gradual transition? Where does the change occur?
The separation between one world and the other creates problems for physicists: for example, how can we describe gravity - explained so well by classical physics - according to quantum mechanics? Quantum gravity is in fact a field of study in which no consolidated and shared theories exist as yet. There are, however, "scenarios", which offer possible interpretations of quantum gravity subject to different constraints, and which await experimental confirmation or confutation.
One of the problems to be solved in this respect is that if space-time is granular beyond a certain scale it means that there is a "basic scale", a fundamental unit that cannot be broken down into anything smaller, a hypothesis that clashes with Einstein's theory of special relativity.
Imagine holding a ruler in one hand: according to special relativity, to an observer moving in a straight line at a constant speed (close to the speed of light) relative to you, the ruler would appear shorter. But what happens if the ruler has the length of the fundamental scale? For special relativity, the ruler would still appear shorter than this unit of measurement. Special relativity is therefore clearly incompatible with the introduction of a basic graininess of spacetime. Suggesting the existence of this basic scale, say the physicists, means to violate Lorentz invariance, the fundamental tenet of special relativity. (The Daily Galaxy)