You can zoom into a high-resolution photo for a long time — until suddenly a smooth face dissolves into individual pixels. Something similar, according to a new study, happens to spacetime itself. The authors propose that tiny intervals of length are not pre-existing 'parts' of the universe but results of measurements. They depend on scale, as if the ruler itself changed its divisions depending on what we measure.
This view leads to a surprising consequence. When you switch to a special description of microscopic lengths, they become discrete and come in equal steps. Any distance at the deepest level can only be assembled from an integer number of 'quanta' of length. Meanwhile, the famous Heisenberg uncertainty relation is not violated but slightly modified, retaining its form.
The behavior of these microscopic lengths follows a flow reminiscent of a river. The flow has 'sinks'—fixed points where the length stops changing. The ordinary continuous space we are used to turns out to be only an unstable regime, like a ball perched on a hilltop. The stable, natural state is a world with a finite minimal length and a grainy structure. The whole construction requires no hard cutoffs or violations of symmetries. The laws of spacetime curvature and speed of light remain intact.
If space were continuous down to infinitesimal scales, an arbitrarily small volume could hold an unlimited amount of information, leading to paradoxes. Quantizing length naturally solves this problem.
In Vernor Vinge's novel 'A Fire Upon the Deep', different zones of the galaxy have different 'graininess' of physical laws, directly affecting the capabilities of civilizations.