Myth: The breakdown of the usual geometric intuition near the Planck scale – sometimes nicknamed the “minimum length” – implies that the length, area, and other geometric observables have to possess a discrete spectrum.
Reality: This implication is incorrect. String theory is a clear counterexample: distances shorter than the Planck scale (and, perturbatively, even the string scale) cannot be probed because there exist no probes that could distinguish them. Consequently, the scattering amplitudes become very soft near the Planck scale and the divergences disappear.
However, there is no discreteness of geometric quantities – such as the radii of compact circles in spacetime. And general “intervals” or “surfaces” inside the spacetime can’t even be localized with the Planckian precision which is also why their proper lengths and areas, assuming their better-than-Planckian accuracy, are not even well-defined observables in string theory: what can’t be measured operationally often can’t be defined theoretically, either. ;-)
— Myths about the minimal length
— Lubos Motl
2013.07.14 Sunday ACHK