2026/02/18 by Jaume Gine
#gr-qc
Can the generalized uncertainty principle (GUP) arise as an effective manifestation of spacetime geometry rather than as a fundamental postulate? More specifically, can the gravitational GUP be interpreted as an emergent uncertainty relation generated by the statistical microstructure of local horizons? Motivated by these questions, this work explores the broader possibility that selected features of quantum-gravitational behavior may originate from the geometric and thermodynamic properties of spacetime itself. We argue that, under suitable assumptions regarding the multifractal structure of microscopic horizons, an effective GUP can indeed be induced by geometry. This perspective suggests that quantum uncertainty may be viewed not as a fundamental ingredient of nature, but as an emergent consequence of the statistical organization of spacetime at the Planck scale. While the present framework does not constitute a complete theory of quantum gravity, nor does it derive the full formalism of quantum mechanics, it provides a proof of concept for a geometric origin of generalized uncertainty relations and establishes a thermodynamic route connecting horizon microstructure, entropy corrections, and effective quantum behavior. The resulting framework is compatible with several modern approaches to quantum gravity through the common notion of scale-dependent geometry, while yielding a unified geometric interpretation of generalized uncertainty relations.