Quantum gravity and minimum length

TL;DR

This work synthesizes multiple lines of reasoning—from microscope thought experiments to path-integral and lattice gravity, string theory, loop representations, and black-hole thermodynamics—arguing for a fundamental length $l_*$ at the Planck scale. It shows that localizing events below $l_*$ inevitably triggers gravitational backreaction, ultraviolet regularization, and a restructuring of spacetime concepts such as causality and the event notion. The paper connects these viewpoints to concrete results, including a universal bound $\Delta x \gtrsim l_*$, UV finiteness of propagators, and discretized geometric observables, illustrating a coherent picture of Planck-scale physics. The findings underscore the significance of Planck-scale structure for low-energy phenomena via horizon measurements, wormhole-induced nonlocalities, and the breakdown of classical spacetime, motivating a quantum theory of gravity with intrinsic bounds on measurement precision.

Abstract

The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients for the appearance of this minimum length are quantum mechanics, special relativity and general relativity. As a consequence, classical notions such as causality or distance between events cannot be expected to be applicable at this scale. They must be replaced by some other, yet unknown, structure.