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The possibility of a minimal physical length in quantum gravity is discussed within the asymptotic safety approach. Using a specific mathematical model for length measurements (COM microscope) it is shown that the spacetimes of Quantum Einstein Gravity (QEG) based upon a special class of renormalization group trajectories are fuzzy in the sense that there is a minimal coordinate separation below which two points cannot be resolved.
Within the asymptotic safety scenario for gravity various conceptual issues related to the scale dependence of the metric are analyzed. The running effective field equations implied by the effective average action of Quantum Einstein Gravity (QEG) an
Studies in string theory and quantum gravity suggest the existence of a finite lower limit $Delta x_0$ to the possible resolution of distances, at the latest on the scale of the Planck length of $10^{-35}m$. Within the framework of the euclidean path
Within asymptotically safe Quantum Einstein Gravity (QEG), the quantum 4-sphere is discussed as a specific example of a fractal spacetime manifold. The relation between the infrared cutoff built into the effective average action and the corresponding
We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic
We put to the test an effective three-dimensional electrostatic potential, obtained effectively by considering an electrostatic source inside a (5+$p$)-dimensional braneworld scenario with $p$ compact and one infinite spacial extra dimensions in the