# Points. Lack thereof

## TL;DR

This paper explores how the classical notion of a point becomes meaningless at quantum gravity scales using noncommutative geometry, showing that point-like structures vanish at Planck distances through spectral action analysis.

## Contribution

It introduces a framework connecting noncommutative geometry with quantum gravity, demonstrating the disappearance of points at Planck scales via spectral action and propagator analysis.

## Key findings

- Points lose meaning at Planck distances.
- Connections between points vanish at high momenta.
- Spectral action reveals the non-existence of classical points.

## Abstract

I will discuss some aspects of the concept of "point" in quantum gravity, using mainly the tool of noncommutative geometry. I will argue that at Planck's distances the very concept of point may lose its meaning. I will then show how, using the spectral action and a high momenta expansion, the connections between points, as probed by boson propagators, vanish. This discussion follows closely [1] (Kurkov-Lizzi-Vassilevich Phys. Lett. B 731 (2014) 311, [arXiv:1312.2235 [hep-th]].