# Spatial cut-offs, Fermion Statistics, and Verlinde's Conjecture

## TL;DR

This paper investigates fermionic statistical effects on Verlinde's conjecture, revealing a quantum-induced lower bound on interaction distance that resembles space discretization in modern gravitational theories.

## Contribution

It extends Verlinde's entropic gravity framework to fermions, demonstrating a quantum statistical lower bound on interaction distance, a novel effect not previously explored.

## Key findings

- Identifies a lower bound on the distance between interacting masses due to fermionic statistics.
- Shows the classical limit of quantum mechanics aligns with previous classical results.
- Reveals a new effect resembling space discretization in quantum fermionic systems.

## Abstract

Verlinde conjectured eight years ago that gravitation might be an emergent entropic force. This rather surprising assertion was proved in [Physica A {\bf 505} (2018) 190] within a purely classical statistical context, and in [DOI: 10.13140/RG.2.2.34454.24640] for the case of bosons' statistics. In the present work, we appeal to a quantum scenario involving fermions' statistics. We consider also the classical limit of quantum (statistical) mechanics (QM). We encounter a lower bound to the distance $r$ between the two interacting masses, i.e., an $r$ cut-off. This is a new effect that exhibits some resemblance with the idea of space discretization proposed by recent gravitation theories