Spatial cut-offs, fermion statistics, and verlinde’s conjecture

Abstract

Verlinde conjectured eight years ago that gravitation might be an emergent entropic force. This rather surprising assertion was proved in Plastino and Rocca (2018) within a purely classical statistical context, and in 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.