Spatial cut-offs, Fermion statistics, and Verlinde’s conjecture

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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.