Where is hbar Hiding in Entropic Gravity?

TL;DR

This paper investigates the quantum origins of entropic gravity, revealing that quantum corrections involving hbar appear in the modified gravity law when considering generalized uncertainty principles.

Contribution

It introduces a GUP-based framework to incorporate quantum effects into entropic gravity, showing how hbar-dependent corrections modify Newton's law.

Findings

GUP modifies black hole entropy with logarithmic corrections

Quantum effects introduce hbar-dependent sub-leading corrections to gravity

Deviations from classical gravity could test entropic gravity hypotheses

Abstract

The entropic gravity scenario recently proposed by Erik Verlinde reproduced the Newton's law of purely classical gravity yet the key assumptions of this approach all have quantum mechanical origins. This is atypical for emergent phenomena in physics, where the underlying, more fundamental physics often reveals itself as corrections to the leading classical behavior. So one naturally wonders: where is hbar hiding in entropic gravity? To address this question, we first revisit the idea of holographic screen as well as entropy and its variation law in order to obtain a self-consistent approach to the problem. Next we argue that when dealing with quantum gravity issues the generalized uncertainty principle (GUP) should be the more appropriate foundation. Indeed based on GUP it has been demonstrated that the black hole Bekenstein entropy area law must be modified not only in the strong but also in the weak gravity regime. In the weak gravity limit, such a GUP modified entropy exhibits a logarithmic correction term. When applying it to the entropic interpretation, we demonstrate that the resulting gravity force law does include sub-leading order correction terms that depend on hbar. Such deviation from the classical Newton's law may serve as a probe to the validity of the entropic gravity postulate.