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One proposal by Verlinde \cite{Verlinde:2010hp} is that gravity is not afundamental, but an entropic force. In this way, Verlinde has provide us with away to derive the Newton's law of gravitation from the Bekenstein-Hawkingentropy-area formula. On the other hand, since it has been demonstrated thatthis formula is susceptible to quantum gravity corrections, one may hope thatthese corrections could be inherited by the Newton's law. In this way, theentropic interpretation of Newton's law could be a prolific way in order to getverifiable or falsifiable quantum corrections to ordinary gravity in anobservationally accessible regimes. Loop quantum gravity is a theory thatprovide a way to approach the quantum properties of spacetime. From thistheory, emerges a quantum corrected semiclassical black hole solution calledloop quantum black holes or self-dual black holes. Among the interestingfeatures of loop quantum black holes is the fact that they give rise to amodified entropy-area relation where quantum gravity corrections are present.In this work, we obtain the quantum corrected Newton's law from theentropy-area relation given by loop quantum black holes. In order to relate ourresults with the recent experimental activity, we consider the quantummechanical properties of a huge gravitational atom consisting in a lightneutral elementary particle in the presence of a loop quantum black hole.

Entropic corrected Newton's law of gravitation and the Loop Quantum Black Hole gravitational atom