Modified Newton's Law of Gravitation Due to Minimal Length in Quantum Gravity

TL;DR

This paper explores how the generalized uncertainty principle from quantum gravity theories modifies the entropy-area relation and results in a revised Newton's law of gravitation, potentially observable at larger scales.

Contribution

It introduces a $ ext{sqrt{Area}}$ correction to the entropy law due to GUP, leading to a novel modified Newton's law of gravitation with implications for extra dimensions.

Findings

Modified entropy-area law with $ ext{sqrt{Area}}$ correction

Derived a new form of Newton's law consistent with quantum gravity effects

Potential observable effects at scales larger than the Planck length

Abstract

A recent theory about the origin of the gravity suggests that the gravity is originally an entropic force. In this work, we discuss the effects of generalized uncertainty principle (GUP) which is proposed by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity theories (DSR), on the area law of the entropy. This leads to a $\sqrt{Area}$-type correction to the area law of entropy which imply that the number of bits $N$ is modified. Therefore, we obtain a modified Newton's law of gravitation. Surprisingly, this modification agrees with different sign with the prediction of Randall-Sundrum II model which contains one uncompactified extra dimension. Furthermore, such modification may have observable consequences at length scales much larger than the Planck scale.