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

Ahmed Farag Ali,A Tawfik

doi:10.1155/2013/126528

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 aarea-type correction to the area law of entropy which implies that the number of bitsNis 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.

Highlights

The earliest idea about the connection between gravitation and the existence of a fundamental length was proposed in [1]
The existence of a minimal length is considered as a consequence of the string theory because strings obviously cannot interact at distances smaller than the string size
The black hole physics suggests that the uncertainty relation should be modified near the Planck energy scale due to the fact that the photons emitted from the black hole suffer from two major errors: the first one is the error by Heisenberg’s classical analysis and the second one is because the black hole mass varies during the emission process and the radius of the horizon changes [2,3,4,5,6,7,8]

Summary

Introduction

The earliest idea about the connection between gravitation and the existence of a fundamental length was proposed in [1]. It was found that polymer quantization suggests the existence of minimal length in a similar way to string theory and black hole physics [11] All these different approaches suggest that the standard uncertainty relation in quantum mechanics is modified to yieldgeneralized uncertainty principle (GUP) [2,3,4,5,6,7,8, 11]. When combining it with the holographic principle and using the equipartition law of energy, Newton’s law of gravitation is obtained It was investigated in [38] modification of the entropic force due to corrections to the area law of entropy which is derived from quantum effects and extra dimensions.

The Generalized Uncertainty Principle

Gravity as an Entropic Force

GUP Impact on the Black Hole Thermodynamics

Modified Newton’s Law of Gravitation due to GUP

Conclusions