Quantum, noncommutative and MOND corrections to the entropic law of gravitation

TL;DR

This paper explores quantum and noncommutative modifications to gravity based on Verlinde's entropic force, deriving a classical MOND-like behavior and explicitly calculating wavefunctions with minimal length effects.

Contribution

It introduces a framework for quantum and noncommutative corrections to Newtonian gravity within an entropic force context, deriving MOND behavior and explicit wavefunctions.

Findings

MOND-like dynamics emerge from entropy corrections

Explicit wavefunctions for minimal length states are computed

A canonical formulation of quantum-corrected Newtonian law is established

Abstract

Quantum and noncommutative corrections to the Newtonian law of inertia are considered in the general setting of Verlinde's entropic force postulate. We demonstrate that the form for the modified Newtonian dynamics (MOND) emerges in a classical setting by seeking appropriate corrections in the entropy.We estimate the correction term by using concrete coherent states in the standard and generalized versions of Heisenberg's uncertainty principle. Using Jackiw's direct and analytic method we compute the explicit wavefunctions for these states producing minimal length as well as minimal products. Subsequently we derive a further selection criterion restricting the free parameters in the model in providing a canonical formulation of the quantum corrected Newtonian law by setting up the Lagrangian and Hamiltonian for the system.