Planck Scale Effect in the Entropic Force Law

TL;DR

This paper explores how Planck scale modifications, via the Generalized Uncertainty Principle, alter the entropic force law by incorporating a minimum measurable length, impacting the quantum uncertainty relation.

Contribution

It introduces Planck scale effects into the entropic force law through a generalized uncertainty relation involving minimum length considerations.

Findings

Modified uncertainty relation with Planck scale effects

Implications for the entropic force law at quantum gravity scales

Potential adjustments to gravitational force descriptions at Planck length

Abstract

In this note we generalize the quantum uncertainty relation proposed by Vancea and Santos [7] in the entropic force law, by introducing Planck scale modifications. The latter is induced by the Generalized Uncertainty Principle. We show that the proposed uncertainty relation of [7], involving the entropic force and the square of particle position, gets modified from the consideration of a minimum measurable length, (which can be the Planck length).