Time varying gravitational constant G via the entropic force

TL;DR

This paper explores how applying the uncertainty principle to Verlinde's entropic gravity leads to a time-varying gravitational constant G and effective mass, suggesting a connection to Dirac's large numbers hypothesis.

Contribution

It introduces a velocity-dependent correction to Newtonian mechanics derived from entropic principles, implying a dynamic G and mass that relate to Dirac's hypothesis.

Findings

Effective mass varies with time near holographic screens

Newton's constant G becomes a time-dependent quantity

Supports the holographic basis of Dirac's large numbers hypothesis

Abstract

If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton's second law of mechanics in the Planck's scale. This curious velocity dependence term inspires a frictional feature of the gravity. In this short letter we address that this new term modifies the effective mass and the Newtonian constant as the time dependence quantities. Thus we must have a running on the value of the effective mass on the particle mass $m$ near the holographic screen and the $G$. This result has a nigh relation with the Dirac hypothesis about the large numbers hypothesis (L.N.H.) [1]. We propose that the corrected entropic terms via Verlinde idea can be brought as a holographic evidence for the authenticity of the Dirac idea.