Stochastic motion of test particle implies that G varies with time

TL;DR

This paper proposes a new holographic approach to gravity where stochastic motion of test particles leads to a time-varying gravitational constant, integrating Dirac's hypothesis with entropic gravity concepts.

Contribution

It introduces a novel framework linking stochastic particle motion to a dynamic gravitational constant within an entropic gravity model.

Findings

Stochastic motion results in a time-dependent Newton's constant.

Equipartition is recovered as time approaches infinity.

The model aligns with Dirac's large numbers hypothesis.

Abstract

The aim of this letter is to propose a new description to the time varying gravitational constant problem, which naturally implements the Dirac's large numbers hypothesis in a new proposed holographic scenario for the origin of gravity as an entropic force. We survey the effect of the Stochastic motion of the test particle in Verlinde's scenario for gravity\cite{Verlinde}. Firstly we show that we must get the equipartition values for $t\rightarrow\infty$ which leads to the usual Newtonian gravitational constant. Secondly,the stochastic (Brownian) essence of the motion of the test particle, modifies the Newton's 2'nd law. The direct result is that the Newtonian constant has been time dependence in resemblance as \cite{Running}.