Entropic Corrections to Coulomb's Law

TL;DR

This paper explores how quantum entropy corrections, inspired by entropic force ideas, modify Coulomb's law and relate to quantum field effects like vacuum polarization, suggesting a link between gravity and electromagnetism.

Contribution

It introduces a novel entropic correction to Coulomb's law based on quantum entropy modifications and connects these to quantum electrodynamics effects.

Findings

Modified Coulomb's law consistent with vacuum polarization at certain distances

Derived entropy-corrected Poisson's equation for scalar potential

Supports unification of gravity and electromagnetism via holography

Abstract

Two well-known quantum corrections to the area law have been introduced in the literatures, namely, logarithmic and power-law corrections. Logarithmic corrections, arises from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, while, power-law correction appears in dealing with the entanglement of quantum fields in and out the horizon. Inspired by Verlinde's argument on the entropic force, and assuming the quantum corrected relation for the entropy, we propose the entropic origin for the Coulomb's law in this note. Also we investigate the Uehling potential as a radiative correction to Coulomb potential in 1-loop order and show that for some value of distance the entropic corrections of the Coulomb's law is compatible with the vacuum-polarization correction in QED. So, we derive modified Coulomb's law as well as the entropy corrected Poisson's equation which governing the evolution of the scalar potential $\phi$. Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.