Entropic Corrections to Coulomb's Law

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 $\varphi$. Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.

17 pages, 5 figures, accepted in IJTP

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• Einstein Equations and MOND Theory from Debye Entropic Gravity
• Modified Friedmann Equations From Debye Entropic Gravity
• Thermodynamical description of the ghost dark energy model
• $q$-Deformed Einstein equations from entropic force
• From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane
• Effects of bosonic and fermionic $q$-deformation on the entropic gravity
• Friedmann equations for deformed entropic gravity
• Generalized entropic gravity from modified Unruh temperature
• Entropic Gravity and Cosmology in Kaniadakis Statistics
• A simple way of unifying the formulas for the Coulomb's law and Newton's law of the universal gravitation: An approach based on membranes
• Nonextensive statistics, entropic gravity and gravitational force in a non-integer dimensional space
• q-Path entropy phenomenology for phase-space curves
• Implications of maximum acceleration on dynamics
• Generalized Second Law of Thermodynamics with Corrected Entropy in Tachyon Cosmology