Casimir Self-Interaction Energy Density of Quantum Electrodynamic Fields

TL;DR

This paper models the Casimir self-interaction energy density of quantum electrodynamic fields, linking it to the fine-structure constant and cosmological observations, suggesting a potential connection to dark energy.

Contribution

It extends a quantum scaling law to describe the polarizability density of quantum fields and derives the Casimir self-interaction energy density in relation to the cosmological constant.

Findings

Calculated energy density aligns with measurements of the cosmological constant.

Model obeys the cosmological equation of state w=-1.

Provides a theoretical link between quantum field fluctuations and dark energy.

Abstract

Quantum electrodynamic fields possess fluctuations corresponding to transient particle/antiparticle dipoles, which can be characterized by a non-vanishing polarizability density. Here, we extend a recently proposed quantum scaling law to describe the volumetric and radial polarizability density of a quantum field corresponding to electrons and positrons and derive the Casimir self-interaction energy (SIE) density of the field, $\bar{E}_{\rm{SIE}}$, in terms of the fine-structure constant. The proposed model obeys the cosmological equation of state $w=-1$ and the magnitude of the calculated $\bar{E}_{\rm{SIE}}$ lies in between the two recent measurements of the cosmological constant $\Lambda$ obtained by the Planck Mission and the Hubble Space Telescope.