Casimir force: an alternative treatment

TL;DR

This paper explores alternative methods to evaluate the Casimir force using models inspired by quantum cavity states and atomic energy levels, revealing dependencies on fundamental constants and estimating the fine structure constant.

Contribution

It introduces novel approaches to calculate the Casimir force by combining cavity quantum states with atomic models, providing new insights into fundamental constants.

Findings

Dependence of Casimir force on particle mass and quantum number cancels out in calculations.

Comparison of models allows estimation of the fine structure constant alpha.

Alternative treatments offer different perspectives on Casimir force calculations.

Abstract

The Casimir force between two parallel uncharged closely spaced metallic plates is evaluated in ways alternatives to those usually considered in the literature. In a first approximation we take in account the suppressed quantum numbers of a cubic box, representing a cavity which was cut in a metallic block. We combine these ideas with those of the MIT bag model of hadrons, but adapted to non-relativistic particles. In a second approximation we consider the particles occupying the energy levels of the Bohr atom, so that the Casimir force depends explicitly on the fine structure constant alpha. In both treatments, the mean energies which have explicit dependence on the particle mass and on the maximum occupied quantum number (related to the Fermi level of the system) at the beginning of the calculations, have these dependences mutually canceled at the end of them. Finally by comparing the averaged energies computed in both approximations, we are able to make an estimate of the value of the fine structure constant alpha.