Quantum Electromagnetic Zero-Point Energy of a Conducting Spherical Shell and the Casimir Model for a Charged Particle

The quantum electromagnetic zero-point energy of a conducting spherical shell of radius r has been computed to be ΔE(r)≅0.09ℏc/2r. The physical reasoning is analogous to that used by Casimir to obtain the force between two uncharged conducting parallel plates, a force confirmed experimentally by Sparnaay and van Silfhout. However, while parallel plates are attracted together because of the zero-point energy, a conducting sphere tends to be expanded. Thus although relevant for the understanding of the quantum-mechanical zero-point energy, the result invalidates Casimir's intriguing model for a charged particle as a charged conducting shell with Poincaré stresses provided by the zero-point energy and a unique ratio for e²/ℏc independent of the radius.