The Casimir effect is usually derived for parallel plates, with the pressure going as the inverse fourth power of the separation. It strikes me that this implies that a tiny spherical shell of charge (approximating opposite walls to be parallel) will feel an attractive force that goes roughly as the inverse square of the radius (since the area goes as the square of the radius). This seems like a suggestive coincidence that would hint that the Casimir effect would provide the attractive force necessary to hold the charge of the electron together. Is this idea trivially ruled out or has it been explored?
Edited to add: I asked a distinct but related question a couple years ago that I think got a nice answer: link.