Connection between time-splitting parameter and surface tension in Casimir problems. Related phenomena in relativistic collapse of a singular shell

TL;DR

This paper explores the interplay between Casimir effects, surface tension, and gravitational phenomena, revealing how these factors influence stability, collapse, and bounce scenarios in quantum and relativistic systems.

Contribution

It introduces a novel connection between the time-splitting parameter and surface tension in Casimir problems, and analyzes stability and collapse phenomena considering these effects.

Findings

Time-splitting parameter relates to atomic spacing and surface tension.

Surface tension stabilizes fluid shells against Casimir-induced instability.

Casimir pressure can cause a bounce in vacuum hole filling and influence gravitational collapse.

Abstract

We discuss four different, though related, fundamental topics related to the Casimir effect: 1) We suggest that the application of Casimir theory to real dielectric materials, thus implying the atomic spacing as a course-grained length parameter, makes it natural to assume that this parameter is of the same order of magnitude as the QFT time-splitting parameter multiplied with the velocity of light. 2) We show that application of Casimir theory to a thick fluid shell (apparently a closed mechanical system), leads actually to an unstable situation if not extra mechanical forces, typically surface tension forces, are brought into consideration. 3) We analyze how the presence of a radial Casimir repulsive pressure modifies the filling process of a spherical vacuum hole in an infinite fluid (the Reynolds problem), with the result that a bounce occurs at a finite though very small radius. 4) As a comment on an apparently similar situation in general relativity, we consider the gravitational collapse of a singular shell. It might seem natural to allow for the presence of a repulsive Casimir pressure in this case also, thereby obtaining a bounce-like situation again. However, we have to conclude that such a procedure implies an omission of the Casimir field's gravitational energy, and is therefore hardly tenable, although it is in our opinion worth mentioning.