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

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.