  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.
