  The Casimir effect continues to be a subject of discussion regarding its
relationship, or the lack of it, with the vacuum energy of fluctuating quantum
fields. In this note, we propose a Gedankenexperiment considering an imaginary
process similar to a vacuum fluctuation in a typical static Casimir set up. The
thought experiment leads to intriguing conclusions regarding the minimum
distance between the plates when approaching the Planck scale. More
specifically, it is found that distance between the plates cannot reach a value
below $(L/L_P)^{2/3}$ Planck lengths, being $L_P$ the Planck length and $L$ the
typical lateral extension of the plates. Additional findings allow the
conclusion that the approach between the two plates towards this minimum
separation distance is asymptotic.
