Playing with Casimir in the vacuum sandbox

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.