Playing with Casimir in the vacuum sandbox

TL;DR

This paper explores a thought experiment involving the Casimir effect, suggesting a fundamental minimum separation between plates near the Planck scale, with implications for quantum vacuum fluctuations.

Contribution

It introduces a novel Gedankenexperiment that proposes a minimum plate separation related to Planck length, offering new insights into vacuum fluctuation limits.

Findings

Minimum plate distance cannot go below (L/L_P)^{2/3} Planck lengths.

Approach to this minimum distance is asymptotic.

Implications for understanding quantum vacuum fluctuations.

Abstract

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.