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.
Highlights
Introduction and aimThe physical vacuum seems to be a “busy place” described as “foamy” by Wheeler [1], and one of the most intriguing phenomena linked to it is the Casimir effect [2]
We propose a Gedankenexperiment based on the Casimir effect by following the tradition of speculating for the playful purpose of thinking through its consequences
This Gedankenexperiment is suggested with the caveat that the relation of the Casimir effect with the vacuum energy of fluctuating quantum fields is still open to debate at the time of this writing [3]
Summary
The physical vacuum seems to be a “busy place” described as “foamy” by Wheeler [1], and one of the most intriguing phenomena linked to it is the Casimir effect [2]. We propose a Gedankenexperiment based on the Casimir effect by following the tradition of speculating for the playful purpose of thinking through its consequences. This Gedankenexperiment is suggested with the caveat that the relation of the Casimir effect with the vacuum energy of fluctuating quantum fields is still open to debate at the time of this writing [3]
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