Mesoscopic Casimir forces in quantum vacuum

Traditionally it is assumed that the Casimir vacuum pressure does not depend on the ultraviolet cut-off. There are, however, some arguments that the effect actually depends on the regularization procedure and thus on the trans-Planckian physics. We provide the condensed matter example where the Casimir forces do explicitly depend on the microscopic (correspondingly trans-Planckian) physics due to the mesoscopic finite-$N$ effects, where $N$ is the number of bare particles in condensed matter (or correspondingly the number of the elements comprising the quantum vacuum). The finite-$N$ effects lead to mesoscopic fluctuations of the vacuum pressure. The amplitude of the mesoscopic flustuations of the Casimir force in a system with linear dimension $L$ is by the factor $N^{1/3}\sim L/ a_{P} $ larger than the traditional value of the Casimir force given by effective theory, where $a_{P}=\hbar/p_{ P}$ is the interatomic distance which plays the role of the Planck length.