Mesoscopic Casimir forces in quantum vacuum

Traditionally, it is assumed that the Casimir vacuum pressure does not depe nd on the ultraviolet cutoff. There are, however, some arguments that the e ffect actually depends on the regularization procedure and thus on trans-Pl anckian physics. We provide the condensed matter example where the Casimir forces do explicitly depend on 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 elemen ts comprising the quantum vacuum). The finite-N effects lead to mesoscopic fluctuations of the vacuum pressure. The amplitude of the mesoscopic fluctu ations of the Casimir force in a system with linear dimension L is a factor of N-1/3 similar to L /a(P) larger than the traditional value of the Casim ir force given by effective theory, where a(P) = (h) over bar /p(P) is the interatomic distance which plays the role of the Planck length. (C) 2001 MA IK "Nauka/Interperiodica".