Generalized uncertainty relations, particles, black holes, and Casimir effect in the three-dimensional quantum vacuum

A modified version of generalized uncertainty relations, which leads to a unifying treatment of microphysics of elementary particles and macrophysics of black holes, is developed in the model of a three-dimensional dynamical quantum vacuum defined by a variable energy density. New suggestive prospects for interpretation of the Casimir effect and cosmological wormholes are obtained in this picture.