Casimir Type Effect in Scale Relativity Theory

Abstract

Navier-Stokes equations in scale relativity theory predict that the (vector) velocity field Fand the (scalar) density field p, on small distances (the same magnitude as the Compton length) behave like wave functions and are transported by the motion of a Newtonian fluid with velocity U. When considering vacuum from Casimir cavities (either two metallic slabs, parallel to each other, placed at a distance d apart or rectangular enclosures of sides d h d) a non-differentiable, Newtonian, 2D non-coherent quantum fluid whose entities assimilated to vortex-type objects become coherent (the coherence of the quantum fluid reduces to its ordering in vortex streets, being trigered by cvasiparticles) due to the constraints induced by the presence of walls. In other words, non-differentiability and coherence of the quantum fluid due to constraints, generate pressure. Casimir type forces are derived which are in good agreement with other theoretical results and experimental data.