Turbulence and Quantum Mechanics from Cosmic to Planck Scales

Abstract:- A scale invariant model of statistical mechanics is applied to describe a modified statistical theory of turbulence and its quantum mechanical foundations. Hierarchies of statistical fields from cosmic to Planck scale are described. Energy spectrum of equilibrium isotropic turbulence is shown to follow Planck law. Predicted velocity profiles of turbulent boundary layer over a flat plate at four consecutive scales of LED, LCD, LMD, and LAD are shown to be in close agreement with the experimental observations in the literature. The physical and quantum nature of time is described and a scale-invariant definition of time is presented and its relativistic behavior is examined. New paradigms for physical foundations of quantum mechanics as well as derivation of Dirac relativistic wave equation are introduced