Abstract

Localized ensemble of free microparticles spreads out as in a frictionless diffusion satisfying the principle of relativity. An ensemble of classical particles in a fluctuating classical scalar field diffuses in a similar way, and this analogy is used to formulate diffusion quantum mechanics (DQM). DQM reproduces quantum mechanics for homogeneous and gravity for inhomogeneous scalar field. Diffusion flux and probability density are related by Fick’s law, diffusion coefficient is constant and invariant. Hamiltonian includes a “thermal” energy, kinetic energies of drift and diffusion flux. The probability density and the action function of drift form a canonical pair and canonical equations for them lead to the Hamilton-Jacobi-Madelung and continuity equations. At canonical transformation to a complex probability amplitude they form a linear Schrödinger equation. DQM explains appearance of quantum statistics, rest energy (“thermal” energy) and gravity (“thermal” diffusion) and leads to a low mass mechanism for composite particles. I. INTRODUCTION Classical character of the particles and the background field Quantum mechanics is based on mathematical axioms, and radically simplified the situation, since this excluded that not on physical principles following from experiments, and element of irrationalism of the standard interpretation, when therefore it is, until now, represented only a successful “quantum” particles supposedly had the ability to fluctuate in mathematical model. The derivation of its formalism from an empty and homogeneous Euclidean space without an physical principles was one of the main problems of quantum external cause, spontaneously changing their energy and physics, since this would complete the long time history of the momentum. Naive attempts to ascribe the appearance of formation of quantum mechanics as a fundamental physical probabilit