Diffusion treatment of quantum theory and gravity. 1. Diffusion quantum mechanics.

On the basis of the observational fact that a wave packet, describing the localized ensemble of micro-objects, spreads according to the diffusion law, the quantum equivalence principle is formulated, that the motion of the ensemble of quantum objects is equivalent to the diffusion of the ensemble of classical objects in a fluctuating background field (physical vacuum). The observations also confirm the validity of the principle of relativity for quantum phenomena, formulating as the principle of constancy of quantum fluctuations, that these fluctuations and the describing them diffusion occur identically in all inertial frames. It is shown that these two physical principles, together with the principles of mechanics, lead to the diffusion quantum mechanics (DQM), containing the formalism of quantum mechanics as a particular case. In DKM the relation between the velocity of the diffusion flow and the probability density is given by the diffusion law (Fick’s law), while the invariance of diffusion leads to its conservatism (diffusion without friction) and the constancy of the diffusion coefficient, fixed from correspondence with quantum mechanics. In DQM the Hamiltonian includes the kinetic energies of the drift, diffusion flux, and interaction potentials, while the probability density and the drift action function of particles S form a canonical pair. The canonical equations for them then lead to the continuity equation and to the Hamilton-Jacobi-Madelung equation. The probability density in them enters nonlinearly, but in the case of a canonical transformation to the complex amplitude of the probabilities, they are linearized and pass into the Schrödinger equation. As a result, the amplitudes of probabilities add up for the alternatives, i.e. their superposition takes place. DQM based on physical principles is a more general theory than quantum mechanics, since along with classical devices and particles it introduces a third participant of all processes - the background field, which is the source of quantum fluctuations of classical particles. In DQM, the quantum potential is the potential energy associated with localization, quantum statistics appears in the system of many classical particles in the fluctuating background, and composite particles of small size can have a small mass. DQM also explains the existence of rest energy, the constancy of the light velocity (velocity of quantum fluctuations) and predicts the existence and properties of gravitation as thermal diffusion in the inhomogeneous background field.