**Conservative Diffusion as a Physical Mechanism ****for Quantum Mechanics and Gravitation**

**Conservative Diffusion as a Physical Mechanism****for Quantum Mechanics and Gravitation****Abstract**

The theory of conservative diffusion and its main applications are reviewed. A basic model for the theory is diffusion of a cold light gas in a warm heavy gas before relaxation when light gas remains cold and mean energy of its particles conserves. Unlike the Lorentz gas, where thermal energies of light and heavy atoms are equal, here the same order are their thermal speeds. Such conservative diffusion is described by two equations – the Hamilton-Jacobi and continuity equations, nonlinear under the probability density. They can be linearized by introduction of a complex probability amplitude, transforming them to the Schrödinger equation where one must add not probabilities, but probability amplitudes of alternatives. Mean free path and the corresponding momentum determine an elementary phase volume and a diffusion coefficient. The theory predicts a number of quasiquantum effects in classical systems. The formalism of quantum mechanics thus describes a classical conservative diffusion and quantum mechanics is only a special case of such diffusion in the vacuum, when the elementary phase volume is equal to the Planck constant. A conservative thermodiffusion at nonzero temperature gradient is studied also. Its properties, such as decreasing of intensity of fluctuations of particles (including redshift of frequencies), drift of particles to colder region and their thermodiffusive acceleration, not depending on the mass of particles, are similar to properties of gravitation. This allows us to identify gravitation by thermodiffusion in the physical vacuum. In the diffusive picture fluctuations of energy-momentum of classical particles due to interaction with vacuum lead to increasing of their mean energy, which appears as quantum phenomena, while corresponding local decreasing of vacuum energy density reveals as gravitation. The diffusive treatment of quantum theory thus leads to the thermodiffusive treatment of gravitation too with natural synthesis of theories of both phenomena. Observable effects following from the new theory are discussed.

PACS: 03.65.Ta, 04.20.Cv, 02.50.Ey, 05.40.Jc

*Key words*:* quantum fluctuations, vacuum energy, thermodiffusion, metrics, curvature*

Vol. **9**, No 2, p. 54 –72, v1, 31 July 2014

Online: TPAC: 4960-038 v1, 31 July 2014; DOI: 10.9751/TPAC. 4960-038

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[1] *Centre for Theoretical Physics and Astrophyics**, Tashkent, Uzbekistan* zahidzakir@theor-phys.org

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