**Comoving to expansion Newtonian potential ****of galaxies and clusters instead of dark matter**

*Zahid Zakir* [1]

**Abstract**

Stretching of the Newtonian potential (NP) at early epochs is investigated and it is shown that observed effects, usually ascribed to a dark matter, can by explained by such stretching only. Increasing by time a radius of the gravitationally-bound region (GBR) and conservation of gravitational energy lead to a new scenario in which values of NP in expanding volume are maintained, while in physical volume are stretched. Really, the energy conservation in expanding volume requires for NP values to be comoving to the expanding shells. In addition, the radius of gravitationally-bound region increases by time due to decreasing of expansion velocity and different shells around galaxy cease expansion at different times. Thus, as far a shell placed from galaxy, as longer it was expanded and thickened, while potential difference on its boundaries remained unchanged. This shifts the values of NP around galaxy proportional to the distance r and, as the result, the gravitational acceleration, from NP’s 1/r^2 dependence, turned to 1/r dependence, as for centrifugal acceleration. This fact naturally explains the known empirical facts, such as flatness of rotation curves and velocity-mass relationships for galaxies and velocity dispersion in clusters.

PACS: 95.30.Sf, 95.35.+d, 98.65.Cw, 98.62.Ck

*Key words*: *gravitation, cosmological expasion, rotation curves, galaxy clusters*

Vol. **9**, No 2, p. 73 –77, v1, 31 July 2014

Online: TPAC: 4960-039 v1, 31 July 2014; DOI: 10.9751/TPAC.4960-039

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

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

*Zahid Zakir* [1]

**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

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

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