## Archive

Archive for the ‘2014 Volume 9’ Category

**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

**New effects in cosmology: frequency and intensity stasis ****for radiation crossed galaxy clusters**

*Zahid Zakir* [1]

**Abstract**

New effects of stasis of radiation due to switching out from expansion flow at crossing largest gravitationally-bound regions (GBR), such as galaxy clusters, are considered and their observational consequences for supernovae and cosmic microwave background (CMB) data are discussed. The stasis of frequency and intensity of radiation at crossing of large number of clusters appreciably decreases observing redshifts z and magnifies apparent luminosities. Only normal redshifts z’ of photons not crossed clusters are directly related with the cosmic scale factor and thus true distances exceed those which follow from z. The effects increase for distant objects because of smaller inter-cluster distances at early epochs. For the relic radiation crossed the clusters the effects lead to the stasis of its temperature and “heating” with respect to a normally expanded flow outside the cluster. As a result, instead of former paradigm about almost sterile propagation of relic radiation from the recombination epoch, there is an opposite picture. Mixing of relic radiation flows, many times isolated from the expansion flow in GBRs along path, leads to their isotropy and loss of earlier perturbations. The observing anisotropy follows from the stasis effects at crossing of multiple layers of clusters at our nearest environment. The stasis effects allow one to do more exact conclusions from data analysis and lead to revising of distances and properties of extragalactic objects.

*PACS*: *04.20.Cv, 98.80.-k, 98.80.Jk 95.30.Sf, 97.60.Lf, 98.35.Jk, 98.54.-h*

*Key words: **cosmological models, redshift, extra dimension*

Vol. **9**, No 1, p. 5 – 17, v1, 6 May 2014

Online: TPAC: 4874-035 v1, 6 May 2014; DOI: 10.9751/TPAC.4874-035

[1] *Centre for Theoretical Physics and Astrophyics**, Tashkent, Uzbekistan*

zahidzakir@theor-phys.org

**A model of the closed universe gravitating in 4-space**

*Zahid Zakir* [1]

**Abstract**

Models of the closed Universe as a thin 3-sphere in 4-space, gravitating along 3-sphere’s radius, are reformulated in a new form, in which at a local environment of an observer the non-relativistic dynamics of a ball is reproduced with a correct energy conservation condition. Corresponding evolution equations for dust matter and radiation in the 3-sphere are obtained and their observational consequences are studied. It is shown that the closed models in 4-space also lead to the “Miniverse” model with a highly oscillating curve for the “distance modulus – redshift” relation.

*PACS*: *04.20.Cv, 98.80.-k, 98.80.Jk 95.30.Sf, 97.60.Lf, 98.35.Jk, 98.54.-h*

*Key words: **cosmological models, redshift, extra dimension*

Vol. **9**, No 1, p. 1 – 4, v1, 6 May 2014

Online: TPAC: 4874-034 v1, 6 May 2014; DOI: 10.9751/TPAС.4874-034

[1] *Centre for Theoretical Physics and Astrophyics**, Tashkent, Uzbekistan*

zahidzakir@theor-phys.org

**Gravitation as a thermodiffusion in the physical vacuum**

*Zahid Zakir* [1]

**Abstract**

An influence of matter on the vacuum energy density is considered and a treatment of gravitation as inhomogeneity of quantum diffusion is developed. A treatment of quantum theory as conservative diffusion [1] is briefly presented, where quantum fluctuations of energy and momentum of a classical particle occur because of interaction with physical vacuum. The increasing of particle’s mean energy at such fluctuations appears as quantum phenomena, while corresponding local decreasing of mean vacuum energy to the same value appears as gravitation. For one a particle the decreasing is extremaly small and in particle physics it can be neglected. However, when large number of particles are concentrated in a small volume, consequences of the vacuum energy decreasing become appreciable and they appear as gravitation. The diffusion treatment of quantum processes thus leads to the diffusion treatment of gravitation with natural synthesis of theories of both phenomena. New properties of inhomogeneous diffusion related by local decreasing of vacuum energy, such as slowering of fluctuations of particles with delay of intensity of processes (including redshift of frequencies), drift of particles toward slower fluctuations region and their diffusive acceleration, which is independent on mass of particles, are studied. Observable effects following from the new treatment are discussed.

PACS: 02.50.Ey, 03.65.Ta , 05.40.Jc * *

*Key words*:* quantum mechanics, diffusion, Brownian motion, kinetic theory of gases*

Vol. **9**, No 1, p. 33 –53, v1, 6 May 2014

*Online: TPAC: 4874-037 v1, 6 May 2014*; DOI: 10.9751/TPAC.4874-037

[1] *Centre for Theoretical Physics and Astrophyics**, Tashkent, Uzbekistan*

zahidzakir@theor-phys.org

**Theory of conservative diffusion **in **classical and quantum systems**

*Zahid Zakir* [1]

**Abstract**

In previous paper [1] conservative diffusion of light particles in a dilute medium of heavy particles was studied by analogue with Brownian motion. In the present paper the theory is formulated in more consistent “hydrodynamic” form by using a conservativity condition only, that mean energy of a light particle is conserved. As a model is taken diffusion of very cold light gas in warm heavy gas a time interval before relaxation when light gas remains cold. Unlike Lorentz’s gas, where thermal energies of light and heavy atoms are equal, here their thermal speeds are equal and this leads to the effects of conservativity similar to quantum effects. Such conservative diffusion is described by two equations – the continuity equation and the energy conservation condition, non-linear under the probability density. At introduction of a complex probability amplitude the equations linearized and turn to the Schrödinger equation. As a result, one must add not probability of alternatives, but probability amplitudes. A free pass length and corresponding momentum define an elementary phase volume and the diffusion coefficient. The predicting new quasi-quantum effects in classical systems are discussed. It is shown that the formalism of quantum mechanics describes the classical conservative diffusion with a constant diffusion coefficient and that quantum mechanics is a particular case of such diffusion in the vacuum where the elementary phase volume of free passage is equal to the Planck constant.

PACS: 02.50.Ey, 03.65.Ta , 05.40.Jc * *

*Key words*:* quantum mechanics, diffusion, Brownian motion, kinetic theory of gases*

Online: TPAC: 4874-036 v1, 6 May 2014; DOI: 10.9751/TPAC.4874-036

[1] *Centre for Theoretical Physics and Astrophyics**, Tashkent, Uzbekistan*

zahidzakir@theor-phys.org

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