On microscopic interpretation of phenomena predicted by the formalism of general relativity.(Report)

1. Introduction

Although Poincaref (1905a) was the first to write the relativistic transformation The general theory of relativity formally predicted such phenomena as the motion of Mercury's perihelion, the bending of light by the gravitational field of the sun and the gravitational red shift of spectral lines (see, e.g. Refs. [1-3]). The predictions were verified experimentally and since then general relativity was widely recognized as the fundamental physical concept of the 20th century. Since general relativity has all attributes of an action-at-a-distance theory, some researchers try to understand its deeper sense coming back to the old idea of retarded potentials, or velocity-depended potentials, which would account for a nature of the motion of the front of the gravitational potential.

Soares [4] considering light as classical massive corpuscles calculated the deflection of a light beam under the Sun's gravitational force, which is described by the central force hyperbolic orbit; in the first approximation he obtained the so-called Newtonian deflection [[delta].sub.N] = 2G[M.sub.sun]/([[c.sup.2][R.sub.sun]) , though Einsteinian's is still [[delta].sub.GR] = 2[[delta].sub.N] where [M.sub.sun] and [R.sub.sun] are the Sun's mass and radius.

Gine [5,6] reviewed tens of works dedicated to the study of the modified Newton's potential, among which there were such potentials as Weber's, Gerber's and others. Gine argues that Weber's potential, which is a velocity dependent potential V = (1 - [r.sup.2] 12[c.sup.2]) */r, allows one to introduce an additional force component. Such a component is the tangential component of the speed of a test particle in the gravitational field of a central mass M, which significantly influences the eccentricity of the hyperbolic orbit of the particle. Thus taking into account the finite propagation speed--the velocity of light c--he [5] concludes that the anomalous precession of the Mercury's perihelion is associated with a second order delay of the retarded potential

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As Gine [6] shows, at some fixed parameters the deflection of a light beam would reach that of derived by Einstein in 1916, i.e. [[delta].sub.GR] = 4GM / ([c.sup.2][r.sub.p]) where [r.sub.p] is the closest approach, i.e. perihelion of the beam.

So far the mentioned phenomena have not been described on the basis of a microscopic approach. Nevertheless, before applying such an approach to the study of the problem, one has to become familiar with major statements of the concept. However, let us initially consider general discrepancies between phenomenological and microscopic standpoints. General relativity, as a typical phenomenological theory, considers matter and space-time as two independent entities, which, however, can influence each other [7]: a matter curves space-time that is treated as a geometric entity resting on the statement of constancy of the speed of light c; photons are massless, they form the world line of light ray. Thus with such an approach the microscopic peculiarities of the real space remain beyond the study of the problem.

Indeed, since photons transfer momentum, they physically have mass. But what is mass? At a scale comparative with the de Broglie wavelength [lambda] of the quantum system in question, a phenomenological description has to make way for a quantum mechanical one. However, conventional quantum mechanics is constructed in an abstract phase space and hence it cannot be used to investigate the behaviour of matter at a sub microscopic size: in line with the theory the less scale, the more indeterminism ... Therefore, to account for the behaviour of matter at extremely small scales we have to rely on a theory developed in the real physical space, which is able to operate at any microscopic scale.

For the first time Bounias and the author [8-12] proposed a detailed theory of the constitution of the real physical space. In line with those researches, which are based on topology, set theory and fractal geometry, the real space emerges as a tessellation lattice of primary topological balls (primary entities of Nature, or 'superparticles') whose size can be estimated as the Planck's one, 1035 m. It has been shown how mathematical characteristics, such as length, surface, volume and fractal geometry generate in this tessellattice the basic physical notions, such as mass, particle, electric charge, the particle's de Broglie wavelength, etc. and the corresponding fundamental laws. In particular, mass emerges from space as its local deformation, i.e. when a volumetric fractal deformation is created in the appropriate cell of the tessel-lattice. Hence matter is no longer separated from space, as it occurs in general relativity, but can reasonably appear at special conditions.

In the present paper we show in what way submicroscopic mechanics [13-19] developed in the real physical space [8-12] is capable …