Figure 1. The continuity of homeomorphic mappings of structures is broken if once a deformation involves an iterated transformation with internal self-similarity, which involves a change in the dimension of the mapped structure.

Figure 2. Topological ball (cell, or superparticle) is represented as a triangle, figuring 3 dimensions, in a metaphorical form. A degenerate ball keeps the same dimension, in contrast with a particled ball endowed with a fractal substructure. A complete decomposition into one single ball (k = 1) conserves the volume without keeping the fractal dimension. The von Koch-like fractal has been simplified to 3 iterates for clarity.

Figure 3. Space net (i.e. the tessellattice) that is made up of cells, or superparticles and the motion of a particle in it.

In papers [12,21,24,33] the exchange dynamics of a moving particle, i.e. exchanges with the tessellattice by fragments of the particle's fractal volumetric deformations carrying by inertons have been studied in detail. Such a mass/fractal dynamics allows the study in the framework of a specific Lagrangian and the corresponding Euler-Lagrange equations. The result shows that inertons scatter from the particle as a standing spherical wave.

The deformation coat made up around the particle in the degenerate space (see Figure 3) plays the key role in the processes of emittion and the following re-absorption of inertons [12]. It seems reasonably to say that the main idea of the research conducted in Refs. [12,21,24,33] may briefly be stated in the words: no motion, no gravity .

An analysis carried out in paper [24] additionally allows us to estimate the velocity of inertons:   v_inerton = 92 c   where   c   is the velocity of light. The inerton standing sperical wave 1/r is developing around the object studied just with this inerton velocity. But in time longer than the time concerened with the inerton dynamics we can talk about a special deformation relief around the object and this relief exactly coincides with Newton's graviational potential G M / r  [12,33]. Since laboratory methods of the study of gravity are mainly optical, we perceive Newton's graviational potential as static, though it is dynamic by its nature!

A detailed analysis [27] enables us to conclude that the inerton field is also responsible for the nucleus stability, i.e. the inerton field generated at the scale from 10^-35 to 10^-30 m also acts on the size 10^-13 m. The same should take place in the case of hadrons: the inerton field may be identified with gluons of quantum chromodynamics that acts at ~10^-18 m.

The notion of the particle spin has been successfully interpreted in Ref. [4]. An actual canonical particle can possess the spin projection to the z-axis equal only to +1/2 or -1/2. Particles with an integer spin (0, 1, 2, ...) are compound particles.

Figure 4. Proper oscillations of the particle in the real space is associated with the notion of its spin. In principle such oscillations can occur not only along/against the particle path but also to the left/right.

In such a manner the proposed line of research develops the model of real space, the mechanics of motion of particles, the submicroscopic theory of gravity and discloses the inner reasons of elementary interactions. Only two fundamental fields are presented in the theory: the inerton field and the photon one called also the electromagnetic field. The phenomenon of "static" gravity is also derived from the dynamic inerton field. The unification of the two said fields is reduced to the space net that is simulated by special building blocks, which using the mathematical language may be called "balls". So the space net is simulated as a tesselation of topological balls (or superparticles, or elementary cells), which are primary blocks of Nature. In other words, saying physically the real space is regarded as a substrate that is densely packed with those balls, or superparticles, which are found in the degenerate state and whose size is on the order of the Planck length, 10^-35 m. A particle is defined as a local curvature, or a local deformation of a superparticle, i.e., the creation of a fractal deformation in a superparticle means the induction of mass in it. Thus the real space can be regarded rather as a kind of a quantum aether that as a medium manifest itself at laboratory measurements. And in fact, we have recorded the inerton field that is the production of the fine-grained structure of space (see below the subsection Experimental verification of the concept).

The electric charge and the photon

A detailed theory of the photon and the electric charge as such, which are generated and move in the tessellattice, has been presented in works [11,19, 22]. The descriptive-geometric sense of the electric and magnetic fields and their carriers - photons - is analyzed. The notion of the scalar and vector potentials of a charged particle and their behavior at the motion of the particle is investigated explicitly. Based on the potentials, the Lagrangian leading to the Maxwell equations is constructed. The distinctive properties of free basic excitations of the tessellattice - the inerton and the photon - are discussed. Work [22] suggests the detailed interpretation of the Maxwell equations in terms of the submicroscopic approach to Nature.

Figure 5. The complete free primary ball, or superparticle (left), which being embedded in the tessellattice becomes crumpled (center), and the charge particle - two opposite polarized surface states correspond to the positive and negative electric charge (right) (from Ref. [22]).

Thus the electric charge is kept and plays on the surface of the particle, which complete agrees with The Rigveda as has recently been decoded by Dr. R. R. M. Roy in his Vedic Physics.

The magnetic charge has appeared at the motion of the particle: it is generated every odd half period λ/2 where λ is the amplitude of spatial oscillations of the particle, i.e. the particle's de Broglie wavelength. The magnetic charge is characterized by the bent state of needles on the surface of the particle [22].

Figure 6. Motion of the charged particle, for instance, the electron. The particle passing the half de Broglie wavelength λ/2 becomes the monopole, but to the end of the next section λ/2 the particle reverts to the initial pure electric state. Standing waves of inerton-photons, i.e. inertons polarized electromagnetically, accompany the particle (from Ref. [22]).

How do a free inerton and a free photon look like? These excitations of the tessellattice migrate from cell to cell transferring their peculiar properties. The motion is characterized by periodicity, namely, the wavelength λ. The inerton carries fragments of cell's deformation: the deformed cell, i.e. mass m, is periodically transferred to the inflatied cell, the so-called antimass', which can be described by the oscillation of the radius of a cell between values R - Δr and R + Δr where R is the effective radius of a superparticle in the degenerate state, i.e. in the non-perturbed tessellattice.

Figure 7. Motion of two basic quasi-particles of the space:
the free inerton and the free photon (from Ref. [22]).

The photon transfers a surface polarization of a cell, which can have two possible orientations. During each spatial period, or wavelength λ, the electric polarizartion changes to the magnetic one.


Experimental verification of the concept

In paper [5] electrons moving in atoms were treated as entities surrounded by their inerton clouds. The investigation of the interaction between such extended entities and a photon flux was curried out in detail. The major peculiarity proposed was the effective cross-section of electrons significantly enlarged due to their inerton clouds spread around the electrons. A number of different experiments aimed at the study of laser-induced gas ionization were in agreement with the theoretical results prescribed by the inerton theory, though other theories failed to account for those data.

The impact of the Earth inerton waves on the behavior of atoms in metals was studied theoretically and then observed experimentally in changes of the fine morphological structure of specimens by the high-resolution electron-scanning microscope [3].

The inerton concept was applied [9] to explain a fine dynamics of hydrogen atoms in the crystal whose FTIR spectra in the 400 to 4000 cm^-1 range showed unexplainable sub maximums. Features observed in the spectra were associated with the overlapping of hydrogen atoms' matter waves that induced the mean inerton field contributing to the paired potential of hydrogen-hydrogen interaction. Such additional interaction brought to the formation of hydrogen clusters that became the origin of the modulated spectra.

The phenomenon of irradiation of aqueous solutions by scalar waves generated by the so-called Teslar^® technology was studied in papers [25,26]. Our study justified that the Teslar watch produced nor the electromagnetic, neither ultrasound radiation. That was the inerton radiation generated by a special electric circuit embedded in the watch (two superimposed electromagnetic waves whose amplitudes are shifted to 180^o are cancelled, but an inerton flow, which continues to transfer the energy, remains). These studies showed that the inerton field, in fact, carries a mass defect Δm, which is absorbed by entities in condensed media.

In our experiment [28] laser illuminating ferroelectric crystal of LiNbO₃ generated stable electron droplets contained around 10¹⁰ electrons, which freely moved with the velocity 0.5 cm/s in the air along the surface of the crystal experiencing the Earth gravitational field. We showed that the cluster stability was possible only due to the weighting of electrons up to millions of times, which happened due to the absorption of the crystal inertons by ejected electrons. Then in a cluster, electrons were interacting through two competitive potentials: the Coulomb one and the inerton field that a solitary one could elastically withstand the Coulomb repulsion.

Consequently, the mass defect Δm becomes an inherent property not only of atomic nuclei but also of any physical and physical chemical systems.

Here is the photos of our recent device that measures the inerton radiation (the intensity, i.e. how many inertons falls on 1 cm² per 1 s and the frequency up to 100 kHz):