Chapter 12. Interactions Carried by the Epola

12.1 The epola deformation around a neutral guest particle

Consider an electrically neutral guest particle of mass $m$ (e.g., a neutron). located centrally in a unit cube of the epola, as shown in Figure 6. The distance from the center of the particle to each of the 8 nearest lattice points is $0.87 \ l_0$, where $l_0$ is the epola lattice constant, $l_0 = (4.4 \pm 0.5) \ \mathrm{fm}$. On such a distance, the repulsive action of the guest particle is very strong, so that the 4 electrons and the 4 positrons are pushed (equally) far out of these lattice points. The second group of 24 lattice sites is at a distance of $1.66 \ l_0$ from the center of the guest particle. At such distance, the direct repulsive action of the guest particle is weak. It pushes (equally) the 12 electrons and the 12 positrons slightly out of their lattice sites. The third group of lattice points is at a distance of $2.18 \ l_0$, out of the range of the direct repulsion by the guest particle.

Each of the outwardly displaced 8 epola particles of the first group pushes strongly outward its three nearest neighbors of the second group of 24 particles, which are also repelled by the guest particle. The 8 particles of the first group also push, though much weaker, the particles of the third group. The 24 particles of the second group push strongly outward the particles of the third group, which are also repelled by the particles of the second group, and so on.

Our first qualitative conclusion is that though the range of the direct repulsion by the guest particle, as well as by each of the involved and displaced epola particles, is limited to $2 \ l_0$, the deformation of the epola continues ad infinitum or up to some boundary in the epola; and, although the deformation is caused by a neutral particle and by the non-electrostatic repulsion, the spreading of the deformation, as well as the actual positioning of the displaced epola particles (more exactly – of their equilibrium points in random vibrations) are influenced by the electrostatic interaction between these particles.

Shadowed arrows show displacements of 8 nearest epola particles. The repulsion by the electron marked 1 and by the positron marked 2 of the three nearest neighbors of each is shown by short arrows. The six particles belong to the second group of 24 particles, which also sustain the direct repulsion by the guest particle.

12.2 The gravitational interaction

Let us now consider the interaction between two neutral guest particles of mass $m_1$ and $m_2$ (e.g., two neutrons). The distance $l_{12}$ between them is large enough (e.g., $l_{12} > 1000 \ l_0$), so that the epola volume around each guest particle, deformed by the repulsion of this particle, is spherically symmetric. This is presented in Figure 7. It is seen that in the epola region behind the first particle, the repulsion of the epola by this particle is strengthened due to the repulsive action on the epola of the second particle. Similarly, in the epola region behind the second particle, the repulsion of the epola by this particle is strengthened, due to the repulsive action on the epola of the first particle. However. in the region between the two guest particles, the repulsion of the epola by one particle is weakened by the repulsion due to the other particle. Hence, the epola deformation behind each guest particle is stronger than in the region between the two particles; therefore, the unevenly-deformed epola reacts by pushing the two guest particle toward each other; this results in an attractive interaction between them.

It is clear from our qualitative analysis that the forces and the energy of this interaction must increase with the increase of each of the masses $m_1$ and $m_2$, and must decrease with the increase of the distance between the particles. We therefore identify this interaction as the gravitational interaction between the particles. It is easy to extend this physical model to the case of the gravitational interaction between conglomerates of particles, i.e., bodies of nuclear matter, atoms and bodies of atom. The model allows us to derive Newton's Law of gravitation with the help of basic calculus, and to approach a calculation of the gravitational constant.

Light arrows 1 and 2 show the repulsion of 6 distant epola particles, caused by the neutral guest particles $m_1$ and $m_2$. The resultant repulsions are marked $R$. Behind each guest particle $R$'s' are increased by the repulsion of the other guest particle, while in the region between them, $R$'s are reduced. Heavy arrows show gravitational forces by which the unevenly deformed epola reacts, pusbing $m_1$ and $m_2$ toward each other.

12.3 The epola as carrier of the gravitational interaction

In Sections 5.3 and 5.5, we have seen that the short-range repulsion is a derivative of the electromagnetic interaction (as are, e.g., adhesion, viscosity and friction). Now, we find that gravitation is due to differences in the short-range repulsion-field in the epola. This agrees with the striking weakness of the gravitational interaction, compared with the known fundamental interactions, nuclear and electromagnetic, which are 39 and 37 orders of magnitude stronger. And, because the gravitational interaction is derived from the short-range repulsion, we must conclude tbat gravitation is not a fundamental interaction, but is of electromagnetic origin. Therefore, all physical phenomena outside the nuclei are governed by one only fundamental interaction – the electromagnetic interaction.

Being the carrier of the gravitational interaction, the epola is also the carrier of the gravitational field. Therefore, the gravitational constant is not universal but is a parameter, depending on the conditions in the epola. These are, mainly, the epola temperature and imperfections (Sections 11.3, 11.4). Regions where the epola is molten or evaporated or just highly-distorted (different kinds of black holes) most strikingly disobey our "universal" laws and constants.

It also follows from our model that there are no separate quasi-particles of energy-transfer in the gravitational field, or gravitons, meant to be photon-analogs. The gravitational field is a "subsidiary" of the electromagnetic field, quite inferior to the main constituents – the electrostatic and the magnetic fields, all sharing the epola as their carrier. Any changes in The electrostatic or the magnetic fields are known to cause in the epola electromagnetic waves with their photons. Similarly, then, any changes in the gravitational field, e.g., mass reduction processes (explosions) and mass production (collapses in the epola) cause electromagnetic waves with their photons. Even the slightest redistribution of masses or motion of particles cause in the epola electromagnetic accompanying waves, with the corresponding de Broglie wavelengths and photons. Thus, there is no function left for separate quasi-particles of the gravitational field, just as there is no need for separate quasi-particles of the electrostatic or magnetic fields.

12.4 Epola deformation around a resting free electron and the electrostatic interaction

Let us consider a resting free electron positioned in the center of an epola unit cube, as in Figure 6. Because of the short-range repulsion, the guest electron pushes the nearest four epola electrons and four positrons equally out of the corners of the unit cube. The guest electron also equally repels the 12 electrons and 12 positrons of the second group of epola particles, as described in Section 12.1. Hence, the deformation in the epola around the guest electron, forced by the short-range repulsion, is identical to the deformation caused by a neutral particle of equal mass. We have seen in Section 12.2 that such epola distortions around two distant neutral particles result in their gravitational interaction. Hence. the gravitational action of electrons, as well as of any charged dense particles, is identical to the gravitational action of neutral particles of equal mass.

The electrostatic action of the guest electron at a distance of $0.87 \ l_0$, where the eight corner particles are, is much weaker than its repulsive action (Section 5.6). Therefore, the electron pushes the four corner electrons slightly farther out than it follows from the short-range repulsion. The four corner positrons, attracted to the guest electron, are pushed out of their lattice sites slightly less, owing to the short-range repulsion. The second group of 24 lattice sites is at a distance of $1.66 \ l_0$, at which the short-range repulsion is much weaker than the direct electrostatic action of the guest electron. The third group of lattice points is at a distance of $2.18 \ l_0$, completely out of range of the short-range repulsion but under its strong electrostatic action, which pulls the positrons nearer in and pushes the electrons farther out. Hence, an electrostatic deformation of the epola around the guest electron is superimposed on the gravitational distortion.

It can be shown that at a distance from the guest electron, where spherical symmetry can be assumed, the electrostatic deformation in the epola forms spherical double-layers of charge, with the positive charge of epola positrons displaced toward the common center of the spheres. and with the negative charge of epola electrons, moved outward. Hence, a deviation from charge neutrality is caused in the epola on the surface of each sphere. We can calculate this deviation and show that

the deviation from charge neutrality in the epola on the surface of any sphere, centered around a charged dense guest particle, which is at rest in the epola, is such as if there were a charge, distributed homogeneously on the surface of the sphere and equal to the charge of the guest particle.

A similar result is obtained in classical electrostatics when the Coulomb and Gauss laws are applied to treat the electric field in a dielectric medium. We got our results from epola considerations alone, without using these laws. Therefore, we may proceed the other way around and derive the laws of electrostatics, just for an additional affirmation of the epola model.

12.5 On magnetic interaction and spin

The magnetic interaction is the most complex among the interactions studied in physics and there is not much the epola model can add towards its understanding on the elementary level developed here. We may divide the magnetic forces into three groups: magnetism of dense particles and their subparticles, including spin; magnetism of atoms and atomic bodies, and the magnetism of electric currents.

The magnetism of dense particles belongs to the fundamental properties of the particles and is not in the domain of the epola model, as also is not the nature of electric charge or nuclear properties. We can only remark that the epola model does allow the original interpretation of the magnetic spin of particles. The magnetic spin-moment of the electron was discovered in 1925 by Goudsmit and Uhlenbeck and explained as due to the rotation of the electron around its axis. This is reflected in the given name 'spin'. The charge of the electron was considered as homogeneously spread over the outer surface of the electron (Section 5.8). The rotation of such charge represents circular currents, the magnetic moment of which would be that of the spin. However, calculation with the assumed 2.8 fm electromagnetic radius of the electron showed that, in order to yield the known value of the spin, the electron would have to rotate so fast that the velocities of its equatorial points would exceed the velocity of light. Hence, this physical model contradicted relativity and was abandoned, leaving us with its name only.

In the epola model, the lumic velocity limit is not absolute and superlumic motion of dense particles is possible (Sections 8.14-8.16). The radius of the electron is also argumented to be quite smaller than 2.8 fm (Section 5.10). Such a guest electron inside an epola unit cube deforms the epola, as discussed in Section 12.4. It is also possible that there is an additional adjustment of the spins (if any) of the neighboring epola particles to the spin of the guest electron. Except for this single adjustment, the spinning of the guest electron with any rotational velocity would not raise an epola resistance, as does sublumic or superlumic translational motion. Hence, a real spinning of dense particles is allowed in the epola model. Whether or not dense particles do really spin or what else might be the physical nature of the magnetic spin relates to the fundamental properties of these particles and is not for the epola model to decide.

The magnetism of atoms and atomic matter is composed of the magnetism of their constituent dense particles and of the magnetism of the electric currents, resulting from the motions of these particles inside the atoms and between them. A microscopic epola analysis of the magnetic interactions here would add more complexities than understanding. We can see it even on the simplest case of the magnetic interaction between two straight and parallel direct electric currents.

12.6 Magnetic interaction of straight currents

The simple experimental fact is that two parallel straight currents attract each other, and antiparallel currents repel each other. This is treated in physics by depicting the magnetic fields with lines of force. The lines of force in the magnetic field of a straight electric current are shown to be concentric circles, centered on the long axis of the current (or of the current-carrying wire) and directed, as shown in Figure 8. A rule is also introduced, stating that:

a current (or current-carrying wire) is pushed in an external magnetic field away from where the magnetic field of the current strengthens the external field, towards the region where it weakens the external field; or, from where the lines of force of the two fields have similar directions to where they oppose each other.

It is seen in Figure 8 that behind each of the two parallel currents, the magnetic field is strengthened by the magnetic field of the other current. Between the two parallel currents, the field of one current weakens the field of the other. Hence, the currents are pushed towards each other. An opposite situation occurs in the case of two antiparallel currents.

The above rule is applicable in all cases of the ponderomotive action of magnetic fields on currents or of the magnetic interaction of currents and can replace all mnemonical rules; it can even be adjusted to yield the direction of electromagnetically induced currents. It works so well that it is accepted as an explanation, though it actually does not explain the physics of the interaction.

A full epola explanation of the magnetic interaction of currents should take into account the following factors: 1.) The displacements of epola particles and the epola deformation caused by the applied electric fields (voltages), which propel the currents. 2.) The effect of these deformations on the accompanying waves of the charged dense particles in the motion of charge carriers (holes, alpha-particles, ions), which carry the current or participate in it, along with free (or "free") electrons, or without them. 3.) The effect of the moving dense particles of the charge carriers on the displacements of epola particles displaced by the applied fields.

Clearly, even in the case of straight currents, the analysis would yield more complexities than understanding. We may reach some understanding when the current is carried by charge-carriers of one polarity, e.g., by electrons. Then we have good reasons to assume, on top of all mentioned complexities, that the moving electrons pull the epola positrons slightly toward their flow, and push the epola electrons slightly away; this action is the stronger, the closer to the current. Therefore, the deformation of the surrounding epola can be presented by cylindrical surfaces, coaxial with the current, as shown in Figure 9. On the insides of the surfaces, there are slightly more epala positrons, and on the outsides – slightly more electrons. If a similar electron-current is placed parallel to the first one, then, as is seen in Figure 9, in the region between the two currents, their cylindrical surfaces face each other with similar charges. The repulsion of these charges acts against the epola deformation, reducing it. Behind each current. the cylindrical surfaces face each other with opposite charges. Their attraction increases the displacements of the epola particles and the deformation of the epola. Therefore, the deforming action of the two parallel currents on the epola is stronger behind the currents than between them. Hence, the reaction of the epola, acting on the currents, is stronger behind the currents than between them. An opposite result can easily be obtained in the case of anti-parallel currents. As a result, the unevenly deformed epola pushes the parallel currents towards each other anti pulls antiparallel currents away from each other. Thus, we obtained a rough explanation of the facts and rules of Section 12.5.

Light arrows show the flow of electrons (opposite to the agreed direction of currents); the $+$ and $-$ represent charges due to the displacements of epola particles; between the currents, the repulsion of the negative charges on the outer sides of surfaces marked 1 and 2 reduce the displacements and the epola deformation; behind each current, surfaces 1 and 2 face each other with opposite charges; their attraction increases the displacements and the epola deformation; heavy arrow show forces with which the deformed epola acts on the currents.

12.7 Comparison of electrostatic, magnetic and gravitational interactions

The cylindric double-layer surfaces around the straight current, representing the epola deformation by the current, differ from the spherical double-layer surfaces around the guest electron or other charged particle (Section 12.4). These spheres have on their outer sides, compared to the charge on their insides, an excess charge, equal to the charge of the guest particle. Hence, the epola around a charged guest particle is electrically charged and induces electrical charges on atomic bodies. In the 'vacuum' or 'field' language, one says that the electric field around a charge induces static electrical charges on atomic bodies.

The electric charges on the insides and outsides of the cylindric surfaces around the straight current are equal to each other; hence, except for small electric dipole moments on the lattice-unit level, the deformed epola around the straight current is electrically neutral or, in the 'field' language, the magnetic field is electrically neutral and does not induce static electric charges in atomic bodies. Similarly neutral is also the gravitationally distorted epola around a neutral dense particle (Section 12.1) or, in the field language, the gravitational field is electrically neutral.

The strengths of the three interactions are usually compared on the interactions between two protons, held at a certain distance. Then, the electrostatic interaction between them is the strongest. Their magnetic interaction, calculated with the known values of their spin magnetic moments, is a hundred times weaker. However, the gravitational interaction forces and energy between two protons are 37 orders of magnitude smaller than in their electrostatic interaction. The weakness of the gravitational interaction is explained in the epola model by it being a derivative of the short-range interaction, directly acting only from point-to-point and from point-to-next-nearest point (Section 12.1). The electrostatic and magnetic interactions, too, can be understood as point-to-point interactions, but they also have a direct range which far exceeds the epola lattice constant.

The electrostatic interaction between two charged particles is due to their action on one another, supported and carried by the epola. However, both the magnetic interaction of currents and the gravitational interaction of neutral particles are due to the action on them of the epola, in response of its deformation by them. Hence, we may say that where there is no epola, as, e.g., in black holes (Section 11.5), there is no gravitation, no magnetic interaction of currents, thus, no electromagnetic radiation, no photons. The presence or absence of electrostatic interaction there, could be clarified if it were possible to observe a stream of charged particles entering such a black hole. Because of the absence of magnetic attraction in the black hole, the streams would not be held together by the magnetic attraction of parallel currents. Therefore, if the stream were to dissipate as a disbanded sheaf, then this would have occured due to the presence of an electrostatic repulsion between the charged particles. If the bundle were to keep its form, then this would mean that there is no electrostatic interaction in the black hole and that the electrostatic interaction too is possible only in the epola.