At this point let us refer to the wave model of the elementary particle which enables us to confront the two types of wave organization we identify with electron and positron. The model influences the behavior of the elementary particles in opposition to that of the respective mirror-images, that is, the corresponding antiparticles. Fig.21 The specular symmetries of electron and positron The behavior of a charged particle, which meets the waves deriving from another charged particle, depends on the structures the waves of the first one meet in the space occupied by the waves of the other particle. It follows that the chirality is the determining factor of interactions. The dynamics of the electromagnetic actions can be understood by confronting the different wave relationships between the secondary waves and the primary waves in the relative orientations taken by particles. The step produced by the discontinuous increase in the radius of curvature of the expanding spherical involute constitutes a surface anomaly which identifies a modular structure in a much smaller scale than that introduced in space-time by the primary waves. As we have already seen, the behavior of a particle which meets the waves deriving from another particle depends on the structures the waves of the first one meet in the space occupied by the waves of the second particle. In the case of a combination of primary and secondary waves, the interactions are influenced by the configurations of the system constituted by both charges. It has a certain number of degrees of freedom and configurations which vary according to the relative orientations of the axes of the particles involved. The vector description appears in this case particularly right for the purpose (even if a spinorial description would be better). We can describe the directional
characteristics of the plane involute by using the vector product With the vector K, tangent to the involute curve, let us describe the direction and the modulus of the secondary wave that is inversely proportional to the radius of curvature of the primary wave, and that is identified with the greatness of the variation in the radius of curvature of the involute. Let us examine, therefore, an electron and a positron isolated in a space lacking in other significant fields, and arranged at a distance greater than the sum of the radii of the resonance orbits. Let us consider an orthogonal coordinate system with origin in the center of the resonance orbit of an electron and, in order to describe the left-hand sense of rotation of the primary wave about the orbit, let us identify the electron's spin with the vector product by using the left-hand rule: 78) x L - y = J e Let us identify the positron's spin with its mirror-image by using the right-hand rule, and express the vector product in the coordinate system of mirror s: 79) x s L- y s = J e+ The vector J e+ describes, with the chirality of the specular world, the right-hand sense of rotation of the primary wave about the positron's resonance orbit.
Some considerations on the nature of the properties of the primitive space, that is, of the empty space lacking in structure, and on the constitution of the particle as a wave organization, lead us to consider isotropy as one of the most influential factors of the mostly directional behavior of charged particles. In an - isotropic - space the existence of a single direction constitutes the maximum anomaly. The preferential orientation introduced in a primitive space in a single direction can be cancelled either by a total disappearance of the directionally defined structure creating such a direction or by the presence of another structure introducing an opposite direction. In both cases the space isotropy would be re-established, and the zone would have the properties of a primitive space again. The thicker the structure of a secondary wave is, the more its influence is. Moreover, it has the characteristic of a directional anomaly. Indeed, its nature of oriented perturbation of the primary wavefront, characterized by the direction of rotation of the variation in curvature of the surface quanta composing it, already explains the reason for its directionally influencing effectiveness. The structure itis able to impose to the space of its existence has a specific orientation connected to the orientation of the source emitting it. In order to know the directional relationship of two organized structures deriving from different sources, it is necessary to know the relative vector state of sources. The wave structure we identify with the electron is constituted by a double wave system having as a common ideal base the plane of reflection on which the resonance orbit lies, and as a common axis the spatial projection of the resonance orbit in the z positive and negative direction. During its propagation, beginning from the orbit, the primary wave creates two helicoids around this ideal tube totally lacking in internal structure. They can be compared to a screw thread of two opposite screws. The helicoids are the edges of the almost spherical wavefronts, which lie on the ideal surface of the cylinder having on the plane of the orbit a plane projection we identify with the evolute of involute( Resonance orbit of involute). The plane of the electron's orbit constitutes the common head of the two screws: a right-hand screw in the direction of the spin and the left-hand screw in the opposite direction. In opposition to the electron's structure, the positron, that is its mirror-image, presents a left-hand screw in the direction of its spin and a right-hand screw in the opposite direction. In order to understand the electric wave interactions, it is necessary, now, to return to the elementary roots of the dynamics of the organized structures called till now particles. The relative symmetry principle acts after the establishment of an energy asymmetry condition. We can say it acts so as to eliminate a directionally privileged state in the energy-wave presence in the vicinity of the particle, and therefore we deduce that the discrete space-time tends to preserve isotropy as its main characteristic. Considering the particle's vector structure, there are many occasions for violating the space - time isotropy, but in each of them there is a response to the behavior of the wave structures - particles, tending to re-establish the lost equilibrium. When two charges interact with each other in absence of waves deriving from other particles, they place themselves so as to obey the tendency of space to mantain itself in isotropy conditions. For each particle the direction of rotation constitutes an anisotropy condition; therefore, the two interactive particles will arrange themselves so as to reduce by minimum the anisotropy state in a zone of space with the spins lying along antiparallel lines. In practice, the system constituted by the two particles always tends to a minimum condition in the sum of the spins. 80) J + (-J) = 0 In the interaction between two electrons the Spins are antiparallel: 81) J e- + (- J e-) = 0 When this condition occurs, the vector K which is identified with the secondary frequency becomes the main agent of the interaction among charges. The presence on the primary
wavefronts of the anomaly we have called secondary wave, enable us to
verify a different condition between the structure in the space between
the centers of the two electrons and that existing on the wavefronts
outside the system. Fig. 23 electron-electron interaction In the zones A outside the system, where the wavefronts are superimposed one upon another, the values of K subtract from one another and tend to zero. In the zone Z inside the system, where the waves are equally superimposed one upon another, the K values add to one another. These two different vector situations
involve privileged orientations that are well defined in space-time. In
next chapter we shall see them to be able to influence the different
wave structures depending on a new geometric principle that seems to be
at the base of the properties of the space - time: the relative isotropy
principle. |