The creation of pairs
At the beginning of the paragraph in which we described the creation of the Spherical Involvent, we considered a wave train diffracted by the field of an electron as in the Compton effect that presented a wave front along a single side of the electron’s wave field.
Let us now consider instead a wave train that collides with the electron frontally and is divided in two with one part of the wave front diffracted toward the right and the other toward the left.
This will ultimately produce “two” evolving spherical planes, the first the specular image of the other and possessing the opposite spin.
When the creator wave front collides frontally with a particle that can diffract it circularly, it divides into two fronts. One rotates clockwise around the particle and the other rotates around it counter-clockwise. Both wave fronts act independently to construct the two resonance orbits that will create two different Spherical Involvent that are identical mirror images of one another.
These will then separate from each other and become two different particle wave sources with opposite charges. One becomes a particle and the other an anti-particle.
Picture 37. The dual Spherical Involvent expressing a model of a particle and its
antiparticle.
Where the wavelength of the incoming photon is less than or equal to:
λi = λe / 2,
and the diffracting obstacle is a free electron, we should find tracks typical of the production of a triplet consisting of an electron and a Dalitz pair in the bubble chamber.
Dalitz pairs are made up of a positron and an electron that, when subjected to a magnetic field, will create the three classic tracks that can be identified easily.
Does this mean we have witnessed the creation of pairs?
It would seem that we really have. Still, it is up to you to judge whether everything that we have illustrated up to now is plausible and consistent with the hypotheses made about the discrete nature of space-time. It is similarly up to you to judge whether our initial hypothesis of the wave-like nature of the electron’s field can now be supported by a model that can be visualized.
On the assumption that you will reach the same conclusion that I have or at the very least will feel sufficiently enticed by “this long and incredible series of curious coincidences”, we will press ahead and show how the wave model as we have conceived it holds true for many other original physical proofs.
Good. In our view, it is time to abandon the physics of “as if” now that we know “what” is rotating in the electron, we know “how” it is rotating and we know “why” it is rotating.
One doubt remains. It goes without saying that we must describe the thing that rotates as the electron’s “spin” and we are fully convinced of this.
But it is natural then to ask ourselves if we must describe the angular momentum in terms of the rotation on the orbit of an entire wavelength of resonance or, as the classical rule of the minimum energy of resonance demands, in terms of half a wavelength.
I personally have not yet been able to decide whether the geometrical representation of the Spherical Involvent would be the same in the two cases.
I am willing to accept a provisory solution “for now” and employ the entire wavelength to describe the construction of the state of resonance.
This of course makes it impossible for the Theory to “explain” spin in terms of the classical energies used by quantum mechanics to express the angular moment which has remained “mysterious up to now” within the particle described in “halves” of the quantum of action:
1 / 2 . h / 2 π.
I believe in any case that, when the physicists finally become aware of its existence in the near future, the debate over the Theory will bring the best solution to this problem to light without invalidating what we present here.
The fact remains that we now have model of the electron and its field of mass based exclusively on waves. We also have a model of the elementary interaction between matter and radiation in the Compton effect. And a model based on the creation of pairs.
An explanation of Lorentz forces in terms of waves,
Let us now see how to take the electron’s dynamics behavior into account by observing the Spherical Involvent in motion in a force field that fixes the axis of the Spherical Involvent in a particular direction.
In other words, let us compare an electron with a spin oriented along the lines of force of a magnetic field with the model of the Spherical Involvent with which we wish to identify it.
We will do this without invoking electromagnetic theory and will only describe the relativistic behavior of the Spherical Involvent’s waves of mass.
In the phenomenon of the creation of pairs actually experimented in the bubble chamber, the effect of the Lorentz forces was to separate the tracks of the positron and the electron in opposite directions.
The Lorentz force curves the trajectory of an electron when its spin is parallel to the lines of force of a magnetic field and its velocity increases on a plane at right angles to the spin.
Picture 38. Classical Lorentz force of a charged particle set in motion by a magnetic field.
In the language of waves, this condition is equivalent to forcing the Spherical Involvent to move on a plane that coincides with the plane of its resonance orbit. When this condition occurs, the creator wave front at different times occupies four physically different conditions:
- The wave front moves on the resonance orbit and creates the involvent plane rotating at velocity “c” in the same direction as the velocity of the center of the resonance orbit. Its wavelength is shortened in this direction by the Doppler effect;
- The wave front then begins to move at right angles to the velocity, and its wavelength remains unchanged in this direction;
- It then moves in a direction opposite to the velocity. In this new direction, its wavelength is lengthened by the opposite Doppler effect;
- And finally it moves perpendicular to the velocity in a direction opposite to the one in 2). Here again its wavelength remains unchanged.
The wave front then returns to condition 1) and repeat the cycle.
The wave front in resonance is in any case subject to the relativistic Doppler effect throughout its entire rotation. Relativity produces an involvent that is deformed and in which the wave fronts are crowded together “to one side” of the involvent.
This creates an asymmetrical variation in the wavelength of the waves emitted at right angles to the direction of the velocity on the plane. In fact, when we observe the front of the involvent that moves along the plane that coincides with the plane of the resonance orbit, we can see that the structure of the curved involvent becomes deformed in keeping with the requirements of the relativistic Doppler effect.
This deformation induces an asymmetrical variation in the wavelength on a single side of the involvent on the resonance plane.
Picture 39. Lorentz force of the evolving plane.
Thus, to reestablish symmetry after the wave variation, the Spherical Involvent moves in keeping with the Principle of Relative Symmetry in the direction opposite to the one in which the variation occurred.
The whole process makes it appear that a force is pushing the Spherical Involvent on one side.
In keeping with the Principle of Relative Symmetry, the trajectory of the electron’s Spherical Involvent also curves in one direction and the plane of its mirror opposite, the positron, in the other.
This leads us to make the following risky but altogether consistent claim.
The fact that an electron that has not been subjected to the influence of a magnetic field travels in a straight line implies that its spin is oriented in the direction of motion unless it has been forced in another direction. This is the case because this position requires the electron to exert the least energy, as it is the most symmetrical condition for an asymmetrical structure like the Spherical Involvent.
Among other things, this explains charged particle’s curly tracks in the bubble chamber. As they have lost velocity by colliding with the atoms in the liquid, they are in an intermediate condition and their spin does not lie either completely on the velocity vector or completely at right angles to the plane of motion.
Consistent with the Doppler effect, the center of the resonance orbit shifts forward in the direction of motion, which shortens the wave surfaces of the evolving plane on one side. This also significantly shortens the distance that was identified with the radius of the resonance orbit in that direction at rest.
This behavior gives the impression that the dimensions of the field of the particle – wave source have been shortened. And this is the justification given for the ever smaller dimensions attributed to particles thrown forward at relativistic velocities that come ever closer to the speed of light in large accelerators.
The wave variation of the wave field that triggers the reaction in the Lorentz force described in the Principle of Relative Symmetry propagates throughout the zone of space-time in which the electron’s field exists at the speed of light. This variation of wave energy is a photon wave train that can be perceived physically and can cause variations in the momentum of other particles.
When the electron achieves relativistic velocities, the wave variation provokes a specific response in the experiment and can be identified with “synchrotron radiation”.
To make the wave interpretation of the Lorentz force more effective and the picture more complete, we should find a plausible explanation in terms of waves of the nature of the electric charge and investigate the behavior of the resonating wave front in detail.
We will do this below in order to explain electrons’ electromagnetic properties as well. But even here we can demonstrate that we can take the Lorentz force into account simply by attributing chiral properties to the electron’s wave field as mass.
Let us take a step back now to examine the explanatory power of the wave model of mass when its waves constitute spherical waves and observe the interactions between macroscopic masses made up of large numbers of elementary wave sources.
Let us first examine the interaction of an ordinary macroscopic body in terms of its wave interactions with the field that surrounds it.