The bidimensional model of involute and evolute, that describes on the orbital plane the resonance state of a wave in the scale of the Schild space-time discontinuity, is full of potential innovations and new possibilities.

One of the new possibilities of the model leads us to the unexpected but totally rational discovery of a wave statistical mechanism that would make the creation of matter under the form of single elementary particles reasonable and consequent.

Let us observe in the wave model of electron the involute on the plane of the resonance orbit.

In terms of quantized lengths, the resonance orbit: 2pr₀ = l₀ is constituted by a definite integer of elementary lenghts L, from which it follows that: nL = 2pr₀, and therefore: nL = l₀.

The resonance orbit is therefore divided into an integer n of elementary lengths L.

The wavefront circulating in a resonance state occupies all the squares composing the quantized physical distance of the resonance orbit.

Let us describe what happens on the scale of the space-time quantization when particle and antiparticle, elementary matter and antimatter meet and annihilate each other.

• As we can experimentally observe, the two particles of opposite motion charge get closer to each other when they are almost entirely lacking in significant momenta.

• Afterwards, the two wave sources orientate their respective surface structural anomalies so as to cancel their respective vector J.

• Finding themselves in opposition to their respective vectors J, the two resonance planes are superimposed upon each other in order to form a single plane.

• The resonance orbits of the two different wave sources are superimposed upon each other.

• The two axes of the resonance orbits form a single axis, so that the rotations of their respective wavefronts are concordant.

• It follows that the two wavefronts circulate on the same orbit which for being a proper resonance orbit should contain only a wavefront.

• At this point we can have n resulting situations.

1) in n-1 cases, the two wavefronts which are on the same resonance orbit lose their resonance condition, the mechanism loses its condition of existence necessary for the resonance, and the condition of perpetual creation of the involute does not exist anymore.

2) where before the spherical involute had appeared, a vacuum hole lacking in perturbation fronts expands at the velocity of light behind the last double frequency waves that had been generated during the extreme approach of the two particles.

Particle and antiparticle are annihilated

3) It can happen that in 1 case out of n cases the two wavefronts are on the same orbit and occupy the same square of discrete lenght L.

The resonance condition in this single case remains unchanged, because the sum of the two superposed perturbations create nothing but another perturbation.

The Positron, which is the antiparticle to electron, has disappeared, and where before there were two particles now there is nothing but one of them.

Once the particle-antiparticle meet, it can happen, with a well precise statistical rythm, that 1 time out of n times they do not annihilate reciprocally, but they exactly interpenetrate superposing their respective perturbation fronts and producing a new matter particle.

The reason why the result produces a particle and not an antiparticle is still unknown, and it will be the object of scientific researchers for the next few years.