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Particle Model

Electron Model

The geometry of the wave-field provides the particle model with a powerful basis for cavity vibrations of any complexity. Subatomic structures arise as a superposition of harmonics. Each harmonic describes a geometric component of the particle and is referred to as a quark excitation frequency. It is only their combination that produces the diverse particle structures which are known from experiments and can be predicted by the model.

 

The particle catalogue summarises known and newly predicted particles. It uses the general formula to calculate the excitation frequencies. This formula distinguishes between the electric, strong and weak interactions.

It follows from the photon model that only the invisible photons shaped orthogonally to the dimensional plane are relevant to particle structures. As soon as they exceed the minimum coupling frequency, they couple to a quantised region – the sphere S. These photons are called fions. Depending on their energy content, they form bundles of rotating fions within the sphere. Due to their orthogonal orientation relative to the dimensional plane , they generate a charge in the wave-field parallel to the electric potential of the universe. The field exchange with the particle-field takes place at the point of contact on . Depending on the geometry and complexity, a different momentum is registered in the particle-field and assigned to the interaction forces.

The illustration shows how a bundle of Fionen forms a positron within a sphere. On the left is the geometry that makes the positron detectable in the particle-field. To the right of this is the same positron, raised above the point of contact – a hidden (dark matter) positron.

Positron, visible or hidden

The simulation illustrates the dynamic behaviour of the positron in space-time. The same applies to the electron, which is situated below the dimensional plane . The beam changes direction every period T because the sphere exhibits its own relativistic dynamics in space-time. This gives rise to a field arising from a ‘stationary’ electromagnetic cavity mode. Through this dynamics, the field reaches its maximum at the point of contact and is mediated into the particle-field. After a period of 2T, the red star marks the location of the field exchange, where all fions arrive in synchronisation with the sphere. The rotation of the particle and each fion proceeds at half the maximum speed, c/2. This geometry explains angular momentum, resulting rotational velocities, isospins, the Pauli principle, as well as the interactions and coupling possibilities between particles.

Simulation:

Dynamics of a positron in a wave-field

Attraction between charges

Particles with different charges attract each other if

a) their exchange fions rotate in the same direction and can fuse with the respective recipient particle, and

b) the active fions of both particles rotate in the same direction above and below the dimensional plane D56.

Attraction between postron and electron

Repulsion between charges

Particles with the same charge repel each other if

c) the exchange fions rotate differently and thus ignore each other, and

d) the active fions rotate in the same direction with their subspaces in sphere S.

Repulsion between postron and electron

Destructive reaction between charges

An annihilation reaction requires a specific spatial structure between two differently charged particles.

e) The active fions from an electron rotate below and the active fions from a positron rotate above the dimensional plane D56.

f) The rotation of their spheres S takes place antiparallel to the dimensional plane D46.

g) These two particles come too close to each other and meet at their respective point of contact in such a way that their fions are exactly or almost exactly in phase at the respective point of contact.

Destructive reaction between charges

Mesons consist of two bosons, which in turn consist of a quark and an exchange fion. The quarks supply a fion from their bundle to produce an exchange fion. Depending on the interaction with other particles, the total charge can drop from 3/3 to 2/3 or even to 1/3. The exchange fion rotates outside the boson at the maximum speed c. The distance to be covered depends on how long a fion must rotate until all of its fions and its sphere S are also synchronously positioned at the point of contact with the receiving boson. After migrating from one meson to the other, its field exchanges with the particle-field during the recombination phase in the boson. The momentum with its field is mediated at the point of contact in the dimensional plane D56. The strong interaction and a mass in the particle-field are registered.

Calculation of quantum states

Simulation:

Interaction dynamics in a meson, two 2/3 quarks with different charges
Schematic representation of a meson consisting of two 2/3 quarks

Simulation:

Interaction dynamics in a meson, a 2/3 quark, a 1/3 quark with the same charge
Schematic representation of a meson consisting of a 2/3 quark and a 1/3 quark
Schematic diagram of the neutron with binding neutrino in the center

Simulation:

Proton for a complete period
Schematic diagram of the proton with binding neutrino in the center

Particle structure of mesons and baryons

Particle-exchange Fion-Particle-Coupling

The particle-exchange fion-particle-coupling models any particle complexity that results in an interaction in any way. It takes into account the geometric conditions and interactions that perform a relativistic rotation in space-time.
 
The field equations yield the structure mn ∝ n/R and the discretisation of the modes. The FSM-specific resonance condition on the dimensional planes D45, D46, D56 requires that only discrete superpositions of fion modes are stable. These superpositions are characterised by the counting parameters BK, KK and TK. Together, these two parts yield the general formula relative to the electron reference.
  • fobj – coupling frequency for arbitrary objects
  • Mobj – mass for arbitrary objects
  • 1/2 – for half the speed of an unbound exchange fion relative to a bound active fion in a particle-exchange fion-particle coupling
  • BC – boson configurationn
  • CC – coupling configuration
  • Power of three for the three possible fions that can be disturbed from the particle field
  • n – nth dimensional family
  • PC – particle configuration
  • Dimfactor for reducing the rotational speed ≤ c
  • Me – mass of the electron
  • fe – frequency of the electron

BC - Boson Configuration

BC counts all fions in the bundle in the numerator and additionally counts fions received for a limited time in sphere S. The maximum possible number of fions in the bundle is counted in the denominator.

CC - Coupling Configuration

CC summarizes the maximum possible number of fions in the bundle in the numerator. In contrast, the denominator shows the number of periods T required to generate synchronization between the bundle fions and the sphere S.

PC - Particle Configuration

PC describes common particle types such as mesons, baryons, electrons, or free fions. In the numerator, the fions in the bundle are counted, plus externally received fions, minus all fions required to produce the required exchange fions. The maximum number of bundle fions remains in the denominator.

Excerpt from the particle folder

Selected particles measured in experiments are presented below. When the mean value from the experiments is compared with the theoretically calculated value without taking the standard deviations into account, there is only an average deviation of 1 – 2 % between them. The source is the Particle Data Group (PDG).

Mass Muon

Mass Pion

Mass Proton/Neutron

Excerpt from the particle folder
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