If the neutrino is the fundamental particle, other particles will be created from this fundamental particle. Much like protons arranging in an atomic nucleus, neutrinos have a specific geometric arrangement to be stable in a particle core. To minimize a particle’s amplitude, they must exist on the node of a wave, separated at multiples of wavelengths. In a 1 dimensional view, this would be easy to be separated at equal wavelengths. But in 3 dimensional view, there are few geometries that allow this configuration to be evenly separated at wavelengths, especially as the number of neutrinos in the particle core grows. This is the reason for decay. A tetrahedron structure is proposed as one of the simplest formations that match the criteria for the separation of neutrinos at wavelengths.

In short, particle formation occurs when neutrinos form a core, in stable arrangement, and constructively add their spherical wave amplitudes. When multiple neutrinos form a core, not only do their amplitudes combine, but the particle radius extends proportional to wave amplitude. Particle radius is defined as the edge where standing waves break down and become traveling waves. Mass is the sum of the standing waves in the particle.

The Longitudinal Energy equation can be used to calculate the rest energies of particles. The key assumptions of this equation is that particles are standing waves of energy where:

1) amplitude is the sum of individual neutrino amplitudes,

2) particle radius is proportional to amplitude,

3) amplitude decreases with the square of the distance from the particle core, and

4) its energy is based on the square of wave amplitude.

This means that a newly formed particle’s energy is not simply the sum of its individual neutrino energy count. It’s much larger. For example, two neutrinos that combine have double the amplitude, double the radius and this standing wave is then squared for energy. As further illustration, using this wave equation, it only takes 117 neutrinos combined in a core to have an energy that is 60 billion times the energy of only one neutrino in the core.

## Evidence

The lepton family of particles, including three neutrinos and three electrons, fit into the same magic numbers seen in atomic element stability. These **magic numbers are: 2, 8, 20, 28 and 50** and represent a configuration of protons and neutrons in an atom core. At certain geometric arrangements that match these numbers, an atom’s core is more stable than other arrangements. Amazingly, lepton particles fall under these same magic numbers:

**Muon Neutrino – 8**

The muon neutrino may be formed from 8 neutrinos. When the value K (# of neutrinos) is set to 8, the rest energy of the muon neutrino is calculated using the Longitudinal Energy equation and wave constants. Compare this value against the measured CODATA value for the muon neutrino – **2.72 x 10 ^{-14} joules**.

**Tau Neutrino – 20
**

The tau neutrino may be formed from 20 neutrinos. The CODATA value for the tau neutrino is **2.48 x 10 ^{-12} joules**.

**Muon Electron – 28
**

The muon electron may be formed from 28 neutrinos. The CODATA value for the muon electron is **1.70 x 10 ^{-11} joules**.

**Tau Electron – 50
**

The tau electron may be formed from 50 neutrinos. The CODATA value for the tau electron is **2.85 x 10 ^{-10} joules**.

Again, these are the same magic numbers 8, 20, 28 and 50 seen in atomic element stability, but now seen in subatomic particle stability. Stability in lepton particles that are found in nature, not manufactured in particle accelerators. Note that magic number 2 is missing. It is possible that this neutrino could be found in sterile neutrino experiments. The rest of energy of a particle with two neutrinos (**K=2**) would be **1.76 x 10 ^{-17} joules**.

The electron’s value is K=10 and its value was confirmed in Electron Mass. Other known particles have been calculated and mapped to values of K (# of neutrinos in core) and can be found in the Wave Equation for Particle Energy and Interaction paper. The Longitudinal Energy equation works well for stable particles because it is assumed that waves are perfectly constructive. When neutrinos are not separated at multiples of wavelengths from each other, the particle’s energy will not be perfectly constructive. Therefore, the equation is not a great fit for particles outside of the lepton family, but may be used as an approximation. For example, the Higgs boson appears at a value of K=117, which in the Periodic Table, is one of the last elements.