The neutrino, also referred to as the electron neutrino, is the lightest and smallest of any elementary particle that has been discovered thus far. It was first proposed by Wolfgang Pauli in 1930 and then detected in experiments in 1956. It is an electrically neutral particle that is found in the weak force, nuclear reactions (such as the process in stars) and some particle collisions. The majority of neutrinos found on Earth originate from the Sun, referred to as solar neutrinos. In fact, billions of neutrinos pass through an area the size of a human fingernail each second. Neutrinos are incredibly small, and because they are neutral and not attracted to particles, they rarely hit another particle in an atom. They can pass through the entire Earth without any collision.

A strange property of the neutrino (ve) is the ability to oscillate to become larger and increase mass. It can become a muon neutrino (vu) or a tau neutrino (vt). Both of these larger particles are still neutral and belong to the neutrino family. The three neutrinos are also a part of the lepton family of particles, which include the electrically charged electrons (electron, muon electron and tau electron).

Three neutrinos

Credit: J-PART




In energy wave theory, the neutrino is the likely candidate for a single wave center, which makes it the fundamental particle that creates other particles. The Longitudinal Energy Equation makes an assumption that there is a collection of wave centers (K) in a particle, similar to how atomic elements are formed from a collection of protons in a nucleus. A single wave center reflecting spherical, longitudinal waves to create standing waves would look like this:

fundamental particle

Neutrino – Standing Waves of Energy from a Single Wave Center


Neutrino Oscillation and Decay

Neutrino oscillations have been found in nature. The neutrino can oscillate to become a larger muon neutrino and a muon neutrino can become a tau neutrino. This occurs naturally as trillions and trillions of neutrinos arrive on Earth, from the Sun. As it was found using the Longitudinal Energy Equation:

  • The neutrino has a particle count of 1
  • The muon neutrino has a particle count of 8
  • The tau neutrino has a particle count of 20

The reason that neutrinos are found to oscillate is that the chance of 20 or less neutrinos randomly merging may occur in nature – kinetic energy traveling from the Sun. This is consistent with neutrino experiments.

nature oscillations


The reason other particles do not oscillate naturally is because they require greater energy to form. Particles with higher particle counts (more than 20) require high-energy experiments such as particle accelerator labs to generate the kinetic energy to combine and form particles. This is consistent with particle accelerator experiments.

high energy experiments particle creation


Stable and Neutral

It is proposed that leptons are slightly more stable, and hence found in nature, because of geometric configurations that are similar to protons and neutrons in the atomic nucleus.  The neutrino family would be relatively stable at these proposed geometric structures (left side of the figure below). At particle counts of 1 (neutrino), 8 (muon neutrino) and 20 (tau neutrino), they are possibly symmetric tetrahedrons, which means they may have no charge if the two tetrahedrons spin in opposite ways. This leaves the possibility of discovering a neutrino with a particle count of 2 (K=2). It would have a rest energy around 110 eV. By comparison, the particle counts for other leptons (electron, muon electron and tau electron) are shown in the right side of the figure. The electron family may also be tetrahedral structures, but non-symmetric. Therefore, as the particle spins, it creates the transverse wave found in the magnetic force.


Leptons at magic numbers


Comparison to Atomic Elements

If neutrinos can oscillate up to a count of 20 (tau neutrino), then what about the other arrangements? For example, why are neutrinos with particle counts of 2, 3, 4, 5, 6 or 7 not found? The next neutrino that is found is the muon neutrino with a particle count of 8. Wave centers centers must be at the nodes of standing waves to be stable and the other geometric arrangements likely do not lead to this stability.

As described in the calculations of particles, leptons appear at the same magic numbers found in atomic elements. The numbers 2, 8, 20, 28, 50, 82, 126 are special in the atomic world because a combination of the stability of these atoms when their nucleons contain these numbers (number of protons or neutrons). The magic numbers align with the orbital shells and how electrons fit within the orbit surrounding the nucleus. Nuclear binding energy levels are found to be higher in these numbers.

magic numbers

Magic Numbers in Atomic Elements




Proof of the energy wave explanation for the neutrino is the calculations and explanation of:

  • Neutrino oscillation – see above
  • Neutrino energy – see below


Neutrino Energy Calculation

The calculation of the neutrino’s energy assumes spherical volume (V) and a radius (r) of one wavelength before standing waves transition to traveling waves. It also assumes that wave amplitude (A) is longitudinal from three dimensions (cubed) and it decreases with the square of the distance.

neutrino geometry with spherical wave amplitude

Neutrino – Geometry 


The Longitudinal Energy Equation is used with a single variable – particle count (K) to calculate rest energy. For the neutrino, there is one wave center (K=1). Using the equation and wave constants, the result is 3.83E-19 joules or 2.39 eV. This is on the high-end of the neutrino’s expected range (~2.2 eV), but the neutrino’s exact energy is still being determined in experiments.

neutrino longitudinal energy equation solved


Calculated Force: 3.83E-19 joules  (2.39 eV)

The rest energy of the muon neutrino (K=8) and tau neutrino (K=20) were calculated using the same method and can be found on the calculations page.