## Equation

**Particle Energy**

Particles are standing waves of energy (stored energy). The equation to calculate particle rest energy uses the energy wave equation and defines the volume (V) of the standing waves given a number of waves centers (K). A detailed explanation can be found below on this page.

## Classical Constant Form |
## Wave Constant Form |

Using classical constants * | Using energy wave constants |

**Variables:**

*K: the number of wave centers at the particle core reflecting longitudinal waves to become standing waves*

* The neutrino’s (E_{v}) can be further derived but is used for readability.

**Particle Mass**

Although rest energy is expressed in both classical constant format and wave constant format, mass is an example of why the wave constant form is the real description and true constants. Particle mass is energy without consideration of wave speed (c), found naturally as c^{2} in the Longitudinal Energy Equation but not in the classical form. For example…

**Particle Rest Mass
**

## Explanation of Equation

The Longitudinal Energy Equation begins with the fundamental equation for calculating energy in a volume:

**Energy Wave Equation**

It assumes that particles consist of a certain number of wave centers (considered a fundamental particle – possibly the neutrino). These wave centers reflect longitudinal waves, creating standing waves of energy. The volume is spherical based on the particle’s radius, which is the transition point from standing waves back to traveling waves.

**Particle Volume – Single Wave Center**

When wave centers combine – stable at the node of a standing wave – the volume being measured changes. This changes the number of wavelengths (n) before standing waves transition back to traveling waves (particle radius). The number of wave centers (K) determines the radius and increased wave amplitude, so the **particle energy can be calculated based on K as the only variable**. An example of this increase is shown below with 2 wave centers.

**Particle Volume – Two Wave Centers**

Energy is represented by two waves: an in-wave and an out-wave. As wave centers combine, constructive wave interference leads to an increase in amplitude in three dimensions (pictured as x, y, z). This is simplified into a picture below showing the transition point of standing waves to traveling waves. A particle is stored energy – its definition is within the boundaries of the standing waves. Beyond the boundary (particle radius), traveling waves are responsible for the electric force.

**Detailed Assumptions**

The Longitudinal Energy Equation was derived from this base equation and these assumptions.

- The wave center is the fundamental particle, which is possibly the neutrino. Longitudinal in-waves are reflected to become out-waves. The amplitude of these waves decrease with the square of distance, with each wavelength, or shell (n).
- Particles are created from a combination of wave centers. A number of wave centers (K) form the core of the particle, resulting in a standing wave formation from the combination of in-waves and out-waves.
- Wave centers prefer to reside at the node of a standing wave, minimizing amplitude. They will move to minimize amplitude if not at the node.
- With sufficient energy, wave centers may be pushed together in arrangement to create a new particle (i.e. neutrino oscillation), but will decay (break apart) if the structure does not lend itself to a geometric shape where each wave center resides at the node in a wave.
- When wave centers are spaced in the nodes, at even wavelengths in the core, waves are constructive. A particle’s amplitude is the sum of its individual wave center amplitudes in the particle core.
- If two wave centers are pi-shifted from each other on the wave (1/2 wavelength) it will result in destructive waves. This is an anti-particle. For example, if the neutrino is the fundamental wave center, then the anti-neutrino is a wave center pi-shifted from the neutrino.
- Particle radius is proportional to the total wave amplitude, and is the edge of where standing waves convert to traveling, longitudinal waves.
- Particle energy is the energy of standing waves within the particle’s radius.

**Calculations and Examples**

A summary of calculations and some examples using the equation are provided here. The remainder of the calculations and examples are detailed in the *Particle Energy and Interaction *paper.