## New Wave Constants and Equations

This section highlights new energy wave equations used in the calculations on this site. As proof of a foundational theory, they can also be shown to derive key energy and force equations from classical and quantum physics (see links on right for derivations). The notation, including new constants and variables, and the equations are found below. The equations on this site, including 23 fundamental physical constants found in physics, can be derived from four universal wave constants in this paper: wave speed, wavelength, amplitude and density and by one variable that is constant to the electron.

## Energy Wave Equation Notation

The energy wave equations include notation to simplify variations of energies and wavelengths of different particles, in addition to differentiating longitudinal and transverse waves.

Notation |
Meaning |

K_{e} |
Particle wave center count (e – electron) |

λ_{l, }λ_{t} |
Wavelength (l – longitudinal wave, t – transverse wave) |

g_{λ}, g_{A}, g_{p} |
g-factor (λ – wavelength, A – amplitude, p – proton) |

F_{g}, F_{m} |
Force (g – gravitational force, m – magnetic force) |

E_{(K)} |
Energy (K – particle wave center count) |

## Constants and Variables

The following are the wave constants and variables used in the energy wave equations, including a constant for the electron that is commonly used in this paper. The remaining constants are derived.

Symbol |
Definition |
Value (units) |

Wave Constants |
||

A_{l} |
Amplitude (longitudinal) | 3.662748116 x 10^{-19} (m) |

λ_{l} |
Wavelength (longitudinal) | 2.835967539 x 10^{-17} (m) |

ρ | Density (aether) | 9.605125782 x 10^{24} (kg/m^{3}) |

c | Wave velocity (speed of light) | 299,792,458 (m/s) |

Variables |
||

δ | Amplitude factor | variable – dimensionless |

K | Particle wave center count | variable – dimensionless |

Q | Particle count (in a group) | variable – dimensionless |

Particle Constants |
||

K_{e} |
Particle wave center count – electron | 10 – dimensionless |

O_{e} |
Outer shell multiplier – electron | 2.138743820 – dimensionless |

g_{λ} |
Electron orbital g-factor (revised) |
0.993643364 – dimensionless |

g_{A} |
Electron spin g-factor (revised) |
0.976448541 – dimensionless |

g_{p} |
Proton orbital g-factor (revised) |
0.958447450 – dimensionless |

## Energy Wave Equations

### Energy

The Longitudinal Energy Equation is used to calculate the rest energy of particles. The Transverse Energy Equation is used to calculate the energy of photons. Both are derived from the Energy Wave Equation.

** Energy Wave Equation
**

**Longitudinal Energy Equation
**(Particles)

**Transverse Energy Equation
**(Photons)

### Forces

Forces are based on particle energy at distance (electric force). The remaining forces are a change in wave amplitude or wave form. The equation for magnetism is the electromagnetic force for an induced current (particles in motion). The equation for the strong force is further derived in *Atomic Orbitals* for an orbital force keeping an electron in orbit in an atom.

**Electric Force**

**Magnetic Force**

**Gravitational Force**

**Strong Force**

**Orbital Force**

### Photon Frequency and Wavelength

Photon energies are often preferred over wavelengths beyond hydrogen, which uses the Transverse Energy Equation. Frequency and wavelength can be calculated using the following equations. The variables for amplitude factor (δ) and distance (r) are obtained from tables in the atom calculations page.

**Photon Frequency**

**Photon Wavelength**

### Relativity & Motion

A particle in motion with velocity (v) changes wavelength. The **complete form** of the in-wave and out-waves are used for Longitudinal Energy (particle energy) at relativistic speeds. The complete form also includes the slight loss of amplitude due to particle spin, used in the equations for gravity and magnetism. The magnetic energy equation uses classical terms for the fine structure constant, Planck length and gravitational coupling constant for the electron in this form, but it can be derived in pure wave constants. It is used in this form to show relationship between gravity and magnetism.

**Longitudinal In-Wave Energy – **Complete Form

**Longitudinal Out-Wave Energy – **Complete Form

**Magnetic (Transverse) Out-Wave Energy** – Complete Form

## Equations Derivation Summary

The following is a derivation of the common equations used in Energy Wave Theory and how they are derived from the energy wave equation.

## Constants Derivations

### Wave Constants – derivations**:**

There are four fundamental, universal wave constants. The speed of light (c) is a known and measured value, leaving three constants that needed to be derived against a known and measured property.

**Wavelength**(longitudinal) is set to the well-measured classical electron radius {r_{e}}.**Amplitude**(longitudinal) is set to the well-measured fine structure constant {α_{e}} and using wavelength calculated from above.

**Density**is set to the well-measured Planck constant {h} and using wavelength calculated from above.

### Particle Constants – derivations**:**

There are two constants used in the equations for the electron. In addition there are three g-factors (two for the electron and one for the proton.

**Electron particle count**is set to 10 based on calculations of K values found for particles (see electron).

**Electron outer shell multiplier**is a constant for readability replacing the summation in the electron’s particle energy.

**Electron orbital g-factor**is set to the well-measured classical electron radius {r_{e}}.*Note that the derivation of this constant and the wavelength constant is circular. The final value was determined through iteration until all constants resolved correctly.*

**Electron spin g-factor**is set to the Planck charge {q_{P}}.

**Proton orbital g-factor**is set proton’s mass {m_{p}}.

In *Energy Wave Equations: Correction Factors,* a potential explanation for the values of these g-factors is presented as a relation of Earth’s outward velocity and spin velocity against a rest frame for the universe.

**Examples: **Examples of the energy, forces and photon equations matching experimental data can be found in the downloadable spreadsheet.