## New 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 22 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 at different particle sizes (K) and shells (n), in addition to differentiating longitudinal and transverse waves. The following notation is used:

Notation |
Meaning |

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

λ_{l, }λ_{t} |
l – longitudinal wave, t – transverse wave |

Δ_{e}, Δ_{Ge}, Δ_{T} |
e – electron (orbital g-factor), Ge – gravity electron (spin g-factor), T – total (angular momentum g-factor) |

F_{g}, F_{m} |
g – gravitational force, m – magnetic force |

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

## 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.

Symbol |
Definition |
Value (units) |

Wave Constants* |
||

A_{l} |
Amplitude (longitudinal) | 3.662796647 x 10^{-10} (m) |

λ_{l} |
Wavelength (longitudinal) | 2.817940327 x 10^{-17} (m) |

ρ | Density (aether) | 9.422369691 x 10^{-30} (kg/m^{3}) |

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

Variables |
||

δ | Amplitude factor | variable – (m^{3}) |

K | Particle wave center count | variable – dimensionless |

n | Wavelength count | variable – dimensionless |

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

Electron Constants |
||

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

Derived Constants** |
||

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

Δ_{e} / δ_{e} |
Orbital g-factor / amp. factor electron | 0.993630199 – (m^{3}) |

Δ_{Ge} / δ_{Ge} |
Spin g-factor / amp. gravity electron | 0.982746784 – (m^{3}) |

Δ_{T} |
Total angular momentum g-factor | 0.976461436 – dimensionless |

α_{e} |
Fine structure constant | 0.007297353- dimensionless |

α_{Ge} |
Gravity coupling constant – electron | 2.400531449 x 10^{-43} – dimensionless |

α_{Gp} |
Gravity coupling constant – proton | 8.093238772 x 10^{-37} – 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**

**Transverse Energy Equation**

### 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 electromagnetic force for an induced current (particles in motion). The equation for the strong force is modified further in *Atomic Orbitals* for orbital forces.

**Force Equation
**(Electric Force)

**Magnetic Force**

**Gravitational Force**

**Strong Force**

### Photons

Photon energies are often preferred over wavelengths beyond hydrogen. A simple version of the Transverse Wavelength Equation is available for hydrogen using longitudinal wavelengths (n). A complete form can be used with known amplitude factors and distances, available here.

**Transverse Wavelength Equation **– Hydrogen

**Transverse Wavelength Equation **– Complete Form

**Amplitude Factor Equation – **1s Orbital

### Relativity & Motion

A particle in motion changes the wavelength. The **complete form** of the in-wave and out-waves are used for Longitudinal Energy (particle energy) at relativistic speeds. Particle acceleration and velocity are independent equations at any speed.

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

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

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

**Acceleration Equation**

**Velocity Equation**

## Equations Derivation Summary

The following is a derivation of the common equations used in Energy Wave Theory and how it is derived from the base 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.

### ** Derived Constants – the derivations for the constants are**:**

The outer shell multiplier for the electron is a constant for readability, removing the summation from energy and force equations since it is constant for the electron. It is the addition of spherical wave amplitude for each wavelength shell (n). Due to a relationship between the energy of the electron and the fine structure constant, the shell energy multiplier can also be rewritten in terms of wave constants. Both versions are provided.

*or*

The three modifiers (Δ) are similar to the g-factors in physics for spin, orbital and total angular momentum. These modifiers also appear in equations related to particle spin and orbitals, however the g-factor symbol is not used since their values are different. This is due to different wave constants and equations being used. The value of Δ_{Ge} was adjusted slightly by 0.0000606 to match experimental data. Since Δ_{T} is derived from Δ_{Ge} it also required an adjustment, although slightly smaller at 0.0000255. This could be a result of the value of one or more input variables (such as the fine structure constant, electron radius or Planck constant) being incorrect at the fifth digit. The fine structure constant (α_{e}) is used in the derivation of the equation below as the correction factor is set against a well-known value. 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. A velocity of 3.3 x 10^{7} m/s (11% of the speed of light) would reduce three g-factors to one based on relativity principles.

The electromagnetic coupling constant, better known as the fine structure constant (α), can also be derived. In this paper, it is also used with a sub-notation “e” for the electron (α_{e}). Since O_{e} is derived in wave constants, two versions of the fine structure are provided.

*or*

The gravitational coupling constant for the electron can also be derived. α_{Ge} is baselined to the electromagnetic force at the value of one, whereas some uses of this constant baseline it to the strong force with a value of one (α_{G} = 1.7 x 10^{-45}). The derivation matches known calculations as α_{Ge }= α_{G }/α_{e} = 2.40 x 10^{-43}.

*or*

The gravitational coupling constant for the proton is based on the gravitational coupling constant for the electron (above) and the proton to electron mass ratio (μ), where μ = 1836.152676.

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