Constants and Equations

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
Ke e – electron (wave center count)
λl, λt l – longitudinal wave, t – transverse wave
Δe, ΔGe, ΔT e – electron (orbital g-factor), Ge – gravity electron (spin g-factor), T – total (angular momentum g-factor)
Fg, Fm 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*
Al Amplitude (longitudinal) 3.662796647 x 10-10 (m)
λl Wavelength (longitudinal) 2.817940327 x 10-17 (m)
ρ Density (aether) 9.422369691 x 10-30 (kg/m3)
c Wave velocity (speed of light) 299,792,458 (m/s)
δ Amplitude factor variable – (m3)
K Particle wave center count variable – dimensionless
n Wavelength count variable – dimensionless
Q Particle count (in a group) variable – dimensionless
Electron Constants
Ke Particle wave center count – electron 10 – dimensionless
Derived Constants**
Oe Outer shell multiplier – electron 2.138743820 – dimensionless
Δe / δe Orbital g-factor / amp. factor electron 0.993630199 – (m3)
ΔGe / δGe Spin g-factor / amp. gravity electron 0.982746784 – (m3)
ΔT Total angular momentum g-factor 0.976461436 – dimensionless
αe Fine structure constant 0.007297353- dimensionless
αGe Gravity coupling constant – electron 2.400531449 x 10-43dimensionless
αGp Gravity coupling constant – proton 8.093238772 x 10-37dimensionless


Energy Wave Equations


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.

Fundamental Energy equation

 Energy Wave Equation


Longitudinal Energy Equation

Longitudinal Energy Equation


Transverse Energy Equation

Transverse Energy Equation



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

Force Equation
(Electric Force)


Magnetic Force

Magnetic Force


Gravity Force

Gravitational Force


Strong Force

Strong Force



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

Transverse Wavelength Equation – Hydrogen


Transverse Wavelength Equation - Complete

Transverse Wavelength Equation – Complete Form


Amplitude Factor Equation - 1s

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 Equation Complete Form

Longitudinal In-Wave Energy – Complete Form


Longitudinal out-wave equation

Longitudinal Out-Wave Energy – Complete Form


Magnetic Transverse Out-Wave Equation

Magnetic (Transverse) Out-Wave Energy – Complete Form


Acceleration Equation

Acceleration Equation


Velocity 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.

Wave Equation Derivations



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.

Amplitude Derivation

  • Density is set to the well-measured Planck constant (h) and using wavelength calculated from above.

Density Derivation


** 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.

Shell Energy Multiplier


Shell Energy Multiplier - Alternative Form
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 ΔGe was adjusted slightly by 0.0000606 to match experimental data.  Since ΔT is derived from ΔGe 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 (αe) 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 107 m/s (11% of the speed of light) would reduce three g-factors to one based on relativity principles.

Orbital G-Factor

Spin G-Factor

Total Anugular Momentum G-Factor

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 (αe).   Since Oe is derived in wave constants, two versions of the fine structure are provided.

Fine Structure Constant


Fine Structure Constant - Alternative Form

The gravitational coupling constant for the electron can also be derived. αGe 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 (αG = 1.7 x 10-45). The derivation matches known calculations as αGe = αG e = 2.40 x 10-43.

Gravity Coupling Constant Electron


Gravitational Coupling Constant - Electron - Alternative Form
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.

Gravity Coupling Constant Proton



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