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 20 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)
Variables
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

 

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

or

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.

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

or

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

or

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

 

Energy Wave Equations

The following are the common equations used on this site, all derived from the fundamental Energy Wave Equation as the equation that describes energy waves.

 

Fundamental Energy equation

 Energy Wave Equation

 

Longitudinal Energy Equation

Longitudinal Energy Equation

 

Transverse Energy Equation

Transverse Energy Equation

 

Transverse Wavelength Equation

Transverse Wavelength Equation

 

Amplitude Factor Equation - 1s

Amplitude Factor Equation – 1s Orbital

 


 

Force Equation

Force Equation

Acceleration Equation

Acceleration Equation

 

Velocity Equation

Velocity Equation