## Force Equation

Wave centers move to *minimize* amplitude, which is why they prefer the node of a wave. This results in a force on the particle as shown below.

** **

**Constructive and Destructive Wave Interference**

The longitudinal wave is responsible for the electric force (*separated from the magnetic force **– described later*). Waves in the same phase are constructive and amplitude increases between particles. Waves in the anti-phase are destructive and amplitude decreases between particles. For example, two electrons are in the same phase and are constructive between the particles. Since particles move to minimize amplitude, they are repelled. An electron and a positron are in the opposite phase. Destructive wave interference causes minimal amplitude between the particles and they are thus attracted to each other.

The energy equation is derived to a Force Equation based on two groups of particles (Q_{1} and Q_{2}) separated at a distance r.

This Force Equation is naturally Coulomb’s Law (k), the electric force, but it is also derived to other forces based on a change in wave amplitude and/or wave form.

## Derivation of the Force Equation

The Force Equation is derived from the Longitudinal Energy Equation with a change in wave amplitude (energy) and a ratio of standing to traveling waves.

1) In expanded form, the change in energy is expressed as constructive/destructive energy of a collection of particles (Q). The ratio of standing waves is r_{particle} (radius of standing waves) relative to the total distance including traveling waves.

2) The boundary of standing waves is the particle radius measured in wavelengths, proportional to wave centers (K). For the electron, this is derived to be the classical electron radius.

3) Substitution of electron energy (E_{e}) and particle radius from (2) into the first equation (1).

4) Simplify (3). **Force Equation.**

This equation is used for the calculation of the electric force. Without any changes to wave form, the Force Equation can be linked to Coulomb’s Law and Newton’s Second Law by mathematically derivation.

A change in wave amplitude and form is the cause of the other forces. Gravity and magnetism are tied by the same force, based on the conservation of energy as shown below. Likewise, the strong force and the repelling force that keeps the electron in an orbital are also linked. Both of these are a result of particle spin, which is addressed next.

## Particle Spin – The Cause of Gravity and Magnetism

Energy is always conserved. When a particle spins, it takes energy, but this energy simply changes forms. Longitudinal in-waves reflect off wave centers, becoming longitudinal out-waves. The combination of these in-waves and out-waves creates the standing wave energy of particles such as the electron.

**Waves reflecting of particles. The resulting in-wave and out-wave forms a standing wave.
**

*Despite the simplistic illustration of in-wave and out-waves, they are spherical and approach the particle from all directions in three-dimensional space.*

A wave with properties of four universal constants (wave speed, amplitude, wavelength and density) and a constant property of the electron (the electron wave center count) results in the standing wave energy of the electron (8.1817 x 10^{-14} joules). This was derived in detail in *Particle Energy and Interaction*.

There is only one wave and it is responsible for particle mass and the forces, as it will be shown. Two of the forces are related to the spin of the particle.

**Particle Spin**

It is known that the electron and proton have spin. In fact, they have a strange spin of ½. If the electron consists of 10 wave centers (K_{e}), then these wave centers would be in a geometric formation that is stable as the electron itself is a stable particle.

Wave centers move to minimize amplitude, positioned at nodes on the wave, thus a potential arrangement for a particle of 10 wave centers is a three-level tetrahedron. In this arrangement, most of the wave centers would be on the node of a spherical, longitudinal wave. The wave centers that are slightly off the node would attempt to move to the node. Once this wave center is on the node, it forces another wave center off the node, and it then attempts to reposition onto the node itself. This process repeats itself constantly as each wave center in the electron’s structure attempts to reposition. This is illustrated below with a red circle representing the wave center off node. This model would explain the electron’s strange spin of ½, which means it has a 720-degree rotation before returning to its original position.

**Particle Spin and Amplitude Effect**

This model of the electron spin would always require energy because the wave center that needs to reposition is constantly changing. The energy for any particle that is required for spin reduces in-wave amplitude as it reflects to become an out-wave (a_{G}). For the electron, it is given a notation of a_{Ge} and is calculated to be a loss of 2.40E-43 for amplitude loss for the electron’s spin. It is a negligible loss when considering one electron, but when considering large bodies containing a significant number of particles, the loss becomes measurable and is the force known as gravity.

Due to the conservation of energy, the loss of longitudinal wave amplitude which becomes the force of gravity is converted to a new, transverse wave form that is the force of magnetism.

**Electric and Gravitational Force**

A new visual of gravity and its relation to the electric force is shown below. Both of these forces are based on the longitudinal wave amplitude between two or more particles.

**Particle Spin and Amplitude Effect
***

*Gravitational force appears when the electric force cancels due to protons/electrons in atoms canceling wave interference. Then, wave amplitude difference begins to appear for a large collection of atoms – such as stars and planets – the force of gravity.*

The longitudinal out-wave is responsible for the electric force, as it was shown earlier deriving the Force Equation. Gravity is the same longitudinal wave force, but with an amplitude difference a_{Ge} as a result of particle spin. The Force Equation is modified with this amplitude loss below as the **gravitational force (F _{g}) equation**. The calculations were proven to match experimental evidence of the gravitational calculations, derive Newton’s law of gravitation, and the gravitational constant G.

**Magnetism**

Magnetism is the energy of a new wave that is created as the electron spins. It creates a new transverse wave, illustrated as red spirals. Since energy is conserved, magnetism is the energy that is gained and released in a new wave form while gravity is the loss of longitudinal wave energy.

**As the electron spins, the wave centers that are off node absorb longitudinal wave amplitude and transfer it to a new transverse wave. This transverse wave becomes the magnetic force.**

The proof that gravity and magnetism are linked is the derivation of the electron’s magnetic moment, known as the Bohr magneton. The gravitational force equation is rewritten to a form before it was simplified, where the in-wave and out-wave frequency and amplitude can be separated in the equation.

In the expanded form of this Force Equation for gravity, the focus is on the mid-section. The electron has an in-wave and an out-wave, with its frequency and amplitude based on the number of wave centers in the electron (K). Amplitude is cubed as it is spherical, in three dimensions. The out-wave experiences an amplitude loss (a_{Ge}) that will become magnetism. This is the mid-section:

To determine the resultant frequency and amplitude for magnetism, the geometric mean is used for the electron’s in-wave and out-wave. One half (½) of the square of this mean is used because there are two axial waves that are created, each traveling in opposite directions from the electron.

**Bohr Magneton – geometric mean of frequency and amplitude**

The frequency and amplitude is apparent from the Force Equation. The in-wave and out-wave frequency (f_{in} and f_{out}), and the in-wave amplitude (A_{in}) is shown in equations below. The out-wave amplitude (A_{out}) is different. It has an amplitude loss (a_{Ge}) that matches the energy loss of gravity, although it is affected by half (½), because the particle’s spin takes two rotations (1/2 spin). One of these rotational waves will become the natural unit of the electron’s magnetic moment – known as the Bohr magneton.

Inserting the above amplitude and frequencies into the equation above titled **Bohr Magneton – geometric mean of frequency and amplitude** and simplifying, the equation resolves to be the Bohr magneton (µ_{B}) – the magnetic moment of the electron. *For a note on the modifier and the units of the Bohr magneton, refer to its dedicated page.*

Particle spin is also the cause of the strong force although a different wave amplitude conversion is used due to two particles being in close proximity.

* Note: *More detailed calculations with instructions to reproduce these calculations is found in the

*Forces*paper.