## Background

The strong force is the most powerful of the forces at roughly 137 times stronger than electromagnetism. It is the force that holds quarks together to form the proton and neutron, and its residual force (nuclear force) holds nucleons together in an atom’s nucleus to form atoms.

Although it is very strong, as the name implies, experiments have shown that the strong force only works at very short distances, about one femtometer, or roughly the radius of a proton.

**Strong force – Neutron**

*(Standard Model representation of 2 down quarks and 1 up quark)*

**Explanation**

The strong force is known to apply only at short distances, less than 2.5 fm, or roughly the radius of the electron. At distances less than the radius of the electron, longitudinal waves are standing in form. Beyond the radius, they are traveling waves. When two particles, such as two electrons, have wave centers that are within the boundary of the standing waves (radius), they are affected by, and contribute to, the standing wave structure of other particles to form a new wave core. In essence, they become a new particle. It would take incredible energy to overcome electromagnetic repelling of two electrons to reach this short distance, but once pushed to within the electron’s radius, two electrons would lock together and take a new form.

Gabriel LaFreniere has modeled quarks and this strong force, which creates gluons, below. At close range, two particles create a strong attraction.

### Quark and Nucleon Attraction

This theory has calculated two key distances for the strong force based on the separation distance between particles at one electron wavelength and two electron wavelengths. *Note, one electron wavelength is equal to ten fundamental wavelengths, as the electron has ten wave centers (K=10).*

Quark attraction is modeled as two particles, possibly electrons, with a separation distance of one electron wavelength. At this wavelength, a new standing wave structure is created and two particles appear as one, highly-energetic particle. A potential visual is provided below. A detailed explanation of the diagram is found in the *Forces *paper.

Nucleon attraction is modeled as two particles with a separation distance of two electron wavelengths. Again, a potential structure is proposed below but the important finding is the separation distance used in the Force Equation that models the peak force.

### Calculating the Force

The Force Equation is used again to calculate the strong force. The strong force calculations model the separation of particles Q_{1} and Q_{2} at three electron wavelengths and four electron wavelengths (one and two electron wavelength separations respectively, if considering the two particles being separated have a particle core distance of an electron wavelength each).

When two particles are separated at distances within the standing wave structure, the amplitude gain is the inverse of the fine structure constant. Amplitude is roughly 137 times greater when these particles are combined. This is shown in the modified Force Equation below. Although the relationship to the fine structure constant is not unexpected, as it is known that the strong force is 137 times greater than electromagnetism, it is interesting to note that the force values only match experimental results when K=10, which is the wave center count for the electron and positron.

Because the fine structure constant can be defined in wave constants, the force equation for the strong force can further be simplified to the following:

**Force Equation – Strong Force**

**Proof**

Proof of the energy wave explanation for the strong force was accomplished by using the Force Equation for the Strong Force to calculate the distance and force for gluons and the nuclear force holding nucleons together in an atom.

The residual of the strong force (beyond the proton’s standing wave radius) was also used as the repelling force from a proton that keeps an electron in orbit. This model successfully calculated the Bohr radius and orbital distances for the first 20 neutral and ionized elements (H to Ca), using classical mechanics.

### Example Calculation

Nucleon Separation at a distance of 1.13E-15 meters:

Using two particles with a separation distance of two electron wavelengths (2Kλ). Considering the radius of each electron core, the total distance between the two particle cores is four electron wavelengths (4Kλ) or 1.13 fm, measured in femtometers. At this distance, the calculated force is 2.488E4 newtons and is consistent with measurements for nucleon binding.

**r = 1.127 x 10 ^{-15} m**

Q

_{1}= -1

Q

_{2}= -1

**Calculated Radius:** 1.127 x 10^{-15} m (*or 1.127 fm*)

**Calculated Value: **2.488E4 newtons

**Comparison Against Measurements:** These values are compared to the measurements of nucleon separation in atoms in the chart below and agree with the maximum force at the calculated distance. Note force is negative due to it being an attractive force.

**Nuclear Force (10 ^{4} newtons)**

* Note: *A summary of strong force calculations is found on this site; more detailed calculations with instructions to reproduce these calculations is found in the

*Forces*paper.