## Background

The strong force is the most powerful of all the known forces. It is roughly 137 times stronger than the electric force. 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. 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. The electrons can “lock” together if at the nodes of standing waves. **At a standing wave node, amplitude is minimal (zero)**, which meets the criteria for particle motion.

### 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 from the edges of the particles – for a total of three electron wavelengths including radii. At this distance, a new standing wave structure is created and two particles appear as one highly-energetic particle. A potential visual is provided below. An animated explanation is found in the proton explanation page.

**Quark separation distance**

Nucleon attraction is modeled as two particles with a separation distance of two electron wavelengths – for a total of four electron wavelengths including radii. Again, a potential structure is proposed below but the important finding is the separation distance used in the strong force equation that models the peak force.

**Nucleon separation distance**

The electric force is used to calculate the strong force with an increase in wave amplitude – proportional to the inverse of the fine structure constant – in an axial direction. The strong force calculations model the separation of particles Q_{1} and Q_{2} at three electron wavelengths for quarks and four electron wavelengths for nucleons, as described above. 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.

**Equation**

**Strong Force**

In simple terms using two groups (Q) of particles separated at distance (r), and the properties of the electron’s energy, mass and radius (E_{e}, m_{e }and r_{e}), the strong force of two electrons are:

When expressed in wave constant terms, it is the strong force:

** Strong Force**

**Proof**

Proof of the energy wave explanation for the strong force is the derivations and calculations of:

- Fine structure constant
- Calculated the strong and nuclear forces at three and four electron wavelength nodes (0.85 and 1.127 femtometers) –
*see example below*

### Calculation Nuclear Force – Calculation

From the explanation of nucleon separation above, using two particles with a separation distance of four electron wavelengths (r=4K_{e}λ) or 1.127 fm.

**Equation: **Strong Force equation

**Variables:**

- Q
_{1}**=**1 - Q
_{2}**=**1 - r = 1.127 x 10
^{-15}m (*1.127 fm – four electron wavelengths*)

**
Result: **2.4891E4 (kg m/s

^{2})

**Comments:**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.

**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.