Strong Force


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 (nucleons), and its residual 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.

quarks and neutron

Strong force – Neutron
(Standard Model representation of 2 down quarks and 1 up quark)


  • Strong force – attractive force to build a composite particle (nucleons) from an arrangement of quarks at a range of the proton’s radius or less
  • Nuclear force – attractive force to build an atomic nucleus from an arrangement of nucleons at a range of the atom’s nucleus radius or less




Similar to the creation of particles, where wave centers may be stable at standing wave nodes where wave amplitude is minimized, the same rule applies for particles made from these same wave centers.  The following summarizes the creation of different types of particles and atoms from this rule:

  1. Particles created from wave centers at standing wave nodes (e.g. electrons, positrons)
  2. Composite particles created from particles at standing wave nodes (e.g. nucleons like protons, neutrons)
  3. Atoms created from nucleons at standing wave nodes and balanced by electrons in orbit (e.g. hydrogen, helium, etc)

The difference between these types of particle and atom formations is placement distance at standing wave nodes.  All have forces at short distances because standing waves eventually transition to traveling waves.  When two particles, such as two electrons, have wave centers that are within the boundary of 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 because at a standing wave node, amplitude is minimal (zero), which meets the criteria for particle motion. The same would be true of protons and neutrons locking together to form the nucleus of the atom, but at longer separation distances.

strong force between particles at standing wave nodes

Strong Force – Two particles placed at standing wave nodes
Increasing transverse out-wave energy and decreasing longitudinal out-wave energy


The particles require significant energy for their spin.  A closer look at a single particle in one dimension shows a major loss in longitudinal out-wave amplitude as energy is converted to a transverse wave, consistent with the conservation of energy principle. This ratio is the fine structure constant.

Fine Structure Constant Explained

Quarks and Gluons

The energy of two particles to reach standing wave nodes is illustrated in the next image. In the Forces paper, the velocity of two electrons to reach standing wave nodes was calculated to be nearly the speed of light. But once at the node and stable, their energy would be stored and converted to the transverse wave, known as the gluon that binds the particles together.  It continually requires energy to maintain a high spin of the particles, reducing longitudinal wave amplitude.  As such, the electrons (or positrons) no longer appear like their typical particle and become a new type of particle, referred to as a quark.

creating protons from quarks


Strong Force Distance – Creating Composite Particles

In three-dimensional space, it takes more than two particles at standing wave nodes to be stable and create a new particle.  This was also seen in particle creation, where tetrahedral structures allow the formation of stable particles.  Four electrons or positrons pushed to standing wave nodes in a tetrahedron shape would fit this criteria.  This is also known as a tetraquark. All four particles continue to spin and create gluons that bind all particles together, creating an empty shell of a nucleon. Later, a positron can be attracted to the center to become a proton, and another electron to become a neutron, matching experimental observations of the decay of these particles. An animated explanation of this process is found in the proton explanation page.

The structure of the nucleon has four particles at its tetrahedral vertices, at a separation distance of one electron wavelength – for a total of three electron wavelengths including radii. Note, one electron wavelength is equal to ten fundamental wavelengths, as the electron has ten wave centers (K=10). This matches the calculations of the strong force at this separation distance, as described in the equation section below.

Strong force - one wavelength separation

Quark separation distance


Nuclear Force Distance – Creating the Atom

After nucleons (protons and neutrons) are created as composite particles, then nucleons may themselves arrange at stable, standing wave nodes. Nucleon attraction is modeled as two nucleons with a separation distance of two electron wavelengths – for a total of four electron wavelengths including radii. It is the same force as the strong force, but now at a slightly longer distance (four electron wavelengths instead of three electron wavelengths).  Because amplitude declines with distance, the force is declining.  It takes less energy to bind nucleons together to form an atom than it takes energy to bind particles together to form a nucleon.

Strong force - two wavelength separation

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 Q1 and Q2 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.


Electron Orbital Distance – Completing the Atom

The strong force is an axial, transverse wave that creates the gluon, but it does not stop just between two particles.  It continues along the axis of spin and is the force that keeps an electron in orbit in an atom. Whereas an electron annihilates with a positron of the same charge as the proton, the proton is a composite particle with this strong force, creating a new type of force that keeps the electron from annihilating with the proton. Because this force travels along an axis through two or more quarks before reaching an electron, the calculation is different than the strong force.  It is referred to as an orbital force and covered in detail on this page.




Strong Force

In simple terms using two groups (Q) of particles separated at distance (r), and the properties of the electron’s energy and radius (Ee and re), the strong force of two electrons are:

Simplified Strong Force


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

Strong Force

 Strong Force




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


Calculation Nuclear Force – Calculation

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

Equation: Strong Force equation

  • Q1 = 1
  • Q2 = 1
  • r = 1.127 x 10-15 m (1.127 fm – four electron wavelengths)

Strong Force Derived and Calculated
2.4891E4 (kg m/s2)
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

Nuclear Force (104 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.