Unification of Forces

Unification

When the complications of charge and mass are removed from force equations, and substituted with a dimensionless count of particles (Q), it can be shown that all force equations are related to the electric force.  These equations are summarized in classical format related to the electron’s energy and radius (Ee and re), in addition to coupling constants (α) explained on this page as a ratio of geometries when wave form changes. The equations are validated on their respective force pages: electric, gravitational, magnetic, strong and orbital. The weak force is excluded, as explained on a separate page.

unified electric gravitational strong and magnetic forces

 

The electric force is the fundamental force, traveling though space as longitudinal waves as granules vibrate in harmonic motion. The magnetic force of electromagnetism, seen as the flow of electrons, is based on electron velocity (v) described in more detail here. It is simply a change of electron energy (electric force) to electron mass times velocity (magnetic force). The remainder of the forces require coupling constants, which is the relative strength of the force relative to the electric force.

 

Forces Summary

A summary of the forces and the simple version of the equation using classical forms with the electron’s energy, mass and radius (Ee, me and re) is found below.  The wave constant form can be derived from these equations. The forces in the following sections are all derived from these descriptions and classical equations.

Forces Summary

 

Coupling Constants and their Geometry Ratio

In the Geometry of Spacetime, all coupling constants are modeled as a ratio of the geometric shapes for transverse and longitudinal waves. A unit cell of the lattice structure of spacetime is shown below in (1).  The wave center (blue) is in motion in (2) passing through a surface area best described by a rectangular geometry.  As it reaches its maximum displacement in (3) it returns to equilibrium.  After returning to equilibrium in (4) it has transferred its energy to granules in the lattice that continue to spread spherically.  The direction of initial motion is also represented by a cone as it propagates outwards from the center. This motion creates two surface areas that will be measured for energy: the surface area of a rectangle, and the surface area of the combination of a sphere and cone.

Vibration of center granule and geometry of spacetime to unify forces

Vibration of Center Granule – Rectangle vs Sphere+Cone Surface Areas

 

Next, this is put into equation format. A transverse wave passing through a surface area (Sr) of a rectangle with length (x) and width (y) is shown below.  A spherical, longitudinal wave with a component that flows from the center in a conical shape with slant length (l) and radius (d) is also shown below as surface area Ss.  This represents the change in wave form from transverse to spherical or vice versa in wave geometry.Fine structure constant and the geometry of a rectangle, sphere and cone

The ratio of Sr to Ss is expressed in equation format with the surface area of a rectangle (x * y), the surface area of a sphere (4 * π * l2) and the surface area of a cone (π * d * l + π * d2).


geometric ratio of rectangle and sphere+cone

Coupling Constant Geometry Ratio

 

Strong, Gravitational and Orbital Forces – Geometry

With the exception of the magnetic force, which is based on electron velocity, the remaining forces that require coupling constants are based on a single geometric ratio. They are based on the electric force, which is why the coupling constants define the relative strength of these forces versus the electric force.

 

Strong Force (x=re ; y=re ; d=re ; l=π*re)

All variables from the coupling constant geometry ratio equation (above) are set to the electron’s radius (re).  This becomes the coupling constant for the strong force, known as the fine structure constant (α or αe). It becomes stronger than the electric force as it converts from spherical, longitudinal wave form to the gluon, which is a transverse wave propagating along one dimension.

Fine Structure Constant Derived from Pi

 

Gravitational Force (Electron) (x=lP ; y=lP ; d=re ; l=π*re)

The variables for the sides of the rectangle from the coupling constant geometry ratio equation (above) are set to Planck length (lP) and the cone radius and slant length are set to the electron’s radius (re). This matches the results for the electron’s gravitational coupling, which is the force of gravity between two electrons. The proton has its own gravitational coupling constant, which can be used for the calculation of gravity for large bodies.

Electron Gravitational Coupling Constant Derived from Pi

 

Orbital Force (x=re ; y=r ; d=re ; l=π*re)

The same variables as the fine structure are used for the coupling constant geometry ratio equation (above), with the exception of the width (y) for the rectangle.  It is now a variable distance (r) as the electron’s distance from a nucleus will vary based on the atomic element. Thus, it cannot be solved directly – the use of the equation is found in calculations in the Atomic Orbitals paper where radius is known for each element and seen on this site in the equations for atoms. When substituted into the equation for atoms, the fine structure constant is now squared (αe2) and the radius distance is now cubed (r3), which is the behavior seen in permanent magnets.

Magnetic Coupling Constant Derived from Pi

 

It is labeled as αMe as it is a force that not only keeps electrons in orbit, as explained here, but also for the static magnetic force seen in permanent magnets (not to be confused with the magnetic force from electromagnetism based on electron velocity).