Geometrical interpretation of 137 in Quantum Mechanics

This geometrical interpretation of quantum mechanics can give us a simple explanation for the fine structure constant or coupling constant 137.

When light waves interact with the spherical electron probability cloud that surrounds the nucleus of an atom there is an exchange of energy formed by the spontaneous absorption and emission of light.

The absorption forms a photon ∆E=hf electron coupling and at that moment in time, the energy levels cannot drop below the centre of the sphere because the process is relative to the radius and the spherical surface. This forms a minimum amount of energy forming a constant of action in space and time that we see mathematically as the Planck constant h/2π linked with 2π representing the circumference of the sphere 2πr.

When the energy levels drop, it also forms another geometrical constant relative to the square of probability and the spherical surface. This is seen mathematically as the fine structure constant or coupling constant 137. The absorption of light is followed by the emission of a new light wave that forms a probabilistic uncertain future, that can be seen mathematically as Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π.

Light is wave with particle characteristics as a probabilistic future unfolds. When there is an exchange of energy formed by the absorption and emission of light, it is relative to radius squared or c². 

We have spherical light waves with particle characteristics of light coming into existence relative to the surface of the sphere, therefore we square the radius r².

Because of this the wave-function ψ² is squared the charge of the electron e² is squared and the speed of the process c is squared as in E=MC² representing one geometrical process. 

When there is an exchange of energy in the form of a photon ∆E=hf electron coupling the energy levels cannot drop below the centre of the sphere because the process is relative to the radius. This forms a constant of action in space and time that we see mathematically as the Planck constant h/2π linked to the circumference 2πr. 

Because the square of probability is relative to the spherical surface (wave-function Ψ²) and the centre of the sphere (Planck constant h/2π), it forms another constant when there is an exchange of energy in the form of the Fine Structure Constant 1/137.