The Parameters 2π & 4π in Quantum Mechanics a Heuristics viewpoint of ∆×...

In quantum mechanics, 2π and 4π represent the limit or boundary condition for a process of mathematical rotation or quantum spin.

 But what is spinning in quantum mechanics, it seems to be probability and uncertainty.

This is like asking the question, what is waving In Schrödinger wave equation Ψ²?

 

I believe we can have an objective intuitive understanding of quantum mechanics if we explain it as a geometrical process based on 4π and 2π.

The 4π can represent spherical 4πr² geometry this can be based on Huygens’ Principle of 1670, that says: “Every point on a wave front has the potential for a new spherical wave”.

 We can think of the ‘point on the wave front’ as a photon ∆E=hf of energy with an uncertain probabilistic future unfolding with each photon electron interaction.

 Because the process is unfolding relative to the spherical surface of the wave front, we have to square the radius r². This is seen in the mathematics of quantum mechanics as c² the speed of the process, the speed of light squared, and e² representing the electron squared.  

 

Spheres always intersect as circles 2πr, and this is why we have 2π in the mathematics of quantum mechanics. The two-dimensional surface of the sphere forms a manifold or boundary condition for positive and negative charge. The inner concaved surface forms negative charge and the outer surface forms positive charge.

 

Light radiates out as a sphere and when the surface of the sphere comes in contact with the electron probability cloud of an atom it forms a photon electron coupling and our three dimensional world changes with the movement of positive and negative charge.

We measure this process as the passage of time with the interior of the sphere forming our three dimensional space. Therefore, we have Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π between position and momentum with 4π in the equation representing the spherical geometry.

If we reformulate the uncertainty using energy and time instead of position and momentum, we have 2π in the equation ∆E∆t≥h/2π representing the surface of the sphere.

This geometrical interpretation of quantum mechanics is supported by the fact that the Planck constant h/2π is also link to 2π.

When there is an exchange of energy in the form of a photon ∆E=hf electron coupling or dipole moment the energy levels cannot drop below the centre of the sphere because the process is relative to the radius. 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 2πr.