Quantum Spin an Artist Animation - Geometrical Explanation for Pauli Exc...

Quantum Spin can be explained by a process of spherical symmetry forming and breaking with the process relative to the spherical surface. The electron is a half spin particle because the process is relative to the radius that is half the diameter of the sphere. It is because we have to square the radius r² to find the spherical surface area that so many properties are squared in the mathematics as in t², c², e², ψ² and velocity v² as in kinetic Eₖ=½mv² energy.

This would be easier to see if we did not use the reduced Planck Constant ħ or h bar but instead used ħ=h/2π. We would then have 2π representing the spherical diameter with the spacing between spin states being h bar.

Because an interior of a sphere 4π is naturally three dimensional at any given moment in time, these spin states can be thought of as a combination pointing in each of our three dimensions.

When the electron is not interacting with anything, and we are not making any measurements there is only uncertainty ∆×∆pᵪ≥h/4π of what the angular momentum is.

The diagram in the video represents light photon ∆E=hf energy interacting with the electron.  Because charge is an innate part of all matter when we make a measurement, it is basically the same interaction.

The moment we make an observation by interacting with the electron of an atom the direction or angular momentum will change to one of the quantum states where it is known with 100% certainty.

In this theory, this represents a probabilistic future unfolding with the exchange of photon ∆E=hf energy.

The photon and electron are different aspects of the same geometrical process; photons being spin one particle represent spherical symmetry. The electron having half spin represents the spherical symmetry breaking forming the potential for the broken imperfect symmetry of our everyday three-dimensional life.

The continuous exchange of photon energy forms our ever-changing world that we measure as a ‘period of time’ relative to the atoms of the periodic table.

But above all this process forms a probabilistic future that is relative to the energy and momentum of our actions. 

There is a direction to ‘time’ the spontaneous absorption and emission of light photon ∆E=hf energy is continuously forming potential photon energy into the kinetic energy of electrons. Kinetic Eₖ=½mv² energy is the energy of what is actually happening. The wave particle duality of light and matter in the form of electrons is forming a blank canvas for us (atoms) to interact with; we have waves over a ‘period of time’ with particles characteristics as an uncertain future unfolds. Within each reference frame, the absorption of light always comes before the emission forming an Arrow of Time for the object or life form of that reference frame. 

The mathematics of quantum mechanics represents the physics of time with classical physics represents processes over a ‘period of time’ as in Newton's differential equations. We have to square the wave-function Ψ² representing the radius being squared r² because the process is relative to the two-dimensional spherical 4π surface. We then see 4π in Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π representing our probabilistic temporal three dimensions life. The charge of the electron e² and the speed of light c² are both squared for the same geometrical reason. This process forms a continuous exchange of energy forming what we experience as the continuous passage of time.

Bosons (photons) are particles whose wave function is symmetric (spherical) under such an exchange or permutation, so if we swap the particles, the wave-function does not change. Fermions (electrons) are particles whose wave-function is antisymmetric, so under such a swap the wave-function gets a minus sign, meaning that the amplitude for two identical fermions to occupy the same state must be zero. This is the Pauli Exclusion Principle: two identical fermions cannot occupy the same state.

This gives rise to the structure and complexity of our three dimensions with this process forming intrinsic magnetic moments that give rise to the macroscopic effects of magnetism, electric charges, such as electric currents and other phenomena, such as electron paramagnetic resonance.  

The spherical surface forms a dynamic two-dimensional manifold for the movement of positive and negative charge. This two-dimensional manifold also forms the two-dimensional aspect within each reference frame in the form of a past and uncertain future, the so-called four dimension of time that we have in Special Relativity. Whenever there is change in our everyday life there is the movement of charge. When object touch it is charge that makes contact and when the bonds between the atoms form and break, there is an exchange of photon energy with the movement of charge. We have an uncertain future continuously unfolding with each photon electron coupling of dipole moment.

A process of spherical 4π symmetry forming and breaking would also form the potential for entropy or disorganization with a built-in potential forever-greater symmetry formation that we see in the complexity of cell life and in the potential forever more abstract mathematics.

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