Apr. 13, 2020

De Broglie's hypothesis provides an elegant and compelling solution for the integer number of wavelengths in a given electron orbit or energy level. The discrete energy levels themselves, indicated by the primary quantum number, follow from a volumetric principle and are not proven by de Broglie. Schödinger's wave equation is used to solve this, however only up to a single orbit or Hydrogen eigenstate at a time, whereas the probabilistic interpretation is a cause of great dissatisfaction.

As shown, the Formal stage of the bifurcative self-interaction (as per the 4C/TAM/QFT model), when synchronized, facilitates dimensionalization or self-localisation. The latter in this case is however still somewhat theoretical. The self-localized state is characterized by self-reference, that is, the principal bifurcation and the physical bifurcation have become the same, but only so far in principle. The self-reference, when taken as an actual bifurcation, constitutes the Final stage.

Thus the Final stage constitutes the actualized self-reference, whereby the final bifurcation pattern confirms that the synchronized bifurcation is indeed self-referent. This confirmational pattern of the Final stage is the Hydrogen eigenstates.

In terms of a spherical potential well, the Hydrogen eigenstates constitute a self-consistent volumetric, surface and radial bifurcation. In terms of TAM, the Triple Attributional Matrix, the eigenstates represent the TAM permutations.

A more generalized approach of 4C/TAM/QFT follows from the assumption that time and space are not fundamental. The field's bifurcative action is geometric in nature, and so there exist no a priori physical (wave) media. Instead, the scaling ratio of the geometrized self-interaction can vary and this accounts for the formation of conformational patterns. In other words the medium is implied in the geometry of the interaction, the interaction is not defined by any pre-existing medium.

The 2 main scaling ratio's are those which create the confirmational patterns of the Formal and Final stages. The Formal stage is fractal, optimized by scaling ratio Phi (Golden ratio, 1.618), the Final stage is arithmetic, optimized by scaling ratio 2. Also, the Formal stage is confined, the Final stage is de-confined.

It should be noted that the self-consistency of the Final Stage is rather satisfactory, suggesting that physics is complete. Technically speaking, it provides no incentive to look for a Formal Stage resp. - Cause. The only incentive is the dissatisfaction with the probabilistic interpretation, as a dubious placeholder for real quantum determinism. This self-consistency however is deceptive, because it silently presumes that time and space are fundamental. Without the latter, there is an instantaneous need for a Formal principle to make physics complete. Here it is shown how the fractally scaled Formal aspect and the arithmetic Final aspect constitute the mutually concommitted confirmational patterns of physical media.

A third important bifurcative scaling ratio is proposed (sqr(3)), associated with the electroweak interaction in QFT, that is, the Intermediary stage. All 3 functional scaling ratio's are directly visible in the Quantum Geometry of Color.

That is, the human visual spectrum spans and truly identifies the spectrum of creation at a fundamental level.

Conclusion: Hydrogen eigenstates are the confirmational pattern of the self-reference of the quantum field's synchronized self-interaction.