Golden Angle to Quantum Oscillators: Fibonacci Operators in Supersymmetric Hierarchies — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The golden angle (137.507°…) emerges from the golden ratio as the irrational rotation that maximises packing efficiency in phyllotaxis; a recent arXiv paper extends this to a quantum calculus of "golden oscillators" with Fibonacci divisor operators, linking golden-ratio spectra to supersymmetric hierarchies. MATH: - Golden angle: \( \theta = 360^\circ \times (1 - 1/\phi) = 360^\circ \times (2 - \phi) = 360^\circ \times (3 - \sqrt{5})/2 \approx 137.507764^\circ \). - Equivalently: \( \theta = 2\pi / \phi^2 \) radians (since \( \phi^2 = \phi + 1 \), \( 1/\phi^2 = 2 - \phi \)). - Fibonacci divisor operator (from arXiv 2410.04169): \( \hat{D}_F = \frac{q^{\hat{N}} - q^{-\hat{N}}}{q - q^{-1}} \) with \( q = \phi \) (golden base) or \( q = \sigma \) (silver ratio \( 1+\sqrt{2} \)), acting on Fock space. Binet form: \( F_n = (\phi^n - (-\phi)^{-n})/\sqrt{5} \) generalised to operator level. - Golden oscillator energy spectrum: \( E_n \propto \phi^{2n} \) or \( \phi^{-2n} \) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7219731598
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