A Parameter-Free Derivation of the Fine-Structure Constant from Information-Theoretic Constraints in Octonionic Space
POSTER
Abstract
The fine-structure constant α ≈ 1/137 remains unexplained within the Standard Model, appearing as a free parameter fit to experiment. We present a complete first-principles derivation yielding α⁻¹ = 137.035999143, achieving 1.62σ agreement with CODATA 2022 (137.035999177 ± 0.000000021) using zero adjustable parameters.
Our approach treats electromagnetic coupling as the channel capacity of information flow between an 8-dimensional octonionic computational substrate and 4-dimensional spacetime. The derivation proceeds through four mathematically necessary components: (1) combinatorial base capacity of 137 channels from (8 choose 4) × 2 − 3 ternary corrections; (2) rotational phase-space normalization of 1/(8π) from octonionic structure; (3) discrete-to-continuous projection loss quantified by the Euler-Mascheroni constant γ; and (4) third-order lattice corrections via Apéry's constant ζ(3). A logarithmic memory term depending on cosmic phase parameter n ≈ 8.07 × 10⁶⁰ reflects 720° spinor cosmology, where α and α⁻¹ occupy conjugate positions.
The framework predicts gravitationally-dependent variation Δα/α ≃ (4.60 ± 0.15) × 10⁻¹⁶ km⁻¹, testable with current optical lattice clock technology achieving 10⁻¹⁹ fractional frequency stability. We propose experimental protocols using ⁸⁷Sr or ¹³³Cs transitions measured at sea level and high altitude (>5 km) to detect the predicted 10⁻¹⁵ level shifts. A null result would falsify the 8D→4D projection mechanism.
This demonstrates that α emerges from mathematical necessity, specifically, from maximal reversible information exchange under octonionic constraints, rather than arbitrary parametrization. The same framework generates other fundamental constants (π, e, φ) from a 42-element basis proven complete by Fano-plane enumeration. If validated, this approach suggests the Standard Model's 26 free parameters may similarly derive from information-theoretic first principles, potentially unifying quantum field theory with discrete computational foundations.
Our approach treats electromagnetic coupling as the channel capacity of information flow between an 8-dimensional octonionic computational substrate and 4-dimensional spacetime. The derivation proceeds through four mathematically necessary components: (1) combinatorial base capacity of 137 channels from (8 choose 4) × 2 − 3 ternary corrections; (2) rotational phase-space normalization of 1/(8π) from octonionic structure; (3) discrete-to-continuous projection loss quantified by the Euler-Mascheroni constant γ; and (4) third-order lattice corrections via Apéry's constant ζ(3). A logarithmic memory term depending on cosmic phase parameter n ≈ 8.07 × 10⁶⁰ reflects 720° spinor cosmology, where α and α⁻¹ occupy conjugate positions.
The framework predicts gravitationally-dependent variation Δα/α ≃ (4.60 ± 0.15) × 10⁻¹⁶ km⁻¹, testable with current optical lattice clock technology achieving 10⁻¹⁹ fractional frequency stability. We propose experimental protocols using ⁸⁷Sr or ¹³³Cs transitions measured at sea level and high altitude (>5 km) to detect the predicted 10⁻¹⁵ level shifts. A null result would falsify the 8D→4D projection mechanism.
This demonstrates that α emerges from mathematical necessity, specifically, from maximal reversible information exchange under octonionic constraints, rather than arbitrary parametrization. The same framework generates other fundamental constants (π, e, φ) from a 42-element basis proven complete by Fano-plane enumeration. If validated, this approach suggests the Standard Model's 26 free parameters may similarly derive from information-theoretic first principles, potentially unifying quantum field theory with discrete computational foundations.
Presenters
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Christian R Macedonia M.D.
- University of Michigan- Ann Arbor