Electrodynamics
MatureFine Structure Constant
The fine-structure constant α ≈ 1/137.036 from Weber electrodynamics. Multiple derivation approaches investigated. Wave-mechanical power-law α¹ scaling confirmed [E]. Full first-principles derivation is [M].
The fine-structure constant is the dimensionless coupling constant of electromagnetism, with a value of approximately . It is fundamental to atomic physics, QED, and atomic structure predictions, yet its numerical value remains one of physics' greatest mysteries.
The fine-structure constant
In the CPT approach, emerges from the ratio of the Weber coupling to the geometric factor of the Clifford torus.
Confirmed Wave-Mechanical Scaling [E]
The wave-mechanical sub-wavelength dipole source coupling gives a power-law scaling. This result is firmly established and banked as of August 2026.
Wave-mechanical scaling result
Full Geometric Derivation [M]
The full first-principles derivation remains a mature work in progress. The leading-order estimate gives where is the torus knot radius and is the Hopf fibre circumference. This estimate yields approximately , but the precise geometric mechanism requires further formalization.
Multiple approaches are under investigation:
- Direct Weber coupling ratio
- Geometric ratio of curvature scales
- Wave-mechanical dipole coupling (confirmed [E] at leading order)
Notably, CPT reproduces the same Sommerfeld fine-structure splitting in hydrogen-like atoms directly through the Weber force acceleration terms.
Source Documents
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