What question did this study set out to answer?

This research aims to derive the fine-structure constant using a single consistency condition and explore its implications for dark sector interactions and condensed matter physics.

June 27, 2026Open Access

Motti Intermediate Physics: Derivation of the Fine-Structure Constant from a Single Consistency Postulate, a No-Go Theorem for Coherential Interactions in Condensed Matter, and the Computational Programme for Dynamical Gap Closure

Key Points

This research aims to derive the fine-structure constant using a single consistency condition and explore its implications for dark sector interactions and condensed matter physics.
The fine-structure constant is derived from the HAL framework using exact algebraic methods without fitted parameters.
A no-go theorem is established regarding cooper pairing in the dark sector of condensed matter systems.
A computational programme is proposed incorporating effective one-body methods and numerical relativity techniques.
The fine-structure constant is derived with 4 parts per million accuracy compared to CODATA 2022.
A unique quantization integer n=27 is identified, connecting SO(4) degeneracy and internal Z_3 multiplicity.
The dark sector cannot produce cooper pairing in condensed matter, leading to a repulsive effective interaction suppressed by 10^-24 eV.

Abstract

The electromagnetic fine-structure constant alphaₑm = 1/137. 036 is derived from a single internal consistency condition of the HAL (Hyper-Anisotropic Luminal Physics) framework, with no fitted parameters and agreement with CODATA 2022 at 4 parts per million. The derivation proceeds through an exact algebraic chain fixing the quartic coupling lambda = 8*pi/9, the instanton action Sᵢnst = 3*pi, the functional determinant TrD*V'' = 6 (Watson 1944), and the renormalization coefficient betaRG = 2/pi. The quantization integer n=27 is shown to be unique: it is the product of the SO (4) degeneracy of the l=2 instanton level (d=9) and the internal Z₃ multiplicity of the complex coherential field (dim=3). From the same postulates, Gₑff = GN/C₀ and a universal gravitational spin-memory correction epsilon = +alphaₑm = +0. 7297% are derived exactly. The prediction is universal, positive, and falsifiable with LIGO O5, LISA and the Einstein Telescope. A rigorous no-go theorem establishes that the dark sector of HAL cannot produce Cooper pairing in any condensed matter system. Exact path integration over dark sector modes yields a ghost mediator with Planck-scale pole (kₚolo = 0. 958 MPlanck) and negative residue (ZD = -0. 00657), generating a repulsive effective interaction suppressed by 10^-24 eV at material scales. Unitarity is preserved by the Lee-Wick mechanism; macroscopic causality is preserved by Yukawa decay at sub-Planckian scales. The dark sector acts as a natural UV regulator that decouples universally from sub-Planckian physics. The dynamical confirmation of Jₜotal = C₀² * JGR remains an open problem. A concrete three-stage computational programme is proposed: effective one-body (EOB) methods for the inspiral, numerical relativity (BSSN/Z4c) for the merger, and an extended Teukolsky equation coupling gravitational perturbations to the coherential Xi operator for the ringdown. All three stages converge on the same observable: the gravitational spin-memory effect at epsilon = +0. 7297%.

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