First-Principles Derivation of the Fine Structure Constant: A Theory Based on Lorentz-Covariant Tensor Fields and Self-Consistent Harmonic Cascades

Abstract This paper presents a theoretical framework aimed at deriving the fine structure constant 𝛼 from first principles. The framework is based on a Lorentz-covariant ”Spacetime Elec?tromagnetic Tensor Field” (EBT), whose constitutive tensor (𝜆, 𝜅) describes the possible nonlinear response of spacetime under strong fields. The EBT constitutive tensor (𝜆, 𝜅) can be interpreted as a higher-order extension of vacuum polarization in strong fields, with mag?nitudes compatible with QED two-loop corrections (|𝜅/𝛼 2 | ∼ 10−8 ). This work truncates to third-order terms, as their contributions dominate the correction to 𝛼. We demonstrate that, within an idealized standing-wave field configuration possessing specific symmetry (𝑙 = 1 spherical dipole), the covariant boundary conditions spontaneously generate an infi?nite yet rapidly convergent harmonic cascade (convergence rate 𝛾 ≥ 0.22). The derivation of how the amplitude of each harmonic order is analytically predicted from the covariant tensor constitutive relations of EBT is provided. The collective feedback of these harmon?ics determines a dimensionless, unique, and stable field drift velocity 𝑥 = 𝑣/𝑐. By making the theory completely dimensionless, the solution process transforms into a system of cou?pled transcendental equations, whose solution (𝜇 ∗ , 𝑥∗ ) is determined solely by the internal structure of the theory. We postulate 𝛼 ≡ 𝑥 ∗ . By computing the harmonic cascade up to the 1/1024 wave (𝑚max = 1024) and employing simulations with 20,000-digit precision, this theory predicts 𝛼 −1 = 137.0359991770010. This prediction agrees with the latest ex?perimental value at the 10−15 level. Its high-order behavior suggests that 𝛼 −1 may be an irrational number, offering a new perspective for understanding its origin