Quantum Gravity and String Theory |
Authors: Aaron Lee Alai
We present a unified theoretical framework — Displacement Spacetime (DST) — in which all fundamental interactions emerge from two geometric axioms: mass is the radial displacement of spacetime, and charge is its rotational displacement. The framework originates in an exact mathematical identity connecting moiré interference patterns to measurements of the quantum Wigner characteristic function [1], numerically verified against five published quantum state experiments to six decimal places.From these two axioms, supplemented by the topology of SO(3) and the geometry of the displacement manifolds, the following results are derived without free parameters: the fine structure constant α = 3/(8 ln(m_Pl/m_e)) to 0.27% at one loop; three generations of matter from the Euler characteristic of CP²; sin²θ_W = 3/8 from SU(5) selection; the Koide lepton mass relation to 0.001%; the proton-to-electron mass ratio m_p/m_e = 6πu2075 to 0.002%; the CP violation phase δ_CP = arctan(8/π) to 0.28%; dark matter mass m_DM = m_e = 511 keV from rotational-radial coupling; the strong coupling α_s × ln(m_Pl/m_e) = 2π/ln(2πu2075) to 0.39% at the Planck scale; the weak coupling α_W × ln(m_Pl/m_e) = 1 from EM and the Weinberg angle; and spin-1/2 uniqueness for all fundamental charged matter from three independent proofs. All four fundamental couplings are now derived from two independent geometric measures.A 0.27% residual appears consistently across multiple independent calculations. This residual is identified as a self-referential correction: α corrects the formula that determines α. The exact corrected formula is α = (3/8)/(ln(m_Pl/m_e) − 9/64), accurate to 0.002%. The consistency of this single correction across all predictions constitutes the principal structural evidence for the framework's validity. Falsifiable experimental predictions are catalogued, including a dark matter detection cross-section and deviations from Standard Model neutrino mixing.
Comments: 52 Pages.
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