This paper represents Part VIII of the comprehensive research series on the Higher-Derivative Lee-Wick (HDLW) Theory, which reconstructs the Standard Model and Gravity from a single scalar progenitor governed by Split-Quaternionic Algebra (H_). In this installment, we address the unification of Quantum Mechanics and General Relativity by proposing that spacetime geometry is not a fundamental entity but an emergent optical phenomenon arising from the scalar vacuum. Building upon the UV-finite framework established in Parts I-VII, we derive the following key results: Algebraic Origin of Lorentz Symmetry: We demonstrate that the Lorentz algebra SO (1, 3) arises naturally as the automorphism group of the internal Split-Quaternionic state space, with the speed of light c emerging from the Berry connection. Optical Gravity: We propose a model where the gravitational field is described as the refractive index of the vacuum, n (r) = (-/c²). We show that this scalar-optical approach reproduces the Schwarzschild metric in isotropic coordinates in the weak-field limit. Classical Tests of GR: The optical metric correctly predicts light deflection and the perihelion precession of Mercury, resolving the historical difficulty of scalar gravity theories in matching observation. Resolution of Singularities: We suggest that the central singularity of black holes is resolved by a ghost-condensation mechanism at the fundamental Lee-Wick scale (M 11. 3 TeV), forming a stable "Black Droplet" instead of a singularity. Thermodynamics: We provide a new interpretation of the Third Law of Thermodynamics, where zero temperature corresponds to the perfect cancellation of observable degrees of freedom by ghost modes. This work suggests that gravity is not a distinct fundamental interaction but a macroscopic manifestation of the same scalar field that constitutes matter and gauge forces, completing the unification program of the HDLW theory.
Masayuki Note (Mon,) studied this question.