An Interior Observer's Holonomic Cosmology

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Abstract

General relativity and quantum field theory divide the world into geometry and matter. We demonstrate that the Lorentz symmetry shared by both theories is sufficient to challenge this duality: the bivector generators that govern spinor propagation in the Dirac equation simultaneously govern how spacetime frames compose in the tetrad formulation of general relativity. When the spin connection acquires nontrivial holonomy in a compact conjugacy class, boost--rotation noncommutativity ($[K_i,K_j] = -\epsilon_{ijk}J_k$) forces the configuration to cycle internally at a rate set by the confinement scale---identifying the Compton frequency with geometric confinement. We construct explicit Einstein--Dirac solitons realizing this mechanism: a massless five-dimensional spinor acquires mass $m_n = |n|\hbar/(cR_0)$ from a discrete topological sector, with no mass parameter in the fundamental Lagrangian. Because matter \emph{is} wound geometry, observers built from it cannot access their absolute gravitational depth---only derivatives and ratios of $\ln\alpha$. The physically meaningful content of those ratios can be packaged covariantly: a depth functional $\mathcal{N}(\tau)$ built from holographic-screen areas is strictly monotone by the Bousso--Engelhardt area theorem, and its projection onto void and wall congruences yields $C(a) = \sqrt{A_w/A_v}$---the lapse-drift variable at the center of Wiltshire's timescape cosmology---reinterpreting cosmic acceleration as an interior-calibration effect within unmodified general relativity.

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