This paper proposes a geometric explanation for nonlinearities observed in multidimensional King plots of atomic isotope shifts. Within the Methane Metauniverse (MMU) framework, spacetime is modeled as a dual-tetrahedral elastic lattice with internal deformation modes. Atomic transitions couple to different combinations of these internal modes, and isotope substitution slightly modifies the internal lattice scale. This leads naturally to second-order corrections in transition frequencies and produces measurable curvature in King plots. Starting from the stiffness matrix of the internal geometry, the paper derives the eigenvalue structure of the internal oscillations and shows how cross-coupling between deformation modes generates nonlinear contributions to isotope shifts. The resulting King-plot curvature is directly related to the cross-coupling matrix and therefore reflects internal geometric dynamics rather than requiring additional new interactions. The model predicts that the magnitude of King-plot curvature scales approximately with the square of the nuclear charge and provides quantitative estimates for several atomic species. Curvature ratios between different elements follow a simple parameter-free relation depending only on nuclear charge, allowing direct experimental tests. Application to ytterbium optical clock transitions yields curvature estimates consistent with recent high-precision isotope-shift measurements. The framework therefore provides a geometric mechanism that can naturally account for observed King-plot nonlinearities while generating testable scaling relations across atomic systems.
Jurgen Wollbold (Thu,) studied this question.