Field–Dependent Geometry of King Plots and Atomic Clocks as Probes of Internal Structure

This article proposes a minimal, experimentally accessible extension of precision atomic clock spectroscopy in which King plots are used as active probes of internal atomic structure rather than as passive consistency checks. Building on recent observations of significant nonlinearity in multidimensional King plots, the work argues that isotope shifts encode information about more than two independent internal degrees of freedom. External electric and magnetic fields are treated as controlled probes that selectively modify these internal contributions through well-known Stark and Zeeman couplings. The central prediction is that the geometry of King plots, including slopes, curvature, and planarity, should change systematically and non-additively when isotopes, electric fields, and magnetic fields are varied independently and in combination. Such field-dependent geometric behavior provides a clear, falsifiable signature of a higher-dimensional internal structure underlying atomic transition frequencies. The proposed framework is model independent at the experimental level and can be tested with existing optical clock technology, while offering a natural interpretation within geometric approaches to atomic structure.