Testing Information-Gauge Entanglement Couplings with Hydrogenic Spectroscopy

This preprint develops a hydrogenic precision-spectroscopy test of information-gauge entanglement couplings in the framework of IG–RUEQFT. Motivated by recent proposals for wormhole-mediated entanglement tests in hydrogen, the work formulates a local alternative in which entanglement-sensitive subsystem data act as a source for a conserved information current (J^μinfo) coupled to a massive Stueckelberg (U(1)Λ) field (Λμ). After integrating out the information-gauge field in the short-range regime, the resulting low-energy description yields three experimentally distinguishable response classes: a hyperfine frequency shift, a neutrality-preserving phase anomaly, and a prepared-state spin-entanglement response. In a minimal spin-contact realization, the relevant relative entanglement matrix elements are computed explicitly, giving (Δ Iₜᵣᵢ=1) for the prepared (m_F=0) versus (m_F=±1) triplet response and (Δ IS- T=2/3) for a singlet–unpolarized-triplet comparison. The manuscript presents benchmark sensitivity estimates in the ((m_Λ,g_Λ)) plane using hydrogen 21-cm spectroscopy, atomic neutrality, muonium hyperfine spectroscopy, positronium hyperfine spectroscopy, and projected hydrogen-maser/Ramsey and leptonic-atom improvements. The plotted curves are benchmark reaches rather than model-independent exclusions. Charge-screening realizations are strongly constrained by atomic neutrality, while neutrality-preserving phase-only and spin-selective realizations motivate dedicated tests using masers, Ramsey protocols, isotope comparisons, muonium, and positronium. No experimental data were generated in this work. The Python source code used to generate Fig. 1 is available separately at Zenodo, doi:10.5281/zenodo.20538702. KeywordsIG-RUEQFT; information-gauge theory; hydrogen spectroscopy; 21-cm line; entanglement; Stueckelberg field; quantum information; muonium; positronium; atomic neutrality; Ramsey spectroscopy; precision tests; quantum field theory; wormhole-mediated entanglement