Temporal Coherence Shear in Bound Matter: A Time-Scalar Field Theory Interpretation of the Migdal Effect

Recent experimental results have reported a statistically significant direct observation of the Migdal effect, wherein atomic electron emission accompanies sudden nuclear recoil induced by interaction with a neutral projectile. Conventional quantum-mechanical treatments model this as a non-adiabatic perturbation of electronic states under rapid displacement of the nuclear Coulomb potential, yielding accurate transition probabilities but offering limited physical explanation for why temporal response inside bound matter is non-instantaneous. Time-Scalar Field Theory (TSFT) proposes that time is a physical scalar field whose local density, gradients, and coherence properties govern persistence and stability of matter. Within this framework, atoms are composite coherence structures stratified across scalar-time response layers. We reinterpret Migdal emission as a manifestation of temporal coherence shear: abrupt nuclear scalar-time displacement exceeds the rephasing capacity of the electronic coherence field,inducing transient decoherence that can be resolved as electron ejection. This interpretation reframes Migdal-sensitive detectors as probes of internal temporal geometryrather than solely recoil-energy transducers. We present a minimal TSFT shear formalism and outline falsifiable predictions, including material-dependent temporal stiffness, orbitalselective emission scaling, and potential coherence-echo signatures relevant to sub-GeV dark matter and ultra-weak interaction searches.