Time Field Theory XIX: Quantum Tunneling from First Principles — Strict Separation of Electric-Phase Coupling and Mass-Phase Locking

This work is the nineteenth installment in the Time Field Theory (TFT) series, succeeding Time Field Theory XVIII: Entanglement, Common Phase Splitting, and the Local Interpretation of Bell Experiments. This work presents a fully transparent, first-principles physical framework with no black-box operations or uninterpreted postulates. All dynamical processes are derived deterministically from time-field axioms, with clear, traceable physical mechanisms at every step. Within the TFT framework, quantum tunneling is derived without reliance on conventional quantum mechanics or probabilistic interpretation. Two fundamental mechanisms are distinguished: (1) electric potential coupling responsible for phase modulation, interference, and tunneling attenuation; (2) mass/time-field gradient responsible for phase locking, measurement, and localization. Tunneling is interpreted as deterministic time-field splitting rather than probabilistic selection: a portion of the time-field oscillation is retained inside the barrier with real energy deposition, while the remainder transmits. The tunneling transmission coefficient is verified against experimental data and shows quantitative agreement. A 2025 observation of under-barrier recollision supports real interactions inside the barrier, consistent with TFT. This work contributes to the unification of gravity, special relativity, and quantum mechanics within a self-consistent, locally realistic, and fully transparent time-field dynamics framework.