This preprint develops a refined TDF-QM formulation within the Time Delay Field (TDF) framework, focusing on the interpretation of quantum phase as a temporal-phase rotation. The central proposal is that the TDF quantum variable (N_t) should be interpreted not as the phase angle itself, but as the local angular rate of temporal-phase rotation, (N_t=\dot{\theta}\tau). Under this definition, the quantum phase becomes (\theta\tau=\int N_t dt), while the standard quantum relation (E=\hbar \omega) is reinterpreted as (E=\hbar N_t).
The paper examines how this definition aligns with core structures of nonrelativistic quantum mechanics, including the wavefunction (\psi=\sqrt{\rho}e^{-i\theta_\tau}), Schrödinger phase evolution, de Broglie momentum, interference, decoherence, uncertainty relations, rest mass as internal phase rotation, and entanglement as temporal-phase locking. In this formulation, Planck’s constant is interpreted as the conversion factor between temporal-phase rotation and physical action/energy, with (h=E_qt_q) representing the action associated with one complete fundamental time-phase cycle.
The work is intended as a conceptual and mathematical bridge between the broader TDF program and effective quantum mechanics. It does not claim a complete derivation of the Standard Model, spin, charge, or quantum field theory, but identifies which standard QM relations are structurally compatible with the TDF time-phase-rate interpretation and which areas require further development.
This work builds on the TDF framework and references the related Zenodo record: https://doi.org/10.5281/zenodo.20633775.
Publication Date: 2026-06-13