Existence of a Dynamical Time Field in the Wheeler–DeWitt Formalism

This work presents a minimal canonical extension of the Wheeler–DeWitt (WDW) framework by introducing an explicit scalar time field Θ(x) with conjugate momentum, restoring intrinsic dynamical evolution without introducing an external background time parameter. The standard WDW equation is recovered as an equilibrium limit in which functional gradients of Θ vanish, while non-equilibrium configurations yield field-driven temporal flow. The formulation preserves spatial diffeomorphism invariance and maintains the canonical constraint structure required by Dirac quantization. The time-field coupling is regulated by a dimensionless constant χ≈0.551, treated here as an effective input parameter motivated by prior Chronos-related work. The result establishes that a dynamical time degree of freedom can exist consistently within the canonical Wheeler–DeWitt formalism.