Quantum Equations from Temporal Field Geometry: Deriving Schrödinger and Dirac Dynamics from Scalar Time

This unified paper derives both the Schrödinger and Dirac equations from the internal dynamics of a scalar temporal field , without relying on traditional quantum postulates. In this model, particles emerge as oscillating temporal vortices whose frequencies define their mass and energy. The Schrödinger equation is recovered as a non-relativistic limit of coherent temporal structures, while the Dirac equation arises naturally when incorporating Lorentz covariance and spinor coupling. This approach provides a novel geometric origin for quantum behavior, predicts particle properties from temporal oscillations, and bridges quantum mechanics with spacetime geometry through a unified scalar field framework.