The Time Wave Field: A Dynamical Scalar Field Model of Time at the Quantum Scale Corrected and Expanded Version

Abstract

This paper presents a unified theoretical framework where time is formulated as a dynamical scalar field τ (x), originating from the intrinsic zitterbewegung fre- quency (ωC ≈ 1.55 × 1021 Hz) of quantum matter. We provide a General Relativity (GR)-compatible action and derive the field equations. By integrating out the τ field fluctuations via the Schwinger-Keldysh formalism, we obtain the emergence of classical coordinate time and predict fundamental decoherence effects. Furthermore, we present a geometric mechanism for dark-matter-like gravitational effects arising from topological phase defects in the internal time field. Numerical Monte Carlo simulations of 104 electron trajectories reveal an intrinsic phase bias at the 10−8 rad scale, offering falsifiable predictions for next-generation matter-wave interferometry and optical lattice clock networks. This framework bridges the Dirac electron clock with the macroscopic temporal flow of General Relativity.