Time Emergence and Local Temporal Degrees of Freedom: A Unified Spacetime Theory, Rigorous Mathematical Derivation and Complete Experimental Scheme

There exists an irreconcilable fundamental logical conflict spanning over a century between the four-dimensional curved spacetime framework of general relativity and standard quantum mechanics. Existing theories cannot self-consistently explain the systematic frequency drift anomalies continuously observed in modern high-precision optical lattice atomic clocks, nor unify macroscopic gravitational dynamics and microscopic quantum nonlocal correlation at the fundamental physical level. Based on fully inheriting all core conclusions of relativity and quantum mechanics firmly verified by experiments, this paper does not subvert the classical paradigm but reconstructs the fundamental spacetime postulates and the essence of time, proposing a unified spacetime theoretical system centered on local temporal degrees of freedom. This paper strictly defines two dimensionless core physical quantities: spacetime coupling strength α and intrinsic recursive locking coefficient β. It constructs a modified gravitational-matter field action compatible with three-dimensional flat spacetime and satisfying general covariance and Lorentz covariance. Starting from the modified action, via the standard variational principle, tensor contraction and asymptotic simplification under limits, the Einstein field equations are rigorously derived step-by-step in the classical macroscopic limit α→1.β→0. Meanwhile, starting from the representation of local proper time evolution, the evolution operator and Schrödinger equation of standard quantum mechanics are fully recovered, proving the self-consistency, compatibility and asymptotic degradability of the proposed theory with established physical theories. The core proposition of this theory is that physical space is an objective rigid three-dimensional Euclidean flat space without traditional spacetime curvature or dimensional coupling; time is not an innate fourth spacetime dimension, but a macroscopic emergent dynamical representation generated jointly by the coupling between material systems and the cosmic background spacetime and by the internal periodic recursive evolution of systems. The local time scaling factor is uniquely determined by α and β. Without introducing extra dimensions, hidden variables, redundant elementary particles or unfalsifiable assumptions, the theory uniformly explains cross-scale physical phenomena including gravitational time dilation, kinematic time dilation, quantum entangled nonlocality, systematic drift of atomic clocks, and human subjective time perception. Two implementable, quantitatively predictive and strictly falsifiable precision experimental schemes are presented: the weak-coupling shielding atomic clock drift control experiment and the lunar independent clock one-way speed of light measurement experiment. This work provides a logically self-consistent, mathematically rigorous and experimentally verifiable fundamental physical paradigm for resolving the quantum-gravity unification dilemma and reconstructing the physical essence of time.