UNIFIED TIME-MASS-ENERGY THEORY (ToE)

This work presents and develops the Unified Time-Mass-Energy Theory (UTMET), which proposes that time is not an independent four-dimensional coordinate but rather the geometric manifestation of local entropy density at the macroscopic scale. At the core of the theory lies the identity T ≡ S: the characteristic macroscopic timescale of a system is equivalent to its local entropic state. A new dynamic scalar field S (x^μ) is introduced, and the Time Field Tensor Z_μν derived from it is added to Einstein's field equations, yielding the extended system G_μν = 8πG (T_μν + Z_μν). Within this theoretical framework, we derive: (i) the M = mc³ micro-to-macro mass scaling relation; (ii) the Time Field Wave Equation — a Klein-Gordon form obtained from the Action Principle applied to the scalar field; (iii) a dynamic cosmological constant Λ (t) ; (iv) a quantum-gravity bridge at the Planck scale; and (v) the singularity origin of universal quantum entanglement. Two independent numerical simulations — a chaotic three-body system and a galactic rotation curve — validate the theoretical predictions. A single dynamic scalar field simultaneously accounts for the two greatest anomalies in modern astrophysics: dark matter and dark energy. No cold dark matter particle hypothesis and no static cosmological constant are required. The paper concludes with concrete falsification criteria and observational test proposals.