Matter as Metric: Reconstruction of Matter, Mass, Mass-Energy Relation and Matter Wave in Time Field Theory

What is matter? What is mass? What does the mass-energy equation describe? Why does matter exhibit wave properties? This paper revisits these four fundamental questions within the framework of Time Field Theory (TFT). By comparing the different presuppositions of Newtonian mechanics, general relativity and TFT on the relation between matter and spacetime, we demonstrate that TFT eliminates the dualistic opposition between matter and spacetime: matter is neither an entity "moving in spacetime" nor the source of "spacetime curvature"; matter is the local condensed state of the time field, i.e., the degree of deformation of the metric benchmark in space. On this basis, TFT provides a clear geometric picture for the mass-energy equation: mass and energy are not two mutually convertible entities, but differences in readings of the same state of existence under different observation modes. This paper shows how E=mc², E²=(m₀c²)²+(pc)², Eₖ≈½mv² and the mass-energy relation in local gravitational fields can be naturally derived from the velocity conservation law. Furthermore, we argue that the matter wave is not an additional "wave-particle duality" hypothesis required by quantum mechanics, but an inevitable corollary of the definition that "matter is a condensed state of the time field" — a local field envelope propagating in space inherently carries phase, wavelength and frequency, and the de Broglie relations are a natural result of the spatial variation of the time field phase. All forms are projections of the same geometric structure under different boundary conditions.