Emergent Time: A Causal-Structural Time Field Coupled to Matter

We propose an extension of General Relativity (GR) in which time is not an independent background dimension but couples dynamically to the presence of matter and propagates outward at the speed of light. Formally, we introduce a scalar causal field Θ(x) ∈ 0,1, determined entirely by the retarded action of matter distributions and carrying no independent energy density. The spacetime metric is modified by weighting its time component with Θ, so that in matter-free regions the temporal structure collapses. Both GR and Special Relativity (SR) are recovered as exact limiting cases for Θ = 1. The theory makes qualitatively new predictions for cosmic voids, type-Ia supernova light curves, and the expansion dynamics of the universe, and provides a potential mechanistic replacement for the cosmological constant Λ.