Five-Dimensional Hydrodynamic Spacetime: Time Density and Dark Energy Complementarity

We propose a theoretical framework in which time is treated as a physical substance characterized by a density field ρtime(x, t). This “hydrodynamic spacetime” theory introduces a complementarity principle between time density and dark energy density: ρtime ×ρDE = E²₀ , where E₀ is a universal energy scale. Time density is interpreted as potential energy, while dark energy is understood as the maintenance cost required for space to exist.By formulating this theory in a five-dimensional spacetime with coordinates (x, y, z, w, t), where w represents the geometric manifestation of time density, we derive observable consequences including gravitational time dilation and provide a geometric foundation for energy-momentum relations. From the metric, we derive the layer-dependent light speed c(w) = (w/w₀)c₀, which serves as the basis for many consequences of this theory.The theory successfully reproduces known effects such as GPS time dilation (∆τ /τ ∼ 10−⁹) and is consistent with general relativity in the weak-field limit.As cosmological implications, we present a conservation law for time density in an expanding universe, a computational framework for five-dimensional proper time,and a new picture of the temporal evolution of the universe. We also discuss the distinction between two types of boundaries in black holes—the electromagnetic event horizon and w = 0—and their implications for the information paradox.The quantum mechanical implications of this framework are developed in Paper II. Dark matter and physical constant evolution are addressed in Paper III.