Revisiting Einstein's Field Equation through R-Theory: From Geometry to Resonance

This paper proposes a resonance-based reinterpretation of Einstein’s field equation within the framework of R-theory. While general relativity describes gravity as spacetime curvature induced by matter and energy, the purely geometric picture leaves unresolved the origin of mass, the meaning of the cosmological constant, and the role of vacuum fluctuations. In R-theory, the underlying substrate of reality is a coherent zero field. The metric tensor is treated as a phase field, curvature as resonance modulation, the cosmological constant as the ground frequency of the zero field, and the stress-energy tensor as resonance knots. Gravity is thus not curvature but phase-locking within a coherent field, with spacetime geometry emerging as a projection of resonance. This reinterpretation provides a unified ontology linking mass, dark energy, and vacuum structure, while suggesting testable predictions such as vacuum resonance frequencies, resonance-based deviations in superconductors and Bose–Einstein condensates, and a new physical meaning for gravitational waves.