The Law of Gravity in TFM: Unifying Time Wave Compression, Space Quanta Merging, and the Critical Radius

This paper presents the Time Field Model (TFM), a unified theory of gravity where gravita tional attraction arises from time wave compression by mass-energy. We introduce space quanta merging to explain why quantum-scale objects (e.g., electrons) exert negligible gravity, while macroscopic aggregates (e.g., stars) significantly warp spacetime. A critical radius rc demarcates the quantum-to-classical transition, modeled via a logistic function. Observational validation includes the Sun’s extended gravitational sphere (∼ 1.059 × 109 m), galactic rotation curves matching SPARC data without dark matter, and black hole entropy derivations from time wave fluctuations. TFM predicts new gravitational wave polarizations (scalar-longitudinal), testable via pulsar timing arrays or advanced interferometers, and replaces dark energy with continuous micro–Big Bangs that generate space quanta. These results bridge quantum mechanics, general relativity, and cosmology under a single theoretical framework.