Self-Consistency of the Whole and Parts: A Precise Reconstruction of Galileo's Free Fall Thought Experiment in Time Field Theory

Galileo's free fall thought experiment — that a large iron ball and a small iron ball hit the ground simultaneously — is traditionally expressed as “all objects fall with the same acceleration, independent of their mass.” This paper points out a logical leap implicit in this formulation: it takes the approximation condition “the Earth’s mass is much larger than that of the iron ball” as a universal conclusion. Within the framework of Time Field Theory (TFT), we provide a precise formulation: In a closed system with a definite and unique mass distribution, the acceleration is fixed, and the whole and its parts are mutually consistent. The correctness of this formulation does not rely on whether the test particle’s mass is negligible, nor on whether the distance changes slowly during the fall — it depends only on one logical principle: measurement must be self-consistent. This paper further shows that this self-consistency is precisely the same logic that the author independently used as a teenager to deduce that “iron balls must hit the ground simultaneously” — self-consistency forces a unique solution. Galileo’s free fall phenomenon receives a more fundamental explanation in TFT than in classical mechanics.