Gravity as the Bridge Between Reference Frames — The Logical Necessity of Cross-Frame Velocity Addition in the TFT Framework

The velocity addition formula of special relativity is derived from the Lorentz transformation between inertial frames in flat spacetime, which presupposes a uniform spacetime background and cannot be directly generalized to scenarios with gravitational fields. This paper first anchors the entire derivation in three universally acknowledged physical facts: the operative definition of the second in the SI, the continuous and differentiable nature of gravitational influence on motion, and the logical requirement of metric self-consistency. By tracing Newton’s omission of this operative definition and Einstein’s retention of geometric a priori, we reveal why a deeper foundation is needed. Within the framework of the Metretics Dynamics (the Time Field Theory, TFT), this paper rigorously demonstrates, starting from the two core axioms of local rate conservation and flux conservation, that the physical essence of a gravitational field is the continuous metric distribution of local reference frames. The local time field strength γ serves as the metric bridge connecting different frames. Velocity addition across inertial frames at the same spatial point must incorporate the covariant scaling of the γ factor to maintain substantial self-consistency of physical laws. The velocity addition formula inherently carries the γ factor, which is the mathematical signature of gravity as a bridge between reference frames. In the uniform limit where γ ≡ 1, the formula naturally reduces to the standard form of special relativity. This paper explicitly defines the applicable boundaries of the conclusion and points out that the deviation of velocity addition rules in strong gravitational fields constitutes a testable theoretical prediction of TFT.