The Geometric Nature of Velocity: A Redefinition of Velocity in the Time Field Theory

Based on the axiomatic system of Time Field Theory (TFT), this paper re-examines the essential definition of spatial measurement and motion velocity, clarifying a core cognitive distinction: three-dimensional space acts merely as a logical coordinate canvas with no inherent physical properties or intrinsic metric benchmarks. All length calibration and physical measurement must rely on the local time field \gamma(r), forming a closed self-referential measurement system constrained strictly by flux conservation. We sort out the fundamental logical defects hidden in the traditional geometric optical calculation of gravitational light deflection, namely directly equating coordinate path element dr to physical length dl under the implicit assumption of an absolute invariant measuring scale. Such approximation is only valid under weak refractive gradient and cannot be transplanted into the gravitational field with continuously varying strong time field gradient. Within the TFT framework, the variable local light speed determined by the time field is converted into equivalent graded refractive index, and the Fermat principle derived from flux conservation is applied with complete self-consistent metric rules, naturally yielding the observed gravitational light deflection value consistent with astronomical measurement data. This study strictly differentiates the ontological concept of flat space in TFT from Newtonian absolute space, and distinguishes projected metric curvature caused by time field gradient from the four-dimensional spacetime curvature hypothesis of General Relativity (GR). While maintaining full compatibility with classical experimental verifications of gravitational effects, TFT retains the flat three-dimensional space framework consistent with Special Relativity, reconstructing gravitational phenomena as the variation of local measurement benchmarks rather than the geometric bending of space itself. Relevant discussions on spatial ontology and self-consistent measurement are supported by dedicated theoretical studies of TFT, breaking the long-standing path dependence of interpreting gravitational effects via spacetime curvature and offering a unified monistic underlying logic for relativity and gravitational phenomenology.