Movement Quantization: A Kinematic and Dynamical Framework from Discrete Displacement to Continuous Physics

This paper proposes a kinematic and dynamical framework in which movement operations—rather than spacetime itself—are quantized. Position coordinates x ∈ ℝ are continuous, but displacement Δx is constrained to integer multiples of the Planck length ℓ_P. The framework rests on five hypotheses: (H1) movement consists of indivisible displacement events; (H2) minimum displacement = ℓ_P; (H3) n·ℓ_P = n sequential events; (H4) each event takes duration ℓ_P/v; (H5) a single event is atomic (binary, no intermediate state). From kinematics (§2–§7): formalization of displacement sequences, emergence of macroscopic continuity, compatibility with Heisenberg uncertainty, Lorentz-frame dependence of displacement spacing, and two falsifiability conditions. From dynamics (§8–§13): Euler velocity mapping for accelerated motion (recovering Newton's equation), g₀₀ correction and equivalence principle correspondence (~10⁻⁵¹), gauge field force as statistical effect, multi-particle EPR/statistics preservation, Liouville's theorem exact (det J = 1), and Einstein field equations compatibility testing (ℓ_P²R ~ 10⁻⁷⁹).