Quantum Discrete-Step Trajectory Dynamics: Emergent Phenomena, Conservation Constraints, and Experimental Tests

QDST Description Quantum Discrete-Step Trajectory Dynamics (QDST) is a theoretical research program investigating whether finite intervals between localized interaction opportunities can produce experimentally distinguishable correlations in quantum propagation and scattering. The model introduces an effective discrete propagation scale L = vτ, where v is projectile velocity and τ is an update interval, without assuming that spacetime itself is fundamentally discrete. Its current formulation studies phase-averaged first-event statistics, velocity- and geometry-dependent correlations in ordered targets, quantum implementations of finite interaction schedules, and the conservation constraints that any physical discrete-update dynamics must satisfy. QDST explores possible connections to inverse-speed reaction behavior, barrier transmission, low-energy nuclear phenomena, reaction structure, and downstream interaction events, while recognizing that these phenomena already have conventional explanations and do not constitute evidence for QDST by themselves. A central objective is therefore experimental falsifiability rather than retrospective explanation. The framework seeks joint predictions across projectile velocity and target geometry that can be compared against calibrated conventional quantum and material-transport models. Its companion Discrete Trajectory Collision Experiment (DTCE) proposes site-resolved ion–graphene measurements as a possible experimental platform. The present QDST formulation is a phenomenological model and research program, not an experimentally established alternative to quantum mechanics. A complete theory would still require a microscopic conservative interaction law, treatment of localization and coherent interference, realistic material and nuclear dynamics, and experimentally calibrated predictions. Authors: Daqian Zhang, GPT6 Astra, SBIL