Phase-Locked Bubble Transport: A Preliminary Mathematical and Conceptual Framework

This preprint develops a preliminary mathematical framework for a speculative transport concept the author calls phase-locked bubble transport. The idea is that a vehicle could become dynamically confined inside a moving low-gradient “bubble” formed by a driven field pattern, and remain phase-locked to the motion of this bubble so that it is carried along with it. Unlike conventional propulsion, the vehicle would not accelerate directly by reaction thrust, but instead would exchange momentum with a traveling field structure that the vehicle helps generate and stabilize. The paper introduces a minimal one-dimensional model based on a moving potential well, derives the phase-locking condition, and discusses stability, failure modes, and analogue experimental setups that could test the underlying dynamical mechanism. This work does not claim technological feasibility or reactionless propulsion. It is presented as a conceptual and mathematical exploration of whether stable, phase-locked transport inside a self-generated traveling bubble is dynamically consistent within classical physics. The author invites constructive technical critique and independent modelling.