Quantum Constraints in Free Particle Motion: A New Perspective on Kinetic Energy Uncertainty and The Critical Velocity.

Quantum mechanics imposes inherent limitations on the precision of simultaneous measurements of conjugate variables, as formalized by the Heisenberg Uncertainty Principle (HUP). These constraints extend beyond position and momentum to define fundamental energy scales for free particles. This work introduces the Critical Velocity—a universal threshold speed below which quantum coherence cannot persist over a defined observational timescale. This concept bridges quantum theory and experimental design, with implications for low-energy quantum systems, decoherence studies, and the quantum-classical transition.