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

Quantum mechanics imposes inherent limitations on the simultaneous measurement ofconjugate variables such as position and momentum. The Heisenberg Uncertainty Principleformalizes these limits, forming the basis for establishing fundamental energy scales in freeparticle motion. This thesis explores how the inherent momentum uncertainty of a freeparticle imposes a lower bound on its kinetic energy. In doing so, we introduce TheCritical Velocity—a universal threshold that defines the minimum velocity a particle musthave to maintain its quantum characteristics. The novel approach presented herein hassignificant implications for quantum electrodynamics (QED), decoherence studies, andpotential experimental validations in low kinetic energy regimes.