A Timing Floor for Phase Transit: Duration Bounds from the Energy-Time Uncertainty Relation

How fast can a phase coordinate be advanced? This paper derives a floor on transit duration from the energy-time uncertainty relation, dt >= hbar/(2 dE), applied to a fifth coordinate whose advance Dchi must be resolved against an available energy spread dE. For one full turn the floor is 3.291e-14 s at a spread of 0.01 eV, 3.291e-16 s at 1 eV, and 3.291e-17 s at 10 eV, corresponding to maximum advance rates of 3.039e+13 and 3.039e+16 turns per second at the two ends of that range. A single readout step of 0.0667 rad at 1 eV has a floor of 3.494e-18 s. The bound is generous at electron-volt spreads and severe at milli-electron-volt spreads, which separates two regimes of transit machinery: devices that can spend electron-volts per turn are not timing-limited, while devices restricted to thermal-scale energies are. Computed from stated assumptions; not measured. SIMULATED, NOT MEASURED.