Heisenberg Uncertainty Relation Derived as a Special Limiting Case of a Single Elementary Phase Cycle.
Hennadii Kovalov
We derive a direct, non-linear relation between the internal phase time per radian , the macroscopically observable coordinate time , and the relative energy fluctuation . Through rigorous differentiation and integration of these phase relations, we demonstrate that for topologically synchronized systems, the product of energy and observable time constitutes a strict dynamic process invariant: . Moving beyond phenomenological interpretations, we deduce the classical Heisenberg uncertainty relation without invoking independent quantum postulates, showing it to be a special boundary limit governing a single elementary phase cycle () under critical fluctuation. Finally, we bridge the gap between microscopic quantum reversibility and the macroscopic thermodynamic arrow of time by analyzing the dynamics of synchronization breakdown and phase slippage ().
•Jun 10, 2026•0 citations