Deterministic Time-Anchoring of Heisenberg's Uncertainty principle: Resolving Quantum Uncertainty and State Covariance via Relativistic Nested Temporal Boundaries

This manuscript introduces a novel theoretical framework that reinterprets the Heisenberg uncertainty principle not as an inherent property of quantum randomness, but as a geometric consequence of incomplete temporal context. By treating time as a nested, two-tiered variable—comprising a macro-time superset (T) and a micro-time subset (t)—we formulate a deterministic time-anchor equation constrained at a scale-dependent discrete interval (t). By defining the fundamental anchor constant at the quantum action threshold and integrating a relative relativistic scaling factor (), we demonstrate how this model accommodates expanding and shrinking time under kinematic constraints. Furthermore, we establish a mathematical bridge to de-Broglie’s matter-wave mechanics by mapping a particle's internal rest frequency directly onto the micro-time subset (t). This mapping allows the framework to delineate two distinct operational states: a fluid, unaligned temporal state characterizing wave-like propagation, and a locked measurement state where temporal synchronization collapses the wave function into a localized particle state. We propose a falsifiable empirical test using high-precision electron diffraction loops subject to an independent time-dilation gradient to distinguish this model from Copenhagen-standard quantum mechanics. Finally, we demonstrate that under macroscopic limits, where Planck's constant becomes negligible and relative scaling forces synchronization to a uniform timeline, the framework smoothly reduces to the absolute trajectories of classical Newtonian mechanics. This model effectively transitions quantum uncertainty into a publishable framework of scale-dependent discrete temporal geometry, bridging the quantum-classical divide without the logical paradoxes of traditional hidden-variable theories.