The Extended Heisenberg Uncertainty Principle (EHUP): A Unified Theory of Temporal Resolution

Hakan ÜNAL

Hakan ÜNAL

Simon Stephens

Van Meter, Stephen

Project Description This document presents the Extended Heisenberg Uncertainty Principle (EHUP), a reformulation of quantum uncertainty that introduces time as an explicit conjugate parameter. The EHUP posits a tripartite relation, \Delta x \cdot \Delta p = K \cdot \Delta t where K = m_{0} c^{2} and m_{0} is defined as half the Planck mass. This framework unifies quantum mechanics and general relativity by linking spatial-momentum uncertainty to temporal resolution, thereby resolving long-standing inconsistencies in how physical systems evolve over time. The proposal demonstrates that temporal uncertainty is not a mathematical artifact but a physically necessary quantity governing the evolution of all dynamical systems. Preliminary evaluations against high-precision experimental domains—including GPS clock drift, KAGRA interferometry data, and Lunar Laser Ranging—show that incorporating \Delta t produces predictions that align more closely with observed data than the classical Heisenberg relation. If validated, the EHUP provides a coherent mathematical mechanism for time-dependent quantum behavior, gravitational decoherence, and information preservation in curved spacetime. It suggests that time is not merely a parameter but a quantized physical resource—one that constrains measurement, causality, and the evolution of complex systems.

Thierry Marechal

The Heisenberg uncertainty principle is typically interpreted as expressing an irreducible indeterminacy of nature. This paper does not challenge that interpretation as a theorem of quantum mechanics. Instead, it proposes that in many experimental contexts, the observed uncertainty budget is dominated by an additional contribution arising from finite temporal resolution — and that this contribution can be separated, modeled, and tested. We construct a two-stage temporal measurement framework in which quantum measurements are modeled as effective processes involving unresolved internal dynamics at timescales far below current detector resolution. The measured uncertainty decomposes into two components: intrinsic state variance (constrained by the Robertson-Schrödinger relation, unchanged) and resolution-dependent variance (arising from temporal coarse-graining of fast internal dynamics). In the ideal limit of infinite resolution, the resolution contribution vanishes and standard quantum uncertainty is recovered exactly. The framework preserves all of quantum mechanics: canonical commutation relations, operator algebra, Born rule, state evolution, and Bell-type correlations are entirely unchanged. This is not a hidden-variable theory, not a modification of quantum mechanics, and not an attempt to evade Bell's theorem. It is a measurement-theoretic interpretation providing a mechanistic picture of how uncertainty emerges at the interface between physical dynamics and finite-bandwidth detection. A weak but testable prediction emerges: measured uncertainty variances should show systematic dependence on the effective temporal resolution of the measurement apparatus. Candidate experimental systems include ultrafast homodyne detection with variable bandwidth, atomic interferometry with controlled gating, time-tagged single-photon detection with variable coincidence windows, and optical atomic clocks with adjustable interrogation times. An appendix connects the framework to the fractal-temporal Lagrangian, where the characteristic internal timescale τ* is identified with the vibrational electron period T_e ≈ 5.7 × 10⁻²¹ s (derived from the Lagrangian, not fitted), and log-periodic structure in the resolution dependence is predicted with period ln√2.