Time-Mass Uncertainty and the Quantum-Gravitational Extension of Heisenberg's Principle

Hakan ÜNAL

Ling Jun Wang

Michael B. Mensky

Espen Gaarder Haug

In this paper we suggest that through working with the Planck mass and its link to other particles in a simple way, it possible to “convert” the Heisenberg uncertainty principle into a very simple quantum probabilistic model. We further combine this with key elements from special relativity theory and get an interesting quantum relativistic probability theory. Some of the key points presented here could help to eliminate negative and above unity (pseudo) probabilities that often are used in standard quantum mechanics. These fake probabilities may be rooted in a failure to understand the Heisenberg principle fully in relation to the Planck mass. When properly understood, the Heisenberg principle seems to give a probabilistic range of quantum probabilities that is sound. There are no instantaneous probabilities and the maximum probability is always unity. In our formulation, the Planck mass particle is always related to a probability of one. Thus, we have certainty at the Planck scale for the Planck mass particle, or for particles accelerated to reach Planck energy. We are also presenting a relativistic extension of the McCulloch Heisenberg-derived Newton equivalent gravity theory. Our relativistic version requires much less mass than the Newtonian theory to explain gravitational phenomena, and initial investigation indicates it is consistent with perihelion of Mercury.

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.

Ijaz Durrani