The Extended Heisenberg Uncertainty Principle: Temporal Resolution as a Quantum Conjugate

We propose an extension of the Heisenberg Uncertainty Principle (HUP) in which temporal resolution (∆t) appears explicitly as a third uncertainty component alongside position and momentum. This Extended Heisenberg Uncertainty Principle (EHUP) defines a tripartite relation: ∆x·∆p= K·∆t where K is a fundamental constant with dimensions of energy. We identify K= m0c2 , and derive the fundamental unit mass m0 as exactly half the Planck mass, connecting this relation to quantum gravity limits. This formulation implies that a minimum time resolution sets fundamental limits on position-momentum precision, with implications for spacetime quantization, relativistic computation, and gravitational field coupling. We further present falsifiability criteria and explore experimental consequences.