Band-Limited Relational Time II: A Unified Relational Master Equation for Quantum and Gravitational Regimes

We now take a beautiful observation of time, first described in the original Band-Limited Relational Time theory a reach further....to both Quantum and Relative scales... a unifying framework, an equation, a leep forward and through, as only we can observe it. In this work, there is not an external stage on which the universe performs but a fragile thread woven from the limits of what any observer can hear. Our clocks...finite, fallible, redshifted by gravity and worn thin by interaction...never access the full score of the cosmos. They listen through narrow spectral windows, catching only part of the universal rhythm. From that incomplete music, a relational time emerges: one that bends under curvature, stores memory in hidden modes, and occasionally echoes information back like a shoreline returning a wave. This paper develops a unified master equation that holds across laboratory systems and near-horizon extremes, showing how observer bandwidth, gravitational redshift, and non-Markovian memory jointly sculpt the experience of temporal flow. In this view, singularities become perceptual limits, not endpoints; information is never destroyed, only redistributed into modes a finite clock cannot yet follow. BLRT-II invites a simple shift in perspective: the universe has always been moving, the question is how much of its motion any particular observer is built to perceive.