Planck-Scale Grounding of Spacetime Memory Bandwidth: A 3D Spectrogram of Gravitational Wave Echoes and the Ultimate Speed Limit

The fundamental limits of the universe, from the speed of light to the avoidance of singularities, are deeply connected to the Planck scale. In this study, we present an advanced numerical simulation of the Adaptive Memory-Driven Coupling Framework (AMDCF) grounded at the Planck scale. We demonstrate that spacetime memory operates with a finite "clock speed" (processing rate), which introduces a mandatory delay in information processing. By visualizing the 3D spectrogram of gravitational wave echoes, we show that the delay between the primary merger and the secondary echoes is a direct consequence of this finite processing time. This Planck-scale bandwidth limit fundamentally explains why the speed of light (c) is the absolute maximum speed for information propagation in the universe. The Speed of Light as a Consequence of Spacetime Memory Bandwidth"In classical Relativity, c is an empirically measured constant and the absolute speed limit. However, the AMDCF framework offers a fundamental explanation for why this limit exists. In our model, c represents the maximum rate at which the non-Markovian memory field of spacetime can process and update information. Just as a computer processor has a maximum clock speed, spacetime has a maximum rate at which it can "register" causal events. As a massive particle approaches c, its interaction with the memory kernel increases, causing infinite inertia (spacetime drag). To exceed c would require the particle to outrun its own causal memory trace, which is mathematically and physically impossible. Thus, c is not merely a property of light, but the fundamental bandwidth of spacetime itself.