Planck’s Constant Physically Derived Through Quantum Substrate Dynamics: A Mode-Ratio and Offload-Based Origin for Quantization and Temporal Structure

Planck’s constant is traditionally treated as a fundamental but unexplained constant of nature—an axiom inserted into quantum mechanics without structural derivation. In this work, we present a first-principles derivation of Planck’s constant within the framework of Quantum Substrate Dynamics (QSD), a Lorentz-invariant physical model in which mass, energy, and time emerge from coherence interactions within a conserved substrate. We show that ℏ arises as a structured ratio of two physically distinct coherence propagation modes: scalar collapse speed (cs) and transverse spread velocity (ct), shaped by local substrate geometry and curvature compliance. The result is an explicit expression: ℏ = (ct4 / cs) * (Lcoh2/ G) where Lcoh is the minimum coherence support area, and G is the substrate’s curvature compliance constant (traditionally Newton’s gravitational constant). This formulation provides a physically interpretable basis for quantization: energy offload occurs in complete wave units, spaced by scalar-mode recovery intervals that define the Planck time. Quantization, causality, and time all emerge from this structural pacing constraint. No parameters are introduced arbitrarily. Dimensional consistency is preserved throughout, and the resulting formulation recovers classical Planck units as mode interactions. This reinterpretation offers a physically grounded explanation of why action is quantized and highlights the role of substrate geometry in defining fundamental constants.