Arrabal-Schrödinger Transition Equation: A Velocity-Based Approach to the Quantum-to-Classical Crossover

Abstract: This thesis introduces the Arrabal-Schrödinger Transition Equation, a novel mathematical framework that integrates velocity as a key parameter influencing quantum decoherence and the quantum-to-classical transition. Building upon the traditional Schrödinger equation and incorporating Arrabal’s critical velocity criterion, the research provides a velocity-dependent decoherence mechanism. At a defined critical velocity vcriticalv_{\text{critical}}vcritical, quantum coherence collapses, facilitating the emergence of classical behavior. This model is designed to account for real-world physical systems, such as high-velocity particles and cosmological scenarios. The framework offers new insights into the limits of quantum behavior, particularly in quantum computing and cosmological structure formation