Physical Formalism Of Directional Quantum Evolution Theory

Abstract: Here, we introduce the Directional Quantum Evolution Theory (DQET), a covariant reformulation of quantum mechanics where evolution takes place along a four-vector-defined arbitrary timelike direction. This method restores space-time symmetry and provides a geometric interpretation of energy as a frame-dependent projection by substituting a directional derivative for the traditional time derivative. DQET establishes a conserved probability current, supports proper-time evolution, and recovers the Schrodinger in suitable bounds. It provides a covariant solution to the quantum twin conundrum and predicts observable phase discrepancies between systems traveling along distinct trajectories. With encouraging extensions to curved spacetime, the theory offers a cohesive framework for relativistic quantum evolution.