2025/04/26 by Tarek Yehia, Yehia, Tarek · 1 voice
Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #Quantum Physics (quant-ph) #physics.gen-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.2504.20100
arxiv published 2025/04/26 · arxiv updated 2025/08/25
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.