Extra Time Dimension: Deriving Relativistic Space-Time Transformations, Kinematics, and Example of Dimensional Compactification Using Time-Dependent Non-Relativistic Quantum Mechanics

We consider a five-dimensional Minkowski space with two time dimensions characterized by distinct speeds of causality and three dimensions. Formulas for relativistic coordinate velocity transformations are derived, leading to new expression the speed limit. Extending ideas Einstein’s Theory Special Relativity, concepts five-velocity five-momenta introduced. get formula rest energy massive object. Based on non-relativistic limit, two-time dependent Schrödinger-like equation infinite square-well potential is developed solved. The extra dimension compactified closed loop topology period matching Planck time. It generates interference additional quantum states an ultra-small oscillation. Some cosmological implications concept four-dimensional versus masses briefly discussed, too.