The Vector Dynamics of Distance and Non-Reversible Temporal Domains: A Multi-Domain Framework of Spacetime Progression

Abstract This paper introduces the Multi-Domain Time-Distance Gateway Framework, proposing that spatial distance ($d$) functions as a translational operator between discrete, non-linear temporal domains ($T$). Analysis indicates that spatial traversal does not merely shift an entity along a singular time dimension, but transitions the entity into autonomous temporal domains ($T_x, T_{kd}$). The framework addresses the Reversibility Paradox: a round-trip trajectory of distance $tm$ to a locus ($W$) and back does not yield a net zero displacement in temporal terms ($tm - tm = 0$), but rather a cumulative compound path ($tm + tm = 2tm$). This cumulative path suggests a non-reversible shift into a synthesized temporal domain ($T_{2tm}$ or $T_{tmtmt}$), indicating that spatial return operates as a forward temporal progression into a novel state. Keywords: Spacetime Dynamics, Temporal Domains, Non-Reversibility, Reversibility Paradox, Distance-Induced Temporal Shift, Multi-Domain Gateway, Entropy of Distance, Intrinsic Mass-Distance Operator, Autonomous Temporal Gateway, Theoretical Physics.