Time Orientation as an Internal Lorentz--Covariant Structure in Special Relativity

This submission presents a kinematic framework for introducing time orientation within special relativity as an internal, Lorentz-covariant structure rather than as a background property of spacetime or an emergent feature of dynamics. Working on fixed Minkowski spacetime, the paper defines an internal orientation field that transforms as a Lorentz scalar and uses it to construct scalar quantities whose spacetime gradients define a local notion of temporal orientation. A central result is a purely geometric monotonicity theorem: any scalar field with an everywhere timelike, future-directed gradient increases monotonically along all future-directed timelike worldlines. This establishes an observer-independent temporal ordering without selecting a preferred inertial frame, foliation, or simultaneity convention. The framework is manifestly Poincaré covariant, preserves the standard causal structure of special relativity, and makes no assumptions about dynamics, thermodynamics, global topology, or entropy-based arrows of time. Any apparent breaking of symmetry arises only at the level of particular field configurations, not from the underlying axioms. By clearly separating internal symmetries from spacetime symmetries, the work clarifies how time orientation can be treated as a minimal, internal kinematic feature fully compatible with special relativity, providing a clean conceptual foundation for subsequent dynamical, geometric, or field-theoretic extensions.