The Relativistic Halting Problem: Computational Complexity Limits on Quantum Hermiticity

This preprint introduces the concept of the Relativistic Halting Problem, proposing that the operational impossibility of constructing inverse quantum evolutions under relativistic and computational constraints leads to effective non-Hermitian dynamics in macroscopic systems. The work argues that standard quantum mechanics implicitly assumes a “Mirror Fallacy”: that inverse operators are ontologically given independent of physical realizability. By treating operators as physically constructed processes bounded by causal horizons, the paper provides an operational account of the emergence of the arrow of time and macroscopic irreversibility. This work is intended as a conceptual and foundational proposal rather than a complete formal theory.