The Relativistic Halting Problem: Computational Complexity Limits on Quantum Hermiticity

This preprint introduces the concept of the Relativistic Halting Problem, proposing that the apparent breakdown of unitarity in macroscopic systems arises from a fundamental conflict between computational complexity and relativistic causality. Core Argument: The work argues that standard quantum mechanics implicitly relies on a "Mirror Fallacy": the assumption that inverse operators (Û^) are ontologically given, independent of the physical resources required to construct them. By treating operators as physically constructed processes bounded by causal horizons, we demonstrate that: When the complexity of inverting a process exceeds the Relativistic Halting Bound, the system must be described by an effective non-Hermitian theory. The Arrow of Time emerges operationally from the computational undecidability of the past. Key Applications & Updates (v1.3): Black Hole Information Paradox: We propose that the paradox is resolved not by modifying quantum mechanics, but by recognizing that the inverse history of a Fast Scrambler (Black Hole) becomes computationally undecidable for any external observer. Quantum-to-Classical Transition: The framework provides an intrinsic bound for the collapse of macroscopic superpositions based on particle number and light-speed constraints.