Unitarity in Quantum Mechanics: A Critical Audit from First Principles

This work presents a rigorous, first-principles audit of unitarity in quantum mechanics, treating unitarity not as a foundational axiom but as a hypothesis whose validity depends on explicit physical and mathematical assumptions. The analysis is conducted entirely within the operational framework of open quantum systems, using completely positive trace-preserving (CPTP) maps to describe the dynamics of reduced subsystems. By systematically isolating and auditing every prerequisite required for unitary evolution—including perfect isolation, Hilbert-space factorization, linearity, the Born rule, and time parameterization—the manuscript demonstrates that unitarity is neither fundamental nor universal, but instead an emergent, scale-dependent consistency condition. The paper distinguishes clearly between mathematical bookkeeping identities and physically meaningful conservation laws, showing that probability conservation does not require unitarity, and that reversibility and energy conservation are not guaranteed by unitary evolution alone. Explicit, mathematically consistent non-unitary evolution models are constructed, including Lindblad dynamics, non-Hermitian Hamiltonians, stochastic Schrödinger equations, non-Markovian evolution, and quantum Darwinism. The work further identifies the precise regimes in which unitary dynamics emerges as an effective approximation—such as weak coupling, short timescales, or limited observational resolution—and delineates the conditions under which it fails. Empirical evidence from atomic spectroscopy, quantum information processing, decoherence experiments, and measurement theory is used to anchor the analysis without assuming fundamental unitarity. The central conclusion is unambiguous: no physically accessible open or effective subsystem undergoes strictly unitary evolution. Unitarity is shown to be an emergent, conditional, and scale-dependent property rather than a fundamental law of nature. This manuscript is intended as a foundational clarification of the status of unitarity in quantum theory and is suitable for researchers in quantum foundations, open quantum systems, quantum information, and quantum gravity. FUSION OS INNOVATIONS