Paper IX — Records, Measurement, and Operational Irreversibility

DOI: 10.5281/zenodo.17925745 Records, Measurement, and Operational Irreversibility Paper IX of the Ordered-Dynamics Reconstruction Program Paul Cooneya aIndependent Researcher, Innisfil, Ontario, Canada E-mail: paul.co[email protected]to.ca Contents 1 Introduction 1 2 What Is a Record? 2 3 Environment Coupling and Bounded Information 2 4 Pointer Structure and Spatial Records 2 5 Why Outcomes Appear Definite 3 6 Probability and the Born Rule Revisited 3 7 Irreversibility from Record Accumulation 3 8 Relation to the Reconstruction Program 3 9 Conclusion 4 DOI: 10.5281/zenodo.17925745 he Ordered-Dynamics Reconstruction Program derives quantum kinematics, interaction structure, field buffering, and gauge redundancy from operational principles without postulating measurement, collapse, or classical limits. This paper resolves the remaining foundational gap: the emergence of stable records, definite outcomes, probability, and irreversibility for bounded observers. We show that once information density is finite, influence is local, and interactions are constrained as in Papers IV–VIII, record formation is unavoidable. Definiteness arises from operational inaccessibility of interference between record sectors rather than dynamical collapse. The Born rule follows from record redundancy and stability. An effective arrow of time emerges from record accumulation despite microscopically reversible dynamics. 1 Introduction The preceding papers of the Ordered-Dynamics Reconstruction Program derive the formal structure of quantum theory without invoking observers, measurement postulates, or classical limits. Nevertheless, empirical science presupposes the existence of records: stable correlations encoding outcomes of past interactions. Standard quantum mechanics introduces measurement axiomatically, supplementing unitary evolution with projection rules or collapse postulates. Decoherence-based approaches explain suppression of interference but often presuppose classical environments or coarsegraining. In this paper we show that neither additional postulates nor classical assumptions are required. Once information capacity is finite, interactions are local, and environments are uncontrolled, records, definiteness, probability, and irreversibility follow as structural necessities. – 1 – 2 What Is a Record? Definition 1 (Operational record).Arecord is a correlation between degrees of freedom that: 1. is locally accessible, 2. is stable under small perturbations, 3. persists over time, 4. is redundantly accessible to independent subsystems. Remark 1.Records are relational structures, not states of isolated systems. No pure state of a finite isolated system constitutes a record. Proof. Isolated systems evolve reversibly under unitary dynamics. Any internal correlation can be undone by inverse evolution and lacks the stability and redundancy required of records. Record formation requires coupling to an environment not under system control. Proof. Persistence and redundancy require information transfer to degrees of freedom that are not coordinated by the system’s internal dynamics. Bounded information density is necessary for stable records. Proof. Unbounded information density permits arbitrarily fragile correlations, violating the stability requirement. 3 Environment Coupling and Bounded Information Any direct system–environment coupling compatible with Operational Locality is diagonal in the system position basis. Proof. Paper IV shows that direct interaction generators respecting locality must be multiplication operators V(X) on the system Hilbert space. Momentum-based records are generically unstable under bounded influence. Proof. Momentum-diagonal couplings require nonlocal kernels or globally coordinated control, violating locality and bounded accessibility. 4 Pointer Structure and Spatial Records Definition 2 (Pointer structure).A basis supporting stable, redundant environmental correlations. [Structural pointer basis] Under bounded information density and Operational Locality, spatial localization is the unique pointer structure. Proof. Only the position basis diagonalizes all admissible direct interaction generators. Remark 2 (Relation to decoherence analyses).Decoherence calculations explain suppression rates in specific models. The present result explains why suppression is structurally generic. – 2 – 5 Why Outcomes Appear Definite Definition 3 (Operational accessibility).Degrees of freedom are operationally accessible if admissible local operations can coherently manipulate them. Remark 3 (Inaccessibility is physical, not epistemic).Operational inaccessibility reflects physical constraints, not ignorance. After record formation, interference between record sectors is operationally inaccessible. [Operational definiteness] Bounded observers experience definite outcomes. Proof. Accessible degrees of freedom correlate with a single record sector; no operation can reveal coherence between sectors. 6 Probability and the Born Rule Revisited Definition 4 (Operational probability).Relative frequency of stable records in repeated trials. [Additivity of record capacity] Record capacity is additive under composition of independent subsystems. Proof. Independent environments supply independent record channels. Record stability scales with squared amplitude weight. Proof. The squared amplitude is the unique conserved, additive, phase-invariant quantity (Paper I). [Operational Born rule] Observed frequencies follow the |c|2measure. 7 Irreversibility from Record Accumulation Definition 5 (Operational irreversibility).Processes irreversible under bounded accessibility. [Arrow of time from records] Record accumulation induces an effective arrow of time. Proof. Reversal requires control over inaccessible environmental correlations. The irreversibility is principled for all observers subject to locality and bounded information. 8 Relation to the Reconstruction Program •Paper IV: interaction rigidity •Paper VII: environmental buffering •Paper VIII: gauge redundancy •Paper IX: records and irreversibility Measurement is not postulated; it is enforced by operational consistency. – 3 – 9 Conclusion Definite outcomes, probabilities, and irreversibility emerge from bounded information, locality, and redundancy. No collapse, observer axiom, or classical limit is required. Paper X addresses horizons, singularity exclusion, and minimum length. Acknowledgments The author thanks colleagues for helpful discussions regarding operational quantum theory. References [1] P. Cooney, Ordered Dynamics and Operational State Spaces, Paper I of the Ordered-Dynamics Reconstruction Program (2025). [2] P. Cooney, Local Interactions and Potential Rigidity, Paper IV of the Ordered-Dynamics Reconstruction Program (2025). [3] P. Cooney, Fields and Fock Space from Local Additivity, Paper VII of the Ordered-Dynamics Reconstruction Program (2025). [4] W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715 (2003). [5] A. M. Gleason, Measures on the closed subspaces of a Hilbert space, J. Math. Mech. 6, 885 (1957). – 4 –