Arc II — Observation Paper 2 Title Measurement as Horizon Activation Zenodo DOI 10.5281/zenodo.18188427 Description This paper reframes quantum measurement as the activation of an operational horizon rather than as wavefunction collapse, branching, or decoherence driven by environmental dynamics. Measurement is defined as the moment when accessible correlations saturate, forcing an irreversible projection of observational structure. Within the finite-accessibility framework, a measurement outcome is not a revelation of a pre-existing value but the stabilization of an inference boundary. Once this boundary forms, further refinement of the measured observable becomes operationally impossible, regardless of improvements in apparatus or control. The horizon is informational, not geometric, and need not coincide with any spacetime boundary. The paper demonstrates that standard features of quantum measurement—outcome definiteness, irreversibility, and apparent randomness—follow directly from accessibility limits without invoking collapse postulates or many-worlds branching. Born-rule statistics emerge as the unique stable weighting compatible with horizon activation and correlation degradation. By treating measurement as a structural transition in accessibility, the work unifies measurement theory with thermodynamic irreversibility and horizon physics. It also clarifies why measurement problems persist when accessibility constraints are ignored. Keywords quantum measurement; wavefunction collapse; horizons; irreversibility; Born rule; operational quantum mechanics Notes Arc II — Observation (core conceptual paper) Measurement defined as horizon formation Collapse reinterpreted as accessibility saturation Born rule emerges structurally Bridges thermodynamics, measurement, and horizons
Arc II — Observation Paper 2 Title Measurement as Horizon Activation Zenodo DOI 10.5281/zenodo.18188427 Description This paper reframes quantum measurement as the activation of an operational horizon rather than as wavefunction collapse, branching, or decoherence driven by environmental dynamics. Measurement is defined as the moment when accessible correlations saturate, forcing an irreversible projection of observational structure. Within the finite-accessibility framework, a measurement outcome is not a revelation of a pre-existing value but the stabilization of an inference boundary. Once this boundary forms, further refinement of the measured observable becomes operationally impossible, regardless of improvements in apparatus or control. The horizon is informational, not geometric, and need not coincide with any spacetime boundary. The paper demonstrates that standard features of quantum measurement—outcome definiteness, irreversibility, and apparent randomness—follow directly from accessibility limits without invoking collapse postulates or many-worlds branching. Born-rule statistics emerge as the unique stable weighting compatible with horizon activation and correlation degradation. By treating measurement as a structural transition in accessibility, the work unifies measurement theory with thermodynamic irreversibility and horizon physics. It also clarifies why measurement problems persist when accessibility constraints are ignored. Keywords quantum measurement; wavefunction collapse; horizons; irreversibility; Born rule; operational quantum mechanics Notes Arc II — Observation (core conceptual paper) Measurement defined as horizon formation Collapse reinterpreted as accessibility saturation Born rule emerges structurally Bridges thermodynamics, measurement, and horizons
Arc II — Observation Paper 4 Title Correlation Degradation, Rank Collapse, and Operational Horizons in Observational Physics Zenodo DOI 10.5281/zenodo.18188547 Description This paper develops a general operational theory of correlation loss in physical observation, showing how finite accessibility leads to systematic degradation of correlation rank across measurement channels. Rather than treating decoherence, noise, or irreversibility as dynamical effects, the analysis reframes them as consequences of constrained inference under finite observational capacity. Using rank as a protocol-independent measure of accessible correlation, the paper demonstrates that successive observations generically induce rank collapse: a reduction in the dimensionality of distinguishable joint states accessible to observers. When rank collapse becomes irreversible, an operational horizon forms, beyond which no experimental refinement can recover lost correlations. The framework applies uniformly to quantum measurement, classical signal processing, and cosmological observation. It clarifies why certain observational limits appear absolute despite differing experimental designs, and why increased resolution or repeated measurement cannot bypass fundamental accessibility constraints. By identifying horizons with rank collapse rather than spacetime boundaries, the paper unifies measurement limits, decoherence, and observational irreversibility within a single operational structure. Keywords correlation rank; decoherence; measurement limits; operational horizons; information loss; observational physics Notes Arc II — Observation (core synthesis paper) Introduces rank collapse as a universal operational phenomenon Horizons defined by irrecoverable correlation loss Applies to quantum, classical, and cosmological observations Bridges measurement theory and horizon physics
Arc V — Gravity & Quantum Theory Paper 8 Title Quantum Mechanics Without Geometry Zenodo DOI 10.5281/zenodo.18226024 Description This paper presents a fully non-geometric formulation of quantum mechanics, completing the quantum arc of the finite-accessibility program. Building on the purification-based reconstruction of Paper V.7, it shows that quantum theory neither requires nor benefits from geometric ontology at the fundamental level. Measurement, collapse, and nonlocality are reinterpreted as changes in operational accessibility rather than physical processes occurring in spacetime. Observables are defined as elements of context-dependent accessible algebras, and measurement is treated as the activation of an accessibility horizon that selects a subalgebra without invoking wavefunction realism or spacetime projection. Within this framework, Bell inequality violations arise from the impossibility of embedding incompatible operational contexts into a single geometric structure, rather than from nonlocal dynamics. Similarly, Wigner-type paradoxes and observer-dependent state assignments are resolved as bookkeeping conflicts between distinct accessibility horizons. The paper demonstrates that all empirical predictions of quantum mechanics are preserved exactly, while the conceptual pathologies associated with geometric interpretation are eliminated. Quantum mechanics is revealed as a theory of constrained inference and context activation, with geometry appearing only later as a classical, intersubjective record structure. This work closes the quantum-reconstruction arc by showing that purification-complete quantum mechanics is intrinsically post-geometric. Keywords quantum foundations; non-geometric quantum mechanics; measurement problem; Bell inequalities; operational horizons; contextuality Notes Arc V — Gravity & Quantum Theory (quantum foundations) Quantum mechanics reformulated without spacetime ontology Measurement as accessibility-horizon activation Bell violations explained without nonlocal causation Conceptual closure of the quantum arc of the program
Arc II — Observation Paper 1 Title Thermalization Without Equilibrium Zenodo DOI 10.5281/zenodo.18180820 Description This paper demonstrates that thermal behavior does not require equilibrium ensembles, microscopic ergodicity, or underlying statistical assumptions. Instead, thermalization is shown to arise from the progressive degradation of accessible correlations under finite observational capacity. The analysis reframes temperature, entropy production, and apparent equilibration as operational phenomena: when observers lose the ability to resolve fine-grained correlations, remaining observables converge toward thermal statistics regardless of the underlying dynamics. Thermal distributions therefore emerge as inference-fixed points under accessibility constraints, not as properties of microscopic phase space. By constructing thermalization without reference to microstates or equilibration timescales, the paper resolves long-standing conceptual tensions between thermodynamics and unitary dynamics. It clarifies why thermal behavior appears robust across systems with vastly different microscopic laws. This framework applies equally to classical, quantum, and gravitational settings, including horizon-induced thermality and detector responses in curved spacetime. Thermal behavior is shown to be a consequence of observational saturation rather than dynamical relaxation. Keywords thermalization; entropy production; irreversibility; operational thermodynamics; accessibility limits; non-equilibrium physics Notes Arc II — Observation (foundational) Thermal behavior derived without equilibrium assumptions Temperature as an inference artifact Applies to classical, quantum, and gravitational systems Conceptual bridge between entropy (Arc I) and measurement
The quantum measurement problem arises from a structural asymmetry in standard formulations of quantum mechanics: while unitary evolution is treated as fundamental, irreversible events are introduced only through ad hoc postulates. As a result, measurement, decoherence, and probability appear conceptually disconnected. In this work, we propose a minimal reformulation in which irreversible interaction events are taken as ontological primitives. An event is defined as a completely positive, trace-preserving map that is not equivalent to any unitary transformation. Unitary evolution emerges as an effective description valid between events. Within this framework, quantum measurement is not a special process but a particular class of irreversible events with outcome-resolving structure. The Born rule arises naturally from the statistical structure of event realizations, and environmental decoherence is reinterpreted as a high density of irreversible events. No collapse postulate, observer-dependent rule, or modification of quantum dynamics is required. This formulation provides a unified and physically grounded resolution of the measurement problem and establishes a conceptual foundation for event-based extensions connecting quantum theory with spacetime and gravity.
Arc VI — Experiment Paper 3 Title Diagnostic and Therapeutic Guidelines for Conceptual Pathologies in Quantum Mechanics Zenodo DOI 10.5281/zenodo.18226039 Description This paper serves as a diagnostic and interpretive guide to longstanding conceptual pathologies in quantum mechanics, reframed through the lens of finite accessibility. Rather than proposing new dynamics or interpretations, it provides a systematic classification of common conceptual failures—such as nonlocality paradoxes, wavefunction realism, and observer-dependent inconsistencies—and traces them to implicit violations of accessibility constraints. Quantum phenomena traditionally regarded as paradoxical are reinterpreted as artifacts of treating geometrical or ontological structures as fundamental in a regime where only operational accessibility is well-defined. Measurement collapse, contextuality, and observer-relative state assignments are analyzed as predictable consequences of horizon activation and algebraic restriction, not physical discontinuities. The paper introduces a set of “diagnostic criteria” for identifying when a quantum argument has exceeded its domain of operational validity, alongside “therapeutic prescriptions” that restore consistency by removing surplus structure. These guidelines are illustrated across canonical examples including Bell tests, Wigner’s friend, Schrödinger’s cat, and delayed-choice experiments. By systematizing these corrections, the paper functions both as a conceptual reference for researchers and as a pedagogical tool, enabling practitioners to recognize and avoid interpretive errors that arise from illicit geometric importation. Keywords quantum foundations; measurement problem; contextuality; nonlocality; operational interpretation; conceptual diagnostics Notes Arc VI — Experiment (conceptual diagnostics and interpretation) No new dynamics or formalism introduced Identifies accessibility violations as root cause of QM paradoxes Provides practical criteria for evaluating quantum arguments Intended as both reference and pedagogical guide
Abstract: The quantum measurement problem has been the deepest conceptual difficulty since the birth of quantum mechanics. Standard quantum mechanics accepts wavefunction collapse as an independent postulate but never provides a physical explanation. The decoherence approach attributes collapse to the interaction between the system and its environment, but faces two fundamental limitations: the “infinite regress” problem and the “insufficiency of decoherence” problem. Within the framework of the Self-Construction Theory (SCT), this paper provides a complete resolution of the measurement problem. The core thesis is that quantum measurement is not a fundamental process independent of the laws of physical evolution, but rather a local manifestation of constructive renormalization—the scale evolution of the spacetime complex field K from microscopic degrees of freedom to macroscopic effective descriptions. The origins of wavefunction collapse, decoherence, and the Born rule receive a unified first‑principles interpretation in this framework. SCT’s spontaneous decoherence mechanism is the key to the resolution. Constructive renormalization inherently involves information loss—the integrated‑out microscopic degrees of freedom no longer exist in the macroscopic effective description. During a measurement, the measuring apparatus possesses a huge number (∼1023) of microscopic degrees of freedom. When the apparatus interacts with the measured system, constructive renormalization triggers information compression of these degrees of freedom—the apparatus can no longer distinguish which branch of the superposition it is in, and quantum coherence is thus spontaneously lost. No “external environment” is needed—the constructive renormalization dynamics of spacetime itself is the ultimate source of decoherence, thereby completely solving the “infinite regress” problem. Among the probability distribution given by the Born rule, the weights of non‑maximal probability branches are further suppressed by information compression under the huge number of microscopic degrees of freedom, so that macroscopic observers can perceive only a definite outcome in the effective description. The information loss caused by constructive renormalization is ontological—it does not rely on any approximation or truncation, thus fundamentally solving the “insufficiency of decoherence” problem. The Born rule—that measurement outcomes occur with probabilities given by the squared amplitudes—is directly derived from the constructive integral structure in SCT. In the constructive renormalization limit, interference terms between different configurations are naturally suppressed by off‑diagonal phase randomization, and the system automatically switches to a classical probabilistic description. In the diagonal density matrix representation, the squared amplitude is the only natural weight that is simultaneously real and non‑negative. Hence the Born rule is not an additional postulate of quantum mechanics but a necessary and unique manifestation of the relative frequencies of the constructive integral in the constructive renormalization limit. This derivation is rigorous within the mathematical framework of constructive renormalization—it does not rely on any approximations or truncations. SCT’s quantum measurement theory is deeply unified with the black hole information paradox. The “collapse” in quantum measurement and the “information loss” in black hole evaporation are different manifestations of the same core mechanism—the redistribution of information due to constructive renormalization—in two extreme physical situations. In quantum measurement, information is redistributed into the degrees of freedom of the macroscopic apparatus; in black hole evaporation, information is redistributed into the time‑point configurations on the horizon. This unification is the strongest proof of the universality of constructive renormalization as an information‑processing mechanism. Keywords: quantum measurement; spontaneous decoherence; constructive renormalization; Born rule; wavefunction collapse; information redistribution; Self-Construction Theory