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
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
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 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
This paper is a conceptual and interpretive companion to "The Dynamics of Discrete Fact: A Phase-Transition Theory of Wavefunction Collapse" (doi:10.5281/zenodo.18748601), which develops a phase-transition theory of wavefunction collapse in full mathematical detail. The interpretive claims made here rest on the physical model established there. The paper identifies a structural conflation at the root of the quantum measurement problem. The standard formulation treats measurement simultaneously as a physical process and as an experiential event without distinguishing between the two. We formalize this distinction as two complementary descriptive frames — a Reality Frame (F_R) for the continuous dynamics of the system–apparatus field, and an Observer Frame (F_O) for the discrete outcomes recorded by an embedded observer — connected by a calculable critical threshold γ_c derived from the companion paper's phase-transition model. The frame distinction is applied to the three sub-problems of measurement, to five foundational paradoxes (Wigner's friend, Frauchiger–Renner, Schrödinger's cat, delayed choice, and EPR), and to seven major interpretations of quantum mechanics, each shown to privilege one frame while neglecting the other. A Frame Complementarity Principle is conjectured as a testable constraint on the simultaneous accessibility of process information and outcome definiteness.
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
Preprint of a conceptual paper that constructs the Special Theory of RelativeMathematics (STRM) — an intermediate framework providing a formal justificationfor the diagnostic method introduced in the author's earlier work (the labelingof switches between incompatible mathematical descriptions), using only existingmathematical concepts and introducing no new formal objects.The paper argues that many quantum-mechanical "paradoxes" — from EPR to theFrauchiger–Renner argument — arise not from an internal inconsistency of quantumtheory, but from the implicit gluing together of incompatible descriptions(wave vs. particle, probability distribution vs. recorded outcome, pre- vs.post-measurement state). The following are introduced and defined: a criterionof incompatibility of descriptions through violation of rigor; the third type ofknowledge as a premise that arises at the transition between incompatible tasks;relative rigor as a construction in which the rules of inference are fixed withineach task but may change at its boundary; and the protocol of switches as anobservable physical act. A structural symmetry is established between differentways of organizing such reasoning — and between different interpretations ofquantum mechanics — from which it follows that the method confers relative rigoron interpretive reasoning regardless of the interpretation used.This paper is currently under peer review at Studies in History and Philosophyof Science.It is the foundational, formal-justification paper of a cycle of five works ofincreasing depth, intended to be read as a whole: 1. Incompatible Mathematical Descriptions and Hidden Switching Errors in Quantum Thought Experiments — the labeling method; openly available on Zenodo (DOI: 10.5281/zenodo.19099007). 2. Incompatible Descriptions and the Structural Gap in the Formalism — a survey of five interpretations; published in the International Journal of Quantum Foundations (https://ijqf.org/archives/8302). 3. The Third Type of Mathematical Knowledge and Relative Rigor in Reasoning with Incompatible Descriptions - (this paper, STRM) — the formal foundation of the cycle; under review at Studies in History and Philosophy of Science. Zenodo, 2026. (https://doi.org/10.5281/zenodo.20720635). 4. An Analysis of Bell's Theorem within the STRM — under review at the International Journal of Quantum Foundations. 5. The Structural Limit of the Axiomatic Approach: Hardy's Axioms… — under review at the International Journal of Quantum Foundations.This record contains three language versions of the same paper (Ukrainian,Russian, English).Keywords: incompatible mathematical descriptions; third type of knowledge;relative rigor; complementarity; foundations of quantum mechanics; applied logic.
This article surveys a selection of key conceptual and interpretational developments in quantum mechanics, tracing the theory from its foundational postulates to contemporary discussions of measurement, nonlocality, and the emergence of classicality. Beginning with the structure of Hilbert space and the postulates governing state evolution and measurement, the epistemic stance of the Copenhagen interpretation and its modern reformulations are examined. The Einstein-Podolsky-Rosen argument, Bell's theorem, and Hardy's paradox are then discussed as probes of locality and realism, alongside the deterministic but explicitly nonlocal de Broglie-Bohm theory. The measurement problem and the implications of contextuality are analyzed in relation to objective collapse models, which introduce new physical dynamics to account for definite outcomes. Finally, the role of decoherence in the suppression of interference and the emergence of classical behavior is explored, together with the interpretational frameworks of many-worlds and consistent histories. This material aims to provide a coherent introductory overview of how several of the most prominent interpretations address the central concern of what quantum mechanics tells us about the nature of physical reality.