Preprint of a conceptual paper on hidden switching errors in quantum thought experiments. The paper argues that many well-known paradoxes arise not from internal inconsistency of quantum theory itself, but from silent transitions between incompatible mathematical descriptions, such as wave and particle models or probabilistic and factual descriptions. A simple labeling method is proposed to mark different reasoning tasks and make such transitions visible. The method is applied to the Frauchiger–Renner argument and to EPR/Klyshko-type scenarios. Full text available in the attached PDF. This version adds full translations of the paper into Russian and Ukrainian, alongside the original English text. All three files contain the same argument, figures and references; the English PDF is unchanged from version 1.0.
Preprint of a conceptual paper on hidden switching errors in quantum thought experiments. The paper argues that many well-known paradoxes arise not from internal inconsistency of quantum theory itself, but from silent transitions between incompatible mathematical descriptions, such as wave and particle models or probabilistic and factual descriptions. A simple labeling method is proposed to mark different reasoning tasks and make such transitions visible. The method is applied to the Frauchiger–Renner argument and to EPR/Klyshko-type scenarios. Full text available in the attached PDF. This version adds full translations of the paper into Russian and Ukrainian, alongside the original English text. All three files contain the same argument, figures and references; the English PDF is unchanged from version 1.0.
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.
Which theories lead to a contradiction between simple reasoning principles and modelling observers’ memories as physical systems? Frauchiger and Renner have shown that this is the case for quantum theory (Frauchiger and Renner 2018 Nat. Commun. 9 3711). Here we generalize the conditions of the Frauchiger–Renner result so that they can be applied to arbitrary physical theories, and in particular to those expressed as generalized probabilistic theories (GPTs) (Hardy 2001 arXiv: quant-ph/0101012 ; Barrett 2007 Phys. Rev. A 75 032304). We then apply them to a particular GPT, box world, and find a deterministic contradiction in the case where agents may share a PR box (Popescu and Rohrlich 1994 Found. Phys. 24 379–85), which is stronger than the quantum paradox, in that it does not rely on post-selection. Obtaining an inconsistency for the framework of GPTs broadens the landscape of theories which are affected by the application of classical rules of reasoning to physical agents. In addition, we model how observers’ memories may evolve in box world, in a way consistent with Barrett’s criteria for allowed operations (Barrett 2007 Phys. Rev. A 75 032304; Gross et al 2010 Phys. Rev. Lett. 104 080402). Ordinary readers, forgive my paradoxes: one must make them when one reflects; and whatever you may say, I prefer being a man with paradoxes than a man with prejudices. Jean-Jacques Rousseau, Emile or On Education
This paper provides a comprehensive analysis of the Frauchiger–Renner paradox (2018), a significant thought experiment that demonstrates a logical contradiction arising when standard quantum mechanics is applied to nested observers. Building on Wigner’s friend scenario, it examines the formal setup, derives the contradiction from assumptions of universality, the Born rule, and self-consistency in multi-agent reasoning, and evaluates proposed resolutions across major interpretations of quantum mechanics (Copenhagen, Everettian/many-worlds, relational, QBism, decoherent histories, and objective collapse theories). The work explores historical context, epistemological implications for observation, objectivity, and intersubjectivity, as well as recent experimental probes and theoretical refinements. It argues that the paradox reveals deep tensions in applying quantum theory to complex, self-referential scenarios involving observers (2026).
Schrodinger's cat and Wigner's friend paradoxes are analyzed using the `wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level' and are shown to be non-paradoxes within the quantum formalism. Then, the extended version of Wigner's friend thought experiment, proposed in a recent article titled, ``Quantum theory cannot consistently describe the use of itself '', Nature Communications {\bf 9}, 3711 (2018), by Frauchiger and Renner (FR) is considered. In quantum mechanics, it's well-known that, statistically observing a large number of identical quantum systems at some particular quantum state, which results in Born's probability, and merely inferring its presence in the same quantum state with the same probability yield distinct physical phenomena. If this fact is not taken care while interpreting any experimental outcomes, then FR type paradoxes pop up. ``What an astonishingly self-consistent the Quantum Theory is!' - is explicitly worked out in the case of FR gedankenexperiment. The present work shows the importance of single-quantum phenomenon for the non-paradoxical interpretation of statistically observed experimental outcomes.
Recent extended formulations of the Wigner's friend thought experiment throw the measurement problem of quantum mechanics into sharper relief. Here I respond to an invitation by Renner to provide a consistent and concrete set of rules for quantum mechanics which can avoid the apparent paradox formulated by Frauchiger and Renner [Nat. Comm. 9, 3711 (2018)]. I propose a slight addition to standard textbook quantum mechanics, in the form of two rules, which avoids the paradox. The first specifies when a given quantum dynamics can be interpreted as a measurement. Potentially any dynamics can, but doing so depends on the context of other performed operations. The second requires that a joint context be used to determine whether several different dynamical evolutions can all be interpreted as measurement. The paradox is then avoided because not every participant in the Frauchiger-Renner thought experiment regards the stated dynamical descriptions of the experiment as measurements.
Considering a complicated extension of a Wigner's friend scenario, Frauchiger and Renner (FR) allegedly showed that "quantum theory cannot consistently describe the use of itself". However, such a result has been under severe criticism, as it has been convincingly argued to crucially depend on an implicit, non-trivial assumption regarding details of the collapse mechanism. In consequence, the result is not as robust or general as intended. On top of all this, in this work we show that a much simpler arrangement--basically an EPR setting--is sufficient to derive a result fully analogous to that of FR. Moreover, we claim that all lessons learned from FR's result are essentially contained within the original EPR paper. We conclude that FR's result does not offer any novel insights into the conceptual problems of quantum theory.