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arXiv:2208.00060

The Frauchiger-Renner Gedanken Experiment: Flaws in Its Analysis -- How Logic Works in Quantum Mechanics

Stuart Samuel

Published Jul 29, 2022• 1 citation
arXivHTMLPDF

Abstract

In a publication (Nature Comm. 3711, 9 (2018)), Daniela Frauchiger and Renato Renner used a Wigner/friend gedanken experiment to argue that quantum mechanics cannot describe complex systems involving measuring agents. They were able to produce a contradictory statement starting with four statements about measurements performed on an entangled spin system. These statements needed to be combined using the transitive property of logic: If A implies B and B implies C, then A implies C. However, in combining successive statements for the Frauchiger-Renner gedanken experiment we show that quantum mechanics does not obey transitivity and that this invalidates their analysis. We also demonstrate that certain pairs of premises among the four statements are logically incompatible, meaning that the statements cannot all be used at once. In addition, to produce the contradiction, Frauchiger and Renner choose a particular run, which they call the `OK' -- `OKbar' one. However, the restriction to this case invalidates three of the four statements. Hence, there are three separate problems with logic in the 2018 Nature Communication publication. We also demonstrate the violation of the rules of logic -- including transitivity -- in certain situations in quantum mechanics in general. We use the Frauchiger-Renner gedanken experiment as a laboratory to explore a number of topics in quantum mechanics including wavefunction logic, Wigner/friend experiments, and the deduction of mathematical statements from knowledge of a wavefunction and obtain a number of interesting results. We show that Wigner/friend experiments of the type used by Frauchiger and Renner are impossible if the Wigner measurements are performed on macroscopic objects. They are possible on certain microscopic entities but then the Wigner measurements are rendered "ordinary" in which case ...

DOI
10.48550/arxiv.2208.00060

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In a publication (Nature Comm. 3711, 9 (2018)), Daniela Frauchiger and Renato Renner used a Wigner/friend gedanken experiment to argue that quantum mechanics cannot describe complex systems involving measuring agents. They were able to produce a contradictory statement starting with four statements about measurements performed on an entangled spin system. These statements needed to be combined using the transitive property of logic: If A implies B and B implies C, then A implies C. However, in combining successive statements for the Frauchiger-Renner gedanken experiment we show that quantum mechanics does not obey transitivity and that this invalidates their analysis. We also demonstrate that certain pairs of premises among the four statements are logically incompatible, meaning that the statements cannot all be used at once. In addition, to produce the contradiction, Frauchiger and Renner choose a particular run, which they call the OK' -- OKbar' one. However, the restriction to this case invalidates three of the four statements. Hence, there are three separate problems with logic in the 2018 Nature Communication publication. We also demonstrate the violation of the rules of logic -- including transitivity -- in certain situations in quantum mechanics in general. We use the Frauchiger-Renner gedanken experiment as a laboratory to explore a number of topics in quantum mechanics including wavefunction logic, Wigner/friend experiments, and the deduction of mathematical statements from knowledge of a wavefunction and obtain a number of interesting results. We show that Wigner/friend experiments of the type used by Frauchiger and Renner are impossible if the Wigner measurements are performed on macroscopic objects. They are possible on certain microscopic entities but then the Wigner measurements are rendered "ordinary" in which case ...
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).
Quantum mechanics has been subject to logical scrutiny since its inception. The behavior of quantum systems, which are fundamentally dissimilar from classical systems, often appears to point to a logical inconsistency in quantum mechanics, allegedly leading to contradictions in the prediction of experimental measurements--though such contradictions have never materialized. A recent example of this type of inquiry into the logical well-posedness of quantum mechanics is the Frauchiger-Renner Gedankenexperiment, which purports to demonstrate that quantum mechanics is logically inconsistent. In this article, we show that by considering the property of contextuality in quantum systems--as predicted by the Kochen-Specker theorem--the supposed contradiction proposed by Frauchiger and Renner becomes logically inaccessible.
Predictions of quantum theory have been confirmed experimentally in the microscopic domain with no known exceptions. This success motivates physicists to assume universal validity of the theory. To put the predictions of the quantum theory to the test in the domain of more complex systems researchers like e.g. Eugene Wigner have proposed carefully designed Gedankenexperiments revealing unexpected difficulties of the theory. Daniela Frauchiger and Renato Renner have recently suggested an extension of the Gedankenexperiment commonly known as Wigner's friend and arrived at a conclusion that one agent, upon observing a particular measurement outcome, must conclude that another agent has predicted the opposite outcome with certainty. Their analysis shows that quantum theory cannot consistently describe the use of itself. Here, we will study the mentioned Gedankenexperiments and introduce an approach leading to consistent predictions of quantum theory, independent of observer using the theory.
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.
Wigner's friend paradoxes highlight contradictions between measurements made by friends inside a laboratory and superobservers outside the laboratory, who have access to an entangled state of the measurement apparatus. Where there are two separated laboratories, the contradictions lead to no-go theorems for observer-independent facts, thus challenging concepts of objectivity. Here, we examine the paradoxes from the perspective of establishing consistency with macroscopic realism. We present versions of the Brukner-Wigner's-friend and Frauchiger-Renner paradoxes in which the spin-1/21/21/2 systems measured by the friends correspond to two macroscopically distinct states. The local unitary operations ${U}_{{\ensuremath{\theta}}_{j}}$ that determine the measurement settings ${\ensuremath{\theta}}_{j}$ at each laboratory are carried out using nonlinear interactions, which are tailored to ensure that measurements need only distinguish between the macroscopically distinct states. The macroscopic paradoxes are perplexing, seemingly suggesting there is no objectivity in a macroscopic limit. However, we demonstrate consistency with a contextual weak form of macroscopic realism (wMR): The premise wMR asserts that each system jjj can be considered to have a definite spin outcome ${\ensuremath{\lambda}}_{{\ensuremath{\theta}}_{j}}$, at the time after the system has undergone the local unitary rotation ${U}_{{\ensuremath{\theta}}_{j}}$ to prepare it in a suitable measurement basis. We further show that the paradoxical outcomes imply failure of deterministic macroscopic local realism and arise when there are unitary interactions ${U}_{{\ensuremath{\theta}}_{j}}$ occurring due to a change of measurement setting at both laboratories, with respect to the state prepared by each friend. In models which validate wMR, there is a breakdown of a subset of the assumptions that constitute the Bell-locality premise. A similar interpretation involving a contextual weak form of local realism exists for the original paradoxes.
Wigner's friend scenarios expose a tension in quantum mechanics: an observer inside a laboratory obtains a definite measurement outcome, while an observer outside describes the laboratory as being in a superposition. The Frauchiger-Renner (2018) extension produces logical contradictions when agents use quantum theory to reason about each other. We show that the recursion-consistency functional K resolves these contradictions without modifying quantum mechanics. The resolution rests on a single physical fact: the friend's measurement creates ~10^20 environmental records inside the laboratory, driving K_rec to its minimum in ~10^-30 seconds. Wigner's description of the laboratory as a superposition is not wrong but incomplete: it omits the internal records that have already selected a definite outcome. The superposition description is operationally correct for Wigner (he cannot access the internal records) but ontologically incorrect (the records exist whether he accesses them or not). This distinction dissolves the Frauchiger-Renner contradiction, resolves the quantum eraser and delayed choice experiments as corollaries, and commits the framework to an ontic interpretation of the quantum state consistent with the PBR theorem.