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arXiv:2011.12716

The Quantum Rashomon Effect: A Strengthened Frauchiger-Renner Argument

Jochen Szangolies

Published Nov 23, 2020• 1 citation
arXivHTMLPDF

Abstract

The Frauchiger-Renner argument aims to show that `quantum theory cannot consistently describe the use of itself': in many-party settings where agents are themselves subject to quantum experiments, agents may make predictions that contradict observations. Here, we introduce a simplified setting using only three agents, that is independent of the initial quantum state, thus eliminating in particular any need for entanglement, and furthermore does not need to invoke any final measurement and resulting collapse. Nevertheless, the predictions and observations made by the agents cannot be integrated into a single, consistent account. We propose that the existence of this sort of \emph{Rashomon effect}, i.e. the impossibility of uniting different perspectives, is due to failing to account for the limits put on the information available about any given system as encapsulated in the notion of an \emph{epistemic horizon}.

DOI
10.48550/arxiv.2011.12716

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The Frauchiger-Renner argument aims to show that `quantum theory cannot consistently describe the use of itself': in many-party settings where agents are themselves subject to quantum experiments, agents may make predictions that contradict observations. Here, we introduce a simplified setting using only three agents, that is independent of the initial quantum state, thus eliminating in particular any need for entanglement, and furthermore does not need to invoke any final measurement and resulting collapse. Nevertheless, the predictions and observations made by the agents cannot be integrated into a single, consistent account. We propose that the existence of this sort of \emph{Rashomon effect}, i.e. the impossibility of uniting different perspectives, is due to failing to account for the limits put on the information available about any given system as encapsulated in the notion of an \emph{epistemic horizon}.
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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).
The concept of an isolated system, and Frauchiger and Renner's extended `Wigner's friend' scenario are discussed. It is argued that: (i) it is questionable whether the approximation of the isolated system is valid when measurement-like processes are involved; (ii) one may infer, from Frauchiger and Renner's thought-experiment, and similar thought-experiments, that any interpretation of quantum theory involving *subjective collapse* fails; (iii) this does not distinguish single-world from many-world (relative-state) interpretations of quantum theory; (iv) reasoning from observations has to take into account the possible quantum-erasure of those observations if it is to be valid reasoning; (v) a single-world interpretation is valid if certain kinds of outcome are not quantum-erased in the future.
The decoherence interpretation of quantum measurements is applied to Wigner's-friend experiments. A framework in which all the experimental outcomes arise from unitary evolutions is proposed. Within it, a measurement is not completed until an uncontrolled environment monitorizes the state composed of the system, the apparatus, and the observer. The (apparent) wave-function collapse and the corresponding randomness result from tracing out this environment; it is thus the ultimate responsible party for the emergence of definite outcomes. Two main effects arise from this fact. First, external interference measurements, trademark of Wigner's-friend experiments, modify the memory records of the internal observers; this framework provides a univocal protocol to calculate all these changes. Second, it can be used to build a consistent scenario for the recently proposed extended versions of the Wigner's-friend experiment. In regard to the work of Frauchiger and Renner [Nat. Commun. 9, 3711 (2018)], this framework shows that the agents' claims become consistent if the changes in their memories are properly taken into account. Furthermore, the particular setup discussed by Brukner [Entropy 20, 350 (2018)] cannot be tested against the decoherence framework, because it does not give rise to well-defined outcomes according to this formalism. A variation of this setup, devised to fill this gap, makes it possible to assign joint truth values to the observations made by all the agents. This framework also narrows the requisites for such experiments, making them virtually impossible to apply to conscious (human) beings. Notwithstanding, it also opens the door to future realizations on quantum machines.