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Entropy

A Consistent Approach to Modeling Quantum Observers

D. Ring

Published Mar 14, 2025• 0 citations
Publisher

Abstract

A number of no-go theorems have shown that Wigner's Friend scenarios combined with various metaphysical assumptions lead to contradictions in any version of quantum theory. We present an alternative constructive approach that only assumes that agents make properly qualified true statements. Quantum observers are modeled rigorously, although simplistically, using quantum circuits. Terminology is suggested to help avoid contradictions. Our methodology is applied to the Frauchiger-Renner paradox and results in statements by all agents that are both true and consistent. Quantum theory evades the no-go theorems because they make an incorrect implicit assumption about how quantum agents behave.

DOI
10.3390/e27030302

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A number of no-go theorems have shown that Wigner's Friend scenarios combined with various metaphysical assumptions lead to contradictions in any version of quantum theory. We present an alternative constructive approach that only assumes that agents make properly qualified true statements. Quantum observers are modeled rigorously, although simplistically, using quantum circuits. Terminology is suggested to help avoid contradictions. Our methodology is applied to the Frauchiger-Renner paradox and results in statements by all agents that are both true and consistent. Quantum theory evades the no-go theorems because they make an incorrect implicit assumption about how quantum agents behave.
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).
Extended Wigner’s friend scenarios (EWFSs) model agents themselves as unitarily evolving quantum systems, going beyond the standard use of quantum theory where agents are treated classically. Several no-go results suggest deep challenges in this setting: Frauchiger and Renner argued that quantum agents reasoning using quantum theory would arrive at logical paradoxes, while the local-friendliness theorem raises difficulties for maintaining objective notions of measurement events and causal reasoning in EWFSs. This prompts a key question: Can the ability to make and test scientific predictions and reason consistently still be maintained if quantum theory applies universally, even to agents and their memories? We answer this positively by developing a general quantum circuit framework for EWFSs without assuming absolute measurement outcomes. We formalize Heisenberg cuts in terms of distinct choices of channels in the circuit, labeled by “settings,” and show that Frauchiger-Renner-type paradoxes are fully resolved by making explicit the conditioning on these channels or settings. We provide concrete reasoning rules for quantum agents that ensure logical, probabilistic, and causal consistency. Our framework captures all perspectives in an EWFS within a single causal structure while allowing events to be fundamentally subjective, and we show how objective events and predictions nevertheless emerge in current real-world quantum experiments. Thus, we demonstrate a relational yet operational framework that overcomes key challenges in EWFSs without altering the Born rule, unitarity, or classical logic and probability for outcomes. This establishes a formal platform to analyze and compare different EWFS arguments and extend quantum information methods consistently into the Wigner’s friend domain.
In his famous thought experiment, Wigner assigns an entangled state to the composite quantum system made up of Wigner's friend and her observed system. While the two of them have different accounts of the process, each Wigner and his friend can in principle verify his/her respective state assignments by performing an appropriate measurement. As manifested through a click in a detector or a specific position of the pointer, the outcomes of these measurements can be regarded as reflecting directly observable "facts". Reviewing arXiv:1507.05255, I will derive a no-go theorem for observer-independent facts, which would be common both for Wigner and the friend. I will then analyze this result in the context of a newly-derived theorem arXiv:1604.07422, where Frauchiger and Renner prove that "single-world interpretations of quantum theory cannot be self-consistent". It is argued that "self-consistency" has the same implications as the assumption that observational statements of different observers can be compared in a single (and hence an observer-independent) theoretical framework. The latter, however, may not be possible, if the statements are to be understood as relational in the sense that their determinacy is relative to an observer.
How can we address the idea of observers in quantum mechanics? The long-standing Wigner’s friend thought experiment provides a conceptual framework for thinking about this question. It considers the the difficulty of reconciling unitary, evolution of systems and non-unitary state update after a making observations. Following from a recent suggested protocol with two friends that share and entangled state, we prove and investigate, in a photonic experiment, a strong no-go theorem for this Wigner’s friend scenario. Specifically, if quantum mechanics applies at the scale of observers, then there are constraints on the set of assumptions: locality; no-superdeterminism; and absoluteness of observed events. We note that this new theorem places strictly stronger constraints on physical reality than Bell’s theorem.
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We present a discussion of the extended Wigner's friend thought experiment proposed by Frauchiger and Renner in [1]. We show by using various arguments, including textbook quantum mechanics and the ontological approach of Contexts, Systems, Modalities (CSM), that no contradiction arises if one admits that agents must agree on what is considered as a system and what is not. In such a contextually objective approach of quantum mechanics, the apparent contradiction is automatically removed. We also discuss why this mutual agreement between agents is already implicit in the standard formulations of quantum mechanics, and why removing it leads to inconsistencies.