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arXiv:2503.00966

Reasoning across spacelike surfaces in the Frauchiger-Renner thought experiment

Jeffrey M. Epstein

Published Mar 2, 2025• 0 citations
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Abstract

The Frauchiger-Renner argument purports to show that the standard framework of quantum mechanics yields a contradiction when used to reason about systems containing agents who are themselves using quantum mechanics to perform deductions. This has been framed as an obstacle to taking quantum mechanics to be a complete theory. I formalize the argument in two closely related ways and elucidate the source of the paradox, clarifying the flaw in the original argument.

DOI
10.48550/arxiv.2503.00966

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The Frauchiger-Renner argument purports to show that the standard framework of quantum mechanics yields a contradiction when used to reason about systems containing agents who are themselves using quantum mechanics to perform deductions. This has been framed as an obstacle to taking quantum mechanics to be a complete theory. I formalize the argument in two closely related ways and elucidate the source of the paradox, clarifying the flaw in the original argument.
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).
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.
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
How can we consistently model the knowledge of the natural world provided by physical theories? Philosophers frequently use epistemic logic to model reasoning and knowledge abstractly, and to formally study the ramifications of epistemic assumptions. One famous example is Fitch's paradox, which begins with minimal knowledge axioms and derives the counter-intuitive result that agent knows every true statement. Accounting for knowledge that arises from physical theories complicates matters further. For example, quantum mechanics allows observers to model other agents as quantum systems themselves, and to make predictions about measurements performed on each others' memories. Moreover, complex thought experiments in which agents' memories are modelled as quantum systems show that multi-agent reasoning chains can yield paradoxical results. Here, we bridge the gap between quantum paradoxes and foundational problems in epistemic logic, by relating the assumptions behind the recent Frauchiger-Renner quantum thought experiment and the axioms for knowledge used in Fitch's knowability paradox. Our results indicate that agents' knowledge of quantum systems must violate at least one of the following assumptions: it cannot be distributive over conjunction, have a kind of internal continuity, and yield a constructive interpretation all at once. Indeed, knowledge provided by quantum mechanics apparently contradicts traditional notions of how knowledge behaves; for instance, it may not be possible to universally assign objective truth values to claims about agent knowledge. We discuss the relations of this work to results in quantum contextuality and explore possible modifications to standard epistemic logic that could make it consistent with quantum theory.