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Refutation of the Frauchiger-Renner Thought Experiment with Modal Operators as a Paradox

Colin James

Published Nov 1, 2018• 0 citations
OpenAlex

Abstract

We use modal logic to evaluate a quantum rendition of the Frauchiger-Renner thought experiment to refute it as paradox (contradiction) and as tautology.

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Electronic Proceedings in Theoretical Computer Science•Jan 31, 2019•9 citations
We test the principles of classical modal logic in fully quantum settings. Modal logic models our reasoning in multi-agent problems, and allows us to solve puzzles like the muddy children paradox. The Frauchiger-Renner thought experiment highlighted fundamental problems in applying classical reasoning when quantum agents are involved; we take it as a guiding example to test the axioms of classical modal logic. In doing so, we find a problem in the original formulation of the Frauchiger-Renner theorem: a missing assumption about unitarity of evolution is necessary to derive a contradiction and prove the theorem. Adding this assumption clarifies how different interpretations of quantum theory fit in, i.e., which properties they violate. Finally, we show how most of the axioms of classical modal logic break down in quantum settings, and attempt to generalize them. Namely, we introduce constructions of trust and context, which highlight the importance of an exact structure of trust relations between agents. We propose a challenge to the community: to find conditions for the validity of trust relations, strong enough to exorcise the paradox and weak enough to still recover classical logic.