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

TL;DR

This paper critically analyzes the Frauchiger-Renner gedanken experiment, revealing logical flaws such as non-transitivity in quantum mechanics and demonstrating the limitations of Wigner/friend experiments on macroscopic systems.

Contribution

It identifies and explains logical inconsistencies in the original analysis and explores the implications of these flaws for understanding quantum logic and measurement.

Findings

Quantum mechanics does not obey transitivity in certain logical inferences.

Some premises in the Frauchiger-Renner experiment are logically incompatible.

Wigner/friend experiments are impossible on macroscopic objects.

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 ...