• Corpus ID: 251223593

The Frauchiger-Renner Gedanken Experiment: an Interesting Laboratory for Exploring Some Topics in Quantum Mechanics

@inproceedings{Samuel2022TheFG,
  title={The Frauchiger-Renner Gedanken Experiment: an Interesting Laboratory for Exploring Some Topics in Quantum Mechanics},
  author={Stuart Samuel},
  year={2022}
}

• S. Samuel
• Published 29 July 2022
• Physics

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 tran- sitive 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’–‘OK’ 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 ex- periments, 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” (such as measurements on a spin using a particular axis of quantization), in which case it is straightforward to perform the Frauchiger-Renner experiment in a real laboratory setting.