Understanding the Frauchiger-Renner Argument

Abstract

In 2018, Daniela Frauchiger and Renato Renner published an article in Nature Communications entitled 'Quantum theory cannot consistently describe the use of itself.' I clarify the significance of the result and point out a common and persistent misunderstanding of the argument, which has been attacked as flawed from a variety of interpretational perspectives.

Testing quantum theory with thought experiments

“…However, as pointed out by Bub [65], the contradiction arising in the FR thought experiment is largely independent of how one interprets the term "certainty", provided that the interpretation is compatible with the reasoning rules Q, C, and S. In other words, Q, C, and S can be themselves ). This measurement may be represented by a circuit diagram with one wire for L and one additional wire where the measurement outcome w is stored.…”

“…(See also the further extension of this theorem in[26]. )13 The necessity of this part of the assumption was noted by Bub[65]. In fact, taking seriously the idea that all statements must be relative to agents, it may be phrased as follows: If an agent A has established the statement "I am certain that agent B observes z = ζ at time t." then A can infer the statement "I am certain that agent B is certain that z = ζ at time t."…”

Agents governed by quantum mechanics can use it intersubjectively and consistently

“…B. The post-FR intellectual landscape FR's discussion with regard to the status of their provisional axioms in various extant interpretations has since been supplemented by others' work that has given detailed interpretation-specific accounts [3][4][5][6][7][8][9][10], addressed the issue in the language of formal logical systems [11,12], examined the FR theorem in connection with the philosophical underpinnings of science [13], and altogether advanced a vast variety of frontiers in light of the theorem.…”

Comment on "Understanding the Frauchiger-Renner argument" by Jeffrey Bub

“…Bub's italics do not make this a true statement. Its falsity becomes clear in Bub's next paragraph but one 1 , where he describes the step in the Frauchiger-Renner thought experiment in which the agent F makes an inference about the result of a future measurement by W of a variable w. This inference is based on the result of a measurement by F of the variable r (the result of a quantum coin toss) and her subsequent action. To make the inference as required for the Frauchiger-Renner argument, F must apply unitary evolution (incorporating the future conduct of the experiment) to the state in which r takes the value given by her measurement, not to the global quantum state -in other words, she must assume that the quantum state undergoes a projection (or "collapse").…”