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Quantum theory has no problem consistently describing the use of itself

Guang Ping He

Published Oct 16, 2018• 1 citation
OpenAlex

Abstract

In a recent publication in Nature Communications by Frauchiger and Renner (Nat. Commun. 9, 3711 (2018)), a Gedankenexperiment was proposed, which was claimed to be able to lead to inconsistent conclusions with a self-referential use of quantum theory. Thus it seems to prove that quantum theory cannot consistently describe the use of itself. Shortly after, Chen and Zhang suggested an improvement (arXiv:1810.01080) which can made the explanation of the Gedankenexperiment become consistent. Here we show that from the viewpoint of any quantum interpretation theory which agrees that there is collapse of the wavefunction when being measured (e.g., the Copenhagen interpretation), the original conclusions of Frauchiger and Renner actually came from an incorrect description of some quantum states. With the correct description there will be no inconsistent results, even without modifying the original Gedankenexperiment.

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We show that the quantum description of measurement based on decoherence fixes the bug in quantum theory discussed in [D. Frauchiger and R. Renner, {\em Quantum theory cannot consistently describe the use of itself}, Nat. Comm. {\bf 9}, 3711 (2018)]. Assuming that the outcome of a measurement is determined by environment-induced superselection rules, we prove that different agents acting on a particular system always reach the same conclusions about its actual state.

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Comments on "Quantum theory cannot consistently describe the use of itself"

Chen, Liang, Ye-Qi Zhang

Recently, a delicately designed Gedankenexperiment was proposed to check the self-consistence of quantum theory in the description of the agents who are using this theory. It was demonstrated that the quantum theory is inconsistent. Here a critical improvement is presented, which can lead to a consistent explanation of the Gedankenexperiment by using quantum theory.

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Comment on Frauchiger and Renner paper (Nat. Commun. 9, 3711 (2018)): the problem of stopping times

P. B. Lerner

The Gedankenexperiment advanced by Frauchiger and Renner in their "Nature" paper was based on an implicit assumption that one can synchronize stochastic measurement intervals between two non-interacting systems. This hypothesis, the author demonstrates, is equivalent to the complete entanglement of these systems. Consequently, Frauchiger and Renner's postulate Q is meaningless and needs to be narrowed. Accurate reformulation of the postulate Q1 does not entail any paradoxes with measurement. This paper is agnostic concerning particular interpretations of quantum mechanics. Nor does it refer to the "collapse of the wavefunction."

arXiv:1906.02333•Jun 5, 2019•0 citations

To the rescue of Copenhagen interpretation

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A recent paper "Single-world interpretations of quantum theory cannot be self-consistent" [arXiv:1604.07422] by D. Frauchiger and R. Renner has attracted a considerable interest of a broader physics audience and shortly elicited a number of replies. In spite of the objections that ensued, we find that significant part of the controversial initial claim has not been refuted - on the contrary, arguments presented both in the initial paper and in the replies seem to leave no longer room for the basic Copenhagen interpretation of quantum mechanics. We revisit the controversy trying to pinpoint the exact phenomenon that lies in its core, pointing out to some aspects of the problem that seem to have been mostly overlooked. Taking all conclusions into account, we here propose novel ways to approach the ostensible paradox, in which the Copenhagen interpretation is naturally preserved. Whereas arguments presented in Frauchiger and Renner paper and the replies that followed revolve over whether Wigner's friend would perceive only one or both of the possible outcomes, we offer the third, pretty obvious solution - namely, that Wigner's friend, in the well known setup, would subjectively perceive {\it none} of the potentially conflicting outcomes. As a side note, we also argue that, contrary to the often stated beliefs, hypothetical real experimental realization of Wigner's friend thought experiment actually would not provide us with any new insight into the quantum mechanics.

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Consistency in the description of quantum measurement: Quantum theory can consistently describe the use of itself

Joseph M. Renes

Recent extended formulations of the Wigner's friend thought experiment throw the measurement problem of quantum mechanics into sharper relief. Here I respond to an invitation by Renner to provide a consistent and concrete set of rules for quantum mechanics which can avoid the apparent paradox formulated by Frauchiger and Renner [Nat. Comm. 9, 3711 (2018)]. I propose a slight addition to standard textbook quantum mechanics, in the form of two rules, which avoids the paradox. The first specifies when a given quantum dynamics can be interpreted as a measurement. Potentially any dynamics can, but doing so depends on the context of other performed operations. The second requires that a joint context be used to determine whether several different dynamical evolutions can all be interpreted as measurement. The paradox is then avoided because not every participant in the Frauchiger-Renner thought experiment regards the stated dynamical descriptions of the experiment as measurements.

arXiv:2107.02193•Jul 5, 2021•34 citations
In a recent publication in Nature Communications by Frauchiger and Renner
(Nat. Commun. 9, 3711 (2018)), a Gedankenexperiment was proposed, which was
claimed to be able to lead to inconsistent conclusions with a self-referential
use of quantum theory. Thus it seems to prove that quantum theory cannot
consistently describe the use of itself. Shortly after, Chen and Zhang
suggested an improvement (arXiv:1810.01080) which can made the explanation of
the Gedankenexperiment become consistent. Here we show that from the viewpoint
of any quantum interpretation theory which agrees that there is collapse of the
wavefunction when being measured (e.g., the Copenhagen interpretation), the
original conclusions of Frauchiger and Renner actually came from an incorrect
description of some quantum states. With the correct description there will be
no inconsistent results, even without modifying the original
Gedankenexperiment.
Theoretical physics has faced many challenges since the advent of quantum mechanics. Recently, Frauchiger and Renner have presented a no-go theorem, which makes quantum mechanics more controversial. However, from our perspective, the process of proving appears questionable. Therefore, we discuss the validity of their proof approach in this letter. Here, we propose a simple thought experiment that clarifies how correctly the attributed quantum state can be written in problems similar to Frauchiger and Renner's Gedankenexperiment. In the next step, with the help of the correct form of the quantum state, it is demonstrated that a fallacy occurred in the proof of the no-go theorem, which means it cannot be valid because of the wrong proof. Ultimately, getting help from Hardy's paradox, we investigate whether there is an approach to modify their proof in order to lend the no-go theorem validity.
The Gedankenexperiment advanced by Frauchiger and Renner in their "Nature" paper was based on an implicit assumption that one can synchronize stochastic measurement intervals between two non-interacting systems. This hypothesis, the author demonstrates, is equivalent to the complete entanglement of these systems. Consequently, Frauchiger and Renner's postulate Q is meaningless and needs to be narrowed. Accurate reformulation of the postulate Q1 does not entail any paradoxes with measurement. This paper is agnostic concerning particular interpretations of quantum mechanics. Nor does it refer to the "collapse of the wavefunction."
A recent paper "Single-world interpretations of quantum theory cannot be self-consistent" [arXiv:1604.07422] by D. Frauchiger and R. Renner has attracted a considerable interest of a broader physics audience and shortly elicited a number of replies. In spite of the objections that ensued, we find that significant part of the controversial initial claim has not been refuted - on the contrary, arguments presented both in the initial paper and in the replies seem to leave no longer room for the basic Copenhagen interpretation of quantum mechanics. We revisit the controversy trying to pinpoint the exact phenomenon that lies in its core, pointing out to some aspects of the problem that seem to have been mostly overlooked. Taking all conclusions into account, we here propose novel ways to approach the ostensible paradox, in which the Copenhagen interpretation is naturally preserved. Whereas arguments presented in Frauchiger and Renner paper and the replies that followed revolve over whether Wigner's friend would perceive only one or both of the possible outcomes, we offer the third, pretty obvious solution - namely, that Wigner's friend, in the well known setup, would subjectively perceive {\it none} of the potentially conflicting outcomes. As a side note, we also argue that, contrary to the often stated beliefs, hypothetical real experimental realization of Wigner's friend thought experiment actually would not provide us with any new insight into the quantum mechanics.
Recent extended formulations of the Wigner's friend thought experiment throw the measurement problem of quantum mechanics into sharper relief. Here I respond to an invitation by Renner to provide a consistent and concrete set of rules for quantum mechanics which can avoid the apparent paradox formulated by Frauchiger and Renner [Nat. Comm. 9, 3711 (2018)]. I propose a slight addition to standard textbook quantum mechanics, in the form of two rules, which avoids the paradox. The first specifies when a given quantum dynamics can be interpreted as a measurement. Potentially any dynamics can, but doing so depends on the context of other performed operations. The second requires that a joint context be used to determine whether several different dynamical evolutions can all be interpreted as measurement. The paradox is then avoided because not every participant in the Frauchiger-Renner thought experiment regards the stated dynamical descriptions of the experiment as measurements.