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arXiv:2308.16220

A review and analysis of six extended Wigner's friend arguments

David Schmid, Yìlè Yīng, Matthew Leifer

Published Aug 30, 2023• 20 citations
arXivHTMLPDF

Abstract

The Wigner's friend thought experiment was intended to illustrate the difficulty one has in describing an agent as a quantum system when that agent performs a measurement. While it does pose a challenge to the orthodox interpretation of quantum theory, most modern interpretations have no trouble in resolving the difficulty. Recently, a number of extensions of Wigner's ideas have been proposed. We provide a gentle introduction to six such arguments, modifying the specifics of many of them so that they are as simple and unified as possible. In particular, we show that all of the arguments hinge on assumptions about correlations between measurement outcomes that are not accessible to any observer, even in principle. We then provide a critical analysis of each argument, focusing especially on how well one can motivate the required assumptions regarding these inaccessible correlations. Although we argue that some of these assumptions are not entirely well-motivated, all of the arguments do shed light on the nature of quantum theory, especially when concerning the description of agents and their measurements.

DOI
10.48550/arxiv.2308.16220

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The Wigner's friend thought experiment was intended to illustrate the difficulty one has in describing an agent as a quantum system when that agent performs a measurement. While it does pose a challenge to the orthodox interpretation of quantum theory, most modern interpretations have no trouble in resolving the difficulty. Recently, a number of extensions of Wigner's ideas have been proposed. We provide a gentle introduction to six such arguments, modifying the specifics of many of them so that they are as simple and unified as possible. In particular, we show that all of the arguments hinge on assumptions about correlations between measurement outcomes that are not accessible to any observer, even in principle. We then provide a critical analysis of each argument, focusing especially on how well one can motivate the required assumptions regarding these inaccessible correlations. Although we argue that some of these assumptions are not entirely well-motivated, all of the arguments do shed light on the nature of quantum theory, especially when concerning the description of agents and their measurements.
This paper presents a critical review of the Wigner’s Friend thought experiment and its modern extensions within quantum mechanics. The study explores observer-dependent reality, measurement theory, quantum state assignment, and interpretational challenges arising from nested observers in quantum systems. Particular attention is given to the Frauchiger–Renner argument and its implications for the consistency of single-world interpretations of quantum mechanics. The paper discusses conceptual tensions between unitarity, observer perspectives, and objective reality, while examining possible resolutions proposed in contemporary quantum foundations research. This work is intended as an independent scholarly review aimed at contributing to discussions in quantum foundations and quantum information theory.
Recent arguments, involving entangled systems shared by sets of Wigner's friend arrangements, allegedly show that the assumption that the experiments performed by the friends yield definite outcomes, is incompatible with quantum predictions. From this, it is concluded that the results of measurements cannot be thought of as being actual or objective. Here, I show that these arguments depend upon a mistaken assumption, regarding the ("mixed") correlations between the results of the friends and those of "the Wigners", which leads to invalid predictions. It is not, then, that the assumption of definite outcomes leads to trouble, but that the results derived with such an assumption are contrasted with faulty predictions. Next, I explore the more famous no-go theorems by Frauchiger and Renner and by Brukner, on which these recent arguments are motivated. Regarding the first, I show that, although it is cast in a different form, it also rests on the mistaken assumption regarding "mixed" correlations--rendering it invalid. Regarding Brukner's theorem, I point out that it depends on the quite unattractive assumption of locality, a fact that fully diminishes its force. Throughout, I illustrate my claims with explicit calculations within pilot-wave theory.
By assuming (i) a universal, observer-independent quantum state, by considering (ii) measurement processes with wave function collapse as part of quantum mechanical time evolution (also within isolated systems), and by (iii) clearly distinguishing the state of a quantum system from the knowledge of conscious observers about this state, we suggest a modified Copenhagen interpretation of quantum mechanics that resolves Wigner's Friend and extended Wigner's Friend paradoxes. The suggested interpretation leads to differences in some outcome probabilities compared to previous analyses which, in principle, make it possible to falsify the suggested modifications or the previous analyses (or both). The fundamental problem of the incompleteness of quantum mechanics in the Copenhagen interpretation regarding the lack of a precise definition and a mechanistic description of the measurement process (including the collapse of the wave function) is not addressed in this study. However, the argumentation regarding the resolution of Wigner's Friend paradoxes also applies to attempts for such a mechanistic description using collapse models with stochastic extensions to the Schrödinger equation or trying to model wave function collapse with unitary time evolution and irreversibility of the measurement process resulting from quantum statistical mechanics.
There has been a surge of recent interest in the Wigner's Friend paradox, sparking several novel thought experiments and no-go theorems. The main narrative has been that Wigner's Friend highlights a counterintuitive feature that is unique to quantum theory, and which is closely related to the quantum measurement problem. Here, we challenge this view. We argue that the gist of the Wigner's Friend paradox can be reproduced without assuming quantum physics, and that it underlies a much broader class of enigmas in the foundations of physics and philosophy. To show this, we first consider several recently proposed Extended Wigner's Friend scenarios, and demonstrate that some of their implications for the absoluteness of observations can be reproduced by classical thought experiments that involve the duplication of agents. Crucially, some of these classical scenarios are technologically much easier to implement than their quantum counterparts. Then, we argue that the essential structural ingredient of all these scenarios is a feature that we call "Restriction A": that a physical theory cannot give us a probabilistic description of the observations of all agents. Finally, we argue that this difficulty is at the core of other puzzles in the foundations of physics and philosophy, and demonstrate this explicitly for cosmology's Boltzmann brain problem. Our analysis suggests that Wigner's Friend should be studied in a larger context, addressing a frontier of human knowledge beyond quantum foundations: to obtain reliable predictions for experiments in which these predictions can be privately but not intersubjectively verified.
The Extended Wigner’s Friend thought experiment, comprising a quantum system containing an agent who draws conclusions upon observing the outcome of a measurement of a quantum state prepared in two nonorthogonal versions by another agent, led its authors to conclude that quantum theory cannot consistently describe the use of itself. It has also been proposed that this thought experiment is equivalent to entangled state (Bell-type) experiments. It is argued in this paper that the assumption of the freedom of choice of the first Wigner’s friend regarding how to prepare a quantum state in one of the two available nonorthogonal versions invalidates such equivalence.
The concept of an isolated system, and Frauchiger and Renner's extended `Wigner's friend' scenario are discussed. It is argued that: (i) it is questionable whether the approximation of the isolated system is valid when measurement-like processes are involved; (ii) one may infer, from Frauchiger and Renner's thought-experiment, and similar thought-experiments, that any interpretation of quantum theory involving *subjective collapse* fails; (iii) this does not distinguish single-world from many-world (relative-state) interpretations of quantum theory; (iv) reasoning from observations has to take into account the possible quantum-erasure of those observations if it is to be valid reasoning; (v) a single-world interpretation is valid if certain kinds of outcome are not quantum-erased in the future.