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arXiv:2009.10218 · Physical Review A

Wigner's friend and the quasi-ideal clock

Vinicius P. Rossi, Diogo O. Soares-Pinto

Published May 14, 2021• 4 citations
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Abstract

In 1962, Eugene P. Wigner [in Philosophical Reflections and Syntheses (Springer, Berlin, 1995), p. 247] introduced a thought experiment that highlighted the incompatibility in quantum theory between unitary evolution and wave function reduction in a measurement. This work resulted in a class of thought experiments often called Wigner's friend scenarios, which have been providing insights over many frameworks and interpretations of quantum theory. Recently, a no-go theorem obtained by D. Frauchiger and R. Renner [Nat. Commun. 9, 3711 (2018)] brought attention back to the Wigner's friend and its potential of putting theories to the test. Many answers to this result pointed out how timing in the thought experiment could be yielding a paradox. In this work, we ask what would happen if the isolated friend in a Wigner's friend scenario did not share a time reference frame with the outer observer, and time were tracked by a quantum clock. For this purpose, we recollect concepts provided by the theory of quantum reference frames and the quantum resource theory of asymmetry, to learn how to internalize time in this scenario, and introduce a model for a feasible quantum clock proposed by M. P. Woods, R. Silva, and J. Oppenheim [Ann. Henri Poincar\'e 20, 125 (2019)] called the quasi-ideal clock. Our results have shown that this approach produces no decoherent behavior, and the disagreement between the superobserver and its friend persists even for an imprecise clock on Wigner's side. However, the Gaussian spread of this clock model can control which observables do not raise a paradox, indicating the relevance of deepening this analysis.

DOI
10.1103/physreva.103.052206

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In 1962, Eugene P. Wigner [in Philosophical Reflections and Syntheses (Springer, Berlin, 1995), p. 247] introduced a thought experiment that highlighted the incompatibility in quantum theory between unitary evolution and wave function reduction in a measurement. This work resulted in a class of thought experiments often called Wigner's friend scenarios, which have been providing insights over many frameworks and interpretations of quantum theory. Recently, a no-go theorem obtained by D. Frauchiger and R. Renner [Nat. Commun. 9, 3711 (2018)] brought attention back to the Wigner's friend and its potential of putting theories to the test. Many answers to this result pointed out how timing in the thought experiment could be yielding a paradox. In this work, we ask what would happen if the isolated friend in a Wigner's friend scenario did not share a time reference frame with the outer observer, and time were tracked by a quantum clock. For this purpose, we recollect concepts provided by the theory of quantum reference frames and the quantum resource theory of asymmetry, to learn how to internalize time in this scenario, and introduce a model for a feasible quantum clock proposed by M. P. Woods, R. Silva, and J. Oppenheim [Ann. Henri Poincar'e 20, 125 (2019)] called the quasi-ideal clock. Our results have shown that this approach produces no decoherent behavior, and the disagreement between the superobserver and its friend persists even for an imprecise clock on Wigner's side. However, the Gaussian spread of this clock model can control which observables do not raise a paradox, indicating the relevance of deepening this analysis.
In 1962, Eugene P. Wigner introduced a thought experiment that highlighted the incompatibility in quantum mechanics between unitary evolution and wave function reduction in a measurement. This work resulted in a class of thought experiments often called Wigner\'s Friend Scenarios, which have been providing insights over many frameworks and interpretations of quantum theory. Recently, a no-go theorem obtained by Daniela Frauchiger and Renato Renner brought attention back to the Wigner\'s Friend and its potential of putting theories to test. Many answers to this result pointed out how timing in the thought experiment could be yielding a paradox. In this work, we ask what would happen if the isolated friend in a Wigner\'s Friend Scenario did not share a time reference frame with the outer observer, and time should be tracked by a quantum clock. For this purpose, we recollect concepts provided by the theory of quantum reference frames and the quantum resource theory of asymmetry, to learn how to internalize time in this scenario, and introduce a model for a feasible quantum clock proposed by Mischa P. Woods, Ralph Silva and Jonathan Oppenheim, called the quasi-ideal clock. Our results have shown that no decoherent behavior comes from this approach, and the disagreement between the superobserver and its friend persists even for an imprecise clock, indicating that the source of paradox in a Wigner\'s Friend Scenario may be elsewhere.
The Wigner’s friend thought experiment has gained a resurgence of interest in recent years thanks to no-go theorems that extend it to Bell-like scenarios. One of these, by us and co-workers, showcased the contradiction that arises between quantum theory and a set of assumptions, weaker than those in Bell’s theorem, which we named ‘Local Friendliness’. Using these assumptions, it is possible to arrive at a set of inequalities for a given scenario, and, in general, some of these inequalities will be harder to violate than the Bell inequalities for the same scenario. A crucial feature of the extended Wigner’s friend scenario in our aforementioned work was the ability of a superobserver to reverse the unitary evolution that gives rise to their friend’s measurement. Here, we present a new scenario where the superobserver can interact with the friend repeatedly in a single experimental instance, either by asking them directly for their result, thus ending that instance, or by reversing their measurement and instructing them to perform a new one. We show that, in these scenarios, the Local Friendliness inequalities will always be the same as Bell inequalities.
This paper offers a comprehensive analysis of Wigner’s Friend paradox (1961), a foundational thought experiment in quantum mechanics that highlights the tension between the internal perspective of a measuring observer (who experiences a definite outcome) and the external perspective of a super-observer who treats the entire laboratory as a quantum system in superposition. It traces the historical lineage from Schrödinger’s cat and von Neumann’s measurement theory, provides a formal mathematical description of the state evolution and logical structure of the paradox, examines implications for major interpretations of quantum mechanics (Copenhagen, Everettian many-worlds, QBism, relational quantum mechanics, and objective collapse theories), and discusses modern extensions such as the Frauchiger–Renner paradox. The work explores profound philosophical and epistemological consequences for the nature of observation, objectivity, intersubjectivity, and the role of consciousness in quantum theory (2026).
How can we address the idea of observers in quantum mechanics? The long-standing Wigner’s friend thought experiment provides a conceptual framework for thinking about this question. It considers the the difficulty of reconciling unitary, evolution of systems and non-unitary state update after a making observations. Following from a recent suggested protocol with two friends that share and entangled state, we prove and investigate, in a photonic experiment, a strong no-go theorem for this Wigner’s friend scenario. Specifically, if quantum mechanics applies at the scale of observers, then there are constraints on the set of assumptions: locality; no-superdeterminism; and absoluteness of observed events. We note that this new theorem places strictly stronger constraints on physical reality than Bell’s theorem.
Wigner’s friend scenarios—in which external agents describe a closed laboratory containing a friend making a measurement—highlight the difficulties of quantum theory when accounting for measurements. The problem is to accommodate for unitary evolution from the point of view of the external agent with the measurements or other operations carried out by the friend. Here, we show in the context of a relativistic thought experiment that an operation that may be accounted for unitarily in a given reference frame cannot be described unitarily in a different reference frame. This result, based on the frame dependence of the state update in relativistic contexts, could point to some fundamental inadequacy when attempting to model actions taken by a complex agent as unitary operations.
The decoherence interpretation of quantum measurements is applied to Wigner's-friend experiments. A framework in which all the experimental outcomes arise from unitary evolutions is proposed. Within it, a measurement is not completed until an uncontrolled environment monitorizes the state composed of the system, the apparatus, and the observer. The (apparent) wave-function collapse and the corresponding randomness result from tracing out this environment; it is thus the ultimate responsible party for the emergence of definite outcomes. Two main effects arise from this fact. First, external interference measurements, trademark of Wigner's-friend experiments, modify the memory records of the internal observers; this framework provides a univocal protocol to calculate all these changes. Second, it can be used to build a consistent scenario for the recently proposed extended versions of the Wigner's-friend experiment. In regard to the work of Frauchiger and Renner [Nat. Commun. 9, 3711 (2018)], this framework shows that the agents' claims become consistent if the changes in their memories are properly taken into account. Furthermore, the particular setup discussed by Brukner [Entropy 20, 350 (2018)] cannot be tested against the decoherence framework, because it does not give rise to well-defined outcomes according to this formalism. A variation of this setup, devised to fill this gap, makes it possible to assign joint truth values to the observations made by all the agents. This framework also narrows the requisites for such experiments, making them virtually impossible to apply to conscious (human) beings. Notwithstanding, it also opens the door to future realizations on quantum machines.