The original Wigner’s friend paradox within a realist toy model

The original Wigner’s friend paradox is a gedankenexperiment involving an observer described by an external agent. The paradox highlights the tension between unitary evolution and collapse in quantum theory, and is sometimes taken as requiring a reassessment of the notion of objective reality. In this note, however, we present a classical toy model in which (i) the contradicting predictions at the heart of the thought experiment are reproduced (ii) every system is in a well-defined state at all times. The toy model shows how puzzles such as Wigner’s friend’s experience of being in a superposition, conflicts between different agents’ descriptions of the experiment, the positioning of the Heisenberg’s cut and the apparent lack of objectivity of measurement outcomes can be explained within a classical model where there exists an objective state of affairs about every physical system at all times. Within the model, the debate surrounding the original Wigner’s friend thought experiment and its resolution have striking similarities with arguments concerning the nature of the second law of thermodynamics. The same conclusion however does not apply to more recent extensions of the gedankenexperiment featuring multiple encapsulated observers, and shows that such extensions are indeed necessary avoid simple classical explanations.

Wigner’s Friend Scenarios and the Internal Consistency of Standard Quantum Mechanics

Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two Observers and two Friends. We investigate this problem by invoking the basic rules of quantum mechanics as outlined by Feynman in the well-known “Feynman Lectures on Physics”. We show here that these “Feynman rules” constrain the a priori assumptions which can be made in generalised Wigner’s friend scenarios, because the existence of the probabilities of interest ultimately depends on the availability of physical evidence (material records) of the system’s past. With these constraints obeyed, a non-ambiguous and consistent account of all measurement outcomes is obtained for all agents, taking part in various Wigner’s Friend scenarios.

Generalized probability rules from a timeless formulation of Wigner's friend scenarios

The quantum measurement problem can be regarded as the tension between the two alternative dynamics prescribed by quantum mechanics: the unitary evolution of the wave function and the state-update rule (or "collapse") at the instant a measurement takes place. The notorious Wigner's friend gedankenexperiment constitutes the paradoxical scenario in which different observers (one of whom is observed by the other) describe one and the same interaction differently, one –the Friend– via state-update and the other –Wigner– unitarily. This can lead to Wigner and his friend assigning different probabilities to the outcome of the same subsequent measurement. In this paper, we apply the Page-Wootters mechanism (PWM) as a timeless description of Wigner's friend-like scenarios. We show that the standard rules to assign two-time conditional probabilities within the PWM need to be modified to deal with the Wigner's friend gedankenexperiment. We identify three main definitions of such modified rules to assign two-time conditional probabilities, all of which reduce to standard quantum theory for non-Wigner's friend scenarios. However, when applied to the Wigner's friend setup each rule assigns different conditional probabilities, potentially resolving the probability-assignment paradox in a different manner. Moreover, one rule imposes strict limits on when a joint probability distribution for the measurement outcomes of Wigner and his Friend is well-defined, which single out those cases where Wigner's measurement does not disturb the Friend's memory and such a probability has an operational meaning in terms of collectible statistics. Interestingly, the same limits guarantee that said measurement outcomes fulfill the consistency condition of the consistent histories framework.

A microscopic model of wave-function decoherence in the double-slit experiment

The act of measurement on a quantum state is supposed to “decohere” and “collapse” the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schr¨odinger’s equation [2]. Progress has, however, been made in studying this problem with two main calculation tools - one uses a time-independent Hamiltonian [18], while a rather more general approach proving that decoherence occurs under some generic conditions [21]. The two general approaches to the study of wave-function collapse are as follows. The first approach, called the “consistent” or “decoherent”’ histories approach [11], studies microscopic histories that diverge probabilistically and explains collapse as an event in our particular history. The other, referred to as the “environmental decoherence” approach[8, 21] studies the effect of the environment upon the quantum system, to explain wave-function decoherence. Then collapse is produced by irreversible effects of various sorts. In the “environmental decoherence” approach, one writes down a Markovian-approximated Master equation to study the time-evolution of the reduced density matrix and obtains the long-time dependence of the off-diagonal elements of this matrix. The calculation in this paper studies the evolution of a quantum system under the “environmental” approach, with a rather important analytic difference. We start from the Schr¨odinger equation for the state of the system, with a time-dependent Hamiltonian that reflects the actual microscopic interactions that are occurring. Then we systematically solve for the time-evolved state, without invoking a Markovian approximation when writing out the effective time-evolution equation, i.e., keeping the evolution unitary until the end. This approach is useful and it allows the system wave-function to explicitly “un-collapse” if the measurement apparatus is sufficiently small. However, in the limit of a macroscopic system, collapse is a temporary state that will simply take extremely long (of the order of multiple universe lifetimes) to reverse. While this has been attempted previously [12], we study a particularly simple and calculable example. We make some connections to the work by Linden et al [21] while doing so. The calculation in this paper has interesting implications for the interpretation of the Wigner’s friend experiment, as well as the Mott experiment, which is explored in Sections V and VI (especially the enumerated points in Section VI). The upshot is that as long as Wigner’s friend is macroscopically large (or uses a macroscopically large measuring instrument), no one needs to worry that Wigner would see something different from his friend. Indeed, Wigner’s friend does not even need to be conscious during the measurement that she conducts. In particular, as a result of the mathematical analysis, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential. Instead, it is the usual Fermigolden rule result. The long-term behavior is, of course, still exponential. This is a second novel feature of the paper - we connect the short-term Fermi-golden rule (quadratic-in-time behavior) transition probability to the exponential long-time behavior of a collapsing wave-function in one continuous mathematical formulation.

Wigner’s friend and Relational Quantum Mechanics: A Reply to Laudisa

Relational Quantum Mechanics is an interpretation of quantum mechanics proposed by Carlo Rovelli. Rovelli argues that, in the same spirit as Einstein’s theory of relativity, physical quantities can only have definite values relative to an observer. Relational Quantum Mechanics is hereby able to offer a principled explanation of the problem of nested measurement, also known as Wigner’s friend. Since quantum states are taken to be relative states that depend on both the system and the observer, there is no inconsistency in the descriptions of the observers. Federico Laudisa has recently argued, however, that Rovelli’s description of Wigner’s friend is ambiguous, because it does not take into account the correlation between the observer and the quantum system. He argues that if this correlation is taken into account, the problem with Wigner’s friend disappears and, therefore, a relativization of quantum states is not necessary. I will show that Laudisa’s criticism is not justified. To the extent that the correlation can be accurately reflected, the problem of Wigner’s friend remains. An interpretation of quantum mechanics that provides a solution to it, like Relational Quantum Mechanics, is therefore a welcome one.

Implications of Local Friendliness Violation for Quantum Causality

We provide a new formulation of the Local Friendliness no-go theorem of Bong et al. [Nat. Phys. 16, 1199 (2020)] from fundamental causal principles, providing another perspective on how it puts strictly stronger bounds on quantum reality than Bell’s theorem. In particular, quantum causal models have been proposed as a way to maintain a peaceful coexistence between quantum mechanics and relativistic causality while respecting Leibniz’s methodological principle. This works for Bell’s theorem but does not work for the Local Friendliness no-go theorem, which considers an extended Wigner’s Friend scenario. More radical conceptual renewal is required; we suggest that cleaving to Leibniz’s principle requires extending relativity to events themselves.

Quantum erasing the memory of Wigner's friend

The Wigner's friend paradox concerns one of the most puzzling problems of quantum mechanics: the consistent description of multiple nested observers. Recently, a variation of Wigner's gedankenexperiment, introduced by Frauchiger and Renner, has lead to new debates about the self-consistency of quantum mechanics. At the core of the paradox lies the description of an observer and the object it measures as a closed system obeying the Schrödinger equation. We revisit this assumption to derive a necessary condition on a quantum system to behave as an observer. We then propose a simple single-photon interferometric setup implementing Frauchiger and Renner's scenario, and use the derived condition to shed a new light on the assumptions leading to their paradox. From our description, we argue that the three apparently incompatible properties used to question the consistency of quantum mechanics correspond to two logically distinct contexts: either one assumes that Wigner has full control over his friends' lab, or conversely that some parts of the labs remain unaffected by Wigner's subsequent measurements. The first context may be seen as the quantum erasure of the memory of Wigner's friend. We further show these properties are associated with observables which do not commute, and therefore cannot take well-defined values simultaneously. Consequently, the three contradictory properties never hold simultaneously.