One of the reasons for the heated debates around the interpretations of quantum theory is a simple confusion between the notions of formalism versus interpretation. In this note, we make a clear distinction between them and show that there are actually two inequivalent quantum formalisms, namely the relative-state formalism and the standard formalism with the Born and measurement-update rules. We further propose a different probability rule for the relative-state formalism and discuss how Wigner's-friend-type experiments could show the inequivalence with the standard formalism. The feasibility in principle of such experiments, however, remains an open question.
One of the reasons for the heated debates around the interpretations of quantum theory is a simple confusion between the notions of formalism versus interpretation. In this note, we make a clear distinction between them and show that there are actually two inequivalent quantum formalisms, namely the relative-state formalism and the standard formalism with the Born and measurement-update rules. We further propose a different probability rule for the relative-state formalism and discuss how Wigner's-friend-type experiments could show the inequivalence with the standard formalism. The feasibility in principle of such experiments, however, remains an open question.
Recently, it has been stated that single-world interpretations of quantum theory are logically inconsistent. The claim is derived from contradicting statements of agents in a setup combining two Wigner's-friend experiments. Those statements stem from applying the measurement-update rule subjectively, i.e., only for the respective agent's own measurement. We argue that the contradiction expresses the incompatibility of collapse and unitarity - resulting in different formal descriptions of a measurement - and does not allow to dismiss any specific interpretation of quantum theory.
Quantum mechanics is one of our most successful physical theories; its predictions agree with experimental observations to an extremely high accuracy. However, the bare formalism of quantum theory does not provide straightforward answers to seemingly simple questions: for example, how should one model systems that include agents who are themselves using quantum theory? These foundational questions may be investigated with a theorist's tool – the thought experiment. Its purpose is to turn debates about the interpretation of quantum theory into actual physics questions. In this article, we give a state-of-the-art overview on quantum thought experiments involving observers, from the basic Wigner's friend to the recent Frauchiger-Renner setup, clarifying their interpretational significance and responding to objections and criticism on the way.
Extended Wigner’s friend scenarios (EWFSs) model agents themselves as unitarily evolving quantum systems, going beyond the standard use of quantum theory where agents are treated classically. Several no-go results suggest deep challenges in this setting: Frauchiger and Renner argued that quantum agents reasoning using quantum theory would arrive at logical paradoxes, while the local-friendliness theorem raises difficulties for maintaining objective notions of measurement events and causal reasoning in EWFSs. This prompts a key question: Can the ability to make and test scientific predictions and reason consistently still be maintained if quantum theory applies universally, even to agents and their memories? We answer this positively by developing a general quantum circuit framework for EWFSs without assuming absolute measurement outcomes. We formalize Heisenberg cuts in terms of distinct choices of channels in the circuit, labeled by “settings,” and show that Frauchiger-Renner-type paradoxes are fully resolved by making explicit the conditioning on these channels or settings. We provide concrete reasoning rules for quantum agents that ensure logical, probabilistic, and causal consistency. Our framework captures all perspectives in an EWFS within a single causal structure while allowing events to be fundamentally subjective, and we show how objective events and predictions nevertheless emerge in current real-world quantum experiments. Thus, we demonstrate a relational yet operational framework that overcomes key challenges in EWFSs without altering the Born rule, unitarity, or classical logic and probability for outcomes. This establishes a formal platform to analyze and compare different EWFS arguments and extend quantum information methods consistently into the Wigner’s friend domain.
This chapter, based on the background information of the previous chapter, will review the formalism of quantum mechanics – its fundamental mathematical structure (the basic contents of Hilbert space representation and operator algebra representation) and physical assumptions (kinematics, dynamics, and measurement theory). These are the premise and foundation for discussing the quantum histories interpretation. Then, in combination with the viewpoints of some literature in recent years, we will explore what is the interpretation of quantum mechanics, analyze the relationship between the theory of quantum mechanics and its interpretation, and declare the author’s basic stance on these two issues. These two are the primary issues that all interpretive work in the philosophy of physics will face (not limited to the interpretation of quantum mechanics), and the necessary clarification here is also conducive to the subsequent discussion. Three common terms – theory, formalism, and interpretation – are explicated and differentiated by offering the necessary definitions of their meanings, based on the works of Acuña and Ruetsche. The clarification will help to make the subsequent related discussions more precise.
Abstract The purpose of this book is to present an interpretation of quantum mechanics. But what are we talking about when we speak of “quantum mechanics?” Are we talking about a single theory or about many related theories? And what do we mean by “interpretation” here? In this chapter, I will address these questions in an introductory way. Of course, I do not intend to take part in the extensive discussions about what a scientific theory is, what is meant by interpreting a theory, in what situation we encounter equivalent theories, and many other questions related to or derived from these. My aim here is to present some preliminary ideas in a way that I hope will be sufficient to avoid misunderstandings in the following chapters. But, above all, I will state my position as to why, after so many years and so much literature on the subject, the interpretation of quantum mechanics deserves further discussion.
Abstract The notorious Wigner’s friend thought experiment (and modifications thereof) has received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In this paper, we formulate a no-go theorem for the persistent reality of Wigner’s friend’s perception, which allows us to conclude that the perceptions that the friend has of her own measurement outcomes at different times cannot “share the same reality”, if seemingly natural quantum mechanical assumptions are met. More formally, this means that, in a Wigner’s friend scenario, there is no joint probability distribution for the friend’s perceived measurement outcomes at two different times, that depends linearly on the initial state of the measured system and whose marginals reproduce the predictions of unitary quantum theory. This theorem entails that one must either (1) propose a nonlinear modification of the Born rule for two-time predictions, (2) sometimes prohibit the use of present information to predict the future—thereby reducing the predictive power of quantum theory—or (3) deny that unitary quantum mechanics makes valid single-time predictions for all observers. We briefly discuss which of the theorem’s assumptions are more likely to be dropped within various popular interpretations of quantum mechanics.