Wigner\'s friend and quantum clocks

A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational formalism which identifies coordinate systems with elements of a symmetry groupG, we define a general operator for reversibly changing between quantum reference frames associated to a groupG. This generalises the known operator for translations and boosts to arbitrary finite and locally compact groups, including non-Abelian groups. We show under which conditions one can uniquely assign coordinate choices to physical systems (to form reference frames) and how to reversibly transform between them, providing transformations between coordinate systems which are `in a superposition' of other coordinate systems. We obtain the change of quantum reference frame from the principles of relational physics and of coherent change of reference frame. We prove a theorem stating that the change of quantum reference frame consistent with these principles is unitary if and only if the reference systems carry the left and right regular representations ofG. We also define irreversible changes of reference frame for classical and quantum systems in the case where the symmetry groupGis a semi-direct productG=N⋊Por a direct productG=N×P, providing multiple examples of both reversible and irreversible changes of quantum reference system along the way. Finally, we apply the relational formalism and changes of reference frame developed in this work to the Wigner's friend scenario, finding similar conclusions to those in relational quantum mechanics using an explicit change of reference frame as opposed to indirect reasoning using measurement operators.

The scientific method relies on facts, established through repeated measurements and agreed upon universally, independently of who observed them. In quantum mechanics the objectivity of observations is not so clear, most markedly exposed in Wigner's eponymous thought experiment where two observers can experience seemingly different realities. The question whether the observers' narratives can be reconciled has only recently been made accessible to empirical investigation, through recent no-go theorems that construct an extended Wigner's friend scenario with four observers. In a state-of-the-art six-photon experiment, we realize this extended Wigner's friend scenario, experimentally violating the associated Bell-type inequality by five standard deviations. If one holds fast to the assumptions of locality and free choice, this result implies that quantum theory should be interpreted in an observer-dependent way.

Considering a minimal number of assumptions and in the context of the timeless formalism, conditional probabilities are derived for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with detection processes described by generalized measurements (POVM). One-time conditional probabilities are unambiguously derived via the Gleason-Bush theorem, including for puzzling cases like the Wigner's friend scenario where their form underlines the relativity aspect of measurements. No paradoxical situations emerge and the roles of Wigner and Wigner can be seen by his friend as being in a superposition.

According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner's conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner's original thought experiment was central to the development of QBist thinking. The focus of this paper concerns two very instructive modifications to Wigner's puzzle: One, a recent no-go theorem by Frauchiger and Renner, and the other a thought experiment by Baumann and Brukner. We show that the paradoxical features emphasized in these works disappear once both friend and Wigner are understood as agents on an equal footing with regard to their individual uses of quantum theory. Wigner's action on his friend then becomes, from the friend's perspective, an action the friend takes on Wigner. Our analysis rests on a kind of quantum Copernican principle: When two agents take actions on each other, each agent has a dual role as a physical system for the other agent. No user of quantum theory is more privileged than any other. In contrast to the sentiment of Wigner's original paper, neither agent should be considered as in "suspended animation." In this light, QBism brings an entirely new perspective to understanding Wigner's friend thought experiments.

The Demon and the Quantum: From the Pythagorean Mystics to Maxwell’s Demon and Quantum Mystery , Robert J. Scully , with endnotes Marian O. Scully , Wiley-VCH, Weinheim, Germany, 2007. $45.00 (271 pp.). ISBN 978-3-527-40688-3 Reviewed by Gian Paolo Beretta Buy at Amazon

Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory \cite{Rovelli.21}. However, there are significant departures from quantum theory: (i) in RQM measurement outcomes arise from interactions which entangle a system S and an observer A without decoherence, and (ii) such an outcome is a "fact" relative to the observer A, but it is not a fact relative to another observer B who has not interacted with S or A during the foregoing measurement process. For B the system S⊗A remains entangled. We derive a GHZ-like contradiction showing that relative facts described by these statements are incompatible with quantum theory. Hence Relational Quantum Mechanics should not be considered an interpretation of quantum theory, according to a criterion for interpretations that we have introduced. The criterion states that whenever an interpretation introduces a notion of outcomes, these outcomes, whatever they are, must follow the probability distribution specified by the Born rule.

CONCEPTUAL FOUNDATIONS OF QUANTUM MECHANICS: THE ROLE OF EVIDENCE THEORY, QUANTUM SETS, AND MODAL LOGIC

The relationship between physics and phenomenology is a blind spot of current literature in a twofold sense. First, while many phenomenologists work on the interface to psychology, the cognitive sciences, biology, artificial intelligence, etc., only very few engage in phenomenological reflections on physics. This is puzzling since, as we shall see below, Husserl and other classical phenomenologists have been quite clear on the significance of such an undertaking, stressing the central role physics plays among the natural sciences. Secondly, while philosophy of physics has emerged as an important sub-discipline of philosophy in the twentieth century, there is hardly any work that addresses the role of phenomenology for the development of modern physics or the philosophical interpretation of physical theories (with notable exceptions that will be discussed below). This is puzzling since, as we shall see below, the father of modern field theory, Hermann Weyl, was inspired by phenomenological considerations when formulating his gauge principle, and there is a long (although usually unnoticed) history of phenomenological motifs in interpretations of quantum mechanics. Section 15.1 addresses the question of how to interpret physical theories and how to estimate the relationship between mathematical models and physical reality. In Sect. 15.2, we shed light on the perspectivist features of Husserl’s philosophy of science and discuss how it relates to current versions of scientific perspectivism. Section 15.3 addresses how phenomenological ideas have influenced the development and interpretation of early modern physics. In Sect. 15.4, we discuss observer-dependence in modern physics and highlight phenomenological motifs in Wheeler’s conception of “observer-participancy.” Finally, Sect. 15.5 sheds light on phenomenological motifs in a novel interpretation of quantum mechanics, namely QBism, and emphasizes similarities between phenomenology and the program of reconstructing quantum mechanics, a program that currently enjoys popularity in the field of quantum foundations. We shall see that the worldviews delivered by phenomenology and physics might be closer than is commonly assumed.

In his 1939 Lectures, the prominent Soviet physicist L. I. Mandelstam proposed an interpretation of quantum mechanics that was understood in different ways. To assess Mandelstam's interpretation, we classify contemporary interpretations of quantum mechanics and compare his interpretation with others developed in the 1930s (the Copenhagen interpretation and the statistical interpretations proposed by K. R. Popper, H. Margenau, and E. C. Kemble). We conclude that Mandelstam's interpretation belongs to the family of minimal statistical interpretations and has much in common with interpretations developed by American physicists. Mandelstam's characteristic message was his theory of indirect measurement, which influenced his discussion of the “reduction of the wave packet” and the Einstein, Podolsky, and Rosen argument. This article also reconstructs what lay behind Mandelstam's interpretation of quantum mechanics. This was his operationalism, by virtue of which his interpretation resembled Kemble's, in which the statistical and Copenhagen views had been combined. Like Popper and Margenau, Mandelstam followed R. von Mises's empirical conception of probability. Mandelstam, like the other proponents of the statistical approach to quantum mechanics, was affected by the culture of macroscopic experimentation with its emphasis on statistical (collective) measurement.

As sketched in the previous chapter, Niels Bohr’s engagement in the development of quantum theory, especially in its crucial phase around the mid-1920s, proceeded with a critical examination of basic concepts such as continuity/discontinuity, space-time and causality, which underlie not only atomic physics, but the modern-scientific view of nature in general. This led to his introduction in 1927 of the idea of complementarity as an interpretation of quantum theory, newly established as quantum mechanics. While closely linked with Heisenberg’s uncertainty relations, Bohr’s complementarity is marked by its own distinctive philosophical notions and implications. Here and throughout this study (as noted in the Introduction), I use the term ‘complementarity’ to refer not only to Bohr’s concept of complementarity, but – following his own and many commentators’ usage – also to his overall philosophical thought revolving around this concept.

The articles provides a phenomenological reading of the Many-Worlds Interpretation (MWI) of quantum mechanics and its answer to the measurement problem, or the question of “why only one of a wave function’s probable values is observed when the system is measured.” Transcendental-phenomenological and hermeneutic-phenomenological approaches are employed. The project comprises four parts. Parts one and two review MWI and the standard (Copenhagen) interpretation of quantum mechanics. Part three reviews the phenomenologies. Part four deconstructs the hermeneutics of MWI. It agrees with the confidence the theory derives from its (1) unforgiving appropriation of the Schrödinger equation and (2) association of branching universes with the evolution of the wave function insofar as that understanding comes from the formalism itself. Part four also reveals the hermeneutical shortcomings of the standard interpretation.

When a physical theory is in its early stages of development, it presents many concepts and constructs that may not be necessary for its interpretation, or may simply be equivocal. As the theory is developed by the physics community, it hopefully passes through a depuration process that washes away many of these constructs and introduces others not initially devised. This process can be viewed, and modeled, as a semiotic process by which the suggested interpretations of the theory, initially dispersed in the space of concepts, taper off in a way that leaves only a small number of possibilities, ideally only one. However, to qualify this process and impose semiotic and epistemological constraints on the depuration process, it seems natural to consider a physical theory as an excerpt of a language and its suggested interpretations as texts, endowed with syntactics and semantics. In this paper we present this framing of general physical theories and apply the resulting semiotic and epistemological constraints we uphold to the special case of quantum mechanics, which shows particular resistance to interpretation tapering. We then show that the findings of this paper are especially important for allowing one to form a hierarchy of interpretations of the same formal structure of a physical theory, even in the case of an experimental underdetermination of these interpretations, which is precisely the case for quantum mechanics. This result is particularly important for more modern physical theories, which are becoming increasingly more abstract and difficult to interpret.

The modal interpretation of quantum mechanics is a no-collapse interpretation that provides a rule for assigning properties to quantum mechanical systems, depending on their (reduced) quantum state, whether this state be pure or mixed. The modal interpretation was originally developed by Kochen (1985), Dieks (1989) and Healey (1989) (with slight differences) modifying ideas by Van Fraassen (1973, 1991), and was further developed by Vermaas and Dieks (1995) and Clifton (1995). In the original version, the rule for assigning properties is applied to all quantum systems. However, a recent series of no-go theorems by Bacciagaluppi (1995), Clifton (1996) and Vermaas (1997) has shown that this unrestricted application of the rule leads to contradictions. This has prompted some authors (Bacciagaluppi and Dickson, 1999; Dieks, 1998) to restrict application of the rule only to ‘elementary’ or ‘atomic’ systems. We call this version the atomic modal interpretation. In this paper, we shall describe the no-go results, and discuss the picture yielded by the atomic modal interpretation. We shall proceed as follows.

The STA is a mathematical system, rather than of itself containing new physics. However, when we employ it in the description of physical phenomena, we usually find that some fresh insight is obtained, often on old questions. The oldest question of 20th century physics is the interpretation of quantum mechanics, and in this lecture we aim to discuss some of the light that an STA approach can throw upon this issue. This will be undertaken in the context of specific examples, and so in the main these lecture notes contain the details of these, rather than the comments that will be made about issues of interpretation. We think these examples stand as interesting and important applications in their own right, irrespective of whether one thinks there is a problem to be solved in the interpretation of quantum theory. This is particularly true for the beginnings of a multiparticle STA approach which we describe here, since it seems undeniable that there is a need for a more coherent and justifiable rationale for the set of recipes and operational procedures that currently constitute relativistic multiparticle theory.KeywordsQuantum TheoryDirac EquationGeometric AlgebraSpin VectorPauli PrincipleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In the framework of an interference setup in which only two outcomes are possible (such as in the case of a Mach–Zehnder interferometer), we discuss in a simple and pedagogical way the difference between a standard, unitary quantum mechanical evolution and the existence of a real collapse of the wavefunction. This is a central and not-yet resolved question of quantum mechanics and indeed of quantum field theory as well. Moreover, we also present the Elitzur–Vaidman bomb, the delayed choice experiment, and the effect of decoherence. In the end, we propose two simple experiments to visualize decoherence and to test the role of an entangled particle. Quanta 2014; 3: 156–170.