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arXiv:2205.08539 · Academia Letters

Randomness in Relational Quantum Mechanics

Gary Gordon

Published Aug 12, 2021• 0 citations
arXivHTMLPDF

Abstract

The relational interpretation of quantum mechanics (RQM), introduced in its present form by Carlo Rovelli in 1996, involves a number of significant departures from other QM interpretations widely discussed in the literature. We begin here by summarizing these unique RQM features, with a focus on those that suggest altered insights into the nature of the randomness exhibited in QM phenomena. One of these RQM features is the assumption that all objects in the universe are quantum objects, regardless of their material complexity. And, the interaction of any two objects can result in new relational quantum states of each of the objects with the other as reference. But such new states do not replace relational states corresponding to previous interactions with other reference objects. In particular, such earlier relational states that include a variable considered to be random do not collapse to define a determined value of the variable, but instead simply take on that specific value in the state relative to the new reference. The concept of randomness associated with quantum state variables in RQM thus differs from that in other QM interpretations. Rather than take the usual pedantic approach of elaborate side-by-side comparisons between the RQM and other common QM interpretations, we illustrate these differences by describing in some detail the well-known "dual-slit" experiment in terms of RQM concepts, pointing out the important advantages over other interpretations along the way. Of course, we suggest no change in dual-slit experiment results, but believe that the interpretative modifications are helpful and profound.

DOI
10.20935/al2764

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The relational interpretation of quantum mechanics (RQM), introduced in its present form by Carlo Rovelli in 1996, involves a number of significant departures from other QM interpretations widely discussed in the literature. We begin here by summarizing these unique RQM features, with a focus on those that suggest altered insights into the nature of the randomness exhibited in QM phenomena. One of these RQM features is the assumption that all objects in the universe are quantum objects, regardless of their material complexity. And, the interaction of any two objects can result in new relational quantum states of each of the objects with the other as reference. But such new states do not replace relational states corresponding to previous interactions with other reference objects. In particular, such earlier relational states that include a variable considered to be random do not collapse to define a determined value of the variable, but instead simply take on that specific value in the state relative to the new reference. The concept of randomness associated with quantum state variables in RQM thus differs from that in other QM interpretations. Rather than take the usual pedantic approach of elaborate side-by-side comparisons between the RQM and other common QM interpretations, we illustrate these differences by describing in some detail the well-known "dual-slit" experiment in terms of RQM concepts, pointing out the important advantages over other interpretations along the way. Of course, we suggest no change in dual-slit experiment results, but believe that the interpretative modifications are helpful and profound.
Abstract The following paper explores the metaphysical significance of Relational Quantum Mechanics (RQM). For this, I will first outline Rovelli’s philosophical framework, and then offer a reconstruction of Rovelli’s seminal argument in favour of RQM. I will then explore some healthy lines of philosophical work that may be undertaken to strengthen RQM. First, I will frame RQM in the debate between realist and antirealist readings of QM and defend the general claim that RQM is compatible with realism. Then, I discuss the main ontological interpretations of RQM, which I classify as “dispositional”, “transcendental” and “structural”, and argue that all of them remain committed to substantialist assumptions that limit the radicality of Rovelli’s proposal. Finally, I analyse recent developments on RQM’s ontology and suggest that preserving its ontological originality requires an assessment on the concept of “pattern”.
Relational quantum mechanics (RQM) purportedly resolves the measurement problem by the postulate that physical variables can take determinate values that are relational in the sense that they are indexed to particular systems. Physical variables take on relational definite values if and only if two systems interact. The discrete nature of interactions required creates an ambiguity as to whether quantum events take place in the context of weak and continuous measurements and interactions. We provide a careful analysis of this problem, explain what a full solution to this problem would require, and then analyse certain proposed resolutions - finding all of them to be insufficient in their present form. Since ‘interactions’ (and the quantum events they underpin) are central to all versions of RQM, no version of RQM presented in the literature so far resolves the measurement problem.
This paper discusses perspectivism and relationalism in the two versions of Relational Quantum Mechanics (RQM): that initiated by Rovelli ( Int. J. Theor. Phys. , 35 (8), 1637–1678 1996) and the other, by Adlam and Rovelli ( Philos. Phys. , 1 (1) 2023). To this end, we offer a substantial discussion of this interpretation. We investigate the issue of the disagreement of results between different observers; distinguish four senses of agreement: strong, weak, very weak, and perspectival; and argue that the old version guarantees only the very weak and perspectival agreement, whereas the new version guarantees the weak agreement as well. The problem that individuals in RQM need to be propertyless when they do not interact is also investigated. Concerning the issue of probabilities in RQM, we argue that to express probabilities involving events relative to different systems, a new kind of probability spaces needs to be devised. The final problem that we identify concerns underspecified dynamics; we argue that some additional postulates are indispensable to make RQM’s dynamics fully specified. The last two points lead to the conclusion that, contrary to declarations of RQM proponents, this interpretation requires some modifications of quantum formalism and not merely conceptual changes. Finally, concerning the problem of testimony, while the new version of RQM was devised to solve it, we argue that in the old version, this problem can be alleviated to the extent that perspectivism permits.
Conceptual Problems in Quantum Cosmology The application of quantum theory to cosmology raises a number of conceptual questions, such as the role of the quantum-mechanical notion of “observer” or the absence of a time variable in the Wheeler–DeWitt equation. I point out that a relational formulation of quantum mechanics, and more in general the observation that evolution is always relational, provides a coherent solution to this tangle of problems. A number of confusing issues appear when we try to apply quantum mechanics to cosmology. Quantum mechanics, for instance, is generally formulated in terms of an observer making measurements on a system. In a laboratory experiment, it is easy to identify the system and the observer: but what is the observer in quantum cosmology? Is it part of the same universe described by the cosmological theory, or should we think of it as external to the universe? Furthermore, the basic quantum dynamical equation describing a system including gravity is not the Schrödinger equation, but rather the Wheeler–DeWitt equation, which has no time parameter: is this related to the absence of an observer external to the universe? How do we describe the quantum dynamics of the universe without a time variable in the dynamical equation and without an observer external to the universe? I suggest that clarity on these issues can be obtained by simply recognizing the relational nature of quantum mechanics and more in general the relational nature of physical evolution. In the context of quantum theory, this nature is emphasized by the so-called relational interpretation of quantum mechanics (Rovelli, 1996). The relational nature of evolution, on the other hand, has been pointed out by the partial-observable formulation of general covariant dynamics (Rovelli, 2002). A central observation is that there is a common confusion between two different meanings of the expression “cosmology”. This is discussed below, in Section 15.1.1. A considerable amount of the difficulties mentioned above stems, I argue, from this confusion. The discussion clarifies on the role of the quantum mechanical observer in cosmology, which is considered in Section 15.1.2. In Section 15.2, I briefly describe the relational interpretation of quantum mechanics and some related aspects of quantum theory.
In this paper I present and defend Rovelli's relation quantum mechanics from some foreseeable objections, so as to clarify its philosophical implications vis a vis rival interpretations. In particular I ask whether RQM presupposes a hidden recourse to both a duality of evolutions and of ontology (the relationality of quantum world and the intrinsicness of the classical world, which in the limit must be recovered from the former). I then concentrate on the pluralistic, antimonistic metaphysical consequences of the theory, due to the impossibility of assigning a state to the quantum universe. Finally, in the last section I note interesting consequences of RQM with respect to the possibility of defining a local, quantum relativistic becoming (in flat spacetimes).Given the difficulties of having the cosmic form of becoming that would be appropriate for priority monism, RQM seems to present an important advantage with respect to monistic views, at least as far as the possibility of explaining our experience of time is concerned.