It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every quantum theory is challenged. In the present essay, we critically discuss this claim by showing that classical logic can be rehabilitated in a quantum context by taking into account Bohmian mechanics. It will be argued, indeed, that such a theoretical framework provides the necessary conceptual tools to reintroduce a classical logic of experimental propositions by virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be shown that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact that is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap.
It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every quantum theory is challenged. In the present essay, we critically discuss this claim by showing that classical logic can be rehabilitated in a quantum context by taking into account Bohmian mechanics. It will be argued, indeed, that such a theoretical framework provides the necessary conceptual tools to reintroduce a classical logic of experimental propositions by virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be shown that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact that is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap.
This paper reviews the structure of standard quantum mechanics, introducing the basics of the von Neumann-Dirac axiomatic formulation as well as the well-known Copenhagen interpretation. We review also the major conceptual difficulties arising from this theory, first and foremost, the well-known measurement problem. The main aim of this essay is to show the possibility to solve the conundrums affecting quantum mechanics via the methodology provided by the primitive ontology approach. Using Bohmian mechanics as an example, the paper argues for a realist attitude towards quantum theory. In the second place, it discusses the Quinean criterion for ontology and its limits when it comes to quantum physics, arguing that the primitive ontology programme should be considered as an improvement on Quine's method in determining the ontological commitments of a theory.
Abstract The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either ‘true ’ or ‘false’, describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of ‘no go ’ theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton ‘uniqueness theorem ’ is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences.
Since its inception Bohmian mechanics has been generally regarded as a hidden-variable theory aimed at providing an objective description of quantum phenomena. To date, this rather narrow conception of Bohm’s proposal has caused it more rejection than acceptance. Now, after 65 years of Bohmian mechanics, should still be such an interpretational aspect the prevailing appraisal? Why not favoring a more pragmatic view, as a legitimate picture of quantum mechanics, on equal footing in all respects with any other more conventional quantum picture? These questions are used here to introduce a discussion on an alternative way to deal with Bohmian mechanics at present, enhancing its aspect as an efficient and useful picture or formulation to tackle, explore, describe and explain quantum phenomena where phase and correlation ( entanglement ) are key elements. This discussion is presented through two complementary blocks. The first block is aimed at briefly revisiting the historical context that gave rise to the appearance of Bohmian mechanics, and how this approach or analogous ones have been used in different physical contexts. This discussion is used to emphasize a more pragmatic view to the detriment of the more conventional hidden-variable (ontological) approach that has been a leitmotif within the quantum foundations. The second block focuses on some particular formal aspects of Bohmian mechanics supporting the view presented here, with special emphasis on the physical meaning of the local phase field and the associated velocity field encoded within the wave function. As an illustration, a simple model of Young’s two-slit experiment is considered. The simplicity of this model allows to understand in an easy manner how the information conveyed by the Bohmian formulation relates to other more conventional concepts in quantum mechanics. This sort of pedagogical application is also aimed at showing the potential interest to introduce Bohmian mechanics in undergraduate quantum mechanics courses as a working tool rather than merely an alternative interpretation.
This book discusses the ontology in the quantum world and argues that it should be interpreted as a historicized ontology. This perspective is advocated by the quantum histories interpretation. Inspired by the nomological interpretation from Bohmian mechanics and the corresponding understanding of the law of nature and logic, the ontology will be useful to solve the difficulties of confusing ontology and perplexing logical inference. Furthermore, this book proposes that the historicized ontology can be generalized to more complicated structures and fit naturally into temporal correlation. Core philosophical issues such as the law of nature, the ontology of events, history, and processes, and the metaphysics of history are coherently discussed, revealing the profound meaning behind the formalism of quantum histories. By providing a new framework for a historicized picture of ontology, it will effectively promote the debates in the philosophy of physics and the fundamental research in quantum mechanics. This book will appeal to scholars and students of the philosophy of science, metaphysics, and quantum theory.
Abstract Despite the successful development of quantum chemistry, the deep breakdown between the conceptual basis of standard quantum mechanics and some implicit ontological assumptions of quantum chemistry is only rarely acknowledged. In fact, in the framework of standard quantum mechanics, quantum systems are not individual objects in the philosophical sense: they cannot be individualized by their positions in space and time and, as a consequence, they have no trajectories. By contrast, the basic magnitude in quantum chemistry is the electronic density, which is commonly interpreted in terms of the definite positions occupied by the individual electron in its motion around the nucleus. In the present paper, it will be argued that Bohmian Mechanics offers an ontological picture that is much closer to the quantum chemists’ way of conceiving their research field.
In recent literature, it has become clear that quantum physics does not refute Humeanism. This point has so far been made with respect to Bohms quantum theory. Against this background, this paper seeks to achieve the following four results: to generalize the option of quantum Humeanism from Bohmian mechanics to primitive ontology theories in general, to show that this option applies also to classical mechanics, to establish that it requires a commitment to matter as primitive stuff, but no commitment to natural properties (physicalism without properties, to point out that by removing the commitment to properties, the stock metaphysical objections against Humeanism from quidditism and humility no longer apply. In that way, quantum physics strengthens Humeanism instead of refuting it.