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arXiv:2305.16194 · Journal for General Philosophy of Science

The Evolution of the Bell Notion of Beable: From Bohr to Primitive Ontology

Federico Laudisa

Published Jun 25, 2024• 1 citation
arXivHTMLPDF

Abstract

Abstract John S. Bell introduced the notion of beable, as opposed to the standard notion of observable, in order to emphasize the need for an unambiguous formulation of quantum mechanics. In the paper I show that Bell formulated in fact two different theories of beables. The first is somehow reminiscent of the Bohr views on quantum mechanics but, at the same time, is curiously adopted by Bell as a critical tool against the Copenhagen interpretation, whereas the second, more mature formulation was among the sources of inspiration of the so-called Primitive Ontology (PO) approach to quantum mechanics, an approach inspired to scientific realism. In the first part of the paper it is argued that, contrary to the Bell wishes, the first formulation of the theory fails to be an effective recipe for addressing the ambiguity underlying the standard formulation of quantum mechanics, whereas it is only the second formulation that successfully paves the way to the PO approach. In the second part, I consider how the distinction between the two formulations of the Bell theory of beables fares vis-a-vis the complex relationship between the theory of beables and the details of the PO approach.

DOI
10.1007/s10838-024-09675-8

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Abstract John S. Bell introduced the notion of beable, as opposed to the standard notion of observable, in order to emphasize the need for an unambiguous formulation of quantum mechanics. In the paper I show that Bell formulated in fact two different theories of beables. The first is somehow reminiscent of the Bohr views on quantum mechanics but, at the same time, is curiously adopted by Bell as a critical tool against the Copenhagen interpretation, whereas the second, more mature formulation was among the sources of inspiration of the so-called Primitive Ontology (PO) approach to quantum mechanics, an approach inspired to scientific realism. In the first part of the paper it is argued that, contrary to the Bell wishes, the first formulation of the theory fails to be an effective recipe for addressing the ambiguity underlying the standard formulation of quantum mechanics, whereas it is only the second formulation that successfully paves the way to the PO approach. In the second part, I consider how the distinction between the two formulations of the Bell theory of beables fares vis-a-vis the complex relationship between the theory of beables and the details of the PO approach.
When discussing quantum ontology, the debate has recently focused on comparing and contrasting wavefunction realism and its rivals. Among them one finds the primitive ontology approach, which is often conflated with the local beables program. In this paper I wish to clarify what I take to be the distinction between the notion of primitive ontology and the one of local beable. I argue that the primitive ontology is the local beable which allows for a dynamical, constructive explanation which preserves symmetries.
Collapse theories are versions of quantum mechanics according to which the collapse of the wave function is a real physical process. They propose precise mathematical laws to govern this process and to replace the vague conventional prescription that a collapse occurs whenever an "observer" makes a "measurement." The "primitive ontology" of a theory (more or less what Bell called the "local beables") are the variables in the theory that represent matter in space-time. There is no consensus about whether collapse theories need to introduce a primitive ontology as part of their definition. I make some remarks on this question and point out that certain paradoxes about collapse theories are absent if a primitive ontology is introduced.
Niels Bohr, considered one of the fathers of quantum mechanics, formulated a complex interpretation \nof quantum mechanics that guided his understanding of quantum experiments. The contemporary dispute \nbetween realism and anti-realism, the two main approaches to the interpretation of quantum mechanics, \nis often based on different attitudes towards or even readings of Bohr. We propose that a better \nunderstanding of Bohr’s philosophical thought can contribute to the contemporary reconciliation of \nthese opposing philosophical views and thus to a better understanding of the quantum world. Unfortunately, \nin many contemporary interpretations, Bohr’s philosophical approach to quantum mechanics \nhas been misunderstood, re-interpreted or labelled as ambiguous. This is mostly due to the dispersion \nof Bohr’s complex and unique interpretation through different texts, never united in a single systematically \nconceptualized work. To comprehensively explain Bohr’s philosophical approach and his main \nphilosophical concepts, we consider the many similarities between Bohr’s and Husserl’s philosophical \napproach to science. Husserl developed his philosophical standpoint in a cultural context similar to \nBohr’s and shared Bohr’s objects of philosophical consideration as well as his approach to these objects. \nParallel reading of Bohr’s and Husserl’s texts reveals the closeness between Bohr’s ontological realism— \nepistemological anti-realism standpoint and Husserl’s phenomenological standpoint. This explains \ntheir similar views on the relationship between mathematical language, scientific method and Nature. \nWhile Bohr’s use of the term phenomenon is not equal to Husserl’s, Husserl’s rigorous philosophical \nexplanation of the term helps us to better understand Bohr’s use. Furthermore, the parallel reading \nfacilitates better understanding of one of Bohr’s main philosophical theses, often labelled as ambiguous \nand interpreted in different ways, that it is necessary to use classical concepts to describe quantum phenomena. \nWe claim that the thesis is connected with the advance of epistemological reconsideration of \nscience at the time of Bohr’s writing. Thus, Bohr considers some parts of argumentation as self-evident, \nwhile they are not evident to the contemporary reader. Husserl’s analysis of the relationship between science and the life-world offers a much-needed background for a comprehensive understanding of \nBohr’s thesis. The insight into the similarities between Bohr’s and Husserl’s philosophical approach \nto science and scientific phenomena enables a philosophically rigorous reading of Bohr’s texts; it can \neliminate some of the disagreements between realists and anti-realists and provide a firmer philosophical \nground for a dialog between them.
I distinguish two senses in which one can take a given physical theory to be `complete'. On the first, a complete physical theory is one that, in principle, completely describes physical reality. On the second, a complete physical theory is one that provides all of the conceptual resources one needs to describe any (in general probabilistic) physical phenomenon to any level of detail one likes, in principle. I argue that while the (neo-)Everettian approach to interpreting quantum mechanics aims to show that it is complete in the first sense, the (neo-)Bohrian approach begins from an understanding of quantum mechanics as being complete in the second sense. I then discuss some of the essential differences between how classical and quantum theory describe phenomena, and the way in which the quantum description can be thought of as a ``natural generalisation'' (to use Bohr's phrase) of the classical description. Finally, I elaborate upon the two visions of physics from which one can motivate the first and the second sense of completeness, respectively: \emph{metaphysical realism}, on the one hand, and what I will call \emph{methodological realism}, on the other -- and discuss what one can say about the significance of the differences between quantum and classical description from each of these points of view. I suggest that there is a sense in which the views of (neo-)Everett and the views of (neo-)Bohr can be understood to be mutually supporting positions, from their respective perspectives, even though they are diametrically opposed.
In this paper, I wish to connect the recent debate in the philosophy of quantum mechanics concerning the nature of the wave function to the historical debate in the philosophy of science regarding the tenability of scientific realism. Advocating realism about quantum mechanics is particularly challenging when focusing on the wave function. According to the wave function ontology approach, the wave function is a concrete physical entity. In contrast, according to an alternative viewpoint, namely the primitive ontology approach, the wave function does not represent physical objects. In this paper, I argue that the primitive ontology approach can naturally be interpreted as an instance of the so-called explanationist realism, which has been proposed as a response to the pessimistic-meta induction argument against scientific realism. If my arguments are sound, then one could conclude that: (1) contrary to what is commonly thought, if explanationism realism is a good response to the pessimistic-meta induction argument, it can be straightforwardly extended also to the quantum domain; (2) the primitive ontology approach is in better shape than the wave function ontology approach in resisting the pessimistic-meta induction argument against scientific realism.
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.