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Philosophy of Science

Idealization and Formalism in Bohr's Approach to Quantum Theory

Scott Tanona

Published Dec 1, 2004• 12 citations
Publisher

Abstract

I reinterpret Bohr's attitude towards quantum mechanical formalism and its empirical content, based on his understanding of the correspondence principle and its approximate applicability. I suggest that Bohr understood complementarity as a limitation imposed by the commutation relations upon the applicability of the idealizations which had grounded the use of the correspondence principle. By discussing this interpretation against the contemporary background of discussions regarding “naïve realism” about operators (as observables), I suggest that a Bohrian view on the empirical content of quantum mechanical operators may provide a middle ground between complete contextualism and an untenable realism about quantum properties.

DOI
10.1086/425233

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I reinterpret Bohr's attitude towards quantum mechanical formalism and its empirical content, based on his understanding of the correspondence principle and its approximate applicability. I suggest that Bohr understood complementarity as a limitation imposed by the commutation relations upon the applicability of the idealizations which had grounded the use of the correspondence principle. By discussing this interpretation against the contemporary background of discussions regarding “naïve realism” about operators (as observables), I suggest that a Bohrian view on the empirical content of quantum mechanical operators may provide a middle ground between complete contextualism and an untenable realism about quantum properties.
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.
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.
The so-called “orthodox” interpretation of quantum physics attributed to Niels Bohr is commonly regarded as abandoning realism. I have already opposed this view elsewhere (Folse 1985) but partially in response to criticism of my position (Shimony 1985), here I propose to relate Bohr’s realism to recent contributions to the realism debate given by Hacking (1983), Cartwright (1983), and Ellis (1985). Specifically, I argue that Bohr’s complementarity viewpoint requires a causal entity realism. Furthermore, labeling Bohr an anti-realist with respect to theories is misleading because it assumes the correspondence theory of truth that Bohr holds quantum theory forces us to reject. Although there are many realist views, I take the root of realism to be the quest for knowledge about the reality producing the phenomena we experience. It is realism in this sense that Bohr defended and that makes science significant to metaphysics.
A conception of the Correspondence Principle which Bohr deployed implicitly in developing a new theory of atomic constitution in 1913, is made explicit through an extensive examination of his classic paper of that year. Arguments are considered which purport to show that the application of the principle must be restricted to few isolated cases. These arguments are either defused or rejected. In particular an extensive review of issues concerning the interpretation of Quantum Mechanics is made to counter the claims that an insurmountable conceptual gap exits between the tenets of this theory and those of Classical Mechanics which makes it logically impossible for the latter to be regarded as the 'limiting case' of the former. In the light of a particular interpretation adopted and defended, a proposal is made that suggests that the Hamilton-Jacobi formulation of Classical Mechanics, as well as Maxwell's electromagnetic theory, can be viewed as 'limiting cases' of Quantum Mechanics. Having established a case for the global validity of the requirement imposed on physics by the Correspondence Principle, it is then argued that this requirement is indispensable if a particular brand of realism is adopted for the interpretation of theories in physics. Taking on board the assumption that an ultimate theory exists which mirrors the underlying physical constitution of the world, it is subsequently argued that the intertheory order established by the global imposition of the principle in physics, can be used to solve the problem of rational theory choice for this brand of realism.
Now that my account of Bohr's philosophy of physics has been completed, it remains for me to give a general assessment of it. What value should we assign to Bohr's main ideas – the notions of correspondence and complementarity? How does his interpretation of quantum physics fare in comparison with some of its rivals? What should our assessment of the Bohr–Einstein debate be? I shall take up these questions in the reverse order. Einstein or Bohr? The final verdict The Bohr–Einstein debate is primarily a dispute about the philosophical foundations in terms of which the interpretation of quantum mechanics should be based: specifically it is a dispute about the intrinsic-properties theory, i.e. about the scope of a realist interpretation of quantum mechanics. Einstein wished to maintain the two realist theses, the intrinsic-properties theory and the objective-values theory, whereas Bohr wished to hold only the latter. My own philosophical leanings are in the direction of realism. To my mind the notion of a physical reality the existence and constitution of which are independent of human thought and perception is coherent and plausible: what physical objects there are, and what properties they have, is not determined by human thought or perception, or by human practical interests. I have sympathy, therefore, with Einstein's position concerning the indefinability thesis and the question of the completeness of quantum mechanics.
In the past both instrumentalism and empiricism have inspired certain pragmatic elements into the Copenhagen interpretation of quantum mechanics. The relation of such pragmatisms with the correspondence principle is discussed. It is argued that neither Bohr nor Heisenberg did take `correspondence' in one of these forms, and that it, in particular, was Bohr's classical attitude which caused him to apply in an inconsistent way his correspondence principle to the Einstein-Podolsky-Rosen experiment, thus causing much confusion. It is demonstrated that an empiricist pragmatism is conducive to an explanation of violation of the Bell inequalities as a consequence of `complementarity' in the sense of `mutual disturbance in a joint nonideal measurement of incompatible observables' rather than as being caused by `nonlocal influences'.