Abstract
This and the following chapter consider Bohr’s new ways (plural) of thinking about quantum phenomena and quantum theory in terms of complementarity that emerged in the wake of Heisenberg’s discovery of quantum mechanics and then of the uncertainty relations. Bohr’s thought on these subjects underwent several changes even at the earlier stages to be discussed in these two chapters, and then was further refined in the wake of EPR’s argument. The first change is the shift from Bohr’s pre-complementarity view of quantum theory in the wake of Heisenberg’s 1925 discovery of quantum mechanics to his view following Schrödinger’s wave mechanics, Dirac’s and Jordan’s transformations theory, and Heisenberg’s uncertainty relations—developments that were instrumental to the invention of complementarity, introduced in the Como lecture in 1927. This change will be discussed in this chapter. The second change, discussed in Chapter 7, was marked by Bohr’s rethinking of the question of causality in quantum theory and occurred under the impact of his exchanges with Einstein in 1927. Section 6.1 gives an introductory discussion of the developments of Bohr’s thought and of the concept of complementarity. Sections 6.2 and 6.3 offer an analysis of the Como lecture. Section 6.3 also critically examines some of the problematic implications of the Como argument, in particular those concerning quantum causality. Section 6.4 considers, from the same critical perspective, the arguments concerning quantum causality offered—in part following Bohr’s Como argument—by Dirac, Heisenberg, and von Neumann.
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Notes
- 1.
It would, accordingly, be difficult to argue that the published version is the definitive statement of Bohr’s views at the time. However, it appears be at least as definitive as any available to be analytically treated as a text; and it was so treated by Bohr himself, for example, in his “Introductory Survey” to Atomic Theory and the Description of Nature (PWNB 1, pp. 9–15). This collection gives 1927 as the article’s date, which is the main reason why I use this date here as well, although this version was not published before 1928. I shall put aside the difference between German and English versions, which are interesting, but ultimately not germane here. For the history and preliminary drafts of the article, beginning with the draft of the lecture (it is not clear to what degree Bohr’s actual presentation followed it), and useful commentary by J. Kalckar, see Volume 6 of Bohr’s collected works (Bohr 1972–1996, vol. 6).
- 2.
These changes in Bohr’s views have been used to criticize Bohr’s argument or “the spirit of Copenhagen,” for example, by Mara Beller, as part of her advocacy of David Bohm’s hidden-variables approach (Beller 1999). As I have argued previously, Beller’s argument appears to me unconvincing; it appears to miss some among the most essential aspects of Bohr’s thinking at all stages (Plotnitsky 2002a, pp. 254–255, n. 33).
- 3.
Bohr uses the phrase “the quantum postulates” (in plural) on earlier occasions, including in “Atomic Theory and Mechanics” (Bohr 1925b), in referring to basic postulates of his atomic theory of 1913. I would argue, however, that, as used in the Como lecture, the phrase designates a new concept.
- 4.
These concerns and some of this misunderstanding are exhibited, for example, by J. Kalckar in introducing Bohr’s work on complementarity in Volumes 6 and 7 of Bohr’s collected works, devoted to complementarity (Bohr 1972–1996, vols. 6 and 7).
- 5.
Later on, Bohr commented on the phrase “choice of nature” as follows in accordance with his post-EPR views: “Needless to say, such a phrase implies no allusion to a personification of nature, but simply points to the impossibility of ascertaining on accustomed lines directives for the course of a closed indivisible phenomenon” (Bohr 1954, PWNB 2, p. 73).
- 6.
An instructive example is Leonard Susskind’s concept of the black hole complementarity, which he extrapolates from the wave–particle complementarity to the mutual exclusivity of the physical picture inside vs. outside a black hole (Susskind 2006, pp. 334–336). While this concept may be more consistent with the Como argument, it is clearly different from Bohr’s ultimate understanding of the concept, as applied, for example, to the position and momentum measurement. For, in contrast with the possibility, always available, of performing either a position or a momentum measurement associated with the same quantum object (part (b) of Bohr’s concept as delineated above), in Susskind’s black hole complementarity no such alternative is obviously available. Bohr’s concept, again, always refers to the role of the observer or of an instrument outside quantum objects and to the mutually exclusive and yet both possible at any given point, which is not the case in Susskind’s concept.
- 7.
A causal quantum-level behavior is a more rigorously established feature in certain alternative interpretations of quantum mechanics, such as the many-worlds interpretation, or alternatives to quantum mechanics itself, in particular in Bohmian theories. The latter maintains not only the underlying causality of the independent quantum behavior but also the view that the probabilistic predictions of the theory (which coincide with those of the standard quantum mechanics) arise only due to our observational interference. No undistorted description of independent quantum behavior is possible, and the uncertainty relations are still valid, which also makes the theory ontological, as well as causal—again, at the cost of nonlocality. In the many-worlds interpretation the observational disturbance plays no role.
- 8.
It is not really a matter of the “smallness” of a given quantum system, since a quantum system could be a large one, but only of the “smallness” of its ultimate quantum constituents. Large quantum systems cannot be observed as quantum systems without using classically described measuring instruments and hence without these systems being “disturbed,” in the way we observe classical systems, by disregarding the role of Planck’s constant, h, which we cannot do in considering quantum phenomena. Indeed, classical systems, at least in Dirac’s (or Bohr’s) view, ultimately have quantum constitution as well, which is unavailable to classical observation.
- 9.
Attributing to Bohr the view that it is possible to establish such relations, even as a form of direct mapping of the independent space–time behavior of quantum objects, is not an uncommon misunderstanding of Bohr’s thinking, including in his later works, in the case of which this claim is especially problematic.
- 10.
I shall bypass the technical details of the procedure, found in any standard treatment of quantum mechanics. See, for example, Feynman’s lucid exposition (Feynman et al. 1977, vol. 3, 16.4–16.16). Some of the problems of relating the formalism to the independent behavior of quantum objects are found in his exposition as well. Feynman, however, avoids speaking of causality in the way von Neumann does, although he does speak of Schrödinger’s equation as deterministic, but, it appears, only in the mathematical sense.
- 11.
Rigorously speaking, in dealing with repeated experiments, even the specification of φ0 is ultimately statistically based, which leads to further complexities that I shall put aside here, since they do not affect and may indeed be used to amplify the present argument.
- 12.
For an (epistemologically) classical ensemble approach and for a more general discussion of the frequentist view of probability, see Khrennikov (2009a, b).
- 13.
Of course, apart from the fact that arguably a majority of physicists and philosophers of quantum theory are dissatisfied with the apparent lack of descriptive capacity in quantum mechanics, the number of physicists who subscribe to alternative views, such as the many-worlds interpretation, is not negligible. (Those subscribing to Bohmian theories are a small minority.) It is also true that certain other approaches to quantum mechanics claim a greater descriptive capacity for quantum mechanics, although, as I noted in the Introduction, these claims may be questioned (e.g., Plotnitsky 2006b, pp. 84–85). The point here is that nonclassical interpretations are logically and experimentally consistent.
- 14.
I especially have in mind Bell’s and related theorems, such as the Kochen–Specker theorem, discussed in Chapter 8. I shall, however, refrain from making definitive claims concerning the situation, given the debate and controversies surrounding them.
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Plotnitsky, A. (2010). Bohr’s Como Argument: Complementarity and the Problem of Causality. In: Epistemology and Probability. Fundamental Theories of Physics, vol 161. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85334-5_6
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