The meaning of complementarity

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The Meaning of Complementarity Carsten Held* 1. Introduction Niels Bohr’s interpretation of quantum mechanics is regarded as the most influential part of the orthodox ‘Copenhagen interpretation’ of that theory, and though it is a matter of dispute whether this interpretation is satisfying, or whether its premises are acceptable, there is broad consensus about the soundness of its central concept, that is, the idea of complementarity. Some interpreters admit that Bohr’s own introduction of the concept is obscure,’ but they apparently imply that this obscurity is due not to the dejkierzs itself, but to the problematic dejiniendum, i.e. the intricacies of quantum phenomena which the concept is intended to depict. Others have even gone so far as to say that, because of the paradoxical quantum phenomena, complementarity only admits of a paradoxical or circular definition.* However, there is no reason why the concept should be, without question, regarded as obscure from the outset. It may be legitimately claimed of every interpretation of quantum mechanics that it tries to make the theory intelligible, thus is intelligible itself. It is a simple demand of text interpretation that the concept be clarified by thorough analysis and given an unambiguous meaning. Only this allows one to evaluate Bohr’s interpretation of quantum mechanics appropriately. Indeed, numerous attempts at such clarification have been made and, as a result, the vast majority of interpreters claim that the meaning of complementarity comprises the two features of ‘mutual exclusion’ and ‘joint completion’ of the descriptions of an atomic object. The tacit additional

assumption,

however, is that this suffices

*Philosophy Department, Princeton University, Princeton NJ 08544, U.S.A. Now at: Philosophisches Seminar I, Universit2t Freiburg, 79085 Freiburg, Germany. Received 29 June 1993; in final form 10 March 1994. ‘H. False, The Philosophy of Niels Bohr (Amsterdam: North Holland, 1985). p. 29, p. 108. P. Gibbins, Particles and Paradoxes (Cambridge: Cambridge Universitv Press. 1987). D. 53 (cf. M. Belier. ‘The Birth of Complementxity: The Context&d the Dialogues’, St&es in History hnd philosophy of Science 23 (1992), 148, note 6); J. Faye, Niels Bohr. His Heritage and Le,qacy (Dordrecht: Kluwer Academic Publishers, 1991), p, 142. *J. Honner, The Description of Nature. Niels Bohr and the Philosophy of Quantum Physics (Oxford: Clarendon Press, 1987), p. 59; C. F. von Weizs&ker, Zum Weltbild der Physik (Stuttgart: Hirzel, 1963), p. 290.

Pergamon

Stud. Hist. Phil. Sci., Vol. 25, No. 6, pp. 871-893, 1994. Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0039-3681/94 $7.00 + 0.00 871

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for clarification,

i.e. that complementarity,

thus

explained,

is an intelligible

concept.3 In the following, it will be argued that the second assumption is false, and that the first is true only in a restricted sense. More exactly, it will be shown that the above interpretation,

though it faithfully mirrors Bohr’s original introduction

of the concept,

creates a fundamental problem for its understanding: complementarity, as it is introduced originally, is indeed paradoxical in the sense that it is an inconsistent concept. It is, however, a mistaken view that this meets Bohr’s intentions; instead he tries hard to develop a consistent version. As a result, there is another, mature notion of complementarity which exhibits a different meaning: complementarity no longer refers to actual descriptions of atomic objects but to incompatible observables. In order to make visible this re-interpretation, it has to be shown that Bohr abandons wave-particle complementarity and re-interprets the complementarity of space-time and causal descriptions. The mature conception of the ‘complementarity of phenomena’ refers only to incompatible observables. The sole purpose of this analysis is to clarify the meaning of the central notion of Bohr’s interpretation from the main texts: how does Bohr explain complementarity, and what does he intend it to explain in turn? This analysis is, in the first instance, developed regardless of Bohr’s philosophical commitments and their development. However, clarification of the meaning of complementarity will in the end-in a final diagnosis-shed some light on both. 2. The Straightforward

Interpretation

of Complementarity

In the Como lecture4 Bohr introduces his idea of complementarity with the remark that quantum mechanics ‘forces us to regard the space-time co-ordination and the claim of causality, the union of which characterizes the classical theories, as complementary but exclusive features of the description’. Referring to the descriptions of wave and particle phenomena, Bohr then explains that ‘again we are not dealing “M. Bunge, ‘Strife about Complementarity’, The British Journalfor fhe Philosophy ofScience 6 (1955), 2; A. Grilnbaum, ‘Complementarity in Quantum Physics and its Philosophical Generalization’, The Journal of Philosophy 54 (1957), 7 17; E. Scheibe, The L.ogicalAnalysis of Quantum Mechanics (Oxford: Pergamon Press, 1973) p. 32; M. Jammer, The Philosophy of Quantum Mechanics (New York: John Wiley, 1974), p. 96; W. Heisenberg, Gesammelte Werke/Collected Works (W. Blum, H.-P. Diirr, H. Rechenberg, eds) (Berlin: Springer, Mtinchen: Piper, 1984) Series C II, p. 32; C. F. von Weizsacker, Aufbau der Physik (Miinchen: Hanser, 1985), p. 507; D. Murdoch, Niels Bohr’s Philosophy of Physics (Cambridge: Cambridge University Press, 1987), p. 60; M. Redhead, Incompleteness, Nonlocality, and Realism. A Prolegomenon to the Philosophy of Quantum Mechanics (Oxford: Clarendon Press, 1989), p. 50; Faye op. cit., Note 1, p. 142. ‘Reference to Bohr’s works is abbreviated as follows: Atomic Theory and the Description of Nature (Cambridge: Cambridge University Press, 1934) = ATDN; Atomic Physics and Human Knowledge (New York: John Wiley, 1958) = APHK; Essays 19X-1962 on Atomic Physics and Human Knowledge (New York: John Wiley, 1963) = EAP; ‘Can Quantum Mechanical Description of Nature be Considered Complete?’ in J. A. Wheeler and W. H. Zurek (eds), Quantum Theory and Measurement (Princeton: Princeton University Press, 1983) = QMD; ‘On the Notions of Causality and Complementarity’, Dialectica 2 (1948) = CC; Collected Works (Amsterdam: North-Holland, 1982-1987) = BCW (with volume number). All emphases in the quotations from Bohr’s and other texts are the author’s,

The Meaning of Complementarity with contradictory

873

but with complementary

together offer a natural generalization

pictures of the phenomena,

of the classical mode of description’,

which only and a few

lines later he says that ‘the complementary nature of the description’ appears in Heisenberg’s indeterminacy relations’ .5 In the introduction of a collection of his essays containing the Como lecture, when paraphrasing its contents, Bohr uses the occasion to give a short definition of ‘complementarity’: the quantum of action ‘forces us to adopt a new mode of description designated as complementary in the sense that any given application of classical concepts precludes the simultaneous use of other classical concepts which in a d$@rent connection are equally necessary for the elucidation of the phenomena.’ He continues, stressing the ‘dilemma’ of waveparticle dualism for both light and matter, and then goes on, emphasizing ‘that this feature of complementarity is essential for a consistent interpretation of the quantum-theoretical methods’. He also stresses again that the indeterminacy described by Heisenberg’s relations ‘exhibits’ complementarity.6 Finally, the most informative explanation given is that the ‘complete elucidation of one and the same object may require diverse points of view which defy a unique description’.’ These few remarks from the late twenties are representative in so far as they give all the information that Bohr presents about his new concept at the time; and they provide full warrant for the interpretation mentioned above: complementarity contains the features of mutual exclusion and joint completion. Moreover, Bohr says that complementarity is a generalized ‘description’ or a ‘new mode of description’; its relata are ‘features of the description’ which consist in the ‘application of concepts’. But ‘features of the description’ are descriptions themselves, and also concepts, are only applied in descriptions. Thus, the complementary relata are descriptions themselves. These descriptions in principle refer to ‘one and the same object’.’ Finally, Bohr introduces no differentiation between the kinds of relata; he intends the new relation to hold for all kinds: wave and particle pictures, space-time and causal descriptions, and incompatible observables. This information about the meaning of complementarity early main writings, but a straightforward interpretation

is easily extracted from of it faces a simple and

‘ATDN, p. 54f. p. 56, p. 57. 6ATDN, p. 10, p. 11. ‘ATDN, p. 96. *It is not always obvious that Bohr means one objecf to be the referent of complementary relata. While unambiguously saying so in general explanations (cf. ATDN, p. 96, APHK, p. 26; see also Note 71). he states the matter ambiguously in concrete physical examples, referring mostly to ‘the phenomena’. This, apparently, happens in view of the consistency problem exhibited below (cf., for example, the emendations in drafts of the Como lecture, quoted in Murdoch, op. cit., Note 3, p. 55f), but it does not mean that Bohr develops a conception denying the sameness of the object. When he says, e.g. that complementary concepts ‘in different connections are equally necessary for the elucidation of the phenomena’, this avoids the informative singular. However, the expression ‘in different connections’ would make no sense, if ‘the phenomena’ meant ‘different objects’; it makes sense only if the sentence is interpreted, in accordance with the general explanations of completion, as ‘. in different connections are equally necessary for the elucidation of the very same object’ (similarly expressions like ‘equally important features of the light phenomena’, APHK, p. 5).

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fundamental

problem.

First, in what sense do complementary

complete each other? A straightforward

features

mutually

answer is: only all of a set of complementary

descriptions provide a complete record of the properties of a quantum object, whereas one of them can only reveal a part of these properties. An appropriate example of this view of mutual completion would be the different features presented by a house as seen from different perspectives which, only together, yield a complete description of it.9 This situation seems, in fact, to be mirrored by quantum phenomena, especially by wave-particle duality: it seems fundamentally incomplete to describe electrons, for example, only as particles, since in experiments they can easily be made to exhibit wave properties; thus a complete description must refer to both sets of properties. It is essential to note that, in this straightforward understanding of joint completion of descriptions of a quantum physical object, the completion idea implies the simultaneity of the described properties. Joint completion of a set of descriptions analytically implies that there is a complete description which is formed by them together; the fact that descriptions of an object hold true together means that the described properties pertain to the object together. A straightforward understanding of this ‘pertaining together’ is that the properties pertain to the object simultaneously. This simultaneity produces no problems for the properties of the house: it is impossible to adopt two perspectives on the house simultaneously; thus not all of its properties can be perceived at the same time, but nevertheless descriptions from different perspectives complete each other in the sense that all properties are said to pertain to the house simultaneously. Again the analogy with quantum phenomena seems perfect: it seems correct to say that electrons sometimes exhibit wave properties, sometimes particle properties; but it seems incorrect to say that sometimes they are waves only and at other times are particles only. This implies that all properties pertain to them always, although they are not always exhibited. Thus, in the quantum as well as the non-quantum case, we understand the completion idea of descriptions as implying actual simultaneity. Secondly, in what sense do complementary features exclude each other? Again, a straightforward understanding seems appropriate. The descriptions exclude each other logically: they are contradictory. In fact, what would be the trouble with wave-particle dualism, if both pictures were compatible like different descriptions of a house? No physical object can simultaneously be localized at one point in space and spread over the whole space, because the latter by definition implies that it is not localized at one point. No physical object can simultaneously interact with another one via scattering and via diffraction, since the latter implies that it is not localized at one point, while the former implies that it is. from M. Drieschner, Voraussag~~Wahrscheinlichkeit-Objekt. iiber die (Berlin: Springer, 1979), p. 152. See also the explanations of complementarity by examples of the two sides of a coin (Honner, op. cit., Note 2, p. .54), and of two incomplete descriptions of a geometrical figure (D. M. McKay, ‘Complementarity’. Proceedings of rhe Aristotelian Society Supplementary Volume 32 (1958), 1 16). ‘The example

begriflichen

is adapted

Grundlagen

der Qunntenmechanik

875

The Meaning of Complementarity

The problem understood

of the straightforward

as above, implies simultaneity,

of the features impossible. be an inconsistent

Therefore,

arising

is obvious.

whereas exclusion

If both readings were conclusive,

concept.

interpreted differently. This simple problem,

interpretation

Completion,

renders simultaneity

complementarity

one of the two characteristics

from a straightforward

attempt

would must be

to understand

complementarity, is what evokes the air of paradox around the notion. However, the problem is hardly ever noticed, perhaps because an equally simple solution suggests itself from Bohr’s writings. Bohr himself vividly denies-as quoted above-that complementarity should imply a contradiction. lo Thus, ‘by exclusion’, he cannot mean logical exclusion of predications of properties, but what then does he mean? An explanation frequently employed by Bohr from 1932 onwards is the following: the observation of a certain quantum mechanical property requires an experimental setup that logically excludes the experimental setup required for the observation of the complementary property;” e.g., measurement of the momentum of an electron requires a moveable diaphragm, while determination of its position requires a fixed one. Thus the properties do not logically exclude each other: only the experiments required for their determination do so. This explanation of ‘exclusion’ is obviously insufficient, because it addresses the measuring of properties, not the properties themselves; it is only an epistemic restriction, while complementarity of properties is an ontic relation. Even if the description of a quantum physical object has to take the experimental setup into account, the description is not only of the apparatus, but includes the object. Therefore, it is decisive whether the exclusion only refers to the setup and, hence, only to the measurement of the object’s properties, or whether it includes the properties themselves. Again, wave-particle duality, if it is in fact a proper example of complementarity, shows that the properties themselves are mutually exclusive. Therefore, the mutual logical exclusion of the setups alone is not a satisfying explanation.‘2 Though Bohr himself sometimes presents this insufficient argument,13 there are, of course, many passages in which his setup argument must be understood as going further. This developed version has it that a physical quantity can only be understood as an observable quantity, and that the latter can only be defined in relation to a concrete experimental setup which is suitable for determining it.r4 Apart from a

“cf. Note 25 below. “APHK, pp. 5, 19, 41, 47, 90, 99; QMD, pp. 148, 149; CC, p. 316; EAP, pp. 12, 60. The argument is foreshadowed in ATDN, p. 17ff. (‘separate experimental arrangements’). “This insufficiency has been particularly emphasized by Griinbaum (op. cit., Note 3, p. 724) and McKay (op. cit., Note 9, p. 114). 13cf. APHK, pp. 5, 26. 14cf. APHK, pp. 40.73, 87,98; EAP, pp. 61, 100. Remarkably, the argument appears already in ATDN, p. 18.

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Studies in History and Philosophy of Science

specified experiment

it is meaningless

to speak of a physical quantity at all. Following

Murdoch, this idea may be referred to as the ‘indefinability thesis’.15 This thesis indeed constitutes an ontic restriction: the meaninglessness propositions

about unobserved

of

quantities implies that nothing empirical exists which

corresponds to these propositions. For example, when a ‘wave-experiment’ performed, the unobservability of particle properties prevents any clear definition

is of

them which in turn excludes them from the physical description. Hence, no contradiction between the two sets of properties can arise, because at a certain instant only one of them can be meaningfully attributed to the object while the contradiction would require the simultaneous attribution of both. The problem with this argument is that it does not save the straightforward interpretation of complementarity. While saving the feature of mutual exclusion from implying contradictory properties, the argument deprives the other feature, i.e. mutual completion, of its meaning. Certain properties of quantum objects are in principle not simultaneously observable, which is reason to conclude that they cannot meaningfully be said to pertain to the object simultaneously. However, this obviously contradicts the interpretation of completion as implying simultaneity. 3. Solution Attempts The problem of comprehending complementarity straightforwardly has, of course, not gone unnoticed. Interpreters who concern themselves with it and thus propose solutions may be divided into three groups. There are those who try to make complementarity intelligible by means of the indefinability thesis, and those who try to do so without. Both intend to show that on a closer look there is no inconsistency in the concept. Finally, there are those who hold that the concept is purposely designed by Bohr in this inconsistent way, in order to capture the paradoxes of quantum mechanics. This is, in effect, a rejection of the indefinability thesis. A representative of the first group is Dugald Murdoch. Clearly seeing that mutual exclusion of descriptions means that the described properties do not simultaneously pertain to the object, he sets out to re-interpret completion without simultaneity; hence, he utilizes the fact that completion, though straightforwardly meaning simultaneity, does not logically entail it. His proposal is that the descriptions in ‘not in the sense of providing a synchronic question are jointly completing, description of the classical state of an object, but in the sense that together they provide a diachronic description’ of it. I6 The descriptions, Murdoch implies, pertain to different times, thus are mutually completing in another sense, perhaps in the sense that together they form a complete history of the object. Now, this is certainly a stretch of language. If Bohr makes no reference to different times of descriptions or to the ‘diachronicity’ of a complete description, there is no reason to understand completion ‘5Murdoch, op. cir., Note 3, p. 139. 16Murdoch, op. cit., Note 3, p. 60f.

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The Meaning of Complementarity

in any other sense than simultaneity.

Hence, there should be some textual evidence

to support Murdoch’s interpretation,

but in Bohr’s early articles there is none. Mostly,

Bohr creates the impression house: a ‘complete viewpoints.17

that the situation is just the same as in the case of the

elucidation

of one and the same object’

requires

different

Clearly, Murdoch takes it that his idea is to be found in the later texts, where Bohr explains that the descriptions are jointly completing in the sense that they ‘jointly exhaust the possibilities of description’.‘8 The development of this idea does indeed go along with Bohr’s abandoning any simultaneity of descriptions, but it does not imply ‘diachronic’ descriptions. ‘Diachronicity’ means a joint completion of actual descriptions of actual states, while Bohr speaks (as Murdoch correctly paraphrases) of possible descriptions, one of which is actualized. To confirm Murdoch’s reading, Bohr would have to insist, for example, that ascription of a determinate position to a particle upon measurement has to be followed by another ascription of a determinate momentum from a subsequent measurement for a complete or exhaustive description. But, of course, Bohr never says this because it is nonsensical. In what sense is the description of an object, having now a determinate position, and now (later) a determinate momentum, complete or exhaustive? Why not include further instances of position and momentum ascriptions? In fact, there is no such sense of completion or exhaustion for a ‘diachronic’ description, since a finite set of descriptions does not in general allow for an exhaustive account of an object’s history. Murdoch’s idea, though avoiding the contradiction, simply does not give a meaning to completion. It has to be accepted that Bohr starts off with the simple and straightforward sense of completion, and even in his later re-interpretation of completion, does not think of a ‘diachronicity’ of descriptions, for this would make no sense. The second line of defense exploits an idea Bohr frequently alludes to before 1935. He underlines a crucial ‘failure of the forms of perception’ and an ‘unavoidable influence on atomic phenomena caused by observing them’, and both ideas may be understood as saying that we do not observe atomic objects as they really are.” This idea is fully developed in Henry Folse’s interpretation. According to Folse, Bohr refers to ‘phenomenal objects’ by the exclusion aspect and to the ‘independent real objects’ causing the phenomenal ones by the completion aspect.*’ It is, of course, essential to know whether or not we are entitled to conclude that the properties of the observed ‘phenomenal object’ also pertain to its cause, the ‘independent real object’. The causal relation suggests that we cannot: an object acting as cause does not necessarily have the same properties as the one which it is acting upon, even if it is causing these properties. In fact, Folse says that ‘the ontologically independent object with its properties not only is not the same as the phenomenal object observed “ATDN, p. 96. “Murdoch, op. cd., Note 3, p. 61. For the Bohr texts Murdoch refers to, see Note 66 below. “False, 1, pp.For183, 238, detailed 19ATDN,op.pp.cit., 93, Note 96, 100. a more interpretation see Section 7 below. 243.

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Studies in History and Philosophy of Science

in an interaction,

but also is not even to be described through the same concepts which

are well-defined in reference to the observable properties through which the phenomenal object is characterized’.*’ This is to be understood as meaning that both objects do not have the same properties because they cannot be described by the same concepts. Their descriptions have nothing in common. Referring

to the completion

aspect,

Folse

says that ‘in the combination

of

complementary descriptions of phenomenal objects we convey information about an independent physical reality’.22 But how is this possible, if the descriptions of both sorts of objects have nothing in common? Does the description of an, apparently phenomenal, atomic object as being a wave or as being a particle ‘convey information’ about the independent object or not? Any clarification here would lead back into the original problem: if the descriptions refer to one object, they ascribe contradictory properties to it; if not, they cannot be jointly completing. The inconsistency of complementarity does not trouble a third group of interpreters: they hold that the notion is purposely designed to be inconsistent. John Honner, for example, referring to a distinction between ‘weak’ and ‘strong’ complementarity (joint completion of non-contradictory and contradictory descriptions, respectively), says ‘It is because complementarity is paradoxical that it has to be “strong”, and vice versa.‘23 Similarly, it has been held that complementarity is a dialectical concept. 24 As answers to the consistency problem, both ideas mean the same thing: the properties in question are contradictory, but nevertheless do pertain to the object simultaneously. Thus a complete description of quantum objects is ineluctably self-contradictory. Given the above difficulty this theory can be characterized as a rejection of the indefinability argument, which asserted that complementary properties do not pertain to the object simultaneously, in order to avoid contradiction. It would certainly be a useless enterprise to start an interpretation of quantum mechanics from a contradictory concept. The puzzle of quantum mechanics is that its phenomena are paradoxical: their explanation seems to involve contradictions, and the interpreter’s task is to dissolve them plausibly. An interpretation which, instead, declares the contradictions to be natural, simply does not accept this task. However, it may suffice here to emphasize that such an interpretation misses Bohr’s own intentions:

it can neither account for his own solution attempts, nor for his untiring

2’Ibid., p. 210. 221bid., p. 243. 23Honner, op. cit., Note 2, p. 59. 24M. H. F. Wilkins, ‘Complementarity and the Union of Opposites’, in B. J. Hiley and F. D. Peat (eds), Quantum Implications. Essays in Honour of David Bohm (London: Routledge, 1987). p. 341; Beller, op. cit., Note 1, pp. 148, 178. These references to dialectics are rather unclear, but in order to solve the problem of complementarity dialectics must be employed in the strong sense of contradictory properties pertaining to an entity; however, Wilkins, by explicitly mentioning Hegel, alludes to this strong sense. See, on the contrary, Bohr’s use of the term in QMD, p. 150 note, APHK, pp. 29, 63, and especially CC, p. 317.

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The Meaning of Complementarity

emphasis of the logical consistency nor does Bohr’s idea of a limitation

achieved especially

through complementarity;25

of the concepts of classical physics support it.

In only one of the earlier articles, is this idea of a ‘peculiar limitation

of our forms

of perception’26 detailed in a way that alludes to dialectics; namely when Bohr explains that quantum theory necessarily transcends those limitations,*’ because it brings about an inevitable ‘revision of our fundamental concepts’ and even ‘logical principles’ .28This, however, is the only allusion to dialectics, and is opposed by many clear statements of consistency. Moreover, as Bohr refines the limitation idea, he turns to emphasizing that his interpretation of quantum mechanics expresses, rather than transcends, the limits of classical concepts.29 His ultimate view is that what the descriptions of quantum phenomena transcend is ‘a deterministic pictorial description’,30 whereas he again underlines the logical consistency of complementarity; this consistency, he now holds, is secured ‘by the mathematical consistency of the formalism of quantum mechanics’.” The conclusion so far, is that there is an insoluble inconsistency in Bohr’s original conception of complementarity which makes the early interpretation as a whole problematic. On the other hand, this problem helps in understanding Bohr’s difficult ideas about the ‘failure of our forms of perception’ or the ‘disturbance of the phenomena’ and even early traces of the indefinability argument, as attempts to overcome that inconsistency. However, as long as Bohr struggles with wave-particle dualism, these attempts remain unsuccessful. 4. Wave-Particle

Complementarity

Neither space-time and causal descriptions nor the values of non-commuting observables are contradictory properties, for they harmonize perfectly in classical theories. Only the wave picture and the particle picture of classical physics are logically incompatible by definition. This suggests that a way of comprehending complementarity is to separate two or more meanings. Few interpreters of complementarity have taken this road, one being Murdoch.32 His differentiation, however, leads him to reject wave-particle complementarity as a classical remnant in Bohr’s interpretation.33 Similarly, Grtinbaum, dismisses this sort of complementarity as meaningless. He says that the full-fledged quantum theory warrants neither the wave nor the particle picture.34 Thus, since co m p lementarity is intended to interpret “The passages where Bohr claims logical consistency for his interpretation Important ones on the consistency of complementarity are: ATDN, pp. 11,55,95; 317; APHK, pp. 59, 74, 92; EAP, pp. 4, 6, 12, 25, 61. 26ATDN, p. 108. *‘cf. ibid., pp. 97, 101. 281bid.,p. 97. 29cf. APHK, p. 39. 30EAP, p. 24. “EAP, p. 25; cf. p. 61. ‘*Murdoch, op. cit., Note 3, p, 60f. “cf. ibid., pp. 77-79, 244. %riinbaum, op. cit., Note 3, p. 722.

in general are legion. QMD, p. 150; CC, p.

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Studies in History and Philosophy of Science

this theory, it must not address either of them. Consequently,

Grtinbaum

rejects

wave-particle complementarity, because ‘it is a misleading carry-over from the classical interpretations of experimental data in terms of waves and particles-an interpretation whose very breakdown is the ratio essendi of the new theory’.35 Grtinbaum’s argument is very compressed, to say the least, for it is certainly incorrect to say that quantum mechanics has nothing at all to do with waves and particles. To be exact, the theory does not warrant thefull wave or particle picture. Quantum mechanics allows for a time evolution of a continuous quantity which is governed by a linear differential equation (thus by a superposition principle), exactly as free waves in classical electrodynamics are subject to the homogeneous Maxwell equations; but it does not warrant that this continuous quantity in interactions continuously transmits energy and momentum as a classical wave would do. On the other hand quantum mechanics allows for a discrete particle to be observed at a certain time, but it does not warrant the classical conception of a trajectory of this particle. Thus quantum mechanics warrants neither the full wave picture nor the full particle picture, but it certainly requires key characteristics of them. Does this differentiation render Grtinbaum’s argument invalid? Obviously not. Bohr does not concern himself in his early conception of wave-particle complementarity with certain characteristics of the classical pictures, but with these pictures as wholes; he addresses the ‘dilemma as regards the choice between the wave description . . and the corpuscular conception’; he calls both pictures ‘indispensable’, although they are ‘mutually contradictory’,36 which is to be made intelligible by complementarity. Thus Grtinbaum’s argument is still valid: Bohr’s idea of wave-particle complementarity starts from the assumption that certain quantum phenomena require the full wave or particle picture for their explanation. Quantum mechanics does not allow for the use of the full pictures. Therefore no interpretation of quantum mechanics may employ wave-particle complementarity.37 Bohr himself never explicitly rejects wave-particle complementarity, but scrutiny of his works shows that Grtinbaum’s argument reflects his own development; over the years Bohr tacitly abandons the idea of wave-particle complementarity. In the early articles the problem of wave-particle dualism stands out as the decisive problem of understanding quantum mechanics, and accordingly serves as the motivation for is instead introducing complementarity, .38 from 1935 on, however, complementarity introduced by means of mutually exclusive experiments.39 The problem of wave-

j51bid., p 717, Note 7. 36ATDN, pp. 10, 57, 107. 37For similar arguments see Heisenberg, op. cit., Note 3, p. 26; M. Born, The Natural Philosophy of Cause and Chance (Oxford: Oxford University Press, 1949), p. 105. ‘scf. ATDN, pp. 93-95 p. 107ff. (without explicit mention of complementarity), APHK, p. 5. In the Como lecture this is less gpparent (cf. ATDN, p. 54f), but see Bohr’s drafts of the lecture in BCW 6, 69, 76. “9APHK, pp. 19, 26, 39f, 74, 90, 99; QMD, p. 148; CC, p. 314; EAP, pp. 4, 12, 19, 92.

The Meaning of Complementarity

particle

dualism

then is only mentioned

complementarity,40 This development

881 as being

‘removed’

but there is no more mention of wave-particle creates the impression

of a conflict

or ‘clarified’

by

complementarity.

between

wave-particle

complementarity and Bohr’s indefinability thesis, and such an impression is well founded. In the case of wave-particle dualism the indefinability thesis simply does not work. First, the thesis is designed to explain why certain descriptive features, which go together perfectly in classical theories, are exclusive in quantum theory; and the explanation given is that they do so because they are observed only in mutually exclusive experiments. However, wave-particle dualism is not in any need of such an explanation, for wave and particle pictures are exclusive even in classical theories. They are not mutually exclusive because of certain experimental circumstances, they are flatly contradictory descriptions. The indefinability thesis is not intended to make sense of wave-particle dualism; it is designed for the explanation of mutually exclusive observables. Secondly, the indefinability thesis could only serve as a solution to the problem of wave-particle dualism, if the mutual exclusion of the experiments could be made to match the logical exclusion of the two classical pictures; in other words, if it were true-like some Bohr interpreters would have it-‘that in experimental situations that are exclusive of each other, quantum physical objects behave either as waves or as particles’,4’ but this is neither an accurate description of typical quantum mechanical experiments, nor is it a faithful interpretation of Bohr’s mature views about these experiments. Consider, for example, Bohr’s very accurate description of the two-slit experiment. This experiment cart be performed in such a way that always only one particle is contained in the apparatus and hits the screen at a definite position and time. Nevertheless, in the long run, the particles produce the puzzling interference pattern4* Now, do the objects in this experiment behave as waves or as particles? Since the single impacts and the interference fringes they form are observed, there is no question here of excluding one classical picture. Some properties of both pictures are somehow ‘blended’: the determinate position of each particle that hits the screen certainly is a particle property; the distribution of all impacts exhibits interference, thus is a wave property.43 Hence, wave and particle properties appear in one well-defined 4”APHK, pp. 40, 90; EAP, p. 25; cf. BCW 5, p. 215f. 4’J. Faye, ‘Review of Dugald Murdoch, Niels Bohr’s Philosophy of Physics’, Isis 81 (1990) 379; cf. False, op. cit., Note 1, pp. 102, 116. “cf. APHK, p. 45f. 43This fact of a ‘blending’ of wave and particle aspects in the two-slit experiment is pointed out clearly by physicists; cf. e.g. Born, op. cit., Note 37, p. 105; L. D. Landau and E. M. Lifschitz, Quanrum Mechanics. Non-Relafivistic Theory (Oxford: Pergamon Press, 1958), p. lff.; R. P. Feynman, R. B. Leighton and M. Sands, The Feynmnn L.ecfures on Physics, Vol. III Quantum Mechanics (Reading/Massachusetts: Addison-Wesley, 1965) p. 1-6: Heisenberg, op. cif., Note 3, Series B, p. 125. However, the point is normally ignored or circumvented by interpreters of complementarity. Compare, e.g. two passages in Murdoch: ‘If [. .] the position of an object has been measured, the object may be conceived of as aparricle localized at that position’. ‘[ . ..I in other experiments in which position may be measured, such as slit experiments in which the diaphragms are rigidly attached to the frame, diffraction and interference effects are observable; in which case the wave mode1 appears to be the more appropriate.’ (Murdoch, op. cit.,

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experimental arrangement, and there is no question of mutual exclusion of them in the sense of their attribution to exclusive experimental arrangements. Those properties of the classical pictures that are conserved in quantum mechanics, appear in one and the same arrangement. The two-slit experiment is a simple counter-example to the defense of complementarity

by the argument from indefinability,

as long

as complementarity refers to waves and particles. Bohr’s tacit abandonment of wave-particle complementarity indicates that he realizes this problem. The conception of complementarity that makes essential use of the idea of mutually exclusive setups does not only have a starting point different from wave-particle complementarity: it is incompatible with this sort of complementarity. The indefinability thesis is a new attempt of Bohr’s to explain complementarity, but not wave-particle complementarity. The problem of wave-particle dualism, Bohr now thinks, is ‘clarified’ by another kind of complementarity, namely the one of incompatible observables.

5. State-Value

Complementarity

Bohr’s original explanation of complementarity in the Como lecture, addresses neither wave-particle duality nor incompatible observables but ‘space-time coordination and the claim of causality’.4 Interpreters have put considerable effort into clarifying Bohr’s intention about this mysterious pair of relata, mostly to the effect that it is reduced to one of the others. 45 Indeed, Bohr often characterizes this pair in an ambiguous manner. For example, he explains that by ‘space-time coordination’ he implies ‘the propagation in space and time’ of light and connects this to the classical ‘electromagnetic theory’, while equating causality with a particle theory of light.46 This seems to be an argument for reducing the relation to wave-particle complementarity. On the other hand, he frequently equates ‘causality’ with ‘conservation laws’ and the latter with a measurement of energy and momentum.47 In such passages he doubtless reinterprets his own idea as an expression of the complementarity of incompatible observables. But all these equations are obscure and cannot hide the fact that Bohr’s original intentions are different. In fact, the relation of space-time description and causality is irreducible to the

Note 3 pp. 66, 67). It seems inevitable to draw the conclusion that in the two-slit experiment, features of the wave picture and the particle picture are blended, though Murdoch does not do so. Quite the contrary, he maintains for wave and particle pictures ‘that the empirical situations in which the two classical models are effectively applicable are in fact mutually exclusive’ (ibid., p. 62). Similarly, Scheibe says that the ‘wave picture’ can sufficiently explain the two-slit experiment (op. cir., Note 3, p. 33). But certainly the wave-picture cannot account for ‘individual processes, each giving rise to a small spot on the photographic plate’ (APHK, p. 46). “ATDN, p. 54. ‘jcf. Scheibe, op. cit., Note 3, p. 32; Murdoch, op. cit., Note 3, p. 58. 46ATDN, p, 55. “ATDN, p. 11; APHK, pp. 40, 58, 72, 89; EAP, pp. 5, I 1, 62.

883

The Meaning of Complementarity other ones when Bohr introduces-as

one between unobserved

he does in the Como lecture-the

relation as

state and observed values.

One of the few interpreters

who explicitly

concern themselves

with this puzzling

state-value Weizsacker

complementarity is von Weizsacker. Contrary to Grtlnbaum, von does not produce an argument in order to reject the relation as

meaningless

but tries to reconstruct

it, and only after correspondence

with Bohr,

accepting the Bohrian restriction to phenomena, does von Weizsacker abandon his reconstruction attempt. Von Weizsacker separates ‘parallel complementarity’ from ‘circular complementarity’ and describes the former in the following way: ‘Complementary magnitudes in quantum theory appear as non-commuting operators.‘48 However, according to von Weizsacker, ‘circular complementarity’ is ‘Bohr’s original conception’, and only space-time description and causality are its proper relata, which is clear from the original introduction in the Como lecture.49 Von Weizsacker interprets this sort of complementarity as a relation between the observed measurement result and the Y-function, 5othus between observed values and unobserved state. This interpretation gains its support from Bohr’s explanations in the Como lecture that the definition of ‘the state of a physical system’ excludes ‘external disturbances’, thus observation, and on the other hand implies ‘causality’,5’ which von Weizsacker interprets as ‘a deterministic description of the time-evolution of the Y-function’;52 whereas ‘space-time description’ refers to the actual observation 53involving the measurement interaction which results in a definite value ascription to the system. However, Bohr in correspondence with von Weizsacker in 1956 rejects the idea of ‘circular complementarity’, emphasizing that complementarity can only hold between phenomena;54 and the wave function certainly does not signify a phenomenon. Von Weizsacker concludes: Thus complementarity between space-time description and causality reduces to the well-known complementarity between position and momentum, or time and energy. Since 1 have to admit that I misunderstood Bohr in these points it is questionable whether the expression circular complementarity should be maintained.55

It is true that Bohr in his mature interpretation confines complementarity to complete phenomena, thus to incompatible observables. In so far as von Weizsacker generalizes the passage from the Como lecture, he indeed ‘misunderstands’ Bohr. He does not, however, misunderstand the passage itself. Instead, Bohr’s rejection of von 48Von Weizslcker, op. cit., Note 2, p, 288. Here and in the following the translations from the German are mine. @Ibid., p. 290; cf. p. 291. 5ocf. ibid., p. 292f. “ATDN, p. 54. j2Von Weizskker, op. cit., Note 2, p. 293. 53cf. ATDN, p. 54; cf. ATDN, p. 61: ‘the space-time coordination of observations’. 54cf. van Weizs%cker, op. cit., Note 2, p. 330. 55ibid.

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Weizsacker’s

Studies in History and Philosophy of Science

interpretation

amounts to an implicit self-criticism

of his original idea.

Closer scrutiny of the text reveals that Bohr’s idea of unobserved state and observed values springs from his reflections on the problem of stationary states.56 This problem consists of the fact that in stable atoms, where electrons are in stationary states, these electrons are in principle unobservable,

as regards their state of motion. Observation

of an electron in such a state, e.g. by means of light, will generally result ‘in the ejection of the electron from the atom ‘,57 but this does not mean that these states are unobservable themselves: the ‘energy of the system’ is very well empirically accessible by means of ‘radiation or collision reactions’.” The ‘complementary nature’ of these different observation results is explicitly clarified only much later. When in the 1950s Bohr explains that ‘energy content and other invariant quantities [can] be strictly defined only for isolated systems’, while on the other hand the system is ‘influenced during any observation by unavoidable interaction with the measurement tools’,59 this must be understood in the way that ‘isolation’ only excludes the direct observation of dynamic observables, whereas the ‘invariant quantities’ are accessible to observation indirectly. Hence, Bohr now explicitly relates bound state and dynamic observables to exclusive observations, for example when he claims that ‘the complementary description offers indeed the adequate approach to the problem of atomic stability’ and explains: . the interpretation of spectral regularities and chemical bonds refers to experimental conditions mutually exclusive of those which permit exact control of the position and displacement of the individual electrons in the atomic systems.60 Here Bohr indeed explains ‘atomic stability’ by the complementarity of ‘mutually exclusive’ experiments, that is by his mature idea of the complementarity of phenomena, the description of which includes a well-defined experimental arrangement.

6. Complementarity

of Incompatible

Observables

Bohr’s mature conception of complementarity refers to ‘phenomena’, the description of which necessarily includes reference to a specified experimental setup.61 This conception does not aim at the problem of wave-particle dualism or the relation of state and values, but is designed solely for incompatible observables. However, a restriction of complementarity to incompatible observables alone does %ompare Bohr’s introduction of the problem in ATDN, p. 54 to an earlier article (ATDN, p. 36) and to a passage later in the same article (ATDN, p. 78), where the problem of stationary states is connected to the observation problem. “ATDN, p. 78. “Ibid., p. 17. 59EAP, p. 78. “Ibid., p. 63; cf. APHK, p. 99. “cf. APHK, pp. 57, 64, 73; CC, p. 317; EAP, p. 4.

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The Meaning of Complementarity

not secure a clear meaning though easily illustrated

of the concept. The straightforward

by wave-particle

dualism-was

regard to the kind of relata. If two descriptions

interpretation-al-

presented

above without

of an atomic object are said to be not

simultaneously well-defined (because of the mutually exclusive setups), they cannot both be true of the object; and, thus, there is no sense, in which they can be jointly completing. This problem remains unsolved, even for incompatible observables. However, it is unmistakably clear to Bohr from 1935 on, that the exclusion of the experimental arrangements must be extended to the object. This is to say, that in 1935 Bohr endorses the whole indefinability thesis: an operationally ill-defined property is not only inaccessible, it cannot be said to pertain to the object-it is simply not rea1.62 Therefore, mutual exclusion must still be understood in the simple, straightforward way that the descriptions in question cannot simultaneously be true of an object, or that the described states of it cannot simultaneously be real. In consequence, the explication of joint completion in the straightforward interpretation must be revised. This strategy is the more promising as Bohr himself pursues it: especially after 1935, he repeatedly tries to make precise his idea of joint completion. The obvious motive for these efforts is the challenge of the famous Einstein-Podolsky-Rosen article, the central argument of which is the alleged incompleteness of quantum mechanics.63 Bohr, on the contrary, tries to argue its completeness, hence he must clarify in which sense the quantum mechanical description of a physical phenomenon is complete, and in which different sense it is incomplete, thus allowing for completion by another description complementary to the first. In order to clarify his counter-argument to Einstein, Bohr now introduces the new expression of an ‘exhaustive description’. In his 1949 Einstein article he writes: In my opinion, there could be no other way to deem a logically consistent mathematical formalism as inadequate than by demonstrating the departure of its consequences from experience or by proving that its predictions did not exhaust thepossibilities of observation, and Einstein’s argumentation could be directed to neither of these ends.@

On the other hand, Bohr now gives a definition employs the concept of ‘exhaustion’:

of complementarity,

which also

Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts thepossible information about the objects.65

%f. QMD, p. 148; APHK, p. 40; CC, p. 315. For an interpretation see Section 7 below. 63A. Einstein, B. Podolsky and N. Rosen, ‘Can the Quantum Mechanical Description of Nature be Considered Complete?’ in Wheeler and Zurek, op. cit., Note 4, pp. 138-141; henceforth abbreviated as EPR. @APHK, p. 57. 65APHK, p. 40.

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Studies in History and Philosophy of Science

From this article on, the idea of ‘exhaustion’ reflections on complementarity.66 However,

though this new expression

problem of completion, of joint completion

it is apparently

is evidence

Bohr’s

argument

This calls for clarification, and incomplete

observables

with the

its meaning. The idea

implies that, in a certain sense, a single against

mechanics is complete in the sense that in one well-defined the maximal set of commuting

place in Bohr’s

of Bohr’s concern

of no help in clarifying

of different phenomena

is incomplete.

phenomenon

occupies a prominent

Einstein

is that quantum

experimental

describes all well-defined

because a phenomenon

arrangement information.67

is said to be complete in one sense

in another, without the latter being specified. And the ‘exhaustion

idea’ does nothing but repeat this ambiguity: in a clear quantum mechanical one well-defined phenomenon does ‘exhaust the possibilities of observation’,

sense while

in another mysterious sense it is ‘complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects’. This ambiguity is never mentioned explicitly, let alone resolved, by Bohr. However, a clue to a clarification is hidden in the quoted passages. In the context of the first quotation, Bohr’s point is that Einstein, in order to prove the incompleteness of quantum mechanics, refers ‘to two different, mutually exclusive arrangements’.68 This, in Bohr’s quantum quantum

view, is an illegitimate

move:

‘any well-defined

application

of

mechanics’ has to ‘specify the whole experimental arrangement’;69 then mechanics yields all well-defined results, and thus ‘exhausts all possible

information’. In the second quotation, however, obtained under different experimental conditions’

Bohr himself refers to ‘evidence as exhaustive information, so that

the information in one specified experiment necessarily is inexhaustive. Consequently, Bohr must have in mind two different meanings of ‘exhaustive’ or ‘complete’, arrangement’

presumably,

differentiating

descriptions

and of ‘objects in different arrangements’.

of ‘an object in a specified This assumption,

however,

has to be made more precise. Bohr, throughout his work, frequently talks about jointly completing information about ‘the objects’ or ‘the phenomena’. By using the plural, he leaves open whether or not in the primitive case the relata of complementarity refer to one object. 7oThis ambiguity seems to be continued in the later articles, when Bohr starts to redefine complementarity,

but in the latest texts he says explicitly that he now

thinks of one object as the primitive referent of complementary relata.” Accordingly, the two senses of completion or exhaustion he has in mind refer to descriptions of ‘one object in a specified arrangement’ and to ‘one object in different arrangements’. But more precision is called for. Bohr does not really mean different actual @cf. APHK, pp. 71, 74, 88, 90, 99; EAP, pp. 3, 4, 12, 25, 60, 92. 67cf. QMD, p. 150. --APHK, p. 57. ;;CC, p. 316. cf. Note 8 above. “cf. EAP, pp. 4, 60, 92; cf. also an unpublished passage quoted by Folse, op. cit., Note 1, p. 258.

The Meaning of Complementarity

887

experimental

The

challenge

arrangements,

where an object exhibits properties ‘diachronically’.

of the EPR argument choose

arrangement

we want to specify.

acknowledges

which

is that we can, without interfering

deliberately

observable

we want to know

with the object,

about,

hence,

And Bohr takes up this challenge,

‘the freedom to choose between the different complementary

which

when he types of

phenomena we wish to study ‘.‘* The different arrangements in question are not actual arrangements but possible choices of a specified arrangement, possible choices of what we want to know in the case of one object. In case there is such a choice, the arrangement has not yet been specified. Consequently a more precise rendering of the two meanings of completion is that they refer to descriptions of ‘one object in a specified arrangement’ or to ‘one object apart from a specified arrangement’. It might be suspected that this distinction is meaningless for Bohr, since now he argues unremittingly that only phenomena can properly be regarded as the subject matter of physics. But Bohr is well aware that, although it may be impossible to investigate an atomic object without the appropriate apparatus, it is certainly possible to EPR that to refer to it apart from the latter. 73 It is Bohr’s counter-argument specifying a certain arrangement, though possibly being delayed to an instant after the physical interaction of particle and apparatus, is indispensable for the unambiguous definition of the phenomenon concerned. Thus, until this specification is made, the object is in fact referred to apart from a specified arrangement, for example when Bohr talks of a particle at an instant where we still have ‘a free choice whether we wish to know the momentum of the particle or its initial position’.74 Moreover, Bohr’s emphasis on the ultimate determination of the arrangement accentuates the difference of the two situations: before a certain experiment is set by determining an appropriate apparatus, it is still possible to measure any observable, but only after determination is the experiment suited to measuring a certain observable. This difference clarifies the two meanings of completion. It was clear before that, considering an actual experimental arrangement, the quantum mechanical description is complete in so far as it yields all possible value ascriptions of the observables specified. The second meaning of completion does not refer to a specified arrangement, but to the stage before an observable is chosen by such specification. It thus can only refer to the choices themselves:

to the observables.

These observables

form a set which in a certain sense can be said to be complete. This interpretation of complementary completion as referring only to observables, has a number of consequences. First, it suggests that its consistency be tested by investigating the other characteristic of complementarity, i.e. mutual exclusion. To ‘%x, p. 317. 73This is clear from passages where Bohr emphasizes a distinction between object and apparatus. Such distinction presupposes that there are entities to be distinguished. cf. APHK, p. 50, QMD, p. 147, EAP, pp. 3, 78. 74QMD, p. 147; cf. APHK, p. 57, CC.

888

Studies in History and Philosophy of Science

assume that one of the characteristics+ompletion-refers

to observables,

other-exclusion-refers

not lead to a consistent

concept.

Thus,

indefinability

mutual

to descriptions, exclusion

would certainly

must also refer to observables.

thesis again. It started from the assumption

while the

Consider

the

that the arrangements

logically exclude each other in the sense that their descriptions

are incompatible

(e.g.

‘the diaphragm

Now observables

are,

is fixed’ and ‘the diaphragm

is moveable’).

according to Bohr, ‘operationally’ defined, namely by the operations by which we specify one or the other arrangement: the mutual exclusion of the arrangements entails only one of the observables being thus defined.75 On the other hand, the mutual exclusion of descriptions is only motivated for by arguing for the mutual exclusion of arrangements of observables. Thus, exclusion also originally refers to observables (or possible arrangements), so both exclusion and completion refer to observables (or possible arrangements) which makes complementarity a perfectly consistent concept. Secondly, it now becomes clear which one of the assumptions of the straightforward interpretation is inappropriate to Bohr’s mature conception: complementarity no longer refers to descriptions of an atomic object; it refers to observables, not to their values. In fact, the only way to solve the consistency problem of complementarity is to leave the level of descriptions: for them the two characteristics of exclusion and completion can only imply that the described properties simultaneously do and do not pertain to the object, an insoluble contradiction. This creates another interpretation problem. There is good textual evidence that Bohr’s mature conception of complementarity refers to phenomena.76 Without qualification, this seems to mean reference to descriptions of actual phenomena, but such qualification is not easily found. It has still to be investigated whether the interpretation proposed is only derivable from Bohr’s remarks, or whether it is really Bohr’s own. And even if further textual evidence supports this interpretation, the formula of complementarity of phenomena has to be criticized as misleading. Thirdly, it is particularly important to note that the jointly completing observables are a set of possibilities, as the arrangements defining them are possible ones before one is actually

selected.

This leads to some further

textual

evidence

for the

interpretation proposed here, which suggests that it is indeed what Bohr himself has in mind. Bohr frequently explains his new completion concept in the way that complementary information exhausts ‘all definable knowledge’ or all ‘possible information’ about the object.77 This cautious wording at least leaves room for avoiding a direct contradiction: all possible knowledge about an object need not at once be actualizable; e.g., we can know the exact position and the exact momentum “This is how I understand the following sentence ‘. the formal representation of physical quantities by non-commuting operators directly reflects the relationship of mutual exclusion between the operations by which the respective physical quantities are defined and measured.’ (EAP, p. 61). 76cf. Scheibe, op. cif., Note 2, p. 32. “APHK, pp. 90, 40. cf. ibid., pp. 26, 99, EAP, p. 4.

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The Meaning of Complementarity

of a particle, but we cannot-beyond Hence, one might identify observables appropriately

a certain limit-know with possibilities

say that there is a complementarity

them simultaneously.

to obtain knowledge and then

of possible pieces of knowledge

or

information about an object. However, though leaving room for this argument, Bohr does not state it. What comes nearest to a clear statement of it is when he says that complementary evidence, though ‘contradictory when combination into a single picture is attempted, exhausts all conceivable knowledge about the object’.” If all the conceivable, thus only possible, knowledge were at once actualized, i.e. ascribed to the object simultaneously, this would be a ‘combination into a single picture’. Thus, possibility must play a decisive role here to avoid contradiction: all conceivable (classical) observables can meaningfully be measured in atomic objects and be predicted by quantum mechanics, but all possibilities cannot be actualized at once. Clearer textual evidence is Bohr’s recurrent metaphor of a specified experiment as a ‘question’ to nature: in order ‘to put questions to nature in the form of experiments’, we must meet ‘the requirement to specify the experimental conditions’;79 this is indispensable for receiving ‘unambiguous answers to our questions’ .80On the other hand-this is clear from the employment of the metaphor for mutually exclusive arrangements-the specification excludes other questions being asked,81 since it prevents simultaneous use of a different arrangement. Expressed by this metaphor, the differentiation of the two meanings of ‘complete’ reads: the ideal description of a quantum phenomenon is complete in so far as it contains the answers to all questions specified by the experiment, and it is incomplete in so far as it does not contain the answers to all possible questions specified by mutually exclusive experiments. Accordingly, complementarity itself can be expressed by the same metaphor: there is a complete set of meaningful questions to ask a quantum system, and to realize an experiment means to ask certain ones of them; but since some experiments are mutually exclusive, some questions cannot be asked simultaneously, thus afortiori cannot be answered simultaneously. Bohr thus says: ‘Far from restricting our efforts to put questions to nature in the form of experiments, the notion of complementarity simply characterizes the answers we can receive.‘82

“EAP, p. 4. 791bid. “Ibid., p. 60. 8’cf. EAP, p. 4. In ‘classical physics’ ’all characteristic properties can in principle be ascertained by a single experimental arrangement’. In quantum mechanics, however, such an arrangement is impossible. This does not mean that our ‘questions to nature’ are restricted, but ‘the notion of complementarity simply characterizes the answers’. This is to say that it restricts the answers, thus the meaningful questions. **EAP, p. 4.

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Studies in History and Philosophy of Science

7. A Diagnosis It is no accident that an intelligible meaning of the key concept of Bohr’s interpretation can only be derived from his later writings, and even there appears only in scattered remarks. The problem of complementarity is symptomatic of Bohr’s struggle for an understanding of quantum mechanics, and in particular the general change his thought undergoes during this struggle. Hence, to learn that the concept is not consistently introduced, nor made consistent in the early interpretation, despite Bohr’s efforts to do so, is of the same importance for an understanding of his thought as is the consistency achieved after 1935. Appropriately put into context, these symptoms allow for a diagnosis: they hint at a radical change in Bohr’s thought concerning the philosophical background of his interpretation. The starting point of complementarity is Bohr’s reluctant acknowledgement of wave-particle dualism.*” In the late twenties he takes it that the crucial experiments about light and matter confirm the classical wave and particle pictures as wholes. The conflict of these pictures seems to force upon us a choice between them which on the other hand is excluded by empirical evidence. Complementarity is designed to show that this ‘dilemma as regards the choice’ between the picturess4 is not a real dilemma; such choice is not necessary. Instead, both pictures together are necessary for ‘a complete elucidation of one and the same object’.” However, Bohr is forced to admit that this is no simple completion in the ordinary sense. Complementary descriptions also exclude each other. 86The obvious difficulty of understanding what this should mean makes the notion problematic right from the start. Complementarity at this point is not a solution, but an indicator of the problem Bohr faces in wave-particle dualism. His explanations before 1935 are attempts to make intelligible what he feels forced to admit, a constellation of exclusion and completion. The claims that the conflict between the descriptions is only an ‘apparent contradiction’, and is and that complementary relata form an instead a problem of ‘visualization’, ‘unvisualizable’ unity, constitute one such attempt;” the idea of an inevitable distortion of the phenomena to be observed, thus the ‘subjectivity’ of all phenomena, which is to explain the incompatible observation results, constitutes another.** But these ideas are abandoned, when wave-particle dualism is no longer Bohr’s main interpretative concernE9 83cf. Murdoch, op. cir., Note 3, chap. 3. a4ATDN, p. 10. 85ATDN, p. 96. 86cf. ibid., p. 54. 87cf. ibid., pp. 95, 5 1, 62, 100. **cf. BCW 6, p, 91; ATDN, pp. 53f, 100. The ‘subjectivity’ of phenomena is implied by questioning their ‘objectivity’ in ATDN, pp. 93, 97f, but directly expressed, ibid., p. 116. 89The ‘real contradiction’ between wave and particle pictures is acknowledged in APHK, p. 5 (indirectly already in ATDN, p. 107). The idea of an ‘unvisualizable unity’ is tacitly abandoned (cf. for example the use of the ‘picture’ metaphor in EAP, p. 4). The idea of a ‘disturbance of the phenomena’ is explicitly rejected in CC, p. 317, APHK, p. 73, EAP, p. 5. The ‘subjectivity of phenomena’ is abandoned, when Bohr starts to insist that phenomena are the only subject matter of physics (cf. Note 61 above), while obviously maintaining the objectivity of physics (cf. for example EAP, p. 24).

891

The Meaning of Complementarity Nevertheless,

these attempts

behind complementarity.

reveal

The conflicting

which is at least ‘unvisualizable’,

the original descriptions

philosophical

presupposition

hint at a state of the object

and which at most is entirely unknowable

to us

because of the insurmountable ‘subjectivity of the phenomena’: the measurement results do not show the objects as they really are. This is the meaning of the obscure remarks about the ‘subjectivity of the phenomena’. Similarly Bohr at the time says, explaining an example of complementarity, ‘that, by the very nature of the matter, we shall always have last recourse to a word picture, in which the words themselves are not further analyzable ‘,90 implying that the picture gives only a blurred view of the object’s real state. Even clearer, is an illustration of complementarity from biology, which Bohr takes to be ‘a close analogy’ to atomic physics: the uncertainty involved in observation of an object ‘will be just large enough to permit it, so to say, to hide its ultimate secrets from US’.~I This reveals the basic idea behind the early conception of complementarity. The concept is to depict an unvisualizable or even unknowable unity behind the observed phenomena, something which in principle remains hidden from us. 92 If the view that reality is independent of what we observe and, in particular, transcends what is actually observed, is called realism, then this starting point of complementarity is indeed fundamentally realist. The later, consistent concept of complementarity, is part of a completely different picture. Bohr, in the EPR rejoinder, endorses the indefinability thesis in its strongest form: an operationally ill-defined property cannot meaningfully be said to pertain to the object; and this meaninglessness implies that the object really does not have this property. Indeed nothing less would cut any ice against the EPR argument. When Bohr stresses the ‘free choice whether we want to know’ the value of one or the other observable, and the ‘inevitable loss’ of knowledge upon a certain choice,93 this is in principle common ground with Einstein and his collaborators. But the latter hold that even if we decide not to measure an observable, but only predict with certainty the outcome of a measurement we never make, then the object really has that property. It would not do as a counter-argument to say that the unmeasured observable is illdefined. Only the additional assumption that, because it is ill-defined, it really has no value, leads to a sufficient argument; and Bohr, though hesitatingly, sets forth this argument, when he argues that specifying an experiment by choosing one

%ATDN, p. 20. 9’APHK, p. 9. 92Folse’s interpretation of an ‘independently real object’ behind the phenomena (cf. F&e, op. ci?., Note 1, mainly pp. 241-257) correctly mirrors Bohr’s early position. However, False’s implication that this is also Bohr’s final word is mistaken. =QMD, p. 147.

892

arrangement

Studies in History and Philosophy of Science

is conditional

for ‘the description

of any phenomenon

‘physical reality’ can properly be attached.94 This, however, is a position which is incompatible

to which the term

with the earlier realism. It is,

in effect, the conviction that only the variables we actually decide to specify by choosing an experiment have determinate values. What is real is only what we actually observe in a specified arrangement. This is a non-realist position which differs radically from the earlier conception. Bohr well realizes that his new interpretation constitutes ‘a radical revision of our attitude towards the problem of physical reality’,95 and it constitutes, in fact, a ‘radical revision’ of his own realist attitude.96 The struggle for a consistent meaning of complementarity, especially the new and different meaning the concept is given in the later articles, reflects this ‘radical revision’; and, accordingly, the consistent meaning is part of this ‘radical revision’. The concept is no longer intended to unite ‘apparent contradictions’; its role now is to depict a certain completeness of quantum mechanics. This theory is complete in the sense that all conceivable ‘questions to nature’ are given unambiguous ‘answers’ in the theory; therefore, it is complete in the sense that it accounts perfectly for all atomic phenomena. 97 This does not mean, however, that all questions can be asked of a certain object at once. We are free to ask any question, but asking certain questions excludes asking certain others9’ The completeness which Einstein and his collaborators question and which Bohr defends is not at all comprised in this explanation. The strong indefinability thesis which Bohr sets forth in order to argue for the completeness of quantum mechanics is, in the first place, an idea independent of complementarity. However, the new meaning of the concept is directly developed from this thesis: Bohr does not explain the exclusion aspect by mutually exclusive experiments only. Because of this exclusion, he explains, the pertaining observable is ill-defined. And this yields not only that we cannot know the value of this observable, but that this value itself is not rea1.99 Hence, the exclusion aspect of complementarity is explained by the indefinability thesis.“’ Both complementarity and completeness are part of the same 94QMD, p. 148. A similar interpretation could be drawn from two further remarks: the unknowability of certain properties raises ‘questions as to the physical reality of two such attributes of the object’ (APHK, p. 4Off.); these questions are answered, when Bohr says that exclusive quantities ‘cannot simultaneously be ascribed definite values’ (ibid., p. 87). An excluded quantity, thus, does not have a definite value: this value is not real. Bohr’s hesitation as to this consequence of his indefinability thesis and the general tendency to compromise his new ‘radical’ position, demand an explanation of course: such explanation, however, transcends the scope of this paper. 95QMD, p. 146. % is apparently the failure to appreciate Bohr’s revision of his own earlier realism which fuels the recent debate about his realism or anti-realism; cf. Folse, op. cit., Note 1, chap. VIII; Honner, op. cit., Note 2, Section 5.2; Murdoch, op. cit., Note 3, chap. 10. 97This is how I understand the remark that ‘a completeness of description like that aimed at in classical physics is provided by the possibility of taking every conceivable experimental arrangement into account’ (EAP, p. 6). 98cf. EAP, p. 4; CC, p. 317. 99cf. Note 94 above. %f. APHK, pp. 40, 99; EAP, p. 5.

The Meaning of Complementarity

893

train of thoughts. Only together do they form what Bohr regards as his final word on quantum

mechanics.

To sum up. The consistent version of complementarity, developed after 1935, is part of Bohr’s ‘radical revision’ of his own earlier thought. His problems of making complementarity comprehensible and his consistent re-interpretation together indicate the ‘radical revision’ of his own earlier realism. In order to assess rightly Bohr’s efforts to develop a consistent concept of complementarity, thus an understanding of quantum mechanics, it is imperative to see that this ‘radical revision’ is his final solution. Acknowledgements-I would like to thank Gerd Buchdahl for his encouragement to write this paper. Moreover, I am indebted for critical remarks to two anonymous referees and to Bas van Fraassen.