Bohr’s philosophy of wave-particle complementarity

905RESONANCE October 2013

GENERAL ARTICLE

Bohr’s Philosophy of Wave–Particle Complementarity

Dipankar Home

KeywordsInterpretation of QM, Comple-mentarity Principle, ‘which path’experiments.

In this article, after briefly providing the pertinent historicalbackground, the underlying motivation and essence of Bohr’sidea of wave–particle complementarity are explained. Towhat extent the Bohrian notion of complementarity is rel-evant in the modern context is discussed. Bohr’s belief in thegenerality of the complementarity framework is also touchedupon.

1. Historical Prelude

We begin by noting that as early as 1914, only a year after hiscelebrated work on the atomic model, Bohr wrote to hisfriend C W Oseen, “.... the possibility for an embracing pictureshould not be sought in the generality of viewpoints but perhapsrather in the strictest possible limitation of viewpoints” [1]. It isindeed striking that even this early, Bohr had believed that theway in which different possible conceptual frameworks for com-prehending quantum phenomena could be reconciled was byfinding a limit to the applicability of each such framework.Nevertheless, a curious fact is that in the years leading up to theeventual founding of the formalism of quantum mechanics andthe uncertainty principle, Bohr had struggled hard to come toterms, in particular, with the duality between wave and particleaspects in the microphysical phenomena whose various aspectswere gradually being revealed.

Although by the beginning of 1920s, it became increasingly clearthat electromagnetic radiation could be conceived of either interms of the wave model or by using the particle model, Bohr wasunable to reconcile himself to the idea of photons or any particle-like model of radiation. This was because, as Bohr had stressed inhis 1923 article in Nature that diffraction and interference effects

Dipankar Home is SeniorProfessor at Department ofPhysics, Bose Institute,Kolkata. He has been

working for the last threedecades on various

foundational problems ofquantum mechanics and inrecent years on the issuesrelated to the interface

between quantuminformation and quantum

foundations.

906 RESONANCE October 2013

GENERAL ARTICLE

of radiation could not be explained without invoking the wavemodel and that “interference phenomena constitute our onlymeans of assigning any closer meaning to the frequency which inEinstein’s theory fixes the magnitude of the light-quantum” [2].At that time, in view of his reluctance to accept the light-quantumor photon hypothesis, Bohr had even contemplated a formulationof quantum theory that would be able to describe the interactionbetween radiation and atomic systems without requiring thenotion of light-quanta. For this purpose, he was also not reluctantto consider that such a theory might require the abandoning ofstrict conservation of energy and momentum in individual emis-sion and absorption processes.

However, when in the early part of 1927, the experiment byDavisson and Germer was reported that showed diffraction ofelectrons, Bohr immediately realised that further resistanceagainstwave–particle duality would be futile because if particles likeelectrons can gave rise to diffraction effects then in the relevantexperimental contexts, phenomena involving even matter mustinevitably be conceived in terms of the wave model. Once herecognized that the feature of wave–particle dualism was ines-capable, then instead of overthrowing the ideas of wave andparticle, Bohr’s approach was to concentrate on formulating anappropriate conceptual framework for reconciling the idea ofwave with that of particle in a way consistent with the mathemati-cal formalism of quantum theory. This led to the birth of the ideaof wave–particle complementarity.

2. Bohr’s Interpretation of Quantum Mechanics and Wave–Particle Complementarity

In his famous address to the International Congress of Physics atComo, Italy on 16 September 1927, where Bohr had presented forthe first time the concept of complementarity, he declineated thecore of his conceptual tenets on the basis of which he sought tointerpret the various features of quantum phenomena. Later, overthe years, Bohr elaborated his views in a number of writings, ofwhich particlularly significant was his book titled Atomic Theory

Once Bohr recognizedthat the feature of

wave–particle dualismwas inescapable, then

instead of over-throwing the ideas of

wave and particle,Bohr’s approach was

to concentrate onformulating an

appropriate concep-tual framework for

reconciling the idea ofwave with that ofparticle in a way

consistent with themathematical

formalism of quantumtheory.


GENERAL ARTICLE

and the Description of Nature published in 1934, where thecentral aspect of Bohr’s entire philosophy as regards quantumtheory was spelled out as follows: “The quantum theory ischaracterized by the acknowledgement of certain fundamentallimitations in the classical physical ideas when applied to atomicphenomena. The situation thus created is of a peculiar nature,since our interpretation of the experimental material rests essen-tially on the classical concepts” [3].

The above point was a recurrent theme in Bohr’s writings; forexample, in his much cited contribution in 1949 to the collectionof articles in honour of Einstein, he wrote: “... however far thephenomena transcend the scope of classical physical explanation,the account of all evidence must be expressed in classical terms”[4]. This contention rested on a view that in order to justify itself,any novel theory like quantum mechanics has to establish acontact between its mathematical formalism and the experimen-tal results, and the most convenient language that can be used todescribe the latter is in terms of theclassical notions. AsHeisenberghad recalled “... just by discussions with Bohr I learned that onecannot go entirely away from the old words because one has totalk about something .... so I saw that in order to describephenomena one needs a language” [5]. Here we may also mentionthat Schrödinger once wrote to Bohr urging him to explain moreclearly his often-expressed conviction about “the indispensableuse of classical concepts” for understanding quantum phenom-ena. Bohr answered concisely: “My emphasis on the unavoidabil-ity of the classical description of the experiment refers in the endto nothing more than the obvious fact that the description of everymeasuring apparatus basically must contain the arrangement ofthe apparatus in space and its function in time, if we are to be ableto say anything at all about the phenomena” [6].

However, Bohr recognised and accepted that his viewpoint inevi-tably gave rise to a tension between two aspects, viz., that al-though classical concepts/models were invoked for the compre-hension of quanum phenomena, their use needed to be constrainedby suitable provisos. It is precisely to resolve this tension Bohr

This contentionrested on a view thatin order to justifyitself, any noveltheory like quantummechanics has toestablish a contactbetween itsmathematicalformalism and theexperimental results,and the mostconvenient languagethat can be used todescribe the latter isin terms of theclassical notions.


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went about to formulate the framework of what he called thephilosophy of complementarity. As Bell had put it, “Rather thanbeing disturbed by the ambiguity in principle, Bohr seemed to takesatisfaction in it. He seemed to revel in contradictions, for ex-ample between ‘wave’ and ‘particle’, that seem to appear in anyattempt to go beyond the pragmatic level. Not to resolve thesecontradictions and ambiguitites, but rather to reconcile us to them,heput forwarda philosophywhichhecalled ‘complementarity”’[7].

There are two crucial ingredients of Bohr’s conception ofcomplementarity – joint completion and mutual exclusiveness.Explaining the idea of ‘joint completion’, Bohr had said: “....evidence obtained under different conditions cannot be compre-hended within a single picture, but must be regarded as comple-mentary in the sense that only the totality of the phenomenaexhausts the possible information about the objects” [4]. Thenotion of ‘mutual exclusiveness’ was introduced by asserting thatquantum theory “forces us to adopt a new mode of descriptiondesignated as complementary in the sense that any given applica-tion of classical concepts precludes the simultaneous use of otherclassical concepts which in a different context are equally neces-sary for the elucidation of the phenomena” [8]. By incorporatingboth these aspects of ‘joint completion’ and ‘mutual exclusive-ness’, a concise statement of how his notion of wave–particlecomplementarity accommodates wave–particle duality was givenby Bohr as follows: “We are not dealing with contradictory butwith complementary pictures of the phenomena, which onlytogether offer a natural generalization of the classical mode ofdescription so that the two views of the nature of light are ratherto be considered as different attempts at an interpretation ofexperimental evidence in which the limitation of the classicalconcepts is expressed in complementary ways” [9].

The literal meaning of complementarity is ‘mutually or jointlycompleting’. It is in this sense that two angles are said to becomplementary if they make up a right angle. As Bell [10] hadpointed out, Bohr’s use of the term ‘complementarity’ impliedgoing beyond its usual meaning. Consider, for example, as Bell

There are two crucialingredients of Bohr’s

conception ofcomplementarity –

joint completion andmutual

exclusiveness.


GENERAL ARTICLE

had suggested, the different descriptions of an elephant from thefront, from the back, from the side, from the top and from thebottom. These various descriptions are complementary in theusual sense. A key point is that they are consistent with oneanother and are not mutually exclusive; together they provide asingle whole image of an elephant. In contrast, Bohr’s wave–particle complementarity is based on elements, viz., the notionsof wave and particle which are, on the one hand, inherentlyincompatible with one another but, on the other hand, eventhough mutually exclusive, are both necessary for a completeunderstanding of this situation.

It is interesting that Bohr did not try to justify his notion of mutualexclusivity of wave and particle pictures as any consequence of arigorous general argument based on the mathematical formalismof quantum mechanics. His strategy was to defend his hypothesiswith illustrative analyses of specific examples confined basicallyto interference effects, since Bohr recognised that two-slit inter-ference type phenomena contain the essential mystery of quan-tum theory. In such analyses, an interference pattern is viewed asa signature of wave-like propagation. If, on the other hand, theexperimental arrangement can provide information about whichof the possible paths a single particle follows from source todetector, this is taken to signify particle-like propagation.

Here it is important to stress that within the framework of Bohr’swave–particle complementarity, the wave- or particle-like pic-ture acts essentially as a prop for visualizing the behaviour ofmicro-objects in a specific context. In other words, within theBohrian framework, one may say that the mental images of waveand particle are like ‘shadows’ of ‘real’ objects. (This is some-thing like the chained prisoners in the cave imagined by Plato inThe Republic, Book VII, where the prisoners facing the wall oftheir prison are doomed to see only the shadows of objects outsidethe cave). However, though not ‘real’, Bohr considered suchmental images to be expedients which could be conveniently usedfor describing, what he called, the “relationship between empiri-cal evidences obtained under different experimental conditions.”

In contrast, Bohr’swave–particlecomplementarity isbased on elements,viz., the notions ofwave and particlewhich are, on the onehand, inherentlyincompatible with oneanother but, on theother hand, eventhough mutuallyexclusive, are bothnecessary for acompleteunderstanding of thissituation.


GENERAL ARTICLE

While providing his interpretation of Bohr’s idea of wave–particle complementarity, Wheeler had invoked the followingmetaphor: A light pulse is imagined to be like a smoky dragonbefore it bites a detector. Expanding on this, Wheeler had stated:“It is wrong to atribute a tangibility to a photon in all its travelfrom the point of entry to its last instant of flight... . What answerwe get depends on the question we put, the experiment wearrange, the registering device we choose. By his choice ofquestion, the observer decides about what feature of the object heshall have the right to make a clear statement” [11]. WhatWheeler essentially meant was that the notion of wave–particlecomplementarity needed to be applied only after the detectionprocess was completed so that one could then infer which of thetwo models, wave or particle, was relevant to the experiment inquestion. Moreover, in applying the idea of complementarity, inorder to avoid any logical inconsistency due to mutual incompat-ibility between the wave and particle pictures, the possibility isprecluded that a single experiment using interference effect mayexist whose observed results would contain one subset of datacomprehensible in terms of wave-like propagation, with anothersubset of coexisting data interpretable by using particle-likepropagation.

3. Some Remarks from Modern Perspectives

If one considers, say, the optical experiments, the rules of quan-tum optics are well-defined and sufficient to predict correctly allobservable results. Electric and magnetic field operators are thebasic dynamical variables in this formalism. The notion of pho-tons enters the theory as excitations associated with normalmodes in terms of which an electromagnetic field can be ex-panded. From this point of view, the particle aspect of radiationcan be regarded as manifested when an emission or a detectionprocess is considered; for example, the quantized decrease infield energy resulting from a detection process can be describedin terms of removing photons from the field.

It is, therefore, clear that if one remains confined within the

While providing hisinterpretation of Bohr’s

idea of wave–particlecomplementarity,

Wheeler had invokedthe following

metaphor: A lightpulse is imagined to

be like a smokydragon before it bites

a detector.


GENERAL ARTICLE

formalism of quantum thoery, the entire issue of wave–particleduality hinges on how one wants to use the ideas of wave andparticle. The Bohrian interpretation of wave–particle dualism, aswe have already emphasized, stems from the consideration that,apart from the formal predictions of observed results, some formof conceptual or intuitive understanding is also required in termsof the visualizable model of particles/waves. Nevertheless, itturns out that the notion of ‘mutual exclusivity’ entailed by theidea of wave–particle complementarity is consistent with thequantum formalism which ensures complete disappearance ofwave-like interference pattern whenever fully efficient which-path information is available in position space, at least in prin-ciple. This is because any measurement scheme capable of yield-ing which-path information couples (entangles) interfering wavefunctions of the observed entity with mutually orthogonal distin-guishable states of the measuring apparatus. Such an entangle-ment between states of the observed entity and those of theobserving device serves to eliminate the interference effectspertaining to the observed entity.

Within the framework of quantum formalism, there have alsobeen analyses of the so-called intermediate experiments [12, 13]where by using inefficient or partial which-path determination,the initial ensemble is split into two – one giving rise to aninterference pattern, while the other (yielding definite which-path information) does not contribute to interference. In terms ofthe languageused in thecontext of wave–particlecomplementarity,such an intermediate experiment furnishes ‘partial wave’ knowl-edge and ‘partial particle’ knowledge using the same arrangment(for example, it may be possible to obtain with 99% certaintywhich-path information while still retaining a significant interfer-ence pattern). Wootters and Zurek [12] have applied wave–particle complementarity in such cases by arguing: “The sharp-ness of the interference pattern can be regarded as a measure ofhow wavelike the light is, and the amount of information we haveobtained about the photon trajectories can be regarded as ameasure of how particlelike it is”.

It turns out that thenotion of ‘mutualexclusivity’ entailedby the idea of wave–particlecomplementarity isconsistent with thequantum formalismwhich ensurescomplete dis-appearance of wave-like interferencepattern whenever fullyefficient which-pathinformation isavailable in positionspace, at least inprinciple.


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Here it is instructive to examine the subtle relationship betweenwave–particle complementarity and double-slit interference ex-periment of the type in which an intereference pattern developsby a gradual accumulation of discrete detection events registeredas spots on a visual screen corresponding to individual particlesreaching the screen one by one. For instance, one can see photo-graphs of results obtained from the electron interferenceexperiement by Tonomura et al. [14]. In such an experiment, oneconsiders an array of detectors on a screen, with all detectorsconnected to an anticoincidence circuit. Then one observesanticoincidence between counts at detectors in the extreme low-intensity limit of single particles being emitted by the source oneat a time. Such observed anticoincidence may appear to providesignature of particle-like behaviour, subsequent to wave-likepropagation. However, note that in such an experiment, which-slit or which-path information for an individual particle is notavailable on its way from source to the detector. Hence, it isarguable that the coexistence of interference with anticoincidencein such an experiment cannot be interpreted to show wave-likeand particle-like behaviour in the same experiment in the senseprohibited by Bohr’s complementarity principle.

The usually used which-path detection methods in actual two-slitinterference experiments (also known as ‘Welcher Weg’ experi-ments – the German word for ‘which path’) involve loss ofinterference by the exchange of momentum with the particlewhose path is being determined. This has prompted the questionof studying quantitatively the amount of momentum transfer thatis necessary for enforcing mutual exclusivity between interfer-ence and which-path information. In this context, Storey et al.[15] gave a general proof that if in a double-slit interferenceexperiment, the magnitude of momentum exchange of the par-ticle with a detector is less than that permitted by a relation thatthey had derived, interference is not completely eliminated andpath detection is not perfectly efficient. Such a demonstrationhas, in turn, stimulated instructive discussions in the literature[16, 17].

This has prompted thequestion of studying

quantitatively theamount of momentum

transfer that isnecessary for

enforcing mutualexclusivity between

interference andwhich-path

information.


GENERAL ARTICLE

Further, we note that in order to observe truly single particle-likebehaviour with appropriate states of light, one needs sourceswhich emit, which is called, the single photon state of light that isan eigenstate of the photon number operator corresponding to theeigenvalue unity. The probability of joint detection of more thanone photon vanishes for an ideal single photon state – in this sensethe single photon states entail particle-like behaviour. It is suchconsideration that motivated the testing of wave–particlecomplementarity by using single photon states, and experimentsfor this purpose were performed by Grangier et al. [18, 19].

The above-mentioned studies, therefore, serve to highlight thatthe idea of wave–particle complementarity, although conceivedentirely on interpretational ground, has stimulated from modernperspectives, a number of theoretical and experimental investiga-tions revealing interesting subtleties in the issue of wave–particleduality as well as revealing an interplay between interference-type effect and which-psath information that have relevant sig-nificance within the formalism of quantum mechanics.

4. Concluding Remarks

Although the scope of this article is confined to discussing wave–particle complementarity, we would like to briefly mention aboutBohr’s belief in the generality of the basic idea of complemen-tarity. Over the years, Bohr’s conviction grew stronger that aframework comprising apparently incompatible and mutuallyexclusive descriptions which jointly complete each other in inter-preting the relevant experimental results should be applicable inwider contexts other than that involving wave–particle duality.For instance, as a statement of his generalized notion ofcomplementarity, Bohr had asserted in his later years that, ingeneral, “phenomena defined by different concepts, correspond-ing to mutually exclusive experimental arrangements, can beunambiguously regarded as complementary aspects of the wholeobtainable evidence concerning the objects under investigation”[20]. In particular, in an application of his extension of the idea ofcomplementarity during his celebrated exchange with Einstein

Over the years, Bohr’sconviction grewstronger that a frame-work comprisingapparentlyincompatible andmutually exclusivedescriptions whichjointly complete eachother in interpretingthe relevantexperimental resultsshould be applicablein wider contexts otherthan that involvingwave–particle duality.


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concerning the Einstein–Podolsky–Rosen paper [21, 22], Bohrhad argued the following.

Since an experimental setup needed for measuring a given physi-cal quantity is incompatible with that needed to measure anotherone if the operators corresponding to these quantities do notcommute, the very concept of the value of a dynamical variable inquantum mechanics acquires meaning only if one specifies theoverall experimental context in which the relevant variable ismeaured. In other words, within the framework of compleme-ntarity, it is not meaningful to discuss about the value a dynamicalvariable may have had in the absence of any measurement. For

Box 1. On Bohr’s Idea of Generality of Complementarity

In his later years, Bohr continually struggled to generalize his notion of complementarity in a way that can beapplied to different disciplines, like psychology and biology. Here we may just briefly summarize Bohr’s finalviewpoint on the possible role of complementarity in the context of, say, biological phenomena.

In one of his last lectures [N Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, John Wiley,New York, p.26, 1963], delivered in honour of his one-time student and pioneer molecular biologist MaxDelbruck, Bohr elaborated on his notion that “the very existence of life must be taken as a basic fact in biologyin the same sense as the quantum of action has to be regarded in atomic physics as a fundamental elementirreducible to classical physical concept.” Bohr argued that in biology, “structure” as described mechanisticallyand “function” as described teleologically represent “complementary manifestations of biological phenom-ena”. The descriptions are “complementary” because, according to Bohr, “a teleological description of thefunctioning of the organs in an organism provides the starting point for a mechanical analysis of that physicalstructure which makes possible such functioning.”

As Bohr put it more elaborately, “Indeed, many terms used in practical physiology reflect a procedure ofresearch in which, starting from the recognition of the functional role of parts of the organism, one aims at aphysical and chemical account of their finer structures and of the processes in which they are involved. Surelyas long as for practical or epistemological reasons one speaks of life, such teleological terms will be used incomplementing the terminology of molecular biology.”

One can, thus, see once again in this last extension of complementarity attempted by Bohr, the reflection of hisstrong commitment to the central philosophy of complementarity that for the advancement of our understand-ing of natural phenomena in any area, it is imperative that we should gain fuller recognition of how our conceptsfunction and their inter-relationship in describing the diverse array of facts of experience relevant to the areain question.


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instance, if one wishes to consider the value of position of aparticle, one can discuss about it only in the context of a well-defined experiment used to measure it. Similarly, for the value ofmomentum of a particle. However, these two experimental ar-rangements are mutually exclusive. This is what Bohr referred toas position–momentum complementarity, alongside its variantwhich he called “kinematic–dynamic” complementarity. For de-tailed discussions of the implications of such extensions of Bohr’snotion of complementarity, see, for example, [1] and [23].

Here it should be worth noting that Bohr’s emphasis on context-dependence of the value to be ascribed to a dynamical variablehas, of late, acquired more concrete meaning in terms of themodern studies, both theoretical and experimental, concerningthe issue of QuantumContextuality which is now an active area ofresearch [24]. Futher, it needs to be stated that while Bohr’sphilosophy of complementarity continues to stimulate intensedebates about foundations of quantum physics, alternative con-ceptual frameworks have been developed over the years forinterepreting/understanding quantum phenomena, includingwave–particle duality; for example, one may mention what isknown as the Bohmian interpretation of quantummechanics [25].For an overall appraisal of Bohr’s approach to quantum theory inthe light of different strands of modern studies concerning quan-tum foundations, see, for instance, [26].

To sum up, we may say that what is usually referred to as aquestion about the nature of reality (e.g., are quantum entitiesreally waves or particles?) is interpreted within the framework ofcomple-mentarity as a problem in redefining the use of availableconcepts. From a general perspective, Bohr’s complementarityviewpoint advocated that as newer experimental results are re-vealed, the necessary improvement in our understanding of therelevant physical phenomena can be made by appropriately refor-mulating the conditions in a way that would enable consistentapplication of the descriptive modes already available, instead ofrequiring to invoke newer concepts. Finally, it should be remem-bered that in the initial years as quantum mechanics was emerg-

This is what Bohrreferred to asposition–momentumcomplementarity,alongside its variantwhich he called“kinematic–dynamic”complementarity.

To sum up, we maysay that what isusually referred to asa question about thenature of reality(e.g., are quantumentities really wavesor particles?) isinterpreted within theframework ofcomplementarity asa problem inredefining the use ofavailable concepts.


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Address for CorrespondenceDipankar Home

Bose Institute, Block-ENSector V, Salt Lake CityKolkata 700 091, India.

Email:[email protected]

ing, while the founding fathers were struggling to come to termswith myriad puzzles thrown up by the new discoveries, Bohr’sapproach towards interpreting quantum phenomena in a prag-matic way played a powerful pivotal role (for relevant historicaldetails, see, for example, Jammer [27]) in shaping what is nowknown as the ‘standard interpretation’ of quantum mechanics.

Suggested Reading

[1] H J Folse, The Philosophy of Niels Bohr, North-Holland, Amsterdam,p.72, 1985.

[2] N Bohr, Nature, Vol.112, p.4, 1923.[3] N Bohr, Atomic Theory and the Description of Nature, Cambridge

University Press, Cambridge, p.53, 1934.[4] N Bohr, in Albert Einstein: Philosopher-Scientist, Edited by P A Schilpp,

Library of the Living Philosophers, Evanston, pp.199–242, 1949.[5] W Heisenberg, quoted by H J Folse in The Philosophy of Niels Bohr,

North-Holland, Amstermdam, pp.96–97, 1985.[6] W Moore, Schrödinger – Life and Thought, Cambridge University

Press, Cambridge, pp.312–313, 1989.[7] J S Bell, Speakable and Unspeakable in Quantum Mechanics, Cam-

bridge University Press, Cambridge, p.189, 1987.[8] Ref. [3], p.10.[9] Ref. [3], p.56.[10] Ref. [7], p.190.[11] J A Wheeler, At Home in the Universe, American Institute of Physics,

New York, pp.120, 311, 1994.[12] W K Wootters and W Zurek, Physical Review D, Vol.19, p.473, 1979.[13] D M Greenberger and A Yasin, Physics Letters A, Vol.128, p.391, 1988.[14] A Tonomura et al, American Journal of Physics, Vol.57, p.117, 1989.[15] P Storey et al, Nature, Vol.367, p.626, 1994.[16] M D Scully et al, Nature, Vol.375, p.367, 1995.[17] P Storey et al, Nature, Vol.375, p.368, 1995.[18] P Grangier, G Roger and A Aspect, Europhysics Letters, Vol.1, p.173,

1986.[19] A Aspect, in Sixty-Two Years of Uncertainty, Edited by A I Miller,

Plenum, New York, pp.45–59, 1990.[20] Ref. [1], p.159.[21] A Einstein, B Podolsky and N Rosen, Physical Review, Vol.47, p.777,

1935.[22] N Bohr, Physical Review, Vol.48, p.696, 1935.[23] D Murdoch, Niels Bohr’s Philosophy of Physics, Cambridge University

Press, Cambridge, 1987.

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Bohr’s philosophy of wave-particle complementarity

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