notions of causality and complementarity

8/12/2019 Notions of Causality and Complementarity

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On the Notions of Causality and ComplementarityAuthor(s): Niels BohrSource: Science, New Series, Vol. 111, No. 2873 (Jan. 20, 1950), pp. 51-54Published by: American Association for the Advancement of ScienceStable URL: http://www.jstor.org/stable/1677100.

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January 20, 1950, VcxlX111 SCIENCE 51

THE CAUSAL MODE of descriptionhas deeproots in our conscious endeavors to utilizeexperience for practical adjustment to ourenvironments,and is in this way inherentlyincorporated n common anguage. By the guidancemrhichnalysis in terms of cause and effect has off redin many fields of human knowledge, he principle ofczeusality as evell come to stand as the ideal for sci-entifie e2rplanation.In physics, causal deseription,originally adapted toShe problems of mechanics,rests on the assllmptionthat the lmowledge of the state of a material systemat a given time permits the prediction of its state atany subsequent im*e. Here, however,already he defi-nition of state requires special considerationand itneed hardly be recalled that an adequateanalysis ofmechanicalphenomena was possible only after therecognition hat, in the account of a state of a systemof bodies,not tnerely heir location at a given momentbut also tlleir velocities have to be included.In elassical mechanics, the forces between bodies

were assumed o depend simply on the instantaneouspositions and velocities; but the discovery of the re-tardationof electromagnetic ffects made it necessaryto consider orce fields as an essential part of a phys-ical system, and to include in the dessription of thestate of the system at a given time the specificationofthese fields in every point of space. lCet, as is wellknown,the establishment f the differentialequationsconnecting the rate of variation of electromagneticintensities in space and time has made possible adescriptionof electromagnetic henomena n completeanalogy to eausal analysis in meehanics.It is true that, from the point of view of relativisticargumentation, uch attributes of physical objects asposition and velocity of material bodies, and evenelectric or magneticfield intensities, can no longer be

1 The purpose of this article is to give a very brief surreyof some epistemological problems rnise(l in atomic phyBics.It was originally published in Dialectwa, InterIlational Ite-view of the Philosophy of }inoavledt,e, Editions elu Griffon,NeucllAtel, Switrerland, Vol. 7/8 ( 1948 ), p. 319. A iulleraccount of the historical development, illustrated by typicalesnmples which have served to clarify tlle general principles,is inclll(led in a chapterzof All)ert Einstein: PhiZosopher-sci-6ntist, being pllblished by The Lxbraryof Living Philosophers,Inc., Eranston, Illinois, under the alitorship of Paul ArthurSchilpp.

given an absolute content. Still, relativity theory,which has endued classioal physies with unpreee-dented unity and scope, has just through its elucida-tion of the conditions for the unambiguoususe ofelementaryphysical conceptsalloweda concise ormu-lation of tWeprinciple of causality along most gen-eral lines.However,a wholly new situation in physical scienaewas created through the discovery of the universalquantum of action, which revealed an elementaryfeature of individuality f atomic processesfar be-yond the old doetrine of the limited divisibility ofmatter originally introduced as a foundation for acausal explanation of the speciSe properties of mat@-rial substances. This novel feature is not only en-tirely foreign to the classical theories of mechaniesand electromagnetism, ut is even irreconcilablewiththe very idea of causality.In fact, the specificationof the state of a physicalsystem evidently cannot determine he choice betwendififerent ndividual proeesses of transition to otherstates, and an account of quantum effects must thusbasieally operate with the notion of the probabilitiesof occurrence of the difEerentpossible transitionprocesses. We have here to do with a situation essen-tially different n character rom the recourseto sta-tistieal methods n the practical dealing with compli-eated systems that are assumedto obey laws of clas-sical mechanies.The e2rtent o which ordinaryphysical pictures failin accounting or atolziiephenomena s strikingly llus-traid by the well-knowndilemmaconcerning he cor-puseular and lvave properties of material particles aswell as of eleetromagnetic adiation. It is further im-portant to realize that any determinationof Planek'sconstant rests upon the comparisonbetween aspectsof the phenomena which-ean be deseribed only bymeans of pictures not combinable on the basis ofclassicalphysical theories. Thesetheories ndeed rep-resent merely idealizations of asymptotic validity inthe limit where the actions involved in any stage ofthe analysis of the phenomena are large comparedwith the elementaryquantum.In this situation, we are aced with the necessityof a radical revision of the foundationfor descriptionand explanation of physieal phenomena. Eere, it

On the Notions of Causality nd ComplementaritylNiels BohrInstitute or TheoreticvGhysics,Universityof Copenhagen,Denmark

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52 SCIENCE January 20, 1950, Vol. 111must above all be recognized hat, however ar quan-tum effects transcend the scope of classical physicalanalysis, the accountof the experimentalarrangementand the record of the observationsmust always beexpressed n common anguage supplementedwith theterminology of classical physics. This is a simplelogical demand, since the word experiment an inessence be used only in referring to a situation wherewe can tell others what we have done and what wehave learned.The very fact that quantumphenomenacannot beanalyzed on classical linesithus implies the impossi-bility of separatinga behaviorof atomic objects fromthe interaction of these objects with the measuringinstruments which serve to specify the conditionsunder which the phenomenaappear. In particular,the individuality of the typical quantumeffects findsproper expression in the circumstance hat any at-tempt at subdividing the phenomenawill demand achange in the experimentalarrangement, ntroducingnew sources of uncontrollable nteractionbetween ob-jects and measuring nstruments.In this situation, an inherent element of ambiguityis involved in assigning conventionalphysical attri-butes to atomic objects. A clear example of such anambiguity s offered by the dilemmamentioned,as tothe properties of electrons or photons, where we arefaced with the contrast revealed by the comparisonbetween observations egarding an atomic object, ob-tained by means of different experimental arrange-ments. Such empiricalevidenceexhibits a novel typeof relationship, which has no analogue in classical'physics and which may convenientlybe termed cons-plewDentartty in order to stress that in the contrastingphenomena we have to do with equally essentialaspects of all well-defined nowledgeaboutthe objects.An adequate tool for the complementarymode ofdescription s offeredby the quantum-mechanicalor-malism, in which the canonical equations of classicalmechanics re retainedwhile the physical variablesarereplaced by symbolic operators subjected to a non-commutative lgebra. In this formalismPlanck'scon-stant enters only in the commutation elations

qp-pq=v-l2 (1)between the symbols q and p standing for a pair ofconjugate variables, or in the equivalent representa-tion by means of the substitutionsof the type

| hdp=-\/-l 2 ,3 (2)by which one of each set of conjugate variables s re-placed by a diSerential operator. According to thetwo alternativeprocedures, uantum-mechanicalalcu-lations may be performed either by representingthevariables by matrices with elements referring to the

individual ransitionsbetween wo states of the systemor by making use of the so-calledwave equation, hesolutions of which refer to these states and allow usto derive probabilities for the transitions betweenthem.The entire formalism s to be consideredas a toolfor derivingpredictions,of definiteor statistical char-acter, as regards nformationobtainableunder experi-mental conditions described in classical terms andspecified by means of parameters entering into thealgebraic or differentialequations of which the mat-rices or the wave functions,respectively,are solutions.These symbols themselves,as is indicated already bythe use of imaginary numbers,are not susceptibletopictorial interpretation; and even derived real func-tions like densities and currents are only to be re-garded as expressing the probabilities or the occut-rence of individual events observableunder well-de-

fined experimental onditions.A characteristic eature of the quantum-mechanicaldescription s that the representationof a state of asystem can never imply the accuratedetermination fboth members f a pair of conjugatevariablesq and p.In fact, due to the noncommutability f such variables,as expressed by (1) and (2), there will always be areciprocalrelationSq- Ap=4x (3)

between he latitudesSq and Ap with whichthese vari-ables can be fixed. These so-called ndeterminacy e-lations explicitly bear out the limitation of causalanalysis, but it is importantto recognizethat no un-ambiguous interpretation of such relations can begiven in words suited to describea situation in whichphysical attributes are objectified n a classical way.Thus, a sentence like we cannot know both themomentumand the position of an electron raises atonce questions as to the physical reality of such twoattributes, which can be answered only by referringto the mutually exclusive conditions for the unam-biguous use of space-time coordination,on the onehand, and dynamicalconservation aws, on the other.In fact, any attempt at locating atomic objects inspace and time demandsan experimental rrangementinvolving an exchangeof momentum nd energy, un-controllable n principle, between the objects and thescales and clocks definingthe reference frame. Con-versely, no arrangementsuitable for the eontrol ofmomentum nd energy balancewill admit precise de-scription of the phenomenaas a chain of events inspace and time.Strictly speaking,every reference o dynamicalcon-cepts implies a classical mechanicalanalysis of phys-ical evidence which ultimately rests on the recordingof space-timecoincidences. Thus, also in the descrip-



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January 20, 1950, Vo1. 111 SCIENCE 53tion of atomic phenomena, use of momentum andenergy variables for- the specificationof initial con-ditions and final observations efers implicitly to suchanalysis and therefore demands hat the experimentalarrangementsused for the purpose have spatixll di-mensions and operate with time intervals sufficientlylarge to permit the neglect of the reciprocal ndeter-minacy expressedby (3). Under these circumstancesit is, of GOurSe,o a certain degree a matter of con-venience to what extent the elassical aspects of th0phenomenaare ineluded in the proper quantum-me-chanical treatmentwhere a distinction n principle ismade between measuring nstrllments, he descriptionof whichmust always be based on space-timepictures,and objects under investigation, about which observ-able predictionscan in general be derived only by thenonvisualizable ormalism.Incidentally, t may be remarked hat the construc-tion and the functioning of all apparatus like dia-phragmsand shutters,serving to definegeometryandtiming of the experimentalarrangements,or photo-graphic plates used for recordingthe localization ofatomic objects, will depend on properties of materialswhieh are themselves essentially determined by thequantumof action. Still, this circumstance s irrele-vant for the study of simple atomicphenomenawhere,in the specificationof the experimentalconditions,wemay to a very high degree of approximationdisregardthe molecular constitution of the measuring instru-ments. If only the instrumentsare sufficientlyheavycomparedwith the atomic objects under investigation,we can in particularneglect the requirements f rela-tion (3) as regards the control of the localization nspace and time of the single pieces of apparatus rela-tive to each other.In representing a generalization of classical me-chanicssuitedwto llow for the existence of the quan-tum of action, quantummechanicsoffersa frame sufR-ciently wide to account for empirical regularitieswhich cannot be comprised in the tlassieal way ofdescription. Besides the characteristic features ofatomic stability, which gave the first impetus to thedevelopment f quantummechanics,we may here referto the peculiar regularitiesexhibitedby systems com-posed of identical entities, such as photons or elec-trons, and determining for radiative equilibriumoressentialpropertiesof materialsubstances. As is wellknown, these regularitiesare adequatelydescribedbythe symmetryproperties of the wave functions repre-senting the state of the whole systems. Of course,such problemscannotbe exploredby any experimentalarrangement uited for the tracing in space and timeof each of the identical entities separately.It is furthermore nstructiveto considerthe condi-tions for the determinationof positional and dynam-

ical variables n a state of a system with several atomicconstituents. In fact, although any pair7q and p, ofconjugate space and momentumvariables obeys therule of noncommutativemultiplication expressed by(1), and thus can be fixed only with reciprocal lati-tudes given by ( 3), the differenceql - q2 between thespace coordinatesreferring to two constituents of asystem will commutewith the sumP1 + P2 of the corre-sponding momentumcomponents,as follows directlyfrom the commutability f ql with P2 and of q2 withP1- Both ql-q2 and P1+P2 can, therefore, be ac-curatelyfixed in a state of the complexsystem and wecan consequentlypredict the value of either q1 or P1if either q2 or P2 respectively, is determinedby di-rect measurement. Since at the moment of measure-ment the direct interaction between the objects mayhave ceased, t might thus appear that both ql and P1were to be regardedas well-definedphysical attributesof the isolated object and that, therefore, as has beenargued, the quantum-mechanicalepresentationo astate shouldnot offer an adequatemeansof a completedescriptionof physical reality. With regard to suchan argument,however, t must be stressed hat any twoarrangementswhich admit accuratemeasurements fq2and P2 will be mutuallyexclusiveand that thereforepredictionsas regards q1 or P1 respectively,will per-tain to phenomena which basically are of comple-mentary character.As regards the question of the completenessof thequantum-mechanical ode of deseription, t must berecognized hat we are dealing with a mathematicallyconsistent scheme which is adapted within its scopeto every process of measurement nd the adequacyofwhich can be judged only from a comparisonof thepredicted results with actual observations. In thisconnection, t is essential to note that, in any well-definedapplication of quantummechanics, t is neces-sary to specify the whole e2cperimental rrangementand that, in particular, he possibility of disposing ofthe parametersdefining he quantum-mechanicalrob-lem just corresponds o our freedom of constructingand handling the measuringapparatus, which in turnmeans the freedom to choose between the differentcomplementary ypes of phenomenawe wish to study.In order to avoid logical inconsistencies n the ac-count of this unfamiliar situation, great care in allquestions of terminology and dialectics is obviouslyimperative. Thus, phrases often found in the phys-ical literature, ike ;;disturbance f phenomenaby ob-servation'2 r ';creationof physical attributes of ob-jects by measurements, epresenta use of words likephetsomenc6and observastzonas well as attrsbqeteandfneasuremetst which is hardly compatible with com-mon usage and practical definition and, therefore, isapt to cause confusion. As a more appropriate way



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4 SCIENCE January 20, 1950, Vol. 111of e2rpression,ne may strongly advoeate imitationofthe use of the word phenornenon to refer exelusivelyto observations btainedunderspeeifiedeireumstanees,ineludingan aeeountof the whole experiment.With this terminology, he observational roblem natomicphysies s free of any speeial intrieaey, inee inaetual experiments all evidenee pertains to observa-tions obtained under reprodueibleeonditions and isexpressedby unambiguous tatementsreferring to theregistration of the point at whieh an atomie partielearrives on a photographieplate or to a eorrespondint,reeordof some other aluplifieationdeviee. Moreover,the ireumstanee hat all sueh observations nvolveproeessesof essentially rreversibleeharaeter ends toeaeh phenomenon ust that inherent featura of eom-pletion whieh is demanded or its well-defined nter-pretationwithin the frameworkof quantummeehanies.

Recapitulating, he impossibilityof subdividing heindividual quantum eSeets and of separating a be-havior of the objects froin their interaetion with thelneasuring nstruments ernng to define he eonditionsunder wvhieh he phenomenaappear implies an am-biguity in assigning eonventionalattributes to atomieobjeets whieh ealls for a reconsideration f our atti-tude towards he problemof physieal explanation. Inthis novel situation, even the old question of an ulti-mate determinaeyof natural phenomenahas lost itseoneeptionalbasis, and it is against this baekgroundthat the viewpoint of eonlplementarity resents itselfas a rational generalization of the very ideal ofeausality.The eomplementarymodeof deseriptiondoes indeednot involve any arbitrary renuneiationof eustomarydemandsof explanationbut, on the eontrary,aims atan appropriatedialeetieexpression or the aetual eon-ditions of analysis and synthesis in atomie physies.Ineidentally, t would seenl that the reeourse o three-valued logie, sometimesproposed as means for deal-ing with the paradoxieal eatures of quantum heory,is not suited to give a eleareraeeountof the situation,sinee all well-definedexperimental evidenee, even ifit eannot be analyzed in tertns of elassieal pllysies,must be expressed in ordinary language making useof eommon ot,ic.

The epistemolot,ieal esson we have reeeived fromthe new development n physieal seience, where theproblemsenable a eomparatively oncise formulationof prineiples, may also suggest lines of approaeh inother domainsof knowledgewhere the situation is ofessentially less aecessible eharaeter. An example Lsoffered in biology, where meehanistic and vitalistiearguments are used in a typieally eomplementarymanner. In soeiolot,y, oo, sueh dialeetiesmay oftexIbe useful, partieularly n problemseonfrontingus inthe study and eoznparison f human cultures, xvherewe have to eope with the element of eomplaeeney n-herent n every national eultureand manifesting tselfin prejudiees whieh obviously eannot be appreeiatedfrom the standpoint of other nations.Reeognition of eomplementary elationship is notleast required n psyehology,where the eonditions oranalysis and synthesis of experienee exhibit strikinganalogy with the situation n atomiephysi. In fact,the use of words like thoql,ghtsand sentiments, equallyindispensableto illustrate the diversity of psyehiealexperienee, pertain to mutually exelusive situationseharaeterizedby a different drawing of tle line ofseparationbetweensubjeet and objeet. In partieular,the plaee left for the feeling of volition is aSordedbythe very eireumstaneehat situationswherewe experi-enee freedom of will are ineompatiblewith psyeho-logieal situations where eausal analysis is reasonablyattempted. In other words, when we use the phraseI will we renouneeexplanatoryargumentation.Altogether, he approaeh towards the problem ofexplanation hat is embodied n the notion of eomple-mentarity suggests itself in our position as eonseiousbeings and reealls foreefully the teaehing of aneientthinkers hat, in the seareh for a harmonious ttitudetowards life, it must never be forgotten that we our-selves are both aetors and speetators n the drama ofexistenee. To sueh an utteraneeapplies, of eourse,aswell as to most of the sentenees n this artiele fromthe beginning o the end, the reeognition hat our taskean only be to aim at eommunieating xperieneesandviews to others by means of language, in whieh thepraetiealuse of every word stands in a eomplementaryrelationto attempts of its striet definition.


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