Copenhagen Interpretation of Quantum Mechanics (Stanford Encyclopedia of Philosophy) Cite this entry Search the SEP • Advanced Search • Tools • RSS FeedTable of Contents• What's New• Archives• Projected ContentsEditorial Information• About the SEP• Editorial Board• How to Cite the SEP• Special CharactersSupport the SEPContact the SEP ©Metaphysics Research Lab,CSLI,Stanford University  Open access to the SEP is made possible by a world-wide funding initiative. Please Read How You Can Help Keep the Encyclopedia FreeCopenhagen Interpretation of Quantum MechanicsFirst published Fri May 3, 2002; substantive revision Thu Jan 24, 2008As the theory of the atom, quantum mechanics is perhaps the mostsuccessful theory in the history of science. It enables physicists,chemists, and technicians to calculate and predict the outcome of avast number of experiments and to create new and advanced technologybased on the insight into the behavior of atomic objects. But it isalso a theory that challenges our imagination. It seems to violatesome fundamental principles of classical physics, principles thateventually have become a part of western common sense since the riseof the modern worldview in the Renaissance. So the aim of anymetaphysical interpretation of quantum mechanics is to account forthese violations. The Copenhagen interpretation was the first general attempt tounderstand the world of atoms as this is represented by quantummechanics. The founding father was mainly the Danish physicist NielsBohr, but also Werner Heisenberg, Max Born and other physicists madeimportant contributions to the overall understanding of the atomicworld that is associated with the name of the capital of Denmark. In fact Bohr and Heisenberg never totally agreed on how to understandthe mathematical formalism of quantum mechanics, and none of them everused the term “the Copenhagen interpretation” as a jointname for their ideas. In fact, Bohr once distanced himself from whathe considered to be Heisenberg's more subjective interpretation(APHK, p.51). The term is rather a label introduced by peopleopposing Bohr's idea of complementarity, to identify what they saw asthe common features behind the Bohr-Heisenberg interpretation as itemerged in the late 1920s. Today the Copenhagen interpretation ismostly regarded as synonymous with indeterminism, Bohr'scorrespondence principle, Born's statistical interpretation of thewave function, and Bohr's complementarity interpretation of certainatomic phenomena.1. The Background2. Classical Physics3. The Correspondence Rule4. Complementarity5. Misunderstandings of Complementarity6. The Divergent Views7. New PerspectivesBibliographyOther Internet ResourcesRelated Entries1. The Background In 1900 Max Planck discovered that the radiation spectrum of blackbodies occurs only with discrete energies separated by the valuehv where v is the frequency and h is a newconstant, the so-called Planck constant. According to classicalphysics the intensity of this continuous radiation would growunlimitedly with growing frequencies, resulting in what was called theultraviolet catastrophe. But Planck's suggestion was that if blackbodies only exchange energy with the radiation field in a proportionequal to hv that problem would disappear. The fact that theabsorption and the emission of energy is discontinuous is in conflictwith the principles of classical physics. A few years later AlbertEinstein used this discovery in his explanation of the photoelectriceffect. He suggested that light waves were quantized, and that theamount of energy which each quantum of light could deliver to theelectrons of the cathode, was exactly hv. The next step camein 1911 when Ernest Rutherford performed some experiments shootingalpha particles into a gold foil. Based on these results he could setup a model of the atom in which the atom consisted of a heavy nucleuswith a positive charge surrounded by negatively charged electrons likea small solar system. Also this model was in conflict with the laws ofclassical physics. According to classical mechanics andelectrodynamics one might expect that the electrons orbiting around apositively charged nucleus would continuously emit radiation so thatthe nucleus would quickly swallow the electrons. At this point Niels Bohr entered the scene and soon became theleading physicist on atoms. In 1913 Bohr, visiting Rutherford inManchester, put forward a mathematical model of the atom whichprovided the first theoretical support for Rutherford's model andcould explain the emission spectrum of the hydrogen atom (the Balmerseries). The theory was based on two postulates: An atomic system is only stable in a certain set of states,called stationary states, each state being associated with a discreteenergy, and every change of energy corresponds to a completetransition from one state to another.The possibility for the atom to absorb and emit radiation isdetermined by a law according to which the energy of the radiation isgiven by the energy difference between two stationary states beingequal to hv. Some features of Bohr's semi-classical model were indeed very strangecompared to the principles of classical physics. It introduced anelement of discontinuity and indeterminism foreign to classicalmechanics: Apparently not every point in space was accessible to an electronmoving around a hydrogen nucleus. An electron moved in classicalorbits, but during its transition from one orbit to another it was atno definite place between these orbits. Thus, an electron could onlybe in its ground state (the orbit of lowest energy) or an excitedstate (if an impact of another particle had forced it to leave itsground state.) It was impossible to predict when the transition would take placeand how it would take place. Moreover, there were no external (orinternal) causes that determined the “jump” backagain. Any excited electron might in principle move spontaneously toeither a lower state or down to the ground state.Rutherford pointed out that if, as Bohr did, one postulates thatthe frequency of light v, which an electron emits in atransition, depends on the difference between the initial energy leveland the final energy level, it appears as if the electron must“know” to what final energy level it is heading in orderto emit light with the right frequency. Einstein made another strange observation. He was curious to knowin which direction the photon decided to move off from theelectron. Between 1913 and 1925 Bohr, Arnold Sommerfeld and others were able toimprove Bohr's model, and together with the introduction of spin andWolfgang Pauli's exclusion principle it gave a reasonably gooddescription of the basic chemical elements. The model ran intoproblems, nonetheless, when one tried to apply it to spectra otherthan that of hydrogen. So there was a general feeling among allleading physicists that Bohr's model had to be replaced by a moreradical theory. In 1925 Werner Heisenberg, at that time Bohr'sassistant in Copenhagen, laid down the basic principles of a completequantum mechanics. In his new matrix theory he replaced classicalcommuting variables with non-commuting ones. The following year, ErwinSchrödinger gave a simpler formulation of the theory in which heintroduced a second-order differential equation for a wave function.He himself attempted a largely classical interpretation of the wavefunction. However, already the same year Max Born proposed aconsistent statistical interpretation in which the square of theabsolute value of this wave function expresses a probability amplitudefor the outcome of a measurement.2. Classical Physics Bohr saw quantum mechanics as a generalization of classical physicsalthough it violates some of the basic ontological principles on whichclassical physics rests. These principles are: The principle of space and time, i.e., physicalobjects (systems) exist separately in space and time in such a waythat they are localizable and countable, and physical processes (theevolution of systems) take place in space and time;The principle of causality, i.e., every event has acause;The principle of determination, i.e., every later stateof a system is uniquely determined by any earlier state;The principle of continuity, i.e., all processesexhibiting a difference between the initial and the final state haveto go through every intervening state; and finallyThe principle of the conservation of energy, i.e., theenergy of a closed system can be transformed into various forms but isnever gained, lost or destroyed. Due to these principles it is possible within, say, classicalmechanics, to define a state of a system at any later time withrespect to a state at any earlier time. So whenever we know theinitial state consisting of the system's position and momentum, andknow all external forces acting on it, we also know what will be itslater states. The knowledge of the initial state is usually acquiredby observing the state properties of the system at the time selectedas the initial moment. Furthermore, the observation of a system doesnot affect its later behavior or, if observation somehow shouldinfluence this behavior, it is always possible to incorporate theeffect into the prediction of the system's later state. Thus, inclassical physics we can always draw a sharp distinction between thestate of the measuring instrument being used on a system and the stateof the physical system itself. It means that the physical descriptionof the system is objective because the definition of any later stateis not dependent on measuring conditions or other observationalconditions. Much of Kant's philosophy can be seen as an attempt to providesatisfactory philosophical grounds for the objective basis of Newton'smechanics against Humean scepticism. Kant showed that classicalmechanics is in accordance with the transcendental conditions forobjective knowledge. Kant's philosophy undoubtedly influenced Bohr invarious ways as many scholars in recent years have noticed (Hooker1972; Folse 1985; Honnor 1987; Faye 1991; Kaiser 1992; and Chevalley1994). Bohr was definitely neither a subjectivist nor a positivistphilosopher, as Karl Popper (1967) and Mario Bunge (1967) haveclaimed. He explicitly rejected the idea that the experimental outcomeis due to the observer. As he said: “It is certainly notpossible for the observer to influence the events which may appearunder the conditions he has arranged” (APHK, p.51). Notunlike Kant, Bohr thought that we could have objective knowledge onlyin case we can distinguish between the experiential subject and theexperienced object. It is a precondition for the knowledge of aphenomenon as being something distinct from the sensorial subject,that we can refer to it as an object without involving the subject'sexperience of the object. In order to separate the object from thesubject itself, the experiential subject must be able to distinguishbetween the form and the content of his or her experiences. This ispossible only if the subject uses causal and spatial-temporal conceptsfor describing the sensorial content, placing phenomena in causalconnection in space and time, since it is the causal space-timedescription of our perceptions that constitutes the criterion ofreality for them. Bohr therefore believed that what gives us thepossibility of talking about an object and an objectively existingreality is the application of those necessary concepts, and that thephysical equivalents of “space,” “time,”“causation,” and “continuity” were theconcepts “position,” “time,”“momentum,” and “energy,” which he referred toas the classical concepts. He also believed that the abovebasic concepts exist already as preconditions of unambiguous andmeaningful communication, built in as rules of our ordinarylanguage. So, in Bohr's opinion the conditions for an objectivedescription of nature given by the concepts of classical physics weremerely a refinement of the preconditions of human knowledge.3. The Correspondence Rule The guiding principle behind Bohr's and later Heisenberg's work inthe development of a consistent theory of atoms was the correspondencerule. The full rule states that a transition between stationary statesis allowed if, and only if, there is a corresponding harmoniccomponent in the classical motion (CW Vol. 3, p. 479). Bohrfurthermore realized that according to his theory of the hydrogenatom, the frequencies of radiation due to the electron's transitionbetween stationary states with high quantum numbers, i.e. states farfrom the ground state, coincide approximately with the results ofclassical electrodynamics. Hence in the search for a theory of quantummechanics it became a methodological requirement to Bohr that anyfurther theory of the atom should predict values in domains of highquantum numbers that should be a close approximation to the values ofclassical physics. The correspondence rule was a heuristic principlemeant to make sure that in areas where the influence of Planck'sconstant could be neglected the numerical values predicted by such atheory should be the same as if they were predicted by classicalradiation theory. The Bohr-Sommerfeld core model of the atomic structure came intotrouble in the beginning of the 1920s due to the fact that it couldn'thandle an increasing number of spectroscopic phenomena. In 1924Wolfgang Pauli introduced a new degree of freedom according to whichtwo electrons with the same known quantum numbers could not be in thesame state. A year later, in 1925, Ralph Kronig, Georg Uhlenbeck andSamuel Goudsmit explained this new degree of freedom by introducingthe non-classical concept of electron spin. It has been suggested,however, that Pauli's proposal meant a lethal blow not only to theBohr-Sommerfeld model, but also to the correspondence principlebecause “how to reconcile the classical periodic motionspresupposed by the correspondence principle with the classicallynon-describable Zweideutigkeit of the electron's angularmomentum?” (Massimi 2005, p.73) Although the exclusion rule and the introduction of spin broke withthe attempt to explain the structure of the basic elements along thelines of the correspondence argument (as Pauli pointed out in a letterto Bohr) Bohr continued to think of it as an important methodologicalprinciple in the attempt to establish a coherent quantum theory. Infact, he repeatedly expressed the opinion that Heisenberg's matrixmechanics came to light under the guidance of this very principle. Inhis Faraday Lectures from 1932, for instance, Bohr emphasizes: “Afundamental step towards the establishing of a proper quantummechanics was taken in 1925 by Heisenberg who showed how to replacethe ordinary kinematical concepts, in the spirit of the correspondenceargument, by symbols referring to the elementary processes and theprobability of their occurrence.” (CC, p.48) Bohracknowledged, however, that the correspondence argument failed too inthose cases where particular non-classical concepts have to beintroduced into the description of atoms. But he still thought thatthe correspondence argument was indispensable for both structural andsemantic reasons in constructing a proper quantum theory as ageneralised theory from classical mechanics. Indeed spin is a quantum property of the electrons which cannot beunderstood as a classical angular momentum. Needless to say, Bohrfully understood that. But he didn't think that this discovery ruledout the use of the correspondence rule as guidance to finding asatisfactory quantum theory. A lengthy quotation from Bohr's paper“The Causality Problem in Atomic Physics” (1938) givesevidence for this:Indeed, as adequate as the quantum postulates are in thephenomenological description of the atomic reactions, as indispensableare the basic concepts of mechanics and electrodynamics for thespecification of atomic structures and for the definition offundamental properties of the agencies with which they react. Far frombeing a temporary compromise in this dilemma, the recourse toessentially statistical considerations is our only conceivable meansof arriving at a generalization of the customary way of descriptionsufficiently wide to account for the features of individualityexpressed by the quantum postulates and reducing to classical theoryin the limiting case where all actions involved in the analysis of thephenomena are large compared with a single quantum. In the search forthe formulation of such a generalization, our only guide has just beenthe so called correspondence argument, which gives expression for theexigency of upholding the use of classical concepts to the largestpossible extent compatible with the quantum postulates. (CC,p.96) This shows that, according to Bohr, quantum mechanics, as formulatedby Heisenberg, was a rational generalization of classical mechanicswhen the quantum of action and the spin property were taken intoaccount. The correspondence rule was an important methodological principle. Inthe beginning it had a clear technical meaning for Bohr. It isobvious, however, that it makes no sense to compare the numericalvalues of the theory of atoms with those of classical physics unlessthe meaning of the physical terms in both theories iscommensurable. The correspondence rule was based on theepistemological idea that classical concepts were indispensable forour understanding of physical reality, and it is only when classicalphenomena and quantum phenomena are described in terms of the sameclassical concepts that we can compare different physicalexperiences. It was this broader sense of the correspondence rule thatBohr often had in mind later on. He directly mentioned therelationship between the use of classical concepts and thecorrespondence principle in 1934 when he wrote in the Introduction toAtomic Theory and the Description of Nature:[T]he necessity of making an extensive use … of theclassical concepts, upon which depends ultimately the interpretationof all experience, gave rise to the formulation of the so-calledcorrespondence principle which expresses our endeavours to utilize allthe classical concepts by giving them a suitable quantum-theoreticalre-interpretation (ATDN, p. 8) Bohr's practical methodology stands therefore in direct opposition toThomas Kuhn and Paul Feyerabend's historical view that succeedingtheories, like classical mechanics and quantum mechanics, areincommensurable. In contrast to their philosophical claims of meaninggaps and partial lack of rationality in the choice betweenincommensurable theories, Bohr believed not just retrospectively thatquantum mechanics was a natural generalization of classical physics,but he and Heisenberg followed in practice the requirements of thecorrespondence rule. Thus, in the mind of Bohr, the meaning of theclassical concepts did not change but their application wasrestricted. This was the lesson of complementarity.4. Complementarity After Heisenberg had managed to formulate a consistent quantummechanics in 1925, both he and Bohr began their struggle to find acoherent interpretation for the mathematical formalism. Heisenberg andBohr followed somewhat different approaches. Where Heisenberg lookedto the formalism and developed his famous uncertainty principle orindeterminacy relation, Bohr chose to analyze concrete experimentalarrangements, especially the double-slit experiment. In a way Bohrmerely regarded Heisenberg's relation as an expression of his generalnotion that our understanding of atomic phenomena builds oncomplementary descriptions. At Como in 1927 he presented for the firsttime his ideas according to which certain different descriptions aresaid to be complementary. Bohr pointed to two sets of descriptions which he took to becomplementary. On the one hand, there are those that attribute eitherkinematic or dynamic properties to the atom; that is,“space-time descriptions” are complementary to“claims of causality”, where Bohr interpreted the causalclaims in physics in terms of the conservation of energy andmomentum. On the other hand, there are those descriptions that ascribeeither wave or particle properties to a single object. How these twokinds of complementary sets of descriptions are related is somethingBohr never indicated (Murdoch 1987). Even among people, like Rosenfeldand Pais, who claimed to speak on behalf of Bohr, there is noagreement. The fact is that the description of light as eitherparticles or waves was already a classical dilemma, which not evenEinstein's definition of a photon really solved since the momentum ofthe photon as a particle depends on the frequency of the light as awave. Furthermore, Bohr eventually realized that the attribution ofkinematic and dynamic properties to an object is complementary becausethe ascription of both of these conjugate variables rests on mutuallyexclusive experiments. The attribution of particle and wave propertiesto an object may, however, occur in a single experiment; for instance,in the double-slit experiment where the interference pattern consistsof single dots. So within less than ten years after his Como lectureBohr tacitly abandoned “wave-particle complementarity” infavor of the exclusivity of “kinematic-dynamiccomplementarity” (Held 1994). It was clear to Bohr that any interpretation of the atomic world hadto take into account an important empirical fact. The discovery of thequantization of action meant that quantum mechanics could not fulfillthe above principles of classical physics. Every time we measure, say,an electron's position the apparatus and the electron interact in anuncontrollable way, so that we are unable to measure the electron'smomentum at the same time. Until the mid-1930s when Einstein, Podolskyand Rosen published their famous thought-experiment with the intentionof showing that quantum mechanics was incomplete, Bohr spoke as if themeasurement apparatus disturbed the electron. This paper had asignificant influence on Bohr's line of thought. Apparently, Bohrrealized that speaking of disturbance seemed to indicate—as someof his opponents may have understood him—that atomic objectswere classical particles with definite inherent kinematic and dynamicproperties. After the EPR paper he stated quite clearly: “thewhole situation in atomic physics deprives of all meaning suchinherent attributes as the idealization of classical physics wouldascribe to such objects.” Also after the EPR paper Bohr spoke about Heisenberg's“indeterminacy relation” as indicating the ontologicalconsequences of his claim that kinematic and dynamic variables areill-defined unless they refer to an experimental outcome. Earlier hehad often called it Heisenberg's “uncertainty relation”,as if it were a question of a merely epistemologicallimitation. Furthermore, Bohr no longer mentioned descriptions asbeing complementary, but rather phenomena or information. Heintroduced the definition of a “phenomenon” as requiring acomplete description of the entire experimental arrangement, and hetook a phenomenon to be a measurement of the values of eitherkinematic or dynamic properties. Bohr's more mature view, i.e., his view after the EPR paper, oncomplementarity and the interpretation of quantum mechanics may besummarized in the following points:The interpretation of a physical theory has to rely on anexperimental practice.The experimental practice presupposes a certain pre-scientificpractice of description, which establishes the norm for experimentalmeasurement apparatus, and consequently what counts as scientificexperience.Our pre-scientific practice of understanding our environment is anadaptation to the sense experience of separation, orientation,identification and reidentification over time of physicalobjects.This pre-scientific experience is grasped in terms of commoncategories like thing's position and change of position, duration andchange of duration, and the relation of cause and effect, terms andprinciples that are now parts of our common language.These common categories yield the preconditions for objectiveknowledge, and any description of nature has to use these concepts tobe objective.The concepts of classical physics are merely exact specificationsof the above categories.The classical concepts—and not classical physicsitself—are therefore necessary in any description of physicalexperience in order to understand what we are doing and to be able tocommunicate our results to others, in particular in the description ofquantum phenomena as they present themselves in experiments;Planck's empirical discovery of the quantization of actionrequires a revision of the foundation for the use of classicalconcepts, because they are not all applicable at the same time. Theiruse is well defined only if they apply to experimental interactions inwhich the quantization of action can be regarded as negligible.In experimental cases where the quantization of action plays asignificant role, the application of a classical concept does notrefer to independent properties of the object; rather the ascriptionof either kinematic or dynamic properties to the object as it existsindependently of a specific experimental interaction isill-defined.The quantization of action demands a limitation of the use ofclassical concepts so that these concepts apply only to a phenomenon,which Bohr understood as the macroscopic manifestation of ameasurement on the object, i.e. the uncontrollable interaction betweenthe object and the apparatus.The quantum mechanical description of the object differs from theclassical description of the measuring apparatus, and this requiresthat the object and the measuring device should be separated in thedescription, but the line of separation is not the one betweenmacroscopic instruments and microscopic objects. It has been argued indetail (Howard 1994) that Bohr pointed out that parts of the measuringdevice may sometimes be treated as parts of the object in the quantummechanical description.The quantum mechanical formalism does not provide physicists witha ‘pictorial’ representation: the ψ-function does not,as Schrödinger had hoped, represent a new kind ofreality. Instead, as Born suggested, the square of the absolute valueof the ψ-function expresses a probability amplitude for theoutcome of a measurement. Due to the fact that the wave equationinvolves an imaginary quantity this equation can have only a symboliccharacter, but the formalism may be used to predict the outcome of ameasurement that establishes the conditions under which concepts likeposition, momentum, time and energy apply to the phenomena.The ascription of these classical concepts to the phenomena ofmeasurements rely on the experimental context of the phenomena, sothat the entire setup provides us with the defining conditions for theapplication of kinematic and dynamic concepts in the domain of quantumphysics.Such phenomena are complementary in the sense that theirmanifestations depend on mutually exclusive measurements, but that theinformation gained through these various experiments exhausts allpossible objective knowledge of the object. Bohr thought of the atom as real. Atoms are neither heuristic norlogical constructions. A couple of times he emphasized this directlyusing arguments from experiments in a very similar way to Ian Hackingand Nancy Cartwright much later. What he did not believe was that thequantum mechanical formalism was true in the sense that it gave us aliteral (‘pictorial’) rather than a symbolicrepresentation of the quantum world. It makes much sense tocharacterize Bohr in modern terms as an entity realist who opposestheory realism (Folse 1987). It is because of the imaginary quantitiesin quantum mechanics (where the commutation rule for canonicallyconjugate variable, p and q, introduces Planck'sconstant into the formalism by pq − qp =ih/2π) that quantum mechanics does not give us a‘pictorial’ representation of the world. Neither does thetheory of relativity, Bohr argued, provide us with a literalrepresentation, since the velocity of light is introduced with afactor of i in the definition of the fourth coordinate in afour-dimensional manifold (CC, p. 86 and p. 105). Insteadthese theories can only be used symbolically to predict observationsunder well-defined conditions. Thus Bohr was an antirealist or aninstrumentalist when it comes to theories. In general, Bohr considered the demands of complementarity in quantummechanics to be logically on a par with the requirements of relativityin the theory of relativity. He believed that both theories were aresult of novel aspects of the observation problem, namely the factthat observation in physics is context-dependent. This again is due tothe existence of a maximum velocity of propagation of all actions inthe domain of relativity and a minimum of any action in the domain ofquantum mechanics. And it is because of these universal limits that itis impossible in the theory of relativity to make an unambiguousseparation between time and space without reference to the observer(the context) and impossible in quantum mechanics to make a sharpdistinction between the behavior of the object and its interactionwith the means of observation (CC, p. 105). In emphasizing the necessity of classical concepts for thedescription of the quantum phenomena, Bohr was influenced by Kant orneo-Kantianism. But he was a naturalized or a pragmatized Kantian. Theclassical concepts are merely explications of common concepts that arealready a result of our adaptation to the world. These concepts andthe conditions of their application determine the conditions forobjective knowledge. The discovery of the quantization of action hasrevealed to us, however, that we cannot apply these concepts toquantum objects as we did in classical physics. Now kinematic anddynamic properties (represented by conjugate variables) can bemeaningfully ascribed to the object only in relation to some actualexperimental results, whereas classical physics attributes suchproperties to the object regardless of whether we actually observethem or not. In other words, Bohr denied that classical concepts couldbe used to attribute properties to a physical world in-itself behindthe phenomena, i.e. properties different from those beingobserved. In contrast, classical physics rests on an idealization, hesaid, in the sense that it assumes that the physical world has theseproperties in-itself, i.e. as inherent properties, independent oftheir actual observation. Complementarity is first and foremost a semantic and epistemologicalreading of quantum mechanics that carries certain ontologicalimplications. Bohr's view was, to phrase it in a modern philosophicaljargon, that the truth conditions of sentences ascribing a certainkinematic or dynamic value to an atomic object are dependent on theapparatus involved, in such a way that these truth conditions have toinclude reference to the experimental setup as well as the actualoutcome of the experiment. This claim is called Bohr'sindefinability thesis (Murdoch 1987; Faye 1991). Hence, thosephysicists who accuse this interpretation of operating with amysterious collapse of the wave function during measurements haven'tgot it right. Bohr accepted the Born statistical interpretationbecause he believed that the ψ-function has only a symbolicmeaning and does not represent anything real. It makes sense to talkabout a collapse of the wave function only if, as Bohr put it, theψ-function can be given a pictorial representation, something hestrongly denied. Indeed, Bohr, Heisenberg, and many other physicists consideredcomplementarity to be the only rational interpretation of the quantumworld. They thought that it gave us the understanding of atomicphenomena in accordance with the conditions for any physicaldescription and the possible objective knowledge of the world. Bohrbelieved that atoms are real, but it remains a much debated point inrecent literature what sort of reality he believed them to have,whether or not they are something beyond and different from what theyare observed to be. Henry Folse argues that Bohr must operate with adistinction between a phenomenal and a transcendental object. Thereason is that this is the only way it makes sense to talk about thephysical disturbance of the atomic object by the measuring instrumentas Bohr did for a while (Folse 1985, 1994). But Jan Faye has repliedthat Bohr gave up the disturbance metaphor in connection with hisdiscussion of the EPR thought-experiment because he realized that itwas misleading. Moreover, there is no further evidence in Bohr'swritings indicating that Bohr would attribute intrinsic andmeasurement-independent state properties to atomic objects (thoughquite unintelligible and inaccessible to us) in addition to theclassical ones being manifested in measurement (Faye 1991).5. Misunderstandings of complementarity Complementarity has been commonly misunderstood in several ways, someof which shall be outlined in this section. First of all, earliergenerations of philosophers and scientists have often accused Bohr'sinterpretation of being positivistic or subjectivistic. Todayphilosophers have almost reached a consensus that it is neither. Thereare, as many have noticed, both typically realist as well asantirealist elements involved in it, and it has affinities with Kantor neo-Kantianism. The influence of Kant or Kantian thinking on Bohr'sphilosophy seems to have several sources. Some have pointed to thetradition from Hermann von Helmholtz (Chevalley 1991, 1994; Brock2003); others have considered the Danish philosopher HaraldHøffding to be the missing link to Kantianism (Faye 1991). But because Bohr's view on complementarity has wrongly beenassociated with positivism and subjectivism, much confusion stillseems to stick to the Copenhagen interpretation. Don Howard (2004)argues, however, that what is commonly known as the Copenhageninterpretation of quantum mechanics, regarded as representing aunitary Copenhagen point of view, differs significantly from Bohr'scomplementarity interpretation. He holds that "the Copenhageninterpretation is an invention of the mid-1950s, for which Heisenbergis chiefly responsible, [and that] various other physicists andphilosophers, including Bohm, Feyerabend, Hanson, and Popper, hav[e]further promoted the invention in the service of their ownphilosophical agendas." (p. 669) Most recently, Mara Beller (1999) argued that Bohr's statements areintelligible only if we presume that he was a radical operationalistor a simple-minded positivist. In fact, complementarity wasestablished as the orthodox interpretation of quantum mechanics in the1930s and therefore often regarded as a consequence of a positivisticoutlook. During the 1930s Bohr was also in touch with some of theleading neopositivists or logical empiricists such as Otto Neurath,Philip Frank, and the Danish philosopher JørgenJørgensen. Although their anti-metaphysical approach to sciencemay have had some influence on Bohr (especially around 1935 during hisfinal discussion with Einstein about the completeness of quantummechanics), one must recall that Bohr always saw complementarity as anecessary response to the indeterministic description of quantummechanics due to the quantum of action. The quantum of action was anempirical discovery, not a consequence of a certain epistemologicaltheory, and Bohr thought that indeterminism was the price to pay toavoid paradoxes. Never did Bohr appeal to a verificationist theory ofmeaning; nor did he claim classical concepts to be operationallydefined. But it cannot be denied that some of the logical empiricistsrightly or wrongly found support for their own philosophy in Bohr'sinterpretation and that Bohr sometimes confirmed them in theirimpressions (Faye 2008). Second, many physicists and philosophers see the reduction of thewave function as an important part of the Copenhageninterpretation. But Bohr never talked about the collapse of the wavepacket. Nor did it make sense for him to do so because this would meanthat one must understand the wave function as referring to somethingphysically real. Bohr spoke of the mathematical formalism of quantummechanics, including the state vector or the wave function, as asymbolic representation. Bohr associated the use of a pictorialrepresentation with what can be visualized in space and time. Quantumsystems are not vizualizable because their states cannot be trackeddown in space and time as classical systems'. The reason is, accordingto Bohr, that a quantum system has no definite kinematical ordynamical state prior to any measurement. Also the fact that themathematical formulation of quantum states consists of imaginarynumbers tells us that the state vector is not susceptible to apictorial interpretation (CC, p. 144). Thus, the state vectoris symbolic. Here “symbolic” means that the state vector'srepresentational function should not be taken literally but beconsidered a tool for the calculation of probabilities ofobservables. Third, Bohr flatly denied the ontological thesis that the subject hasany direct impact on the outcome of a measurement. Hence, when heoccasionally mentioned the subjective character of quantum phenomenaand the difficulties of distinguishing the object from the subject inquantum mechanics, he did not think of it as a problem confined to theobservation of atoms alone. For instance, he stated that already "thetheory of relativity reminds us of the subjective character of allphysical phenomena" (ATDN, p. 116). Rather, by referring tothe subjective character of quantum phenomena he was expressing theepistemological thesis that all observations in physics are in factcontext-dependent. There exists, according to Bohr, no view fromnowhere in virtue of which quantum objects can be described. Fourth, although Bohr had spoken about "disturbing the phenomena byobservation," in some of his earliest papers on complementarity, henever had in mind the observer-induced collapse of the wavepacket. Later he always talked about the interaction between theobject and the measurement apparatus which was taken to be completelyobjective. Thus, Schrödinger's Cat did not pose any riddle toBohr. The cat would be dead or alive long before we open the box tofind out. What Bohr claimed was, however, that the state of the objectand the state of the instrument are dynamically inseparable during theinteraction. Moreover, the atomic object does not posses any stateseparate from the one it manifests at the end of the interactionbecause the measuring instrument establishes the necessary conditionsunder which it makes sense to use the state concept. It was the same analysis that Bohr applied in answering the challengeof the EPR-paper. Bohr's reply was that we cannot separate thedynamical and kinematical properties of a joint system of twoparticles until we actually have made a measurement and thereby setthe experimental conditions for the ascription of a certain statevalue (CC, p. 80). Bohr's way of addressing the puzzle was topoint out that individual states of a pair of coupled particles cannotbe considered in isolation, in the same way as the state of the objectand the state of the instrument are dynamically inseparable duringmeasurements. Thus, based on our knowledge of a particular state valueof the auxiliary body A, being an atomic object or an instrument, wemay then infer the state value of the object B with which A onceinteracted (Faye 1991, pp. 182-183). It therefore makes sense whenHoward (2004, p.671) holds that Bohr considered the post-measurementjoint state of the object and the measuring apparatus to be entangledas in any other quantum interaction involving an entangled pair. Finally, when Bohr insisted on the use of classical concepts forunderstanding quantum phenomena, he did not believe, as it issometimes suggested, that macroscopic objects or the measuringapparatus always have to be described in terms of the dynamical lawsof classical physics. The use of the classical concepts is necessary,according to Bohr, because by these we have learned to communicate toothers about our physical experience. The classical concepts aremerely a refinement of everyday concepts of position and action inspace and time. However, the use of the classical concepts is not thesame in quantum mecahnics as in classical physics. Bohr was well awareof the fact that, on pains of inconsistency, the classical conceptsmust be given “a suitable quantum-theoreticalre-interpretation,” before they could be employed to describequantum phenomena (ATDN, p. 8).6. The Divergent Views The Copenhagen interpretation is not a homogenous view. This is stillnot generally recognized. Both James Cushing (1994) and Mara Beller(1999) take for granted the existence of a unitary Copenhageninterpretation in their social and institutional explanation of theonce total dominance of the Copenhagen orthodoxy; a view theypersonally find unconvincing and outdated partly because they readBohr's view on quantum mechanics through Heisenberg's exposition. Buthistorians and philosophers of science have gradually realized thatBohr's and Heisenberg's pictures of complementarity on the surface mayappear similar but beneath the surface diverge significantly. DonHoward (2004, p. 680) goes as far as concluding that "until Heisenbergcoined the term in 1955, there was no unitary Copenhageninterpretation of quantum mechanics." The term apparently occurs forthe first time in Heisenberg (1955). In addition, Howard also arguesthat it was Heisenberg's exposition of complementarity, and notBohr's, with its emphasis on a privileged role for the observer andobserver-induced wave packet collapse that became identical with thatinterpretation. Says he: "Whatever Heisenberg's motivation, hisinvention of a unitary Copenhagen view on interpretation, at thecenter of which was his own, distinctively subjectivist view of therole of the observer, quickly found an audience." (p. 677) Thisaudience included people like Bohm, Feyerabend, Hanson, and Popper whoused Heisenberg's presentation of complementarity as the target fortheir criticism of the ortodox view. Following up on Don Howard's research, Kristian Camilleri (2006,2007) points to the fact that complementarity was originally thoughtby Bohr (in his Como-paper) to exist between the space-timedescription and the causal description of the stationary states ofatoms — and not between different experimental outcomes of the freeelectron. So the formulation of complementarity was restricted to theconcept of stationary states because only there does the system have awell-defined energy state independent of any measurement. Thisobservation deserves general recognition. But when Bohr rather soonthereafter began analysing the double slit experiment in hisdiscussion with Einstein (1930), he had to extend his interpretationto cover the electron in interaction with the measuring apparatus. Camilleri then shows how Heisenberg's view of complementarity, inspite of Heisenberg's own testimony, radically differs from Bohr's. AsHeisenberg understood complementarity between the space-timedescription and causal description, it holds between the classicaldescription of experimental phenomena and the description of the stateof the system in terms of the wave function. A quotation fromHeisenberg (1958, p. 50) shows how much he misunderstood Bohr in spiteof their previously close working relationship.Bohr uses the concept of ‘complementarity’ atseveral places in the interpretation of quantum theory … Thespace-time description of the atomic events is complementary to theirdeterministic description. The probability function obeys an equationof motion as did the co-ordinates in Newtonian mechanics; its changein the course of time is completely determined by the quantummechanical equation; it does not allow a description in space and timebut breaks the determined continuity of the probability function bychanging our knowledge of the system. So where Bohr identified the causal description with the conservationof energy, Heisenberg saw it as the deterministic evolution ofSchrödinger's ψ-function. In other words, Heisenberg, incontrast to Bohr, believed that the wave equation gave a causal,albeit probabilistic description of the free electron in configurationspace. It also explains why so many philosophers and physicists haveidentified the Copenhagen interpretation with the mysterious collapseof the wave packet. The transition from a causal description in termsof the evolution of the ψ-function to a classical space-timedescription is characterized by the discontinuous change that occursby the act of measurement. According to Heisenberg, these two modes ofdescription are complementary. In a very recent study Ravi Gomatam (2007) agrees with Howard'sexposition in arguing that Bohr's interpretation of complementarityand the textbook Copenhagen interpretation (i.e. wave-particle dualityand wave packet collapse) are incompatible.7. New Perspectives After the 1950s a number of alternative interpretations to Bohr'scomplementarity were articulated and they all found their proponentsamong physicists and philosophers of science. The Copenhageninterpretation started to lose ground to other interpretations such asBohm's interpretation, the many worlds interpretation, the modalinterpretation and the decoherence interpretation, which have beenmore in vogue the last couple of decades. But parallel with thegrowing awareness of the essential differences between Bohr's andHeisenberg's understanding of quantum mechanics several philosophersof science have revitalised Bohr's view on complementarity. Around themillennium a new recognition of the Copenhagen interpretation hasemerged. Rob Clifton and Hans Halvorson (1999, 2002) argue that Bohm'sinterpretation of quantum mechanics can be seen as the special case ofBohr's complementarity interpretation if it is assumed that allmeasurements ultimately reduce to positions measurement. OriginallyJeffrey Bub and Clifton were able to demonstrate (given some idealizedconditions) that Bohr's complementarity and Bohm's mechanics fallunder their uniqueness theorem for no-collapseinterpretations. Clifton and Halvorson improve this result by showingthat Bohr's idea of position and momentum complementarity can beexpressed in terms of inequivalent representations in the C*-algebraicformalism of quantum mechanics. It turns out that either position ormomentum are dynamically significant, but it is not permissible toassume that position and momentum are both dynamically significant inany single context. From these assumptions they deduced Bohm'mechanics by adding the metaphysical postulate that positionmeasurement is always dynamically significant, but this metaphysicalrestriction requires, as they emphasize, that positions have a dubiouspriviledged ontological status. Rather, Clifton and Halvorson (1999)and Halvorson (2004) believe that complementarity may give us arealist interpretation of quantum field theory. Another insight into Bohr's view of complementarity is due to MichaelDickson (2001, 2002). By using the contemporary theory of referenceframes in quantum theory, he proves that Bohr's reponse to the EPRthought-experiment was in fact the correct one. Moreover, he alsomaintains that Bohr's discussions of spin, a property much less framedependent than position and momentum, were very different from hisdiscussions of the latter, and based on these differences he offers aBohrian account of Bell's theorem and its significance. A re-assessment of Bohr's philosophy of quantum mechanics is made byWhitaker (2004) on the basis of Clifton and Halvorson's and Dickson'sworks and in the light of quantum information theory. Besides theseattempts to apply Bohr's notion of complementarity to the contemporarydiscussions of the interpretation of quantum mehanics and quantumfield theory there is an ongoing attempt to understand Bohr's idea ofsymbolic representation (Tanona, 2004a, 2004b) and his notion ofcomplementarity with respect to trends in philosophy and generalepistemology (Plotnitsky, 1994, and Katsumori, 2005).BibliographyReferences to Work by BohrCW Bohr, N. (1972-2006), Collected Works, Vol. 1-12,Amsterdam: Elsevier. ATDN Bohr, N. (1934/1987), Atomic Theory and the Description ofNature, reprinted as The Philosophical Writings of NielsBohr, Vol. I, Woodbridge: Ox Bow Press. APHK Bohr, N. (1958/1987), Essays 1932-1957 on Atomic Physics andHuman Knowledge, reprinted as The Philosophical Writings ofNiels Bohr, Vol. II, Woodbridge: Ox Bow Press. Essays Bohr, N. (1963/1987), Essays 1958-1962 on Atomic Physics andHuman Knowledge, reprinted as The Philosophical Writings ofNiels Bohr, Vol. III, Woodbridge: Ox Bow Press. CC Bohr, N. (1998), Causality and Complementarity,supplementary papers edited by Jan Faye and Henry Folse as ThePhilosophical Writings of Niels Bohr, Vol. IV, Woodbridge: Ox BowPress. Other ReferencesBeller, M. (1992), “The Birth of Bohr's Complementarity: TheContext and the Dialogues”, in Studies in History andPhilosophy of Science, 23, pp. 147-180.Beller, M. (1999), Quantum Dialogue: The Making of aRevolution, Chicago: University of Chicago Press.Brock, S. (2003), Niels Bohr's Philosophy of Quantum Physicsin the Light of the Helmholtzian Tradition of TheoreticalPhysics, Berlin: Logos Verlag.Bunge, M. (1967), “The Turn of the Tide”, in MarioBunge (ed.) Quantum Theory and Reality, New York: Springer,pp. 1-12.Camilleri, K. (2006), “Heisenberg and the Wave-particleDuality”, in Studies in History and Philosophy of ModernPhysics, 37, pp. 298-315.Camilleri, K. (2007), “Bohr, Heisenberg and the DivergentViews of Complementarity”, in Studies in History andPhilosophy of Modern Physics, 38, pp. 514-528.Chevalley, C. (1991), “Introduction: Le dessin et lacouleur" ”, in Niels Bohr, Physique atomique et connaissancehumaine. Edmond Bauer and Roland Omnès (trans.), CatherineChevalley (ed.). Paris: Gallimard, pp. 17-140.Chevalley, C. (1994), “Niels Bohr's Words and the Atlantisof Kantianism”, in J. Faye and H. Folse (eds), Niels Bohrand Contemporary Philosophy, pp. 33-55.Clifton, R. and H. Halvorson (1999), “Maximal BeableSubalgebras of Quantum Mechanical Observables ”, inInternational Journal of Theoretical Physics, 38,pp. 2441-2484 Clifton, R. and H. Halvorson (2002), “Reconsidering Bohr'sreply to EPR”, in Placek, T. and J. Butterfield (eds.)Non-locality and Modality Dordrecht: Kluwer AcademicPublisher, Cushing, J. (1994),Quantum Mechanics, Historical Contingency,and the Copenhagen Hegemony, Chicago: University of ChicagoPress. Dickson, M. (2001), “The EPR Experiment: A Prelude to Bohr'sReply to EPR”, in Heidelberger, M. & F. Stadler (eds.)History of Philosophy of Science — New Trends andPerspectives Dordrecht: Kluwer Academic Publisher,pp. 263-275.Dickson, M. (2002), “Bohr on Bell: A Proposed Reading ofBohr and Its Implications for Bell's Theorem”, in Placek, T. andJ. Butterfield (eds.) Non-locality and Modality Dordrecht:Kluwer Academic Publisher, Einstein, A., B. Podolsky and N. Rosen (1935),“CanQuantum-Mechanical Description of Physical Reality Be ConsideredComplete?”, Physical Review, 47, pp.777-780.Faye, J. (1991), Niels Bohr: His Heritage and Legacy. AnAntirealist View of Quantum Mechanics, Dordrecht: KluwerAcademic Publisher.Faye, J. (2008), “Niels Bohr and the Vienna Circle”,in Manninen, J. and F. Stadler (eds.) The Vienna Circle in theNordic Countries. (Series: The Vienna Circle InstituteYearbook, 14). Dordrecht: Springer Verlag.Faye, J., and H. Folse (eds.) (1994), Niels Bohr andContemporary Philosophy. (Series: Boston Studies in the Philosophy ofScience, vol. 158.) Dordrecht: Kluwer Academic Publisher.Folse, H. (1985), The Philosophy of Niels Bohr. The Frameworkof Complementarity. Amsterdam: North Holland.Folse, H. (1986), “Niels Bohr, Complementarity, andRealism”, in A. Fine and P. Machamer (eds), PSA 1986:Proceedings of the Biennial Meeting of the Philosophy of ScienceAssociation, vol. I, East Lansing: PSA, pp. 96-104.Folse, H. (1994), “Bohr's Framework of Complementarityand the Realism Debate”, in J. Faye and H. Folse (1994),pp. 119-139.Gomatam, R. (2007), “Niels Bohr's Interpretation and theCopenhagen Interpretation — Are the two incompatible?”, inPhilosophy of Science, 74, December issue.Halvorson, H. (2004), “Complementarity of Representations inQuantum Mechanics”, in Studies in History and Philosophy ofModern Physics, 35, pp. 45-56.Heisenberg, W. (1955), “The Development of theInterpretation of the Quantum Theory”, in W. Pauli (ed),Niels Bohr and the Development of Physics, 35, London:Pergamon pp. 12-29.Heisenberg, W. (1958), Physics and Philosophy: The Revolutionin Modern Science, London: Goerge Allen & Unwin.Held, C. (1994), “The Meaning of Complementarity”,Studies in History and Philosophy of Science, 25,871-893.Honner, J. (1987), The Description of Nature: Niels Bohr andThe Philosophy of Quantum Physics, Oxford: Clarendon Press.Hooker, C. A. (1972), “The Nature of Quantum MechanicalReality”, in R. G. Colodny (ed.), Paradigms andParadoxes, Pittsburgh: University of Pittsburgh Press,pp. 67-305.Howard, D. (1994), “What Makes a Classical ConceptClassical? Toward a Reconstruction of Niels Bohr's Philosophy ofPhysics”, in Faye and Folse (1994), pp. 201-229.Howard, D. (2004), “Who Invented the "CopenhagenInterpretation?" A Study in Mythology”, Philosophy ofScience, 71, pp. 669-682.Kaiser, D. (1992), “More Roots of Complementarity: KantianAspects and Influences”, Studies in History and Philosophyof Science, 23, 213-239.Katsumori, M. (2005), Niels Bohr's Complementarity. ItsStructure, History, and Intersections with Hermeneutics andDeconstruction, Vrije University Amsterdam(Ph.d.-dissertation)Massimi, M. (2005), Pauli's Exclusion Principle. The Originand Validation of a Scientific Principle. Cambridge: CambridgeUniversity Press.Murdoch, D. (1987), Niels Bohr's Philosophy of Physics,Cambridge: Cambridge University Press.Petruccioli, S. (1993), Atoms, Metaphors and Paradoxes,Cambridge: Cambridge University Press.Plotnitsky, A. (1994), Complementarity: Anti-Epistemologyafter Bohr and Derrida, Durham: Duke University Press.Popper, K. R. (1967), “Quantum Mechanics Without ‘theObserver’”, in Mario Bunge (ed.) Quantum Theory andReality, New York: Springer, pp. 1-12.Tanona, S. (2004a), “Uncertainty in Bohr's Response to theHeisenberg Microscope”, in Studies in History and Philosophyof Modern Physics, 35, pp. 483-507.Tanona, S. (2004b), “Idealization and Formalism in Bohr'sApproach to Quantum Theory”, in Philosophy of Science,71, pp. 683-695.Whitaker, M.A.B. (2004), “The EPR Paper and Bohr's Response:A Reassessment”, in Foundation of Physics, 34,pp. 1305-1340.Other Internet ResourcesEntry on Niels Bohr (MacTutor History of Mathematics Archive, University of St. Andrews)Related Entries quantum mechanics | quantum theory: the Einstein-Podolsky-Rosen argument in | Uncertainty Principle Copyright © 2008 byJan Faye<faye@hum.ku.dk> |
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