Complementarity and reconciliation
Yoav Ben-Dov
Cohn Institute for the History of Science
Tel-Aviv University
Lecture given at the conference Einstein Meets Magritte, VUB, Brussels, June 1995
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In this paper, I try to sketch in general lines the idea of complementarity, which was first suggested by Niels Bohr as an answer to the conceptual problems of quantum mechanics, but later extended by him to other domains, both within science and outside it. In these applications, the idea of complementarity allows for the acceptance of different sets of beliefs and principles, which contradict each other but have all their value. In particular, it may help to ease the conflict between the scientific approach and human aspirations.
The idea of complementarity was first introduced by Bohr in 1927, in a lecture given at Como, Italy, and repeated at the fifth Solvay conference in Brussels [1]. Its aim was to come to terms with the new and conceptually problematic situation in atomic physics. On one hand, the new quantum theoretical formulations introduced by Heisenberg and Schroedinger in 1925-26 could account with impressive exactness for the atomic experimental results. On the other hand, these formulations could not be cast in a way that clearly identifies the quantum object as something which exists by itself, independently of the manner in which we choose to observe it. Thus, the new quantum mechanics fails to satisfy one of the basic tenets of physics, and science in general, as these terms were understood from the 17th century onwards: it does not give an objective description of an observer-independent reality. For Einstein, this was a good enough reason to reject the new quantum mechanics, and to look for a better theory (which, in spite of much effort, was never found). For Bohr, on the other hand, this situation called for the re-formulation of the scientific concept of "objectivity", or, in other words, for a re-evaluation of the relation between human language and reality. However, this re-formulation was perceived by him as pertaining not only to the understanding of atomic physics, but also to much broader issues.
In the original Como lecture, Bohr applied the idea of complementarity to the possible modes of description of an atomic electron. On one hand, he conference "Einstein Meets Magritte", Brussels, June 1995. we can in some cases know precisely the energy of an atomic electron, and apply concepts of conservation of energy to it. But in order for these concepts to be valid, the atom has to be kept isolated from any external influence. On the other hand, we may wish to have a space-time account of the detailed motion of the electron inside the atom. But in order to give such an account, we have to perform a position measurement, for example with the aid of a gamma-ray photon which collides with the electron. But now the atom is no longer isolated, and the atomic energy is defined only up to a relatively large degree of uncertainty. The space-time description thus excludes the energy-conservation description: both are possible, but not at once. In this sense, the two descriptions are "complementary": they exclude each other when applied simultaneously, but only their conjunction gives the complete story about the atomic electron.
Up to this point, one can understand Bohr's idea in terms of a classical image, in which the electron "really" has both a well-defined space-time location and a well-defined energy, but we cannot know them together because of the perturbation caused by the act of measurement. But Bohr later clarified his position, and stated explicitly that it is not a question of a mechanical disturbance of the particle by the measurement, but something deeper, which concerns the very definition of the physical phenomenon. One cannot speak of "the quantum object" as something which exists independently of its act of being measured, but rather one should give a full account of the experimental set-up which actually was implemented [2]. This description can be formulated only in classical terms. However, no single description in classical terms can exhaust all the knowable features of the quantum phenomenon, so that we have to use "complementary" descriptions. In other words, the quantum phenomena exhibit a richness and complexity which surpass our ability to give a full account of them in the language accessible to us. Instead of trying in vain to look for a better language, we should accept that any description of the quantum world is partial, and be ready for the possibility that different descriptions, which seem to be incompatible with each other, are all correct. A logical contradiction does not arise in practice, because at any given moment, only a single description is accessible. But this means that no description will be taken as "objectively true", independently of the practical context in which it applies.
In the domain of quantum mechanics, Bohr applied the principle of complementarity not only to the different possible descriptions of the electron's state, but also to the different possible answers to the question "what is the electron". The electron, like any quantum object, behaves in experiments sometimes like a particle and sometimes like a wave. The classical concepts of particle and wave exclude each other. The wave is a physical entity which extends over space, and two waves can annihilate each other through interference, when the crest of one falls on the trough of the other. In contrast, a particle is located at each moment at a specific point in space, and two classical particles can never annihilate each other. The application of these concepts together to the same electron thus leads to a contradiction.
Again, one could look for a new language, in which terms the electron will be described using a single well-defined concept. But Bohr thought that such a language is not required. Physicists should not look for alternatives to the classical language. Instead, they should examine the circumstances in which descriptions formulated in classical terms are used. It is possible to construct an experimental arrangement in which the electron behaves like a particle, and another arrangement in which it behaves like a wave. But these two experimental arrangements cannot be realized simultaneously. The particle and the wave descriptions are thus applicable each in its own experimental arrangement, and never together in the same arrangement. Since in Bohr's view it is not possible to define the physical phenomenon outside its experimental context, the question "is the electron really a wave or a particle" is meaningless.
The statements "the electron is a particle" and "the electron is a wave" therefore stand in a relation of complementarity: excluding each other when applied at once to the same object, but giving together, along with the specification of their corresponding experimental arrangements, the complete account of the electron's entity.
One could, of course, ask about the relation between these two applications of complementarity. For an answer, it is important to note that complementarity is not a feature of the quantum object (although its description in physics textbooks sometimes gives the impression that it is). Rather, it is a general point of view which concerns the relation between language and the objects which it describes, or more exactly, between different descriptions in human language of what is taken to be the same object. Further, it is perhaps not even essential that complementarity always should involve only two descriptions and not more - although Bohr did not discuss such cases. Thus, the two applications of complementarity described here are not directly related, and it is "the same" complementarity only in the sense that they both reflect the use of human (classical) language to describe quantum phenomena.
Bohr's approach can be extended to other formulations of the conceptual problems of quantum mechanics, for example to Von Neumann's [3] formulation, which serves as a starting point for some of the new interpretations. In this formulation, the state of the electron is described by a quantum wave function. For this mathematical function, two modes of temporal evolution are assumed: one when no measurement is performed, and the other during a measurement. The coexistence of these two modes is usually considered as a serious problem, for it implies that a measurement is different from an ordinary process in which the electron is undergoing some physical interaction. It is therefore necessary to include the concept of measurement, which implies a reference to the observing agent, in the definition of the electron, which was supposed to be a physical object existing to itself. To solve this difficulty, Von Neumann treats the measurement device as a quantum object, which has its own wave function. But now it has to be assumed that the wave function of the device evolves differently when nobody is looking at it and when somebody is looking, so that the (implicit) reference to the observing agent still remains.
Bohr did not share Von Neumann's account, because he believed that the measuring device should be described in classical terms, so that no wave function is assigned to it. And as to the fact that the definition of the measured object includes a reference to the measurement procedure, as we saw, Bohr accepted it as unavoidable. Against Bohr's position one can claim that the measuring apparatus is made of atoms, which are quantum objects, so that the complete device should be describable in quantum terms of a wave function. But Bohr could point out that in order to demonstrate the quantum behavior of the atoms in the measuring apparatus, one should construct an experiment in which this apparatus serves as the object measured by another device. In such a case, we can treat it as a quantum object, but now it no longer serves as the measuring device. The role of the apparatus as a measured object and its role as a measuring device thus occur in different and incompatible experimental arrangements. Therefore, the description of the apparatus as a quantum object with a wave function, and its description in classical terms as a measuring device, are complementary, and it is meaningless to ask what the apparatus "really" is.
Bohr did not think that the principle of complementarity is limited to the new quantum theory. As he saw it, atomic physics was not even the basis of this principle, but only its clearest exemplification. Complementarity is a general epistemological principle, which should apply to all the domains of human thought and activity - from the hard sciences of physics and biology to the study of man, society and morality. Bohr tried to show the relevance of complementarity to problems in all these domains. As he insisted, these extensions from physics to other domains are not superficial analogies, but something fundamental.
Some of these extensions are perhaps related to his own background. His father, Christian Bohr, applied in his physiological researches the mechanistic view of the biological organism as a physical machine. But as he claimed, a description of the living creature in vitalistic terms, in which "life" is an irreducible concept, is also necessary, although not in the same observational context. The reason is that in order to study the living creature in mechanistic terms we have to dissect it, and for this we have to kill it. As Pais [4] points out, Bohr spoke explicitly about the need to apply the principle of complementarity to the mechanistic and the vitalistic descriptions of living creatures until the discovery of the structure of DNA in 1953. Then he changed his terminology, and spoke of a complementarity between a mechanistic description in terms of active factors and a finalistic description in terms of goal and purpose.
Regarding this position of Bohr's, one can claim that within the domain of biology, the application of the complementarity principle between a mechanistic and a finalistic description of the living organism seems unnecessary. The theory of evolution makes it possible to use finalistic expressions like "the eye is made for seeing", and still to regard them as short forms for a mechanistic description in terms of embryology and natural selection. The relation between the finalistic and the mechanistic accounts can therefore be a reduction, in which one of them is considered to be more fundamental then the other, and not complementarity, in which both have the same status. Thus, biologists can apply in their studies any combination of mechanistic and finalistic considerations, while their basic beliefs remain purely mechanistic. Clearly, Bohr did not think of such a "complementarity of practice", but of something more fundamental. After all, even Einstein was ready to admit that in actual practice, the physicist is an "opportunist" as regards conceptual systems, using whatever serves his needs at any moment.
If the principle of complementarity has any place at all in the description of living organisms, this place may lie outside the strict domain of biological research, and concern the perception of the living creature as a subject with which one can sympathize, identifying oneself with its feeling of purpose. For example, one can perhaps regard the description of a cat as a physical mechanism that can be dissected for research purposes, and its description as a living creature which suffers on the dissection table, as complementary. The key point here is the existence of consciousness in the living creature. As Bohr put it [5]:
"The fact that consciousness, as we know it, is inseparably connected with life ought to prepare us for finding that the very problem of the distinction between the living and the dead escapes comprehension in the ordinary sense of the word. That a physicist touches upon such questions may perhaps be excused on the ground that the new situation in physics has so forcibly reminded us of the old truth that we are spectators as well as actors in the great drama of existence".
The idea of a language that is imposed on us by our modes of communication but does not reflect reality as it is, as Bohr describes the classical language, bears a resemblance to the ideas of Kant. Bohr did not mention Kant as a direct influence on him. However, at the time when Bohr got his education, Neo-Kantian ideas were very much in the air, and it is difficult to assume that Bohr could have completely avoided their influence. Kant indeed argues in his Critique of Judgment that a complete mechanical description of living creatures are impossible, and that finalistic considerations should also be applied to their study. However, as we saw, Bohr's treatment of living creatures is problematic as long as consciousness is not mentioned, and consciousness can be ascribed with certainty only to humans. Therefore, even if there is a resemblance here between Bohr and Kant, in concerns a rather weak point.
Concerning humans, however, it is perhaps possible to say that Kant applies different kinds of considerations in a complementary way. We can regard the human person as a phenomenon, and study it with the scientific tools of physics, chemistry and biology. In this case, its description is limited by the principles laid down in the Critique of Pure Reason: we do not know another person as a thing to itself but only the phenomena related to him, and therefore the causal laws that we discover reflect the structure of our system of perception as much as they reflect the properties of the human object observed. On the other hand, as Kant states in the Critique of Practical Reason, each one of us perceives his own mind as a thing to itself, without the mediation of sense perception. In this self-perception, the contents of mind appear as finalistic. The same person can therefore be described in terms of two systems of concepts - the causal description as an object, and the finalistic description as a moral agent. In each of these systems, his laws of conduct obey different constraints: in the scientific description all his actions are determined by the causal laws of classical mechanics, while in the moral description, we have to assume the existence of free will. The antinomy between the assumption of determinism in classical mechanics (or the randomness in quantum mechanics) and the assumption of free will is thus solved, without a need to settle any contradiction: each one of these assumptions is valid in a different description of the same person, and the correct description at any moment depends on the kind of questions that we ask.
However, there is an important difference between Bohr and Kant. For Kant, the description of the person "from within," as he perceives himself, is completely subject to rational considerations, and Kant derives the principles of morality from such considerations. His analysis is abstract, and does not concern any feeling of human empathy. Bohr, on the other hand, describes the moral dilemma which arises in a concrete human situation, for example between the need to punish a beloved child and the tendency to forgive him [6]:
"Through the closest possible combination of justice and love presents a common goal in all cultures, it must be recognized that in any situation which calls for the strict application of justice there is no room for the display of love, and that, conversely, the ultimate exigencies of a feeling of love may conflict with all ideas of justice".
Since a similar dilemma arises in other circumstances, it is possible to say that Bohr uses here the word "love" in a somewhat Christian sense, as a kind of Grace. The feeling of love in this sense enables one to identify with the internal experience of the other person, and to feel a sort of communality with him. In contrast, the principles of justice are objective, and belong to the description of the person "from without". Thus, Bohr puts the duty to act according to some general rules in the external and objective description of the person, and human empathy in the internal experience, as complementary components of what can be called "morality". Kant, on the other hand, assigns the concept of duty to a moral imperative which is supposed to belong exclusively to the rational description of the person "from within".
In the previous sections, we discussed several applications of the concept of complementarity to different domains, as suggested by Bohr. As can be appreciated from these applications, complementarity reflects a general epistemological approach, which can be applied on several levels. For example, within atomic physics, complementarity is applied to different descriptions of the quantum object. In a broader context of physics in general, Bohr mentioned the possibility of applying the atomistic and the energetistic description to thermodynamical systems [4]. And in a still broader framework, complementarity can be applied to the relation between the physical and the mental-teleological descriptions of living beings. This again stresses the point mentioned above, that complementarity is not a feature of "reality", but rather of the language used to describe reality.
The idea of complementarity thus runs counter to a very old tradition in western thought, which predates the scientific revolution. In fact, already in the 13th century one can find in this tradition the central idea that reality (or, if we prefer, "truth") can be given a single, complete and unambiguous description in human language. The fact that the content of this description has undergone very radical changes, for example from the Aristotelian-theological dogma of the late middle ages, to the mechanistic world-picture of the 17th-19th centuries, is secondary in this respect. The alternatives to mechanism reflected a similar tendency: for example, German idealism in the 19th century rejected physical materialism along with mechanism, but still tried to find the single set of principles which would account for all existence, for example Hegel's dialectical evolution of the spirit through history. One could continue this trend to 20th-century positivism, which rejected metaphysical accounts of "reality" as meaningless, but still looked for a single set of methodical principles which would generate the collection of all meaningful statements about the world. In this sense, as Henri Atlan calls it [7], western culture has kept a basic "monotheistic" obsession throughout its intellectual evolution.
The idea of complementarity suggests a different approach, much more modest, which is perhaps the only way to cope with the conflicting accounts of reality which today cannot be denied their claim to validity. One should not look for the single "True" account of reality, which should be cast in human language (either the existing language, or a new ideal language, as the positivists tries in vain to formulate). Instead, one should ask, for any given description of reality, what is its domain of useful application. In quantum mechanics, this domain is defined by the experimental set-up, in a more or less unambiguous way. In other domains, the question of useful applicability can be more difficult to answer. However, it is of the essence of the approach of complementarity that no clear-cut answers can be generated in advance to all possible questions (because there is no universally valid set of principles to generate these answers). One might therefore be called to make, in specific cases, a choice which is not dictated by a general set of principles. It is exactly in this choice that human existence as a moral agent is manifested. In this sense, complementarity reflects not only the ability to reach a reconciliation between conflicting views of reality, but also our reconciliation with the finite and limited nature of any form of human knowledge.
As an example, we can try to apply the concept of complementarity to a debate which cuts through the academic world, and consists of the relative priority of the scientific and the humanistic disciplines. The fact that such a debate exists, and that it is sometimes expressed in virulent terms, needs hardly to be pointed out: One could follow, for example, C.P. Snow's [8] concept of "the two cultures" to its recent manifestations in some scientists' attacks on the humanistic disciplines as "higher superstition". However, it is today clear that hostilities along the dividing lines between the disciplines can be dangerous and harmful, in a situation in which the central problems facing humanity involve both scientific and human aspects.
As long as we insist on the (supposed) existence of a single set of methods and principles which regulate all valid knowledge, a peaceful and productive coexistence between scientific and humanistic disciplines is impossible. The reason is that the two domains (Snow's "two cultures") rely on radically different basic assumptions. One of the central points of this cleavage involve the use of teleological considerations. In natural science, teleology is explicitly rejected. In the humanistic disciplines, in contrast, teleology is indispensable: one cannot arrive at any understanding of human affairs without recourse to concepts like volition and purpose. And in particular, one cannot formulate any acceptable precepts of morality without using such finalistic terms.
As we saw, Bohr's use of the concept of complementarity allows us to apply different sets of concepts, without asking which one is "absolutely true". In this issue, one should not ask whether there "really" are purposes in the world. Instead, one should ask in which domains the use of finalistic terms is productive. Therefore, scientific and humanistic approaches can coexist in the same cultural framework, without the need to choose one of them as the only "true" one.
Behind the mechanistic-finalistic distinction lies, of course, a deeper issue, that of the mind-body question. Ever since Descartes' separation of these two substances, western philosophy has been involved in a hopeless attempt to determine, once and for all, which of the two "really" exists, or, if both exist, what is the exact relation between them. In our terms, the body (brain included), which is made of matter, can be studied by the natural sciences, which involve no finalistic concepts. On the other hand, the most important features of the subjective experience of mind appear to itself as finalistic: I want, I choose, I hope. But the distinction between mind and body is not between two substances which exist separately in the world: in the living human, they always come together. Thus, we can regard the mind-language and the body-language as two different descriptions of the same human entity, to be applied in different circumstances. The basic assumptions of these two languages are contradictory, and therefore, they cannot be applied at once. but each one of them is applicable in a different context. Therefore, the relation between mind and body can be regarded as complementarity between two different descriptions, and not as some mysterious connection between two distinct substances.
The interesting questions arise, of course, on the borderline between the two languages. For example, at which point does a collection of cells become "alive"? More specifically, if we speak of a human embryo, it is sometimes necessary for practical and very definite purposes to decide whether or not it should be regarded as a human being. As mentioned above, an approach based on complementarity will not be able to give a clear-cut answer, which should be valid in any circumstances. What we have is two different languages - in one of them, we have a biological object, and in the other a human being - and none of them can determine where the borderline between their respective domains of applicability exactly lies. It is in such circumstances that we have to rely on our moral autonomy, and make a choice which is not dictated by a previously given set of principles. In other words, in such cases we cannot have recourse to anything external - God, science, categorical imperative or whatever - to relieve us from our moral responsibility. Thus, at least in this example, and maybe also in others, the approach of complementarity does not give a general solution to problems which should perhaps be left without one.
[1] Bohr, N., The quantum postulate and the recent development of atomic theory, Nature 121, 580-590, 1928.
[2] Bohr, N.,The causality problem in atomic physics", in: New Theories in Physics, Nijhoff, the Hague, p. 11, 1939.
[3] Von Neumann, J.,: Mathematische Grundlagen der Quantenmechanik, Springer-Verlag, Berlin, 1932; English Translation: Mathematical Foundation of Quantum Mechanics, Princeton University Press, Princeton, N.J., 1955.
[4] Pais, A., Niels Bohr's Times In Physics, Philosophy and Polity, Clarendon Press, Oxford, 1991.
[5] Bohr, N., Naturw. 18, 73, 1930, Cited in Ref. 4.
[6] Bohr, N., in: Studia Orientalia Ioanni Pedersen, Munskgaard, Copenhagen p. 385, 1953.
[7] Atlan, H., A tort et a raison, Le Seuil, Paris, 1986.
[8] Snow, C.P., The Two Cultures, Cambridge University Press, Cambridge, 1959.