Having discussed the meaning of complementarity in general and wave particle complementarity in particular, I wish now to explicate Bohr's subtle argument for the thesis that certain pairs of classical concepts which are mutually compatible in classical physics are mutually exclusive in quantum physics, i.e. the thesis of kinematic–dynamic complementarity. It is generally held that Bohr regarded the mutual exclusiveness in question as being not only epistemic but also ontic or semantic, in the sense that the uncertainty principle expresses a restriction not only on the joint measurability of canonically conjugate observables but also on the joint instantiation of the properties corresponding to these observables. I shall consider the question of the ontic or semantic construal of kinematic–dynamic complementarity in Chapter 7. Bohr's argument for complementarity in the epistemic sense is, however, more fundamental: it goes to the heart of his theory of observation and measurement in quantum physics. What, then, is Bohr's argument? The mutual exclusiveness of kinematic and dynamic properties Kinematic and dynamic attributes in quantum mechanics are mutually exclusive in the sense that they cannot be simultaneously measured; they are, in this sense, epistemically incompatible. Why did Bohr think this? His reasons may seem intricate, but they are basically quite simple. Two main factors, he maintains, account for the epistemic incompatibility: ( a ) measurements of these two different sorts of properties require mutually exclusive experimental arrangements, incompatible measurement procedures; ( b ) the indeterminability of the interaction between the object and the instrument of measurement precludes extrapolation of the different measurement results to one and the same time.
Having discussed the meaning of complementarity in general and wave particle complementarity in particular, I wish now to explicate Bohr's subtle argument for the thesis that certain pairs of classical concepts which are mutually compatible in classical physics are mutually exclusive in quantum physics, i.e. the thesis of kinematic–dynamic complementarity. It is generally held that Bohr regarded the mutual exclusiveness in question as being not only epistemic but also ontic or semantic, in the sense that the uncertainty principle expresses a restriction not only on the joint measurability of canonically conjugate observables but also on the joint instantiation of the properties corresponding to these observables. I shall consider the question of the ontic or semantic construal of kinematic–dynamic complementarity in Chapter 7. Bohr's argument for complementarity in the epistemic sense is, however, more fundamental: it goes to the heart of his theory of observation and measurement in quantum physics. What, then, is Bohr's argument? The mutual exclusiveness of kinematic and dynamic properties Kinematic and dynamic attributes in quantum mechanics are mutually exclusive in the sense that they cannot be simultaneously measured; they are, in this sense, epistemically incompatible. Why did Bohr think this? His reasons may seem intricate, but they are basically quite simple. Two main factors, he maintains, account for the epistemic incompatibility: ( a ) measurements of these two different sorts of properties require mutually exclusive experimental arrangements, incompatible measurement procedures; ( b ) the indeterminability of the interaction between the object and the instrument of measurement precludes extrapolation of the different measurement results to one and the same time.
To resolve the challenges (paradoxes) attending the genesis of quantum theory, Niels Bohr in 1927 proposed a generalization of the conceptual framework of classical physics, termed complementarity, which posited pairs of classical concepts that could be manifested only in mutually exclusive experimental arrangements with both needed to embrace the full range of physical experience. In this context particle–wave complementarity has encountered two major obstacles; (1) No formulation of it has commanded a general consensus; and (2) empirical evidence abounds that contradicts the claim of mutual exclusivity of particle and wave properties of quantum objects in a single experiment. These problems are rooted in the unrestricted scope of this claim. It is shown that a restricted version of particle–wave complementarity, here called “which value–interference” complementarity, is consistent with observations, is naturally contained in the mathematical formalism of quantum theory and, in fact, holds in any representation of quantum theory defined by the eigenvectors of a complete set of commuting observables, such as the configuration space position (kinematic) variables or the complementary linear momentum (dynamic) variables. Thus, the which value–interference form of particle–wave complementarity exists within kinematic–dynamic complementarity, a “layered” complementarity, so to speak. It is hoped that a consistent and valid exposition of particle–wave complementarity will be helpful to those who find the framework of complementarity useful and appropriate for some purpose.
In Bohr's view, what ontological significance does measurement have in quantum physics? How, exactly, are we to conceive of the physical properties which we attribute to microphysical objects on the basis of measurement? As we have seen, Bohr regards such properties as objective in the sense that in general they characterise the object immediately before the measurement. But what exactly is their ontological status? In order to answer this question, we shall have to consider in detail Bohr's view of the ontological significance of kinematic-dynamic complementarity. It is generally believed that Bohr held that in quantum physics an object cannot meaningfully be said to possess simultaneously an exact position and an exact momentum. Did he, and if so, why did he? The interactive-properties theory Some hold that the process of measurement does not so much create the value of the measured observable as disturb a pre-existing value. On this view the measured value characterises the observable only after the measurement, and not before: the measured value may be said to be a ‘created’ or ‘disturbed’ value. Bohr, as I have already said, seems to have toyed with this view in his earlier years: even as late as 1933 he says: Indeed, even in a position or momentum measurement on the electron in a hydrogen atom in a given stationary state one can assert with a certain right that the measuring result is produced only by the measurement itself.
Niels Bohr asserted both that (i) the properties of quantum systems are specifiable, in general, only in relation to mutually exclusive experimental arrangements which may be freely chosen by experimenters, and that (ii) observed physical behavior is objective. In a move that reduces the apparent tension between those two assertions, Bohr put forward an analogy between quantum complementarity (in effect, the dependence of property values on measurement apparatus configuration in quantum mechanics) and the principle of relativity (in effect, the dependence of property values on the inertial reference frame in special relativity). Here, Bohr's analogy is considered in a theoretical context. The elements of quantum mechanics and special relativity involved are set side by side, the analogous elements are identified with their roles in the analogy spelled out, and a number of dissimilarities that impact the force of the analogy are indicated-for example, quantum value determination, in general, requires an uncontrollable interaction during measurement, whereas non-quantum relativistic value determination does not. These dissimilarities point to weaknesses in the analogy, which he did not highly develop, and suggest that any stronger such analogy involving the two theories must take these differences more fully into account.
Bohr's general thesis of complementarity conveys the idea that we can, and perhaps must, make use of the classical physical concepts in quantum physics, notwithstanding the inadequacies of these concepts; but we can use them only within the limits circumscribed by the quantum of action – beyond these limits the classical concepts cease to be well defined. This idea originated in his thesis that the conceptual structure of the quantum theory is in a sense a generalisation of the conceptual scheme of classical mechanics; and this thesis was a corollary of the correspondence principle. During the first months of 1927 Bohr regarded quantum mechanics as the quantum-theoretical generalisation of classical mechanics to which he had been looking forward. He came also to think that quantum mechanics required in a sense the generalisation of the two classical models of particle and wave. In classical physics these two models generally pertain to different theories, the particle model to the mechanical theory of matter, the wave model to the electromagnetic theory of radiation. In quantum physics, however, the two models pertain to one theory, quantum mechanics, and each is applicable to matter and radiation. Where discontinuity obtains, the standard classical models of matter and radiation cease to be well defined, and the alternative, non-standard models may be used. There is no logical inconsistency in this dual use of the models since each is appropriately applicable only in different empirical circumstances.
One of the various interpretations of quantum mechanics occupies a privileged position in the opinion of the majority of physicists. This is the Copenhagen view, which owes its fame and popularity not only to historical reasons but also to its simplicity and practical efficiency. As is well known, the Copenhagen outlook was elaborated collectively. Nevertheless, Niels Bohr's and W. Heisenberg's contributions should be singled out as particularly outstanding. This chapter describes two principles, which are in fact the two pillars on which Bohr's doctrine is built. These are: The working of measuring instruments must be accounted for in purely classical terms . Another one is quantum systems that should not even be thought of as possessing individual properties independently of the experimental arrangement. In the particular case of the pair of observables "position" and "momentum," the Heisenberg uncertainty relations can be considered as a generalization of the complementarity principle.
Updating the wave-particle duality Maria C. Bosca e-mail: bosca@ugr.es Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Granada E-18071. Granada Spain The wave-particle-duality, the fundamental component of the new quantum formalism in Bohr’s opinion, must be reformulated by incorporating the results of some experiments accomplished in the last decades of twentieth century. The Bohr´s complementarity principle stated the mutual exclusiveness and joint full completeness of the two (classical) descriptions of quantum systems; after Einstein-Podolsky-Rosen’paper, the wave-particle duality, or wave-particle complementarity, could be expressed by stating that it is impossible to build up an experimental arrangement in which we observe at the same time both corpuscular and wave aspects. In a two-slit experiment, they would correspond, respectively, to the which-way knowledge and the observation of interference pattern. Bohr showed this mutual exclusivity in numerous examples , and linked it to the unavoidable disturbance inherent in any measurement event. In quantum mechanical formalism, the complementarity principle has a clear mathematical expression: two observables are complementary if precise knowledge of one of them implies that all possible outcomes of the other are equally probable; their extension to classical concepts (as wave and particle) is not concerned. In 1991 Scully et al published a variant of the two-slit experiment that incorporates two micromasers cavities and a laser beam to provide which-path information without net momentum transferred during the interaction ; the impossibility of know which slit an atom went through and still observe the interference fringes is preserved by the establishing of quantum correlations between the measuring apparatus and the system being observed. They claimed that complementarity, of which wave-particle duality would be to them a manifestation, is more fundamental than the uncertainty principle . In 1996 B-G. Englert, following an approach originally due to Wooters and Zurek , derived , without making use of Heisenberg’s uncertainty relation, an inequality that quantifies the mutual compatibility relation between fringe visibility and which-way information. The inequality, that they denominated as “interferometric duality”, has the expression D^2 + V^2 ≤ 1, where D stands for the distinguishability of the ways and V for the fringe visibility; both of them are mathematical expressions that can be measured to check experimentally the inequality . Today, it is clear that intermediate particle-wave behaviours exist and, in addition to that, there are single experiments in which both classical wave-like and particle-like behaviours are showed total and simultaneously on an individual system. For instance, in the Bose’s double-prism experiment , tunnelling and perfect anticoincidence were observed in single photon states. Consequently, the meaning of the wave-particle duality must incorporate the simultaneous use of the two classical descriptions in the interpretation of experiments, loosing their original mutual exclusivity , which is incorporated as an extreme case in the new interferometric duality, a continuous quantum concept . The wave-particle duality, therefore, must be formulated as an interpretative addition to quantum mechanics, to which is possible to renounce if any pretension of visualize quantum phenomena in terms of classical concepts and intuitions is abandoned.