5. Misunderstandings of complementarity
Complementarity has been commonly misunderstood in several ways, some of which shall be outlined in this section. First of all, earlier generations of philosophers and scientists have often accused Bohr's interpretation of being positivistic or subjectivistic. Today philosophers have almost reached a consensus that it is neither. There are, as many have noticed, both typically realist as well as antirealist elements involved in it, and it has affinities with Kant or neo-Kantianism. The influence of Kant or Kantian thinking on Bohr's philosophy seems to have several sources. Some have pointed to the tradition from Hermann von Helmholtz (Chevalley 1991, 1994; Brock 2003); others have considered the Danish philosopher Harald Høffding to be the missing link to Kantianism (Faye 1991).
But because Bohr's view on complementarity has wrongly been associated with positivism and subjectivism, much confusion still seems to stick to the Copenhagen interpretation. Don Howard (2004) argues, however, that what is commonly known as the Copenhagen interpretation of quantum mechanics, regarded as representing a unitary Copenhagen point of view, differs significantly from Bohr's complementarity interpretation. He holds that "the Copenhagen interpretation is an invention of the mid-1950s, for which Heisenberg is chiefly responsible, [and that] various other physicists and philosophers, including Bohm, Feyerabend, Hanson, and Popper, hav[e] further promoted the invention in the service of their own philosophical agendas." (p. 669)
Most recently, Mara Beller (1999) argued that Bohr's statements are intelligible only if we presume that he was a radical operationalist or a simple-minded positivist. In fact, complementarity was established as the orthodox interpretation of quantum mechanics in the 1930s and therefore often regarded as a consequence of a positivistic outlook. During the 1930s Bohr was also in touch with some of the leading neopositivists or logical empiricists such as Otto Neurath, Philip Frank, and the Danish philosopher Jørgen Jørgensen. Although their anti-metaphysical approach to science may have had some influence on Bohr (especially around 1935 during his final discussion with Einstein about the completeness of quantum mechanics), one must recall that Bohr always saw complementarity as a necessary response to the indeterministic description of quantum mechanics due to the quantum of action. The quantum of action was an empirical discovery, not a consequence of a certain epistemological theory, and Bohr thought that indeterminism was the price to pay to avoid paradoxes. Never did Bohr appeal to a verificationist theory of meaning; nor did he claim classical concepts to be operationally defined. But it cannot be denied that some of the logical empiricists rightly or wrongly found support for their own philosophy in Bohr's interpretation and that Bohr sometimes confirmed them in their impressions (Faye 2008).
Second, many physicists and philosophers see the reduction of the wave function as an important part of the Copenhagen interpretation. But Bohr never talked about the collapse of the wave packet. Nor did it make sense for him to do so because this would mean that one must understand the wave function as referring to something physically real. Bohr spoke of the mathematical formalism of quantum mechanics, including the state vector or the wave function, as a symbolic representation. Bohr associated the use of a pictorial representation with what can be visualized in space and time. Quantum systems are not vizualizable because their states cannot be tracked down in space and time as classical systems'. The reason is, according to Bohr, that a quantum system has no definite kinematical or dynamical state prior to any measurement. Also the fact that the mathematical formulation of quantum states consists of imaginary numbers tells us that the state vector is not susceptible to a pictorial interpretation (CC, p. 144). Thus, the state vector is symbolic. Here “symbolic” means that the state vector's representational function should not be taken literally but be considered a tool for the calculation of probabilities of observables.
Third, Bohr flatly denied the ontological thesis that the subject has any direct impact on the outcome of a measurement. Hence, when he occasionally mentioned the subjective character of quantum phenomena and the difficulties of distinguishing the object from the subject in quantum mechanics, he did not think of it as a problem confined to the observation of atoms alone. For instance, he stated that already "the theory of relativity reminds us of the subjective character of all physical phenomena" (ATDN, p. 116). Rather, by referring to the subjective character of quantum phenomena he was expressing the epistemological thesis that all observations in physics are in fact context-dependent. There exists, according to Bohr, no view from nowhere in virtue of which quantum objects can be described.
Fourth, although Bohr had spoken about "disturbing the phenomena by observation," in some of his earliest papers on complementarity, he never had in mind the observer-induced collapse of the wave packet. Later he always talked about the interaction between the object and the measurement apparatus which was taken to be completely objective. Thus, Schrödinger's Cat did not pose any riddle to Bohr. The cat would be dead or alive long before we open the box to find out. What Bohr claimed was, however, that the state of the object and the state of the instrument are dynamically inseparable during the interaction. Moreover, the atomic object does not posses any state separate from the one it manifests at the end of the interaction because the measuring instrument establishes the necessary conditions under which it makes sense to use the state concept.
It was the same analysis that Bohr applied in answering the challenge of the EPR-paper. Bohr's reply was that we cannot separate the dynamical and kinematical properties of a joint system of two particles until we actually have made a measurement and thereby set the experimental conditions for the ascription of a certain state value (CC, p. 80). Bohr's way of addressing the puzzle was to point out that individual states of a pair of coupled particles cannot be considered in isolation, in the same way as the state of the object and the state of the instrument are dynamically inseparable during measurements. Thus, based on our knowledge of a particular state value of the auxiliary body A, being an atomic object or an instrument, we may then infer the state value of the object B with which A once interacted (Faye 1991, pp. 182-183). It therefore makes sense when Howard (2004, p.671) holds that Bohr considered the post-measurement joint state of the object and the measuring apparatus to be entangled as in any other quantum interaction involving an entangled pair.
Finally, when Bohr insisted on the use of classical concepts for understanding quantum phenomena, he did not believe, as it is sometimes suggested, that macroscopic objects or the measuring apparatus always have to be described in terms of the dynamical laws of classical physics. The use of the classical concepts is necessary, according to Bohr, because by these we have learned to communicate to others about our physical experience. The classical concepts are merely a refinement of everyday concepts of position and action in space and time. However, the use of the classical concepts is not the same in quantum mecahnics as in classical physics. Bohr was well aware of the fact that, on pains of inconsistency, the classical concepts must be given “a suitable quantum-theoretical re-interpretation,” before they could be employed to describe quantum phenomena (ATDN, p. 8).
