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Now that my account of Bohr's philosophy of physics has been completed, it remains for me to give a general assessment of it. What value should we assign to Bohr's main ideas – the notions of correspondence and complementarity? How does his interpretation of quantum physics fare in comparison with some of its rivals? What should our assessment of the Bohr–Einstein debate be? I shall take up these questions in the reverse order. Einstein or Bohr? The final verdict The Bohr–Einstein debate is primarily a dispute about the philosophical foundations in terms of which the interpretation of quantum mechanics should be based: specifically it is a dispute about the intrinsic-properties theory, i.e. about the scope of a realist interpretation of quantum mechanics. Einstein wished to maintain the two realist theses, the intrinsic-properties theory and the objective-values theory, whereas Bohr wished to hold only the latter. My own philosophical leanings are in the direction of realism. To my mind the notion of a physical reality the existence and constitution of which are independent of human thought and perception is coherent and plausible: what physical objects there are, and what properties they have, is not determined by human thought or perception, or by human practical interests. I have sympathy, therefore, with Einstein's position concerning the indefinability thesis and the question of the completeness of quantum mechanics. [ABSTRACT FROM AUTHOR]

Now that Bohr's philosophy of quantum physics has been surveyed in detail, it is time to provide a general description of his philosophy that illuminates the details. The question which I wish to address, then is: what is the general philosophy, or philosophical point of view, that underlies Bohr's philosophy of physics? Can his philosophy be neatly categorised in terms of any well known philosophical position? Apropos his philosophy of physics in particular, the question of primary interest is: to what extent, if any, is Bohr's philosophy of physics realist? No simple answer to this question can be given: indeed, certain realist and non-realist components are subtly interwoven in his philosophy, and to unravel them we shall need a fairly refined conception of what constitutes a realist interpretation of physics. Realism in the interpretation of physics The basis of realism is the view that statements of a certain class predicate properties of real objects, the truth-values of these statements being determined by reality as it is independently of how it appears to us to be. This notion is captured in the following characterisation of what constitutes the adoption of a realist interpretation of a physical theory. [ABSTRACT FROM AUTHOR]

Bohr's response in 1925 to the failure of the Bohr–Kramers–Slater theory was, as we have seen, to regard wave–particle duality as having a formal, rather than realistic, significance; he saw it as a ‘limitation of our usual means of visualization’. That same year, however, wave–particle duality was generalised by Louis-Victor de Broglie to cover the theory of matter. Moreover, the advent of quantum mechanics (i.e. matrix mechanics and wave mechanics), rather than dispelling the duality problem, heightened it. How did Bohr respond to these new developments in the quantum theory? A matter of waves In the autumn of 1923 de Broglie put forward the extremely bold hypothesis that any particle whatever is associated with a wave whose wavelength λ and frequency ν are proportional to the particle's momentum and energy respectively: λ = h/p, v = E/h. De Broglie regarded his hypothesis as the basis of a new mechanics, a wave mechanics related to classical mechanics in the same way as wave optics is related to ray optics. On this view the trajectory of a particle corresponds to the ray of the wave associated with it (i.e. the normal to the equiphase surface of the wave), and the velocity of the particle corresponds to the group velocity of the wave. De Broglie suggested, moreover, that in certain circumstances particles should exhibit diffraction effects: a stream of electrons, for example, which passes through a slit in a screen should undergo diffraction. [ABSTRACT FROM AUTHOR]

Between 1927 and 1936 no one had a greater influence on Bohr's thinking than Einstein. It was Einstein's unremitting criticism which provided the severest test of Bohr's interpretation of quantum physics, and which forced him to clarify and refine his arguments. The debate between Bohr and Einstein concerning the interpretation of quantum physics is generally recognised as one of the great intellectual disputes in the history of science. What was the nature of the disagreement between them, and what were the arguments with which each defended his position? The fifth Solvay Conference, 1927 Einstein was not present at the Volta Centennial Conference at Como in September 1927, where Bohr first presented his theory of complementarity; Einstein first learned of Bohr's interpretation of quantum mechanics at the fifth Solvay Conference of Physics at Brussels in October 1927. In the discussion following Bohr's paper Einstein examined an imaginary experiment in which an electron passes through a slit in a diaphragm and impinges at a point on a hemispherical screen. This experiment, Einstein suggested, could be interpreted in either of two ways: the de Broglie–Schrödinger waves represent either (a) an ensemble of electrons spread out in space (but not an individual electron), or (b) a wave-packet corresponding to an individual electron. There is, he noted, a difficulty with the latter interpretation. [ABSTRACT FROM AUTHOR]

The EPR paper and Bohr's reply to it brought to an end the public debate between Einstein and Bohr. In the aftermath, Bohr's construal of quantum mechanics established itself as the basis of the orthodox interpretation – the ‘Copenhagen interpretation’ as it came to be called. The vast majority of physicists regarded Einstein's criticism as reactionary, and dismissed it with disdain. One of the main causes of this disdainful attitude was the general opinion that Einstein's criticism committed him to the existence of hidden states, and the existence of these, it was thought, had been conclusively ruled out by the work of von Neumann and others. What light does the subsequent work on the question of hidden states, and in particular the work of Bell, throw on the Bohr–Einstein dispute? Completeness and hidden states There are three distinct questions concerning hidden states. First, might there be such states, unbeknown to quantum mechanics? Second, can quantum mechanics, as it stands, take account of such states? Third, could some theory containing descriptions of such states reduplicate the predictions of quantum mechanics? Concerning the first of these questions, Einstein's view was that it is very likely that such states exist, and since quantum mechanics takes no account of them, it is incomplete and best regarded as a statistical theory analogous in some respects to classical statistical mechanics. [ABSTRACT FROM AUTHOR]

What was Bohr's response to the problem of wave-particle duality? Before considering this question in detail it will be useful to survey briefly Bohr's work in physics between 1911 and 1923. Bohr and the ‘old’ quantum theory In 1911 Bohr completed his doctoral dissertation on the classical electron theory of metals. Developed by Sir J.J. Thomson and Lorentz, the theory explained electrical, magnetic and thermal properties of metals in terms of the motions of free electrons. Although Bohr made no use of the quantum hypothesis in his dissertation, he noted that classical electrodynamics was incapable of explaining Planck's radiation law and entailed the ultraviolet catastrophe. After completing his dissertation Bohr pursued his post-graduate studies under Thomson at Cambridge University. Finding that Thomson was little interested in his work, Bohr went on to Manchester University in March 1912, to work under Ernest Rutherford. Bohr's move to Manchester was very opportune: the quantum hypothesis was just beginning to receive a wider recognition, thanks largely to the first Solvay Conference in 1911, which Rutherford attended; Rutherford's laboratory, moreover, was one of the most active centres in the investigation of radio-activity. In order to explain the results of experiments on the passage of alpha and beta particles through matter Rutherford had revived Hantaro Nagaoka's (1904) planetary model of the atom. On this model an atom consists of a positively charged nucleus which is orbited by negatively charged electrons, the number of which corresponds to the number of charges on the nucleus. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

I propose now to examine Bohr's informal theory of measurement from a somewhat more formal point of view, and to consider how his theory relates to the orthodox theory of measurement in quantum mechanics. This is a difficult task, since Bohr nowhere discusses the theory of measurement in formal terms. My discussion, therefore, will be less closely tied to Bohr's own statements. I shall also consider some important objections to the theory. The objective-values theory of measurement Before we look into this theory, it will be useful to have a brief sketch of some of the relevant formal elements of quantum mechanics. In the Hilbert space formulation of quantum mechanics the measurable physical properties (‘observables’) of an object are represented by linear Hermitian operators A, B, … which have complete orthonormal sets of eigenvalues an, bn, … corresponding to the subspaces (closed linear manifolds) of a Hilbert space H. These operators are in one-to-one correspondence with the projection measures PA, PB, … on the Hilbert space such that PA = ΣnanPn, where Pn are the projections of the eigenvectors ψn belonging to the eigenvalues an of A, and an are discrete, non-degenerate values (for simplicity I shall deal only with operators which have such values, and shall denote observables and the corresponding operators by the same symbols). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Niels Bohr's theory of complementarity was an attempt to solve the enormous problems of interpretation – especially the problem of wave particle duality – that beset the quantum theory in the mid-twenties. By 1920 electromagnetic radiation could be conceived of either in terms of the wave model or in terms of the particle model, though neither conception alone was wholly adequate to the empirical data. By the mid-twenties the duality problem was quite general, applying to matter as well as to radiation. Quantum mechanics, the new quantum theory, could be interpreted partially in terms of one or other of the two models but not comprehensively in terms of either. Bohr's theory can be fully understood only against the background of the interpretative problems which it was intended to solve; and the root of these problems goes back to the very origin of the quantum theory, viz. the quantum hypothesis to the effect that in certain physical processes energy is transferred discontinuously in discrete amounts. Wave-particle duality was a development of the continuity-discontinuity duality which the quantum hypothesis introduced into physics. How did wave-particle duality arise? [ABSTRACT FROM AUTHOR]

What exactly is Niels Bohr's interpretation of quantum physics? And what general philosophical position underlies it? In the following pages I try to present clear and thorough answers to these questions. Bohr's interpretation is undoubtedly of major importance, but there is no universal agreement about what that interpretation is, owing largely to the notorious obscurity of his writings and the fact that his own views are often confused with those of others within the Copenhagen tradition which he founded. My reading is based solely on Bohr's own writings, and it is supported with liberal citations; I defend it against rival readings, but I try to keep polemical discussion to a minimum. When it illuminates Bohr's views, I have made use of material in the Niels Bohr Archive, much of which has now been published in Niels Bohr: Collected Works (six vols., eds. Léon Rosenfeld & Erik Rüdinger, North-Holland, Amsterdam, 1972–85). All translations are my own, unless the contrary is stated. Bohr's interpretation of quantum physics, I believe, contrary to a widely held view, was not the outcome of a ready-made philosophy; rather, it developed gradually from his day-to-day grappling with the problems of the physics. It is best understood, therefore, when seen against the historical background of these problems. My account of this background in the first few chapters is selective, highlighting only those ideas and problems which played a prominent part in the formation of Bohr's views. [ABSTRACT FROM AUTHOR]