Atoms, Metaphors and Paradoxes: Niels Bohr and the Construction of a New Physics.
The discovery of the quantum of action meant, in the eyes of Bohr, that the physical description of the quantum world had to forsake some principles that had been so essential for the development of classical physics. They were the principles of causation, determinism, space and time, continuity, and conservation of energy. Already, in 1913, Bohr's original model of the atom introduced a radical break with several of these principles, when he postulated that the electron can move around the nucleus only in stable and stationary states defined by quantized orbits. Although the atom radiates discontinuous spectra of energy as an electron jump from more remote states to some closer to the nucleus, it is impossible, according to Bohr's model, to say what causes the electron to make the jump, and to describe its passage from one orbit to another in terms of some trajectory in space and time. As a result of this failure of classical principles to apply to the atom, physics for Bohr had to give up the ability to visualize atomic processes.
While Bohr held that the discovery of the quantum of action in physics ruled out the unlimited applicability of such classical principles, he also argued on philosophical grounds that the use of classical concepts, like those of position, momentum, and energy, is necessary for any understanding of physical experiments. His grounds were that he saw classical concepts as a physical specification of everyday notions of space, time, and causation: notions that were prerequisites for the distinction between the subject and the object of experience, and therefore as forms of perception essential for an objective and unambiguous description of physical phenomena. Eventually, Bohr realized that space, time, and causation were notions buried in our ordinary language as informal conditions for the description of observations. So although quantum phenomena could no longer be explained according to classical principles, they still must be described in terms of classical concepts in order for such descriptions to have unambiguous meaning.
The result of this analysis was his complementarity interpretation of quantum mechanics which calls attention to the fact that different and mutually exclusive experimental arrangements yield information that precludes a precise and simultaneous application of classical concepts such as position and momentum, or concepts such as waves and particles. To Bohr these experimental situations were not merely complementary to each other, but also they serve as the conditions under which it is unambiguously meaningful to ascribe such attributes to the object under investigation. Bohr often compared the new epistemic situation in quantum mechanics with the introduction of the frame of reference in relativity theory.
In general, Bohr scholars now acknowledge both the physical and philosophical premisses as the basis of Bohr's interpretation. Where scholars mainly disagree is on the question of which consequences for the representation of reality follow from these premisses. A new book on Niels Bohr's philosophy, Atoms, Metaphors and Paradoxes, by Sandro Petruccioli, an Italian historian of science, apparently differs with respect to Bohr's presumptions from other recent books on this topic. Petruccioli believes, naively I think, that Bohr's epistemological claims regarding the interpretation of quantum mechanical formulas can be reached by a purely physical reconstruction without taking into account Bohr's philosophical background. For instance, regarding Bohr's reply to the EPR argument he says: 'This did not, however, require [Bohr] to embark on a dispute as to the ontological implications of the new physics. His arguments were theoretical and concerned the nature of the quantum phenomena . . .' (p. 195). It is therefore quite baffling to read two pages later: 'Since in Bohr's view the expression "physical reality" can only refer to the phenomenon, it makes no sense to speak of an incomplete description of physical reality' (p. 197). One would never have thought it possible that an argument which concludes that phenomena as observed objects are considered to make up physical reality could be derived from premisses restricted to theoretical physics. Here we need a clearer indication of where purely theoretical considerations of atomic physics end and philosophical reflections begin.
The same failure to distinguish physical from philosophical claims leads Petruccioli to give an equivocal characterization of Bohr's ontology. For if observed phenomena are nothing but the physical reality, how then is it possible to state the following?
The paradox [of dualism of waves and corpuscles] disappears only if it is admitted - to put it in traditional terms - that the use of classical concepts to describe the phenomenal manifestations of objects does not necessarily imply that the objects themselves possess properties corresponding to such terms when they are not observed (p. 207).
This claim only makes sense if one thinks that Bohr held that there is a kind of reality behind the phenomenal reality. In my judgement nothing in Bohr's writings suggests this. But, had it been true, one may wonder at Petruccioli's insensitivity to Einstein's arguments, namely that it is just such an underlying reality that a complete theory of quantum phenomena must take into account. And, again, Bohr's position that any such theory must be confined to the world of phenomena, since these constitute physical reality, can never be solely justified by arguments in theoretical physics.
Despite these critical remarks Petruccioli's book is not without merits. Because he is mainly a historian and not a philosopher, Petruccioli has a keen eye for the physical conditions behind Bohr's interpretation. He traces many of them back to Bohr's atomic model of 1913. And, in spite of many problems built into the research program that arose from this model, Petruccioli sees the significance of Bohr's contribution in his introduction of the concept of discontinuity as an essential and irreducible element in atomic physics. Accordingly, he believes that Bohr's correspondence principle was called upon to ensure the consistency of the theory. Furthermore, Petruccioli shows how the Bohr, Kramers, and Slater theory is Bohr's last attempt to reconcile the quantum of action and a classical picture of continuity. Although Petruccioli doesn't mention it, his painstaking analysis of the BKS theory none the less reveals remarkable similarities between this theory and Bohm's theory of nonlocal quantum potentials.
In his chapter on the emergence of Bohr's view of complementarity, Petruccioli emphasizes, in particular, the importance of the Planck-Einstein-de Broglie equations and Schrodinger's wave mechanics for Bohr's understanding of the complementarity between definitions and observations. However, this very formal perspective on Bohr's interpretation is open to a serious objection. According to such an approach, position and time can be associated with particles, and the conservation of energy and momentum with waves through the Planck-Einstein-de Broglie equations. But Bohr's analysis of an electron's movement in the double-slits experiment shows that the determination of momentum - so that we can trace the trajectory of the electron through one of the two slits - prevents the occurrence of any wave pattern, whereas the determination of position allows the existence of the interference pattern. Consequently, here Bohr's analysis reaches the opposite conclusion from Petruccioli's formal approach. Since Bohr believed that the experimental apparatus plays a fundamental role in the specification of conditions under which the classical concepts may be used unambiguously, Petruccioli's formal perspective on the road leading to complementary generates its own problems.
In the beginning of his Como paper, Bohr speaks of the quantum of action as preventing us from defining the classical state of a physical system independently of an observation of that system. From the context it is clear that by the phrase 'the definition of state' Bohr is thinking of the classical union of space-time and causality into a deterministic description of a future state. The concepts of space and time require, on the one hand, an observation in order for the position to be determined. But because of the quantum postulate this act of observation excludes, on the other hand, any determination of energy and momentum, and therefore the application of causality and thus the possibility of defining a classical state of the system. The same is also true the other way around. These remarks cause Petruccioli to conclude that conditions of observation and possibilities of definition stand in relation of complementarity to each other. For instance, the conditions under which the position of the electron is observed preclude any definition of its momentum. One should therefore not focus on the operational element of the definition of position but on the fact that momentum is not unambiguously defined as one would have expected in a classical state description (p. 171), Nevertheless, this conclusion is strange, for it is clear from many of Bohr's other statements, which Petruccioli mainly leaves untouched in his formal approach, that Bohr also considered the conditions of observation as essential for a well-defined application of the attribute being measured. Here an obvious inconsistency can be avoided only if one distinguishes (as Bohr did) between the formal definition of states in classical physics and the definition of classical concepts in quantum mechanics as an operational application.
The final chapter deals with Bohr's discussions with Einstein, and especially their incompatible views on reality as they surfaced in the EPR dispute. Here Petruccioli does not add anything new to our understanding of Bohr. On the contrary, for my part, I think he misses the important point that the EPR argument induced a change in Bohr's way of thinking of complementarity.
Nevertheless, Petruccioli's book is welcome as a good and rewarding addition to the fast growing literature on Bohr's philosophy. In particular, it gives us a fine analysis of Bohr's early atomic model and its violation of classical physical principles, and how this violation can be connected to his later interpretation of quantum mechanics.