(and more importantly that we can live in both of these apparently mutually exclusive worlds), I need to introduce the idea of complementarity. Complementarity is a logical framework for the analysis of ideas in which the exclusive binary relationships between categories found in classical Aristotelian logic no longer hold. Although we will be much concerned with Niels Bohr’s famous formulation of complementarity, let’s start with a simpler example: Imagine a certain piece of music. Now imagine further that this piece of music is played by a solo violin. How would we describe the music? One option is to specify completely the overtone frequencies in the sound emitted by the violin, which in principle specifies everything we can hear and would thus want to know (it is this kind of information that is engraved on a recorded CD). But this description is solely in terms of the physical sound. Alternatively, we could specify the musical notes, i.e. each pitch and its duration; in this case, there is no sound at all associated with our description, except insofar as the notes can be played (if desired) on some instrument to create a sound. If the instrument is chosen to be a trumpet, the actual sounds will quite different from our first description, and yet the piece of music will be the same. So, we have two alternative descriptions, and they are very different from each other (to the point of being mutually exclusive, at least in a limited sense) since one description is in terms of physical sounds and the other description is in terms of symbolic notations. Of course, the two descriptions are intimately related; they are both describing the same piece of music. Indeed, we can claim that both of these descriptions are necessary in order to have a complete understanding of the piece of music. With only one or the other, we would be missing something essential. This is the essential meaning of complementarity: there are situations in which mutually exclusive alternative descriptions of some phenomenon are not only logically compatible but are both essential in order to have a complete understanding. We refer to such descriptions as complementary descriptions of the phenomenon.
An excellent overview of complementarity, including its relationships to classical logic, to medieval theological thought, and to Kantian philosophy has been given by MacKinnon1. More recently, based upon many years of work, Reich2 has broadened the ideas inherent in complementarity and relabeled the broadened set of ideas as “relational and contextual reasoning” (RCR), which he contrasts with binary, dialectic, and analogical reasoning. Reich carefully examines the logical status of RCR and develops a set of heuristic methods to apply this form of reasoning to issues and problems; a number of specific issues and problems are analyzed in some detail to illustrate the application of RCR thinking and the value it has. An early champion of complementarity was MacKay3, who has contributed both a rigorous analysis of the logical status of complementarity and who has also urged its use in clarifying the relationships between scientific and religious thought. Mackay emphasizes the status of complementarity as a purely logical concept that defines relationships different in kind from other logical concepts such as contradiction, independence, and identity. It’s this added set of possible relationships that make complementarity valuable as a framework for examining concepts, and MacKay notes that this value is especially apparent at the science/religion boundary. “…whether we like it or not, we need it; and by ‘we’ I mean […] anyone […] who wants to avoid logical blunders in seeking to bring science and faith into confrontation.”4 In emphasizing complementarity as a logical relation as opposed to its well-known role in modern physics, however, we need to be careful to not underplay the extremely important work done by Niels Bohr in developing complementarity along several novel lines of thought. It’s also important to disentangle the use of complementarity as a generic logical or heuristic analytic tool from the more specialized development of Bohr and the implications of that development.
Bohr’s Work
The problem that Bohr set out to solve arose in the context of early attempts to understand quantum physics. The experimental results that were available for understanding the properties of matter and radiation at a microscopic level had become very puzzling. One set of experiments demonstrated unequivocally that both radiation (e.g. light) and matter (e.g. electrons) were wave phenomena: undulations that are not localized in space. Contrariwise, another set of experiments demonstrated unequivocally that both radiation and matter were composed of pointlike particles, quite localized in space and bearing no resemblance to waves. The energies of the particles were found to be in discrete states, which changed discontinuously, and these discontinuities were related in some way to a physical constant of nature, Planck’s constant h. A more detailed discussion of all this work and its implications is presented in Chapter 6. Eventually, a self-consistent and rigorous mathematical theory was developed for quantum physics, and this theory has been applied to particular physical systems with spectacular success ever since. The major unresolved problem was the interpretation of the theory, i.e. trying to figure out just what the mathematics is telling us about the structure of physical reality. Not surprisingly, the strange features of the experimental results were also found in the mathematical theory. The peculiar discontinuities, the presence of both wavelike and particlelike properties, and the lack of classical determinism were all inherent in the mathematics but not well understood in any sense. In 1927, Niels Bohr presented a piece of work in which he hoped to clarify all these murky points.
The work that Bohr presented was not well understood (or well received) by the physics community, because it turned out that the issues Bohr addressed were not issues in physics but rather issues in epistemology. The heart of his solution to the interpretive problems of quantum theory was complementarity, and Bohr had a specific and precisely defined meaning for complementarity in this context. The starting point for Bohr’s line of reasoning is the discontinuous energy changes that occur in the microworld due to the existence of Planck’s constant. Bohr refers to this as the “quantum postulate” and it is a contingent fact of nature, not a logical necessity. The quantum postulate is a fact of the world as we find it, and Bohr asserts that this fact carries an implication: due to the quantum postulate, all interactions with physical systems are liable to uncontrollable discontinuous exchanges of energy. The importance of these discontinuities hinges on Bohr’s next assertion, which is an epistemological statement. Bohr argues that we only know the properties of a physical system by interacting with it. A totally isolated system has no real meaning for us, because it can disclose no information. Hence, all of our knowledge of the system is acquired through interactions, and all of the interactions include uncontrollable discontinuities. Our knowledge of the world is thus severely limited, not by technological restrictions but by deep issues linked to how we know the world at all. Developing these themes further, Bohr shows that we can define the state of a system if we wish to, but only by giving up any knowledge of the space and time coordinates associated with the system. Alternatively, we can know the space and time coordinates of the system but this then precludes our ability to know its dynamical properties (such as energy and momentum). This latter restriction is extremely important, because conservation of these dynamical quantities is what insures the orderly dynamical behavior of the system (what Bohr refers to as “the claim of causality”). In this way, Bohr arrives at the conclusion that to understand these physical systems we need to use two complementary pictures, that of spacetime coordination and that of cause/effect relations. They are complementary because each picture excludes the other yet both are needed for a complete understanding of the system. Using this framework, Bohr was then able to explain the observed wave/particle duality and the famous Heisenberg Uncertainty Principle in terms of complementarity.
A more detailed and extensive treatment of Bohr’s development of complementarity in the interpretation of quantum physics is given in Chapter 7. Excellent expositions of this material are also given by Folse5 and by Faye6 (on both of whom I draw extensively in this work) and also by MacKinnon1. For our present purposes, we should merely note two further points: First, the combined and integrated spacetime and causal views form the basis of classical determinism, and that’s why determinism of this sort is not possible in quantum theory. Second, and perhaps more germane to the arguments we are developing here, Bohr carefully notes that which picture we employ depends on the manner in which we observe the system. In other words, the knowledge we have about a system depends on the experimental arrangement, i.e. on the details of how we acquire this knowledge. This may sound trivial, but it’s not; put succinctly, whether we see a wave or a particle depends on how we look. This conclusion of Bohr’s development
