THE PRIMER PROJECT
COMPLEMENTARITY
JOHN L. HITCHCOCK
This article is excerpted from Chapter 4 of Atoms, Snowflakes & God. Wheaton: Quest Books, 1986.
With rack and screw I put Nature through A thorough inquisition: But She was so afraid that if I were disappointed
I should hurt Her more that Her answers were disjointed- I did. I didn't I will. I won't She is just as big a liar, in fact as we are.
To discover how to be truthful now Is the reason I follow this star. WH. Auden, “For the Time Being”
The nonrational seems always to be worming its way into our attempts to reduce the world to order and rationality. Specifically, the nonrational somehow finds its way into philosophy and mathematics as well as into theology and physics. It now seems possible to say why this occurs, for the problem has taken a singularly acute form in physics.
That there are opposites (conscious/ unconscious, spirit/ matter, good/evil, and others) is not the problem, but rather that single things must be described in terms of such opposites. Without these contradictory descriptive terms, the description is incomplete. As modern a philosopher as Whitehead rejected the notion that a situation can require contradictory concepts in its description. He repudiated the belief that “logical inconsistencies can indicate anything else than some antecedent errors.” (Whitehead, 1969, pp. vii, viii)
Whitehead's point of view here is characteristic of 19th century thought. In the 20th century, first in physics and then in mathematics, this kind of thinking has begun to give way under the pressure of evidence and theoretical proof. Since the primary aim of this article is to describe the evidence found in quantum physics, the work in mathematics will be mentioned briefly here at the beginning.
Two years after Whitehead wrote the words quoted above, G6del proved that finite logical systems of a certain minimum complexity cannot be shown to be free of contradiction. A finite system is one which has a limited number of axioms for its foundation. Godel also proved that there will always be true statements which should be included in the system but which remain outside unless they are incorporated as new axioms. At one stroke, then, he proved that in order to be complete, a system must be infinitely complex, i.e., have an infinite number of axioms, and that such a system could not be shown to be internally consistent
It had also long been proven that if a statement and its formal contradiction are both derivable by[ correct] deduction from a given set of axioms, then any statement is correctly derivable. Therefore it would seem that Godel has given a deathblow to all logical limitation of thought. This is precisely what \Whitehead was aiming at in his. repudiation above.
But now that it is known that internal consistency cannot be guaranteed and that logical systems are always essentially incomplete, what is to be done? The point of view taken here is that one must begin in the middle and base theoretical work upon facts rather than upon arbitrary axioms. That is also why the major weight of this article is given to physics.
Yet it is to be noted that even the facts of physics are secondary in importance to the guiding fact that consciousness has arisen out of that which is unconscious. The physics provides a model for thought -that of complementarity-for viewing all situations in which contradictions arise in the description of single entities.
The problem is that a single entity exhibits contradictory characteristics. The knowledge that this is the case has arisen in the attempts of physicists to interpret the results of certain experiments. These experiments were designed to answer the question as to what concepts apply to the basic recognized constituents of the physical world, energy and matter. Ordinary visible light was taken as representative of energy, and the electron was seen as the easiest-to-handle representative of matter. It was thought that energy would be a “wave” phenomenon, i.e., would exhibit continuity, and that matter was “atomic,” i.e., particulate or discontinuous. By means of the experiments, however, it was discovered that both entities, light and electrons, exhibited both of the contradictory aspects, continuity, and discontinuity, though they did not exhibit both simultaneously.
Actually, one kind of experiment excluded discontinuity for light when done with light, and for electrons when done with electrons. In these two terms, continuity and discontinuity, the logical contradiction or mutual exclusiveness of those two theories is made clear.
Thus we have two experiments, both of which, after sixty years of refinement and discussion, are considered correct and factual. Each absolutely excludes the theory which is the necessary basis for the explanation of the other- necessary, that is, if we must think in such terms as waves and particles. On this point, Nobel laureate Richard Feynman emphasizes, “All our experience is with waves and particles.” The wave and the particle natures are two sides of one thing whose nature cannot be rationally expressed. This one thing is light, which seems both continuous and discontinuous, and which the experiments show is neither continuous nor discontinuous, but which we know at a level beyond rational knowledge is a unity.
Physicist Max Jammer, who will shortly be quoted more fully, says of this situation that we are “applying to the description of a physical phenomenon two categories of notions which, strictly speaking, are contradictory to each other.” We must distinguish between this logical [“hard”] contradiction and mutual exclusion (“soft”] contradiction. The former strictly applies to descriptive concepts in conflict at an instant of time. Mutual exclusion is less strong in that it says that the contradictory aspects cannot arise simultaneously but can arise successively. wlhich of the two aspects is exhibited depends upon the experiment, and the experiments which give the contradictory results cannot be set up simultaneously. Since the contradictory concepts cannot be brought into rigorous conflict simultaneously, it might be thought that mutual exclusion is as strong a statement as can be made about the complementarity of the descriptive situation. This brings us to the heart of the problem.
It is contended here that we have a case of the stronger criterion of logical contradiction, for it is a single entity which exhibits the two aspects, wave and particle, continuity and discontinuity. A physicist who does either of the two kinds of experiments uses the same source of light [or the same source of electrons] in both. The experiments indicate both a wave nature and a particle nature for light. The light is thus one thing with two contradictory aspects. We may say, as physicists do, that light travels as a wave and interacts as a particle, but between traveling and interacting is a qualitative “leap” into a contradictory aspect.Thus we ma truly say that there is a problem in the description of light. These last sentences could be repeated by replacing light vath electrons, so that there is the same problem in the description of the latter.
The succinct presentation by Edward Teller of the notion of complementarity employs no technical terms whatsoever:
“The idea of complementarity is that in order to describe a situation you have to use [at least on certain occasions] two mutually exclusive approaches. If you omit either, the description is incomplete. Both must be used. Because they are mutually exclusive, it is necessary to adjust the two approaches in a manner that is by no means obvious.”
Here is a more precise, but more extended amplification by Jammer:
“It was this mutual exclusion and, at the same time, indispensability of fundamental notions and descriptions which led Bohr to the conclusion that the problem with which quantum physics found itself confronted could not be solved by merely modifying or reinterpreting traditional conceptions. What was needed, he concluded, was a new logical instrument He called it 'complementarity,' denoting thereby the logical relation between two descriptions or sets of concepts which, though mutually exclusive, are nevertheless both necessary for an exhaustive description of the situation. In Heisenberg's reciprocal uncertainty relations he saw a mathematical expression which defines the extent to which complementary notions may overlap, that is, may be applied simultaneously, but, of course, not rigorously. The uncertainty relations, Bohr contended, tell us the price we have to pay for violating the rigorous exclusion of notions, the price for applying to the description of a physical phenomenon two categories of notions which, strictly speaking, are contradictory to each other.” 2
From the two statements just quoted, we will begin to describe characteristics of complementaiity, amplifying with other sources as we proceed. In an earlier work [Hitchcock, 19761 1 developed nine characteristics of complementarity of which the following apply to the present discussion.
a. Completeness of description requires both contradictory aspects to be incorporated. They are neither synthesized nor superseded. They are [ 1 ] mutually exclusive but [2] both necessary. Since a complete description requires both contradictory aspects to be incorporated, the words incomplete or approximate separability of the contradictory concepts applying to a microphysical entity will also be used to indicate the property[a-2]. And, if “perfection” can be identified with the absence of contradiction, we might say that completeness requires imperfection.
b. The observer is essentially involved in the situation which he or she is attempting to observe or to know. c. The unity behind the complementary conceptual opposites is not ultimately susceptible of a rationalistic description [at least as complementarity stands]. It is a nonrational unity. d. The single entity exhibits both aspects so that reversal [or exchange] of aspect occurs-a qualitative “leap” into the contradictory manifestation. e. As a universal principle, causality is denied, at least within complementarity as developed here. This will be seen as following from the ultimate inseparability of the object or entity from the instrument through which knowledge of the nature of the entity is obtained. f. There is an essential dynamism or disequilibrium in the complementarity of contradictory aspects of entities, though this is not explicit in the statement to be quoted. This characteristic is not considered essential to the argument of the study, but helpful insights can be obtained by carrying it along.
[a] Let us consider the first point. Jammers words, “concepts which, though mutually exclusive,are nevertheless both necessary for an exhaustive description,” and Teller's “both must be used” [for completeness], as related to the nature of a single entity[ the photon of light, or the electron], point to the relatedness of opposites in spite of the exclusion. [a-1 I In emphasizing that both opposites are necessary, Holton stresses their “irreducibility” or the impossibility of “attempting to dissolve one member of the pair in the other” as essential to Bohr's point of view: specifically, Bohr asked that physicists accept both [antithetical descriptions]-though both would not be found in the same plane of focus at any given time'. Holton stresses Bohr's view that the contradictory but necessary themes are not to be converted, or mutually absorbed, into a single new entity but remain as an eitherlor [recalling Kierkegaard ]. This either/or appears as nature putting a situation of choice before physicists as to which information will be tested for and which will be excluded. Physicists did not like this at all. They wanted to have all information which might be applied to, or obtained from, a phenomenon at once. Tellees words “both must be used” and Jammer's “overlap” increase the sense of “both/and.”
Our knowledge that it is light, a unity, or electron, another unity, to which the opposites apply, emphasize a “both/ and” which links the two and highlights their contradictory character.
Notes
1. Edward Teller. Niels Bohr and the idea of complementafity. In Great Men of Physics. Edited by Marvin Chachere. Los Angeles: Tinnon Brown, 1969. 2. Max Jammer. The Conceptual Development of Quantum Mechanics. New York. McGraw? Hill, 1966. 3. EdvAn? Adler. Basic concepts of analytical psychology- Guild Lecture No. 174. London: The Guild for Pastoral Psychology, 1974. Quotes a letter of Jung's vath similar import: The language I speak must be ambiguous, must have two meanings in order to be fair to the dual aspect of our psychic nature. I strive quite consciouslyand deliberatelyforambiguityof expression, because it is superior to unequivocality and reflects the nature of life. My whole temperament inclines me to be very unequivocal indeed. That is not difficult, but it would be at the cost of truth. I purposely allow all the overtones and undertones to be heard, partly because they are there anyway, and partly because they give a fuller picture of reality. Unequivocality makes sense only in establishing facts, but not in interpreting them. Adler goes on to say. One is reminded of a remark by the physicist Niels Bohr that there is a relationship of complementarity between the clarity and the rightness of a statement, so much so that a statement which is too clear always contains something false. [p. 15] 4. Gerald Holton. Thematic Origins of Scientific Thought- Kepler to Einstein. Cambridge, MA: Harvard University Press, 1973
