Science in Christian Perspective



The Relevance of the Quantum Principle of Complementarity to 
Apparent Basic Paradoxes in Christian Theology.

Research Solid-State Physicist*
Mountainview Road, Belle Mead, N. J.

From JASA 8 (December 1956): 4-7.

In a recent article1, J. A. Wheeler, one of our most renowned theoretical physicists, has offered the support of his reputation to the basic applicability of the quantum principle of complementarity, not only for science itself, but even for other aspects of life. This is by no means the first time that this has been done, for Bohr himself, who formulated the principle of complementarity in the first place2, envisioned its importance beyond the realm of the physical for the solution of a number of apparent paradoxes.

The principle of complementarity is simply this (following Wheeler's rewording): "The use of certain concepts in the description of nature automatically excludes the use of other concepts, which however in another connection are equally necessary for the description of the phenomenon."

In this paper we shall consider briefly the meaning of the principle of complementarity in physics and will find that we are naturally led, by its importance for the most basic understanding of nature, at least to speculate about its applicability to other problems out side of physics. We will be careful. to recognize that the absolute validity of the principle, however,. is still a matter of debate among philosophers of science, and that we must not imply that we have a principle which has been proven valid with finality even in physics itself.

A The importance of our consideration will lie in:

(1) A comparison by analogy between the use of the principle of complementarity in physics and the  use of a similar principle in illuminating our present 0 position on certain apparent basic theological paradoxes;

(2) The suggestion that, as the complexity of nature has led scientists to formulate the principle of complementarity to bridge the gap between human ability to form concepts and the essence of nature itself, even so we may be forced to rely on a similar principle in trying to describe Truth in other forms in terms of idealized human concepts; and

(3) The possibility that the principle of complementarity may indeed have not only heuristic, but also real significance.

*At the RGA lAboratories, Princeton, N. J.

Experiments on the nature of light have shown that it is necessary to think of light as having a nature, only one aspect of which is discernible at time. Whenever light is absorbed, emitted, or scattered for example, it behaves as if the fight were compo of a steam of particles called photons, each with a fix discrete energy equal to the-product of Planck's constant, h, and the frequency of the light. The of light by solids, showing a continuous absorption a function of wavelength terminated by a sharp off at a certain wavelength of light, can be describe satisfactorily by considering the cut-off to be at a wavelength for which the photon energy is just enough to produce ionization or excitation in the Similarly, the emission of light by solids, as in luminescence, behaves as if photons were being emitted an energy, and hence a wavelength corresponding to energy given up when an excited. electron returns to its ground state. The photoelectric effect, in which electrons are ejected from solids as the result of absorption of light and the Compton effect, in which the wavelength of light is altered after an electron because of a transfer of energy from the light to the electron, are all examples of cases which the description of experimental results naturally calls for a particle (photon) picture of light.

On the other hand, whenever light is active in interference, polarization or diffraction, the results are completely described by considering light to be a wave motion. The experiments ma be treated in detail using Maxwells wave theory with lyth no mention of Planck's constant at all. The spreading of light after passing through a small opening, the bending of light around edges, and the phenomena which make the diffraction grating such a useful instrument, are examples which naturally call for a wave picture of light.

But this duality of particle-wave nature is not restricted to light alone. It extends to all matter. Electrons, which were thought to be tiny charged particles because of such experiments as Millikan's oil experiment, in which the charge of the electron was determined, and such experiments as the deflection of a beam of electrons in vacuum by electric and magnetic fields, were shown to have a definite wave nature the Davisson-Germer experiment. In this experiment  it was shown that electrons reflected from the suface of a crystal show a selective reflection phenomenon; the direction of maximum reflectivity (hence the effective wavelength) varies with the velocity of the electron. The definition of the DeBroglie wavelength for an electron equal to Planck's constant divided by the electron momentum enabled the experiments to be explained by the wave nature of the electron. In the Ramsauer effect, it was shown that the diffraction of electrons with a wavelength of the same order as the atomic cross-section of the material scattering the electrons produced variations from the smooth dependence of scattering cross-section on electron velocity which would have been expected for particle-electrons. Similar results were found for alpha-particles (helium nuclei); in the study of radioactive decay in which alpha-particles were emitted, it was found that a particle with an energy smaller than the barrier preventing emission could still escape from the nucleus by "tunneling" through the barrier in a wave phenomenon similar to the classical case of total reflection.

just as entities in matter which were thought to have particle nature have been shown to exhibit wave nature under the proper circumstances, so also experiments have shown the presence of discrete variations in nature. The basic need for a discrete-energy-state description of the atom to explain the absence of radiation from moving planetary electrons, for example, together with the characteristic line spectra emitted by excited atoms, shows that energy states in matter are quantized, Le., matter partakes of a discontinuous particle-nature as well as a continuous wave-nature.

It was on the basis of a situation such as this, that Bohr3 formulated his principle of complementarity. Bohr4 believed that our whole attitude toward physical reality should undergo a major change. As summarized by DeBroglies the point is that our understanding of nature has arrived at such grips with the very complexity of matter, that we should not expect our ability to formulate pictorial-concepts to be able to adequately describe nature At one time one concept will be the most useful, at others another will be the most useful.

But, one may ask, is there no conflict between two such opposite pictures as particle and wave? The answer is that conflict is impossible because any attempt to force a conflict will run head-on into the Uncertainty Principle- The Uncertainty Principle set forth by Heisenberg is simply a statement of the fact that two quantities cannot both
be known with complete accuracy. This is because "every experiment destroys some of the knowledge of the system which was obtained by previous experiments." The Uncertainty Principle gets its name from the fact that its mathematical form states that the product of the uncertainties in two complementary quantities must never be less than Planck's constant in magnitude. Two such complementary quantities are (position" and "momentum". The position and the momentum of an electron cannot both be known accurately at the same time; an effort to measure the position will destroy past information about the momentum and vice versa, because of an interaction between the measuring process and the quantities to be measured. If we come back to the opening question of this paragraph and consider an electron, we will find that conflict between the particle and wave pictures of the electron cannot occur because either (1) the electron will have a wavelength well-enough defined to interact with itself (to produce wave effects), in which case it is not localized in position and does not correspond to the particle picture, or (2) the electron is localized in position, in which case it no longer can interact with itself to produce interference or other wave effects.+ Basically, conflict is impossible because there is not present both a particle and a wave-there is present only one entity: an electron.

Bohr's principle of complementarity goes to the very heart of quantum theory itself.8 Being a human theory, it is bound by the same conceptual limitations as our other views of nature. It is possible to describe nature in the classical perspective of space-and-time, but then the description becomes non-causal because the Uncertainty Principle must be incorporated. to limit the accuracy with which two complementary quantities may be simultaneously known. On the other hand, it is possible to describe nature by foregoing a description in terms of space-and-time and retain a causal description by using instead a mathematical formulation which is based on the "psi" function and the laws which apply to "psi" functions. One can go from one representation to the other by well-known laws of transformation. Thus in quantum theory itself, space-and-time description and causal description are complementary concepts.9

Most scientists have followed in the steps of Bohr in accepting the principle of complementarity as basic, at least in the field of science itself. In the words of Wheeler, "Complementarity is battle-tested. No one knows an acceptable alternative. The new viewpoint is part of the working attitude of the great majority of physicists of this generation. It would be hard to name a part of science better established than the quantum principle, more thoroughly analyzed for self-consistency, or able to account for a more fantastic range of experience. There is no going back on complementarity !"

But we would leave an incomplete picture if we intimated that there have been no dissenting voices. The most eminent of these was Einstein10 himself who looked throughout his life for a form of theoretical expression which would describe events themselves in nature and not just their probability as is the case with the "psi" formulation. Margenau,11 as a philosopher-scientist, points out the major disadvantages of the principle: (1) it leaves nature forever in a dilemma without any hope of a final resolution, and (2) it invites I the speculation that other dilemmas outside of science are capable of no further elucidation beyond that interpretation of the complementarity principle. Bohr12 himself warned against extremism in the latter direction.

But with these warnings noted, let us go on to consider some of the other complementary concepts which seem suited for discussion on the basis of the principle. We have spoken thus far of three such concepts: (1) position and momentum, (2) the particle-aspect and the wave-aspect of nature, and (3) a description of nature in space-and-time and a causal description of nature.

Another complementary set in physics is that of "energy" and "time"; it is not possible to know accurately the energy of a system and the time simultaneously.

Other complementary concepts quoted by Wheelel1 are the following (1) the use of a word to communicate information and the analysis of the meaning of the word; (2) justice and love; (3) free will and determinism. Let us consider the last of these in somewhat greater detail to make clear the actual implication of considering these as complementary concepts. It may be simply shown that the experimental conditions which would have to be established to confirm the existence of determinism would automatically rule out the exercise of free will and vice versa. To demonstrate determinism one would have to prove that the future of a person is determined by the past; to accomplish, this, one would have to carry out detailed experiments on the potentials of various portions of the brain and the attendant bio-chemical functions of the body. Such an approach, however, would sever the natural course of existence for the person and make exercise of free will impossible. Similarly if the person is pu~ in such a situation that the exercise of free will ' can be demonstrated, it is impossible to show that determinism is or is not acting. Thus Wheeler' argues that free will and determinism are not contradictory-but complementary.

It is not difficult to think of other complementary concepts in everyday life. The use of art forms, such as music or painting, to convey aesthetic impressions is complementary to an analysis of such art forms into their basic components of frequency-and-amplitude variation and brush strokes. Such examples are directly analogous to that given above for the use and analysis of words.

When we turn to the subject of Christian theology, we again find a number of concepts which seem to partake of the nature of complementarity at least to some extent. Probably this "nature of complementarity" can be redefined as the existence of two apparently contradictory concepts to fully describe reality, the cause of their contradictory appearance lying in our inability to pictorialize to an extent required by reality.

Certainly the basic concepts of the Unity and the Trinity of God, and of the divine nature and human nature of Christ partake of at least some of this quality of complementarity. We might also consider as complementary the concepts of the holy position of the Christian in Christ and the sinful state in which he yet lives this life. Faith and works also possess a definitely complementary nature as is evident by a comparison of Romans 4:14 with James 2:21-23. Even the duties of Christian burden-bearing are complementary as indicated in Galatians 6:2, "Bear ye one another's burden", and Galatians 6:5, "For every man shall bear his own burden."

But above and beyond these concepts of Christian theology there is the one apparent basic paradox that rests in the very deepest heart of the Scriptures, that apparent paradox upon which is centered our deepest understanding of God and His purpose: the co-existence of man's responsibility and God's- sovereignty. There can be no doubt that the Bible teac -, each of these doctrines with absolute finality. Let us consider a few examples:

(1) When God sent the king of Assyria against the Samaritans to carry out His sentence of judgement against them, the king of Assyria had no knowledge of being used in this way and acted out of his own evil motives. By one act the sovereign purpose of God was accomplished and the holy law of God was transgressed; the king of Assyria was held responsible for the sin which he had committed. (Isaiah 10:5-13).

(2) God announced to Solomon that He would the kingdom from his descendents -in judgment against him (I Kings 11:11). This judgment came into effect when Rehoboam, Solomom's son, accepted the evil counsel of his young companions to threaten the people with worse hardships than before, and ten of tribes of Israel rebelled. God's purpose was achieved and yet Rheoboam was fully responsible for his sin before God.

(3) Jesus warned against the great sin of leading-little children astray, and said, "Woe unto the world because of offenses! for it must needs be that offenses come; but woe to that man by whom the offense cometh!" (Matthew 18:7).

. (4) The co-existence of God's sovereignty and man"s responsibility is clearly brought out in the betrayal of Jesus by Judas Iscariot. Here are the words of Jesus

'The Son of man goeth as it is written of him  but woe unto that man by whom the Son of man is betrayed! it had been good for that man if he hadnever been born" (Matthew 26:24)

"While I was with them in the world, I kept them in thy name: those that thou gavest me I have kept, and none of them is lost but the son of perdition; that the sc:riptures might be fulfilled." (John 17:12)

  "I speak not of you all : I know whom I have chosen: but that the scripture may be fulfilled, He that eateth bread with me hath lifted up his heel against me." (John 13:18)

If ever an event were part of God's eternal sovereign purpose, it was that His Son Jesus Christ should come to pay the penalty f or men's sins by dying in their place:

"Him, being delivered by the determinate counsel and foreknowledge of God, ye have taken, and by wicked hands have crucified and slain:" (Acts 2:23)

And yet there can be no doubt on the basis of the Scriptural record that Judas was guilty and responsible for his sin of betrayal before God, since he acted in accord with his own evil will.

We can sum up the situation in this way: "Perhaps the most important fact to recognize in studying the scriptural revelation concerning God's purposes is that the truth is presented from two distinct points of view. Many passages present the truth of God's purpose from God's point. of view. Many other passages present the same truth from man's point of view. If we fail to recognize that the same truth is being described in both cases, we find ourselves facing a paradox which seems to make God's point of view and man's point of view irreconcilable. "13

Is not this the very same language as that of the principle of complementarity? We have here at the very heart of Christianity an example of complementarity which matches the scientific applications of the principle perfectly.

To be sure, we can soften this apparent paradox between man's responsibility and God's sovereignty without invoking the principle of complementarity, in a way which affords some satisfaction to Christians.13 By considering rmn's inheritance of an unregenerate nature as the result of the Fall, we can place man's responsibility on his own sinful actions dictated by the desires of his sinful will. By considering the saving grace of God's election by which He bestows salvation as a free gift upon those whom He has chosen, we can see the exercise of His sovereignty. But it is clear that we cannot see Christian's responsibility and God's sovereignty in action at the same time, so as to understand how all of men's actions infallibly fulfill God's purpose. We have softened the paradox and made it easier to build upon in our Christian life and service, but its essence remains unchanged as far as our knowledge in this life is concerned.

It may be that the principle of complementarity in physics is a result only of inherent limitations on our 
experimental ability and is not a final picture of the true nature of things. And it may be that some day 
science will penetrate beyond the Uncertainty Principle by discovering bidden variables which permit both a causal and a space-and-time description of nature, as Einstein had hoped. These things must be admitted as possibilities, albeit seemingly unlikely ones at the present time.

Even if science were able to overcome this limitation, however, it is likely that our grasp of spiritual Truth the created mind seeking after those things of the Creator-will never be able in this life to go beyond a position like that in which science finds itself today. Our feeble attempts to invent and use concepts to describe the purpose and -the plan of Almighty God will very likely not get beyond those concepts such as man's responsibility and God's sovereignty which present an apparent paradox. Man will probably always find his best refuge in those heart-felt words of Paul: "0 the depth of the riches both of the wisdom and knowledge of God! how unsearchable are his judgments, and his ways past finding out!" (Romans 11:33).

An understanding of the principle of complementarity demonstrates to us that the existence of apparent paradoxes in our theology cannot be used against the Bible as evidence of its falsehood; such apparent paradoxes are seen to be common in human experience and to exist even at the very heart of modern physics.

An understanding of the principle of complementarity also shows us that we need not retreat from the complete Scriptural revelation by denying either the real meaning of man's responsibility or of God's sovereignty, as some have been led to do in order to remove from themselves what they considered to be the intolerable burden of the apparent paradox.

We are led once again to the conclusion that the Bible is the infallible Word of God, presenting to us the truth of Himself and His purpose insofar as it can be revealed in human language to human beings.


1. J. A. Wheeler, Am. Sci. 44, 360 (1956).
2. N. Bohr, "Atomic Theory and the Description of Nature" Cambridge Univ. Press (1933), p. 28.
3. N. Bohr, chapter in "Albert Einstein: Philosopher-Scientist", edited by P. A. Schilpp, Library of Living Philosophers, Inc-, Evanston, Ill. (1949), p. 199.
N. Bohr, Phys. Rev. 48, 702 (1935).
5. L. deBroglie, "The Revolution in Physics", Noonday Press, N.Y. (1953), p. 218.
6. W. Heisenberg, "Quantum Theory", Dover Pub. Inc., (1930), P. 20.
7. L. deBroglie, loc. cit., p. 217.
8. N. Bohr,
Nature 121, 580 (1928).
9. N. Bohr,
Nature 131, 422 (1933).
10. 1. Rosenthal-Schneider, chapter in Ref. 3, p. 14Z
11. H. Margenau, "The Nature of Physical Reality", McGraw-Hill Book Co., Inc., N.Y. (1950), p. 418.
12. N. Bohr, Phil. Sci. 4, 289 (1937)
13. R. H. Bube, "To Every Man an Answer", Moody Press,  Chicago, Ill. (1955), p. 200.