CONJUGATE PROPERTIES AND THE HYPOS TA TIC UNION
Michael J. Bozack
Surface Science Center, Department of Chemistry
University of Pittsburgh
Pittsburgh, PA 15260
From: PSCF 39 (June 1987): 105-107
The emergence of complementarity as a way to reconcile problems in theology has been beset with several difficulties. The major difficulty lies in determining exactly what Bohr meant by the "principle of complementarity." As eminent a scientist as Einstein remarked that he had not been able to achieve a "sharp formulation" of the principle. This lack of clarity has led to increasing criticism of the validity of viewing theology in complementarian terms.
In this paper. we propose a method of dealing with
complementarity which does not depend on the obscurities of
Bohr nor on redefinition of terms. In doing so, we circumvent
the difficulties of past approaches while maintaining strict
adherence to modern quantum mechanics. By consideration
of the relationship between the hypostatic union of Christian
theology and the modern theory of waves and particles, it is
possible to handle complementarity without recourse to Bohr
or Bohr redefined. The modern viewpoint accepts that quantum theory is not afflicted by paradox and does not require
Bohr's semiclassical interpretation of physical phenomena.
Quantum mechanically, a particle is represented by a wave disturbance confined to a region of space. The localized wave phenomenon is called a wave packet. The intensity of the wave packet at a given location in space gives the probability of finding a particle at the location in space. All physical objects possess varying degrees of "particleness" and "waveness" depending on the degree of localization of the wave packet. The localization is governed by the uncertainty relation for the linear momentum and position of the wave-particle. Uncertainty relations show that as one tries to "squeeze" nature into revealing both particle and wave properties with equal precision, there is an unavoidable interaction which frustrates the attempt. The pair of complementary quantities which satisfy the uncertainty relations are called canonically conjugate variables.
In Bohr's original analysis, no matter how far physical phenomena transcended the scope of classical physics, their account was to be sought in classical terminology. On the microscopic level, however, one cannot make the sharp distinction between the natural phenomena and the instrument with which it is observed. Whether an electron or a photon appears as a wave or as a particle depends on the nature of the measurement that is made. A physical situation cannot be completely specified with classical variables, but must be described by an imprecise specification of a pair of complementary quantities whose sharpness in a given environment is defined by the uncertainty principle.
We have chosen the wave-particle duality as the paradigm
for our discussion; however, similar comparisons hold
between any pair of conjugate variables. It is possible to
identify at least eight points of comparison between the
theological principle of hypostatic union and the modern
complementary view of waves and particles.
1. Both models have two natures in a single entity.
The hypostatic union and the wave-particle duality postulate the existence of two natures which are integrated into one entity. The wave and particle natures pertain to a single entity properly called the wave-particle, while the divine and human natures pertain to a single person properly called the God-man. The coexisting natures cannot be separated, and, at a certain level, appear to be incompatible. However, this is due to the limitations of human perception and the unjustified transferral of concepts familiar in one domain into another.
2. The God-man and the wave-particle have properties which transcend either nature acting separately.
The synergism between divine and human, and between
wave and particle, endows both wave-particle and God-man
with properties transcending those of either nature acting
separately. For example, without the dual nature of electrons, it is difficult to explain the existence of the atom,
diffraction, scattering, et cetera. Likewise, many theologians
hold that if Christ were not both God and man, atonement
for sin would not be possible. There is no flexibility in the
hypostatic union to account for Christ's resurrection in
purely human terms, nor is there any possibility of explaining
physical phenomena by purely wave or purely particle phenomena.
3. Both models possess properties described by conjugate variables.
Canonically conjugate properties occur in both the hypostatic union and the wave-particle dualism. The description of
an event in either realm proceeds by specification of a pair of
mutually complementary quantities. When measuring the position of a particle, for example, one seeks to squeeze the
wave packet representing the particle into a small region of
space. Since waves are not easily localized in space, measurement of the position is subject to uncertainty, making it
difficult to tell how "wavelike" and "particlelike" is the
resulting phenomena. A similar situation exists Christologically. The God-man is described by both human and divine
attributes, and it is difficult to determine in a given situation
which attribute is operative. At a certain level, the complementary properties appear dualistic and incompatible; however, both descriptions are necessary to fully characterize the
properties of the God-man.
4. The conjugate properties in both models obey an uncertainty principle.
Once it is shown that the hypostatic union and the wave-particle duality contain a principle of complementarity, the existence of uncertainty relations between the conjugate properties follows necessarily. For example, if an experiment is performed to reveal both particle and wave aspects of matter to infinite precision, an unavoidable interference takes place which frustrates the attempt. A given experiment will emphasize the details of only one complementary property at a time, depending on the choice of measurement.
It is also difficult to perceive both human and divine natures at the same time in the God-man. Either the divine or the human nature is featured, depending on the interaction of Christ with the universe. It is possible to envision a relationship similar in form to the Heisenberg uncertainty principle, which describes the combination of divine and human in the God-man. In symbols:
d(divine) x d(human) ~ C
where d(divine) and d(human) represent the uncertainties
expected during an attempt to specify the divine and human
natures of the God-man simultaneously, and C is a constant.
Such a relation shows that absolute precision in the specification of the divine nature of Christ is accompanied by
complete uncertainty in his human nature, and provides a
possible explanation of how Christ could walk on water in
spite of being human. Although both natures are necessary
for a full description, only one or the other is featured at a
given time. The other attributes are retained in the complementary nature of Christ and are hidden, not absent. The
same is true for waves and particles.
5. Viewing the complementary properties as classical entities leads to irrational conclusions.
According to Bohr, physical phenomena must be expressed in classical terminology. The point of the modern theory, however, is that quantum entities cannot be described in classical terms without leading to absurdities. By making a classification according to waves or particles, we force a classical description on things that are by nature unclassical. Photons and other quanta do not obey the laws of classical mechanics; they obey the laws of quantum mechanics.
In the same way, to press the hypostatic union into a "classical" description of what is divine and what is human leads to the same logical absurdities that arise when trying to reconcile waves and particles. For example, it is impossible to explain how Christ could turn water into wine and rise from the dead based on our limited "classical" perspective of what constitutes humanity. On the other hand, from a "classical" view of what constitutes divinity, it is difficult to explain why a divine being would need to eat and sleep. The impasse is avoided by postulation of complementary natures which cannot be viewed in all detail at all times. In a given situation, either the divine nature or the human nature will be featured, depending on the interaction of the God-man with the world. At a deeper level, the two natures of Christ are not incompatible; the paradox merely reflects the inadequacy of human comprehension to achieve a rational understanding based upon our limited notions of what constitutes "human" and "divine."
There are at least eight alternative models that have been
proposed for the union of God and man. These theories differ
from the classical doctrine in that they deny either: 1) the
reality of the two natures (Ebionism and Docetism); or
2) the integrity of the two natures (Arianism, Apollinarianism, and the theory of incomplete humanity); or 3) the union
of the two natures in one person (Nestorianism, Eutychianism, and the theory of gradual incarnation). The properties
of conjugate variables are incompatible with the alternate
models for the following reasons. First, the uncertainty
relation governing the conjugate variables is an explicit
statement that there is reality to particle and wave interpretations of matter. Second, there is no subordination or loss of
nature implied in the statement that matter has a dual
nature. Third, there is no incomplete integration of the two
natures. Either waves or particles can be featured, depending
on the experiment, but the wave-particle has not "given up"
any of its wave or particle nature during the integration. The
measurement has merely dictated whether waves or particles
are seen by the observer. Matter at its most fundamental
level is both wave and particle, just as Christ is both God and
man. There is no provision in either model for a "halfman/half-God," or a "half-wave/half-particle."
7. In spite of the union, the two natures are retained in both models.
In traditional doctrine, the two natures are unchanged by the hypostatic union. The argument is: if divine attributes are conferred to man, man ceases to be man. Therefore, the divine and human natures cannot be mixed to form a third nature which is neither one or the other. The humanity in Christ is not deified.
Can the same be said of waves and particles? This is a difficult question, but the answer is probably yes. In the classical view of particles and waves, the answer is surely yes. Particles and waves are mutually exclusive concepts, and there is no intermixing of the natures. In the modern viewpoint, however, the answer is more elusive. It is a "chicken and the egg" issue. In order to find out if the wave nature of an electron has been modified by the presence of the particle nature you have to make a measurement; but when you make a measurement, you change the very Lhing that you sought to measure. In spite of the dilemma, the majority of physicists believe that conjugate properties such as position and linear momentum are potentially present in nature, but not actually present until a measurement is made. For example, in the single slit experiment, as the slit is closed, the diffraction pattern shrinks and begins to look as though it is caused by straight-line motion of particles through the aperture. As the wave nature of the electrons appears to vanish as the slit is closed, however, it still must be potentially present to produce the interference pattern, which can only arise by wave interference. Hence, while one complementary nature is featured the other is suppressed, but not changed into something other than of wave or particle nature. There may be less of one nature than the other during a measurement, but the wave and particle natures are unchanged. This is similar to what theologians mean when they propose that the union occurs without corruption of the natures.
8. Reconciliation of the hypostatic union and the waveparticle dualism is dependent on the role of human perception.
Whether an electron appears as a wave or a particle depends on the nature of the measurement that is made. The wavelike or particlelike character of an electron lies only in the eye of the beholder. No one can really say when a wave packet has been localized "enough" to be considered a particle. A similar situation occurs when viewing a threedimensional cube drawn on paper-a paradox arises when the observer is asked to specify which side of the cube is facing forward. Some individuals see the "back" surface as forward; some see the '6front" surface as forward. In forcing a notion of meaning upon a series of lines, or in pressing matter to fit a classical model of either particles or waves, an antinomy is created which forces us to conclude that the universe is by nature irreconcilably dualistic. In other words, we as observers are the true source of the paradox due to our insistence to describe things by particular models. In the case of the hypostatic union, the God-man seems impossible because of our deep-seated convictions of what is divine and what is human. In our insistence on preconceived views of humanity and divinity, we arc forced to regard the hypostatic union as paradoxical and dualistic. This no longer need be true, as it is possible to resolve a similar paradox in quantum physics by way of conjugate variables.