Part IV Cosmology and Physics

Quantum Theory and Theology

RODNEY D. HOLDER

Anyone not shocked by quantum theory has not understood it.

(Niels Bohr)

If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.

(Erwin Schrödinger)

Quantum mechanics is certainly imposing. But an inner voice tells me that it is not the real thing. The theory says a lot, but does not bring us any closer to the secret of the old one. I, at any rate, am convinced that He [God] does not throw dice.

(Albert Einstein)

I think I can safely say that nobody understands quantum mechanics.

(Richard Feynman)

Introduction

The above quotations from some of the founders of quantum theory plainly demonstrate the radical revolution in our understanding of the world which the theory has wrought. In this chapter I describe some simple experiments, including thought experiments, which illustrate this revolution. I then go on to explore what implications or opportunities for theology there may be in the light of these developments.

The Two-Slit Experiment and Wave-Particle Duality

Richard Feynman thought that the whole mystery of quantum theory was encapsulated in the following experiment. Neutrons are fired at a screen with two slits in it, so as to be detected by a photographic plate on a target screen beyond. Unsurprisingly individual neutrons behave like particles in that each produces a definite mark. However, as more and more neutrons are fired, the pattern that builds up comprises not two clusters of hits, but alternating bands of high and low intensity. This is exactly like an interference pattern arising from a wave motion, whereby peaks combine with peaks to reinforce the intensity but peaks and troughs cancel out.

If one of the slits is closed, the interference pattern disappears. However, the results from the two slits considered separately do not add up to the pattern produced when both slits are open. The inference is that the neutron possesses both particle and wave properties. Neutrons arrive at the target as distinct “hits,” but with an intensity pattern characteristic of a wave.

One way of thinking about this is to observe the bands of zero intensity on the screen. These are places which an individual neutron could reach when only one slit was open, but when both slits are open, even if the neutrons are fired individually, no neutron can now reach these points!

Suppose we try to resolve the wave-particle ambiguity by attempting to determine by observation which slit an individual neutron actually passed through on its way to the target. If we do this we find, amazingly, that the interference pattern disappears.

How on earth can we resolve these strange ambiguities? The only way seems to be to say that when both slits are open an individual neutron interferes with itself. In fact we are forced to say that an individual neutron passes through both slits!

Suppose we replace the neutrons by light, which had been classically thought of as a wave motion. The pattern observed is the same as that for neutrons. However, light has been shown to occur in discrete quanta of energy known as photons. Therefore light arrives at the screen as individual localized units of energy, just as the neutrons did. When the light intensity is low one can make out the individual spots. But wavelike behavior is observed when both slits are open and there is strong light intensity. Then one obtains just the same sort of interference pattern as with the neutrons. Again, if a photon detector is placed at one slit to determine which slit any photon has gone through, the interference pattern disappears.

The two-slits experiment shows that atomic particles such as neutrons or electrons have wavelike properties and that light, which propagates as a wave, also has particle properties. Which kind of property is exhibited in an experiment depends on the question being asked by the experiment itself, that is, just what is being measured. This phenomenon is known as wave-particle duality.

This experiment, and others, have led to the formulation of the rules of quantum mechanics, according to which a system remains in a combination, called a “superposition,” of alternative possible states until a measurement is made. The state of a system is described by a quantity called the wave function, whose change over time is described by a differential equation, Schrödinger’s equation. But this wave function only gives us the probability of finding the system in any of the possible states at any given time. When a measurement is made we say that the wave function “collapses” to a particular value.

Heisenberg’s Uncertainty Principle

In the year 1814 the French mathematician the marquis de Laplace famously made the leap from Newton’s laws of motion, discovered a century earlier, to universal determinism. He said:

We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it – an intelligence sufficiently vast to submit these data to analysis – it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.

(Laplace 1902, 4)

The Laplacian universe runs by itself on mechanical principles, just like a watch that has been wound up and allowed to run. The laws of physics, as discovered by Newton, imply that the universe is a closed causal system. We can imagine God upholding or sustaining these mechanistic laws, but not of having any further interaction with his creation.

That picture of the way the world works has been completely overturned by quantum mechanics. This is made particularly clear by Heisenberg’s Uncertainty Principle, which tells us that it is not possible simultaneously to measure with total precision (for example) both the position and the momentum of an electron. If we measure the one accurately, the other is infinitely imprecise.

Heisenberg conducted a thought experiment in which a γ-ray microscope was used to measure the position of the electron. This is done by bouncing photons off the electron into the microscope. The problem is that if light of long wavelength is used then the accuracy of position measurement is poor, but using short-wavelength (high-frequency) light (γ-rays) imparts energy to the electron and makes its momentum more uncertain.

Most physicists believe that this indeterminacy reflects “the way the world is,” that is, it is ontological and not merely epistemological. It is not due to some fault or inaccuracy in our measuring instruments. The wave function does indeed evolve deterministically (according to Schrödinger’s equation), but it only tells us the probability of a particular event occurring.

The main alternative interpretation is that of David Bohm. This maintains determinism but at the cost of introducing “hidden variables.” It must also account for “non-locality,” that is, the possibility that widely separated particles can form a unified quantum system, as discussed below. Most physicists consider this to be too ad hoc to be plausible, though in doing so they are making a metaphysical decision rather than adopting a position demanded by the science.

The picture that emerges is one in which successive events occur according to chance, though with a definite probability, in total contrast to the Laplacian deterministic picture, in which each successive event is totally determined by those which have gone before. However, when matter is aggregated together to the macroscopic scale, the scale of everyday objects, the quantum uncertainty tends to disappear and determinism rules again. The motion of all the atoms comprising a billiard-ball is probabilistic, but when these motions are aggregated, the motion of the ball is determined by Newton’s laws. Newton’s laws are a highly accurate approximation to the laws of quantum mechanics at the macroscopic scale, so accurate that all uncertainty is effectively removed. However, quantum theory has more surprises in store, as we now discuss.

Schrödinger’s Cat

This unfortunate animal, in Schrödinger’s vivid thought experiment, is incarcerated in a sealed box which also contains a radioactive atom with a fifty-fifty chance of decaying in the next hour, emitting a γ-ray in the process (Polkinghorne 2002, 51–52). If this emission takes place it is recorded by a Geiger counter, which triggers the breaking of a vial of poisonous gas into the box, and this quickly kills the cat. If the atom does not decay in the allowed time the cat survives. The experiment ends when we lift the lid from the box to see if the cat is alive or dead.

The paradox arises because the orthodox interpretation of quantum theory tells us that before I lift the lid from the box the cat is in a fifty-fifty superposition of the two states “alive” and “dead.” The question as put by John Barrow is:

When and where does this crazy mixed-up, half dead, half alive cat change state from being neither dead nor alive into one or the other? Who collapses the cat’s wave function, the cat itself, the Geiger counter, or the physicist? Or does quantum theory not apply to “large”, complicated objects, though it does to the smaller ones of which the large are composed?

(Barrow 1988, 152).

This seems to be a macroscopic effect of considerable magnitude arising out a quantum mechanical substrate and posing some perplexing philosophical questions.

The Einstein-Podolsky-Rosen Experiment

Einstein was deeply skeptical about quantum theory, as indicated by the quotation at the beginning of this chapter. He and two collaborators, Boris Podolsky and Nathan Rosen, conceived a famous thought experiment which they believed undermined the theory and which has given rise to what is now known as the Einstein-Podolsky-Rosen (EPR) paradox.

In quantum theory, elementary particles possess a property called “spin” and for convenience we can think of them as tiny tops, although in reality they are unpicturable. Suppose that an electrically neutral particle with spin 0 decays into an electron and a positron, each possessing spin ½ in natural quantum mechanical units. Suppose these particles move directly outwards in opposite directions. Since spin is conserved in this process, if we measure the spin of the electron in some direction, then the spin of the positron must automatically be in the opposite direction. These particles might now be light years apart, even at opposite ends of the universe. Measurement on the one seems to communicate its effect to the other faster than the speed of light – in fact, instantaneously – in violation of Einstein’s own theory of relativity.

Everything would be alright for this experiment on a classical picture, since the spin states would then be fixed at the decay time. The experiment would only bring to light an already existing state of affairs. The problem arises because in quantum theory it is the act of measurement which fixes the spin of the electron – it is indeterminate up to that point. Hence the instantaneous transmission of the opposite value to the positron and hence the paradox.

It is possible to design an experiment to test whether quantum mechanical systems have the property known as “local realism.” If a system is “locally realistic” then measurement on it is independent of measurement on another system from which it is widely separated. John Bell derived a set of inequalities which would apply to the classical case but be violated in the quantum case, and experiments by French physicist Alain Aspect have confirmed the reality of the EPR paradox – these effects do in essence travel faster than light. Quantum theory thus exhibits non-local effects; there is an interrelatedness between different parts of the universe of a most fundamental kind. Isolation of the phenomena under discussion, as traditionally done in science, is intrinsically impossible, and a new holism reigns.

Physics has traditionally been thought of as the most reductionist of the sciences. Physicists have always wanted to split things up into smaller and smaller constituents with a view to treating these constituents independently and isolating systems from extraneous effects. The EPR experiment and the verification of its paradoxical predictions show that holism, and not reductionism, reigns at the most fundamental level in physics (Polkinghorne 2002, 80).

Interpretation: Quantum Reality?

Quantum theory is quite clearly saying something very strange about reality. Most physicists just get on with the job, and ignore the philosophical implications of their subject. Quantum mechanics is highly successful. It has been verified by countless experiments and keeps making predictions which are verified. But what does it all mean?

The interpretation we have been implicitly working with is the so-called “Copenhagen interpretation,” associated especially with Niels Bohr, who worked in Copenhagen. This would be the working interpretation of most physicists who give any thought to such issues. It embraces the features we have described: wave-particle duality, ontological indeterminism, and collapse of the wave function when a quantum system interacts with a classical, macro-scale measuring device.

One way of understanding this interpretation is in a positivist or instrumentalist sense, as Bohr himself appeared to do. The concern then would be with only what is measurable – pointers on scales, marks on photographic plates, and so on. Reality would be understood as “created” by acts of measurement, and physics would be merely a set of calculational procedures. I agree with Polkinghorne that such an approach should be rejected, on the grounds that it denies a fundamental motivation which physicists generally have in doing science – that is, to understand the underlying reality (Polkinghorne 2002, 84–86).

One of the main problems with the Copenhagen interpretation is that it creates a divide between the classical and the quantum mechanical. The classical measuring instrument is made up of parts which are ultimately quantum-mechanical in character. How does it come about that the quantum-mechanical level is obliterated in the large-scale instrument? This is the so-called “measurement problem.” One development which seems to help in solving this problem is the notion of “decoherence.” This relates to the interaction of a classic object with its environment. For example Schrödinger’s cat, whether alive or dead, will interact with the air molecules in the box and the “alive” and “dead” states will not interact but “decohere.” The upshot would be that the cat is not in a superposition of states but definitely alive or dead.

An extreme interpretation of quantum theory is that reality is not instrument-created but “observer-created.” This idealist view gives consciousness pride of place in bringing about reality through a kind of “backwards causation.” The physicist John Wheeler has adopted a view like this which he calls “it from bit.” It is, however, highly paradoxical to assert both that non-conscious matter pre-exists and causes my existence and that I cause its existence. And surely the result of an experiment is decided by the imprint on the photographic plate at the time the experiment happens, rather than by me three months later when I take the plate out of the cupboard and look at it! However, there is an interesting theological analog to this. As noted by Barrow and Tipler (1986, 470–471), this line of speculation can lead to the idea that all quantum events are coordinated by an Ultimate Observer who, by making the Final Observation, brings the whole universe into existence. This being would resemble the idealist Bishop Berkeley’s picture of God, albeit a resemblance which Wheeler may well not welcome (Midgley 1992, 206–211).

A realist interpretation in contrast stresses the belief that the world has an objective existence independent of any observer; it stands over against us as an entity in its own right. This world is populated by entities such as electrons and positrons. By observation we can probe what this world is like and attempt to understand its laws. In doing so we submit to the way things actually are.

This realist view is certainly the way scientists in general view their activities and their discoveries. It is supported by the success of science, and the way in which the world has a habit of surprising us (not least through quantum phenomena) speaks against it being merely constructed by our minds. But quantum theory clearly leads us to question a straightforwardly objective view of the world.

The wave function must play a pivotal role in our interpretation. It is clearly not a physical object in the way a billiard-ball is a physical object. Yet it would seem that neither is it merely a calculational device. It describes the objectively real state of the electron even if the reality of the electron itself is “veiled” from us and unpicturable. The wave function evolves in time according to Schrödinger’s equation, which is a differential equation just like the differential equations of classical physics. The difference is that the wave function gives only the probability that a measurement will give a particular result. To say that the electron does not exist between measurements seems far too pessimistic: it is a real entity which has the potentiality to exhibit definite properties when measurements are made.

There is another, highly extreme and quite bizarre, version of realism. This is Hugh Everett III’s many-worlds interpretation. This states that wave functions do not actually collapse, but that all possibilities are realized. Each time an experiment is done which has several possible outcomes, the world splits into different branches which have no causal contact with each other. I am being repeatedly cloned as copies of myself multiply and pursue separate lives in the many worlds into which my world is splitting.

William of Occam advocated that in any explanation entities should not be multiplied beyond necessity. This principle of “Occam’s razor” has proved highly successful in sifting and selecting scientific theories. Everett’s many-worlds interpretation of quantum mechanics would seem to be highly anti-Occamite.

Critical Realism in Science and Theology

One area of comparison between science and theology is the realist–positivist–idealist debate. It would seem that in both science and theology some form of critical realism is the preferred option. In the case of physics, realism states that there is a real world out there to be discovered. Genuine scientific discoveries disclose something about real things. Theology would endorse that, the doctrine of creation telling us that this world is the free creation of an omnipotent, omniscient, all-good God. Orthodox theological discourse would also speak of God as real, indeed as the ultimately real who gives reality to everything else.

In physics, quantum theory shows us that a naive, common-sense realism is inadequate, but that some form of critical realism is more appropriate. Subatomic particles exist as real entities but are totally unlike the macroscopic objects we can readily grasp. Similarly in theology, God is real and has effects, but, since he is “qualitatively other,” his reality is veiled and our knowledge of him has to be mediated in a number of ways – through creation itself; through revelation in Scripture; and through religious experience, which is mediated through the senses. All of these sources of revelation need careful interpretation, of course. So again, a critical realist position is reasonable (Polkinghorne 1998, chapter 5).

The great Protestant theologian Karl Barth said that we have to know God as he has revealed himself to be, on his terms, and for Barth this is uniquely in the person of the incarnate Son and as Trinity. This is why Barth (1957) repudiated all natural theology, which he saw as the human attempt to have God on our terms, not his. Barth’s disciple Thomas Torrance took a similar line (Holder 2009). While I take a more positive view of natural theology than Barth or Torrance, I agree that God’s clearest disclosure of himself to humans is in Christ. The analogy here with quantum theory is that just as we have to accept the reality of the world, in all its strangeness, as it is disclosed to us by observation and experiment, and not according to any preconceived notions we might have, so also if God has revealed himself to us in Christ then that is where to look for the reality of God. Moreover, the methods and tools of theology need to be appropriate to the task of theology, just as the methods and tools of quantum theory are appropriate to that realm of enquiry and not simply adopted from elsewhere, which in this case would be classical physics.

Determinism, Human Free Will, and Divine Action

Quantum theory, at least under the interpretation favored by the overwhelming majority of physicists, shows that nature is not deterministic but probabilistic. Determinism is, I believe, damaging for a religious perspective. It means that we have no genuine free choice. How then could we be held responsible for our actions?

One answer to this question would be to affirm the compatibilist account of free will. This merely requires that I do what I want and am not constrained, say by another person, to do what I do. The determining factors of my actions are within my biological makeup (my neurons really did “make me do it” and their deterministic behavior does not negate this kind of free will).

Many philosophers, however, conceive of free will in the libertarian sense whereby I could have acted otherwise. There are genuine choices open to me and I choose which of several possible actions to take. For this kind of freedom indeterminism is a necessary but not sufficient condition. Thus the standard probabilistic, Copenhagen interpretation makes libertarian freedom possible but by no means guarantees it. Similarly with regard to divine action, God is not simply upholding deterministic laws which he has decreed from the foundation of the world but is able to act within the openness and flexibility of indeterminate, unpredictable processes.

Compatibilism therefore fits with the Bohmian interpretation of quantum theory because it does not require genuine uncertainty. The many-worlds interpretation is also deterministic, insofar as all possible outcomes of my decisions occur, but that makes both compatibilist and libertarian freedom look decidedly odd. Of course it may be preferable to speak of clones of me making these alternative choices, but then, if they are all of identical makeup, there is no sufficient reason for me to do what I do in this particular universe.

For some significant figures in the modern dialogue between science and religion, then, it is the probabilistic nature of quantum theory as standardly interpreted which makes possible both human free will and divine action in the world. A significant recent exemplar would be Robert John Russell.

Russell calls his a “bottom-up, noninterventionist, objective approach” to divine action. It is clearly “bottom-up” since it sees God as acting at the lowest level of the hierarchy of sciences rather than through higher-level influences of complex systems on their parts (“whole–part influence” or “downward causation”). However, Russell stresses his belief that other modes of divine action besides that at the quantum level will be required in an overall picture (Russell 2001, 294). His view is non-interventionist because the probabilistic laws of quantum physics are not violated. It does not, therefore, invalidate a “methodologically naturalist” approach to the scientific enterprise, nor does it invoke a “God of the gaps.” It is objective because these acts are objectively special acts, bringing about objective changes in the physical world which would not occur otherwise. Russell lists many quantum events which are not simply acts of measurement, and many ways in which quantum events influence the macro level.

Does God act in every single quantum event on this kind of model? The danger here is that determinism returns, albeit in the different sense that God determines everything and there is no real role for secondary causes. This was the view of physicist-turned-theologian William Pollard (1958), who pioneered this way of thinking about divine action, and also of neuroscientist Donald MacKay (1978, 30–31). Chance events at the level of physics would then not really be chance events at the deepest level of theological truth about reality. This theological determinism would, like physical determinism, negate the possibility of libertarian free will, and in addition exacerbate the theodicy problem.

Nancey Murphy, another significant contributor to the discussion, believes that God does indeed act intentionally in all quantum events. Regarding Pollard’s view as occasionalism (God alone determines every natural process), Murphy is more nuanced, seeing God’s action as mediated, that is, God acts together with nature. Thus on the one hand subatomic particles possess innate powers given to them by God, such as that of electrons to repel rather than attract other electrons, and God respects the integrity of these devolved powers. On the other hand, there is no sufficient reason for the results of quantum measurements to come down one way rather than another. Murphy says that “God must not be made a competitor with processes that on other occasions are sufficient in and of themselves to bring about an effect,” and there is indeed no such competition because “the efficient natural causes at this level are insufficient to determine all outcomes” (Murphy 1995, 343).

Russell is impressed by Murphy’s approach (Russell 2001, 315) but disagrees with Murphy about human free will. Murphy thinks that quantum indeterminacy is not necessary for top-down causation to be effectual for this, whereas for Russell “the somatic enactment of incompatibilist human freedom requires lower-level indeterminism” (317). This leads Russell to see God acting in all quantum events in the universe until life and consciousness arise but then gradually refraining from determining outcomes (318). Both Russell and Murphy agree that God is continuously active in upholding the laws of nature with which he has endowed the universe, but see this as insufficient adequately to describe God’s action in history as revealed in Scripture. They also believe that divine action in their sense is necessary for intercessory prayer to be meaningful.

A problem arises because, as noted above, quantum indeterminacies tend to disappear at the macroscopic level. Peter Clarke, for example, argues that they are irrelevant at the level of brain function (Clarke 2010), and in any case free will requires more than randomness. For both human and divine action, quantum events would need to be agent-controlled and yet would not have to conflict with the probabilistic laws. John Polkinghorne sees the influences that do or might occur, by their “episodic nature,” to be inadequate to describe the “flexible actions of agents” (Polkinghorne 2001, 189), and therefore turns to chaos theory as a more promising locus for both human and divine action in the world.

Chaotic systems are theoretically deterministic but unpredictable in practice. This is because errors in the initial measurements propagate exponentially, rather than linearly as in predictable systems. To obtain accurate predictions the initial errors will ultimately have to be reduced to infinitesimal proportions. Polkinghorne gives the example of molecules in a gas, which behave essentially like small billiard-balls:

After less than a microsecond, fifty or more collisions have taken place for each molecule. After even so few collisions the resulting outcome is so sensitive that it would be affected by the variation in the gravitational field due to an extra electron on the other side of the universe – the weakest force due to the smallest particle the furthest distance away!

(Polkinghorne 2005, 35)

Of course unpredictability and indeterminism are not the same thing. However, the requirement of infinitesimal accuracy leads us back to the quantum world with its intrinsic uncertainty. But then a further problem arises owing to the severe, and as yet unsolved, technical problems of matching the quantum and macroscopic realms.

Meanwhile Polkinghorne questions whether we are right to stipulate deterministic laws with unpredictable behavior following from them. “Which is the approximation and which is the reality?” he asks (Polkinghorne 1991, 41). Indeed, why should we take deterministic laws as anything other than useful approximations to reality, especially when we know we have free will because we experience it? Moreover, we have obtained the lower-level laws by treating systems as if they were isolated from the whole, a procedure intrinsically impossible. Polkinghorne writes:

There is an emergent property of flexible process, even within the world of classical physics, which encourages us to see Newton’s rigidly deterministic account as no more than an approximation to a more supple reality.

(Polkinghorne 2005, 35–36)

Polkinghorne suggests a form of downward causation through the input of active information, whereby the simple deterministic, and approximate, laws emerge at a lower level from high-level behavior which does not possess this property (Polkinghorne 1998, 63ff.). To see God acting by downward causation would be analogous to our minds influencing matter. This happens in any act of will, for example when I intentionally raise my arm, and without violating any laws of nature. Might not the mind of God similarly, yet far more powerfully, act on the matter of his created universe?

Whether God acts in any of the ways suggested is of course highly speculative, and it would be dangerous to dogmatize, yet modern science does seem to be opening up possibilities denied to us by the viewpoint of Laplace. The world of modern physics is a world of regularities described by natural law (these laws given and faithfully sustained by God), but also a world with a genuine openness, flexibility, and freedom. Within that freedom lies man’s own free will as a conscious, rational being, and also God’s freedom to fulfill his special providential care for humans and the rest of creation. And rather than focusing on one route to divine action, perhaps we should humbly leave the question open as to exactly how in fact God does act.

Consonance with Christian Doctrine

Although we could not predict the kind of world shown to us by quantum theory without doing the experiments, it does seem to be a world consistent with the kind of world the Christian God would create. And we can say more about this with regard to specifically Christian doctrine as opposed to mere theism: these strange features are consonant with the kind of world one would expect the God described by the Nicene and Chalcedonian formulations to create.

According to Christian doctrine, God is fundamentally relational. God is one, yet God is also Trinity; God is three persons enfolded in a relationship of perfect love. Moreover, each of the persons is fully God. The persons are distinct yet inseparable and interrelated. According to the doctrine of perichoresis formulated in the early Church, the three persons are bound together in a kind of mutual indwelling.

Quantum holism, as demonstrated by the EPR thought experiment, is analogous to this. The electron and positron, though distinct and widely separated, yet form a unified quantum system (Polkinghorne 2004, 73ff.; 2010).

According to the Chalcedonian definition, our Lord Jesus Christ is fully God and fully man. He is one person, the Son of God, but with two natures, divine and human. This reminds us of the wave-particle duality of subatomic particles discussed above. An electron is one thing but possesses both particle and wave properties.

A further analogy might be drawn with the distinction made by the Fathers between the “immanent” Trinity and the “economic” Trinity. The idea of the immanent Trinity concerns what God is in himself, the inner relations between the persons. The economic Trinity concerns how he reveals himself for the sake of the “economy,” that is, how in the divine plan the persons of the Trinity relate to the world and its salvation. Thus, while the Son and Spirit are eternally one with the Father in the being of the Godhead, they are manifested in the economy, and thus made known to us as distinct from the Father, in the Incarnation and in our sanctification. In a somewhat analogous way, the electron’s reality is veiled until a measurement is made.

Of course, none of this is to claim that quantum theory proves Christian doctrine correct. However, I believe it does two things. First, it shows that theology and science are alike in using analogical language, even apparently paradoxical language. For example, the mystery of God is expressed in the phrase “one God, Father, Son and Holy Spirit.” Wave-particle duality would be doing a similar job in quantum theory to express the veiled mystery of the electron.

Second, it links theology to science by saying that the world revealed by quantum theory is consonant with what would be expected on the basis of Christian doctrine, so that a relational God is likely to create a relational world. As Polkinghorne rightly says, this is indeed not to prove that God is relational, or that theology can make predictions from its doctrines about the physical world, but it is to say that theology and science fit together very comfortably and are far from contradictory.

References

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Barth, K. 1957. Church Dogmatics, vol. 2.1. Edinburgh: T. & T. Clark, pp. 162–178.

Clarke, P. G. H. 2010. Determinism, Brain Function and Free Will. Science and Christian Belief, 22(2), pp. 133–149.

Holder, R. D. 2009. Thomas Torrance: “Retreat to Commitment” or a New Place for Natural Theology? Theology and Science, 7(3), pp. 275–296.

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