GOD, CHAOS, AND THE QUANTUM DICE by Jeffrey Koperski Abstract. A recent noninterventionist account of divine agency has been proposed that marries the probabilistic nature of quantum mechanics to the instability of chaos theory. On this account, God is able to bring about observable effects in the macroscopic world by determining the outcome of quantum events. When this determina- tion occurs in the presence of chaos, the ability to influence large systems is multiplied. This paper argues that, although the proposal is highly intuitive, current research in dynamics shows that it is far less plausible than previously thought. Chaos coupled to quantum mechanics proves to be a shaky foundation for models of divine agency. Keywords: chaos; divine agency; noninterventionist; quantum mechanics. "If active force should diminish in the universe by the natural laws which God has established, so that there should be need for him to give a new impression in order to restore that force, like an artist's mending the imperfections of his ma- chine, the disorder would not only be with respect to us but also with respect to God himself: He might have prevented it and taken better measures to avoid such an inconvenience, and therefore, indeed, be has actually done it. ” -G. W. Leibniz Although some of the terms in this passage are no longer part of the physicist’s vocabulary, the issue addressed by Leibniz endures. This quote is from his famous Correspondence with Newton’s disciple Samuel Clarke. Jeffrey Koperski is Assistant Professor of Philosophy at Saginaw Valley State Univer- sity, 7400 Bay Road, University Center, MI 48710. His e-mail address is koperski@svsu. edu. Earlier versions of this paper were read at Theology and the New Physics, a confer- ence at Calvin College in April 1999, and at Religion and Science: Tension, Accommoda- tion, and Engagement, a conference at Ohio State University in May 1999. Work on his paper was supported by the Pew Charitable Trusts through the Summer Seminars in Chris- tian Scholarship at Calvin College 1998. Zygon, vol. 35, no. 3 (September 2000): 545-559. © 2000 by the Joint Publication Board of Zygon. ISSN 0591-2385 545 In it Leibniz stakes out a position at the intersection of science and philo- sophical theology. The question is this: How does the theistic God inter- act with the physical universe? Clarke had been arguing for the more traditional view in which God intervenes in the natural order from time to time. Some of these interventions are miraculous; others are unobserved physical nudges (say, to keep the planets in their proper orbits). Leibniz argues that Clarke’s tinkering God would lack either knowledge or ability. A perfect being would not need to make periodic adjustments to its cre- ation; hence, God does not intervene in the natural order. Current work on divine agency deems Leibniz’s God too passive, too deistic. Whatever the causal joint between God and the cosmos, it must allow for a more active, ongoing governance. On the other hand, Clarke’s God is considered by many to be too intrusive, and so the Leibnizian intu- ition about a tinkering deity continues to shape the debate. Several pro- posals have been offered as part of a noninterventionist program that pur- ports to steer a middle way. Many of these appeal to the probabilistic character of quantum mechanics (see Murphy 1995; Tracy 1995; Russell 1995). According to one version of what might be called a “quantum determination” view of divine agency, If there are causal gaps in the ultimate physical processes of the cosmos, those gaps provide space for [divine] intervention that would still be wholly within the bound- aries of natural law. For example, God could either bring about or prohibit the radioactive decay of a particular atom at a particular time, but given the way proba- bilistic laws function, either of those would be totally within the bounds of all of the relevant physical laws. (Ratzsch 1996, 187) Thus, God can manipulate the ontic probabilities (in contrast to mere epistemic uncertainty) found in quantum mechanics to exercise will in creation without violating any law of nature. It seems to me--and to others, John Polkinghorne the most prominent among them--that quantum determination (QD) is too limited in scope to provide a robust account of divine agency. (For recent critiques see Polkinghorne 1995; Saunders 2000.) The bottom line is this: QD does not provide sufficient freedom for God to significantly influence macro- scopic events. Probabilities enter into the quantum mechanical picture only during the so-called collapse of the wavefunction. Schrodinger's equa- tion itself is completely deterministic. Indeterministic events occur only during measurements,’ at least on the orthodox interpretation of quantum mechanics that QD advocates (Nancey Murphy, for example) seem to pre- suppose. The problem is that such events seldom influence macroscopic systems-one of the enduring lessons of the Correspondence Principle. Nonrelativistic macroscopic bodies (almost always) obey classical mechan- ics, and no amount of quantum manipulation can change that. Hence God's ability to influence the macroscopic world would be quite limited Jeffrey Koperski 547 under QD. Granted, these matters deserve a more rigorous treatment, but on the basis of this proto-argument I press on to consider the most promis- ing descendant of this approach. A recent refinement of QD makes use of advances in nonlinear dynam- ics (chaos theory). Murphy has taken some very cautious steps in this direction (Murphy 1995, 348-49); Thomas Tracy also leaves the door open but recognizes that there are problems yet to be addressed (Tracy 1995). The idea is that systems displaying sensitive dependence on initial condi- tions (SDIC) enhance God's ability to work through quantum probabili- ties: a slight fluctuation determined by God at the quantum level can dra- matically affect the evolution of nonlinear macroscopic systems. Let’s call this view chaotic quantum determination (CQD)3. The argument is this: 1. Every material system, including those that evolve chaotically, is ulti- mately composed of subatomic particles. 2. The behavior of these particles is governed by QM. 3. QM entails the existence of stochastic/probabilistic events rather than the purely deterministic events found in classical mechanics. 4. The outcome of these probabilistic events can produce a change of state in the classical chaotic systems in which the particles are found. 5. God can determine the outcome of these probabilistic events. 6. Therefore, God can determine the future state of every chaotic system. In this paper I argue that, although CQD is highly intuitive, it rests on questionable assumptions. The first assumption is that nature is suff- ciently chaotic for it to be an effective amplifier of quantum fluctuations. Most philosophical and theological discussions of nonlinear systems fail to consider that chaos comes in degrees. As we will see, real-world systems are not as chaotic as one might infer from popular accounts. But if chaos is not as prevalent as CQD advocates believe, then the motivation for mov- ing from QD to CQD is diminished. Second, I argue that premise 4 is at best oversimplified and perhaps just false. The difficulty lies in a fundamental mismatch between QM and classical chaos, sometimes referred to as the problem of quantum chaos. For the amplifying effects of chaos to come into play, quantum events under CQD must have a specific manifestation at the macroscopic level: they must produce a change of state. That such events have this effect on cha- otic systems is obvious to CQD advocates. I maintain that tracing the causal chain from one realm to the other is not a simple task.4 Moreover, if this presupposition proves false, the entire program fails. Before considering these challenges in detail, let us briefly review why CQD is an improvement over QD. CHAOTIC QUANTUM DETERMINATION Murphy describes QD this way: . the general character of the entire macroscopic world is a function of the char- acter of quantum events.... We can imagine in a straightforward way God's effect on the quantum event that the experimental apparatus [for Schrödinger’s cat] is designed to isolate; we cannot so easily imagine the cumulative effect of God's action on the innumerable quantum events that constitute the cat's existence. Yet this latter is equally the realm of divine action. (Murphy 1995, 357; emphasis added) The picture presented is straightforward: the behavior of the parts (quan- tum events) determines the behavior of the whole (macroscopic events). Every material object is therefore subject to quantum determination. Just as a sufficient accumulation of snowflakes can eventually produce an ava- lanche, God’s determination of a massive number of quantum events can have observable effects. The problem is that indeterministic quantum events very seldom influ- ence the behavior of macroscopic objects, for reasons already mentioned. (The subatomic parts of macroscopic objects typically obey the fully deter- ministic Schrödinger's equation.) The trick for QD is to find a way for God to amplify tiny quantum fluctuations in order to significantly influ- ence the material world. CQD has evolved from QD as a means to bolster this weakness in the causal chain. For any system evolving chaotically, a slight perturbation will produce a dramatic change in the future state of the system. How slight? When astronomers plot the orbits of the planets in our solar system, they ignore the gravitational pull of everyday objects. Mount Rushmore, my house, and Arthur, our family cat, are simply too small to make a difference. If, however, Arthur suddenly disappeared from the surface of the earth, the gravitational change would significantly affect the motion of Hyperion, the chaotically tumbling moon of Saturn.