Fortnightly Club of Redlands

Table of Contents

Introduction………………………………………………………………………...	1

Part I: Quantum Theory…………………………………………………………...	3
A History of Quantum Theory……………………………………………………..	3
Hidden Variables Theories………………………………………………………...	15
David Bohm: Causal Interpretation………………………………………………	17
Another Deterministic Interpretation of Quantum Mechanics…………………….	20
“Many Worlds” Interpretation……………………………………………………..	22
“Many Minds” Interpretation……………………………………………………...	23
Bell’s Theorem…………………………………………………………………….	24
The Case for the Copenhagen Interpretation………………………………………	26

Part II: Divine Action……………………………………………………………...	27
Defining God………………………………………………………………………	27
The Nature of Approaches to Divine Action………………………………………	28
Quantum Divine Action……………………………………………………………	29

Part III: Proponents of Quantum Divine Action…………………………………..	31
William Pollard…………………………………………………………………….	31
Thomas Tracy……………………………………………………………………...	33
Nancey Murphy…………………………………………………………………..	37
Robert John Russell………………………………………………………………..	39

Part IV: A New Perspective……………………………………………………….	43
A Panentheistic Construction…………………………………………………….	43
The Trouble with Quantum Divine Action………………………………………...	48
Chaos……………………………………………………………………………….	52
Quantum Chaos…………………………………………………………………….	53

Conclusion………………………………………………………………………….	54
About the Author…………………………………………………………………...	55
Works Cited………………………………………………………………………..	56

Introduction
“For the belief in a single truth is the root cause for all evil in the world.” Bravo Max Born, for summarizing such a profound concept in this elegant succinct statement. This idea has been instrumental in my spiritual and intellectual growth. Science and religion were both integral parts of my growing up experience. I can recall as a young child being conscious of subtle differences in plants and living creatures, playing with my miniature chemistry lab, and exploring tangram puzzles. Both of my parents have a deep understanding and appreciation of mathematics and the sciences, and they made every effort to expose me to those disciplines. When I took my first physics class in high school, I had a passion for it unlike anything I had ever experienced. I did not experience that same passion again until my sophomore year in college when I took a course in World Religions. I was raised Catholic and have experienced and dealt with many questions and concepts that are relevant to a given faith tradition. I remember my Pentecostal great-grandmother telling me as a young child that her beliefs were true because “the Bible says so”. While I love, respect, and deeply appreciate everything she stands for, I knew at an early age this kind of thinking would not fit into my meaning of life paradigm. I fully embraced science and Catholicism, and knew in my heart that they were both true for me—I had faith that there was no conflict between the two. Growing up, I found that establishing this connection was difficult for me. I tended to think of ideas as very cut and dry, at least I wanted them to be that way. Unfortunately, life does not work like that. This paper really challenged my thought process and in doing the research and the writing, I feel able to understand the material on science and religion on a deeper level. In light of the topic of this paper, Born’s choice of using the word “evil” may not be the best. Evil in the world is not easily defined, but the implications of this statement capture the essence of my sentiments on the topic.
Throughout history, people have taken many views of the interaction between science and religion. The four main views presented by Richard F. Carlson in 2000 are creationism, independence, qualified agreement, and partnership. Neither discipline is superior to the other: While science is subject to critical reevaluation and paradigm shifts, religion is exceedingly difficult to interpret and does not give undisputed answers to ultimate questions. Robert Millikan was correct when he said, “The first fact which seems to me altogether obvious and undisputed by thoughtful men is that there is actually no conflict whatever between science and religion if each is correctly understood.” I believe that the two disciplines of science and religion should be integrated as partners to attain a deeper and more meaningful understanding of the world in which we live. Only then can the two be used to address issues whose complexity requires the explanatory power of both disciplines. Divine action in the world is an example of such an issue. Neither science nor religion succeeds in explaining this issue sufficiently on its own. Theories of quantum divine action suggest ways that God can act in the world through microscopic phenomena, and hence can be understood in terms of quantum physics without suspending natural law. The quantum world is attractive for trying to account for divine action because it is an avenue to indeterminacy, and therefore provides an account that is consistent with natural law and thus an interventionist view of divine action is avoided. This paper will outline the discovery of the strange behavior at the microscopic level and discuss several interpretations of quantum mechanics. It also discusses several views of God and His relationship with the universe. The arguments of four major proponents of quantum divine action, William Pollard, Thomas Tracy, Nancey Murphy, and Robert Russell will be presented. The aim of this paper is to show that a panentheistic view of God and the Copenhagen Interpretation of quantum mechanics can be used to construct an approach to a noninterventionist divine action at the quantum level.
Part I: Quantum Theory
A History of Quantum Theory
From the 16th to the Twentieth Century, a single way of thinking dominated the scientific theory of physics. Newtonian mechanics in combination with Maxwell’s electrodynamics were believed to be a model and a method of answering any and all physical questions. In 1687, Isaac Newton strongly states in his Principia that “[gravity] act[s] according to the laws which [I] have explained, and [those laws] abundantly serve to account for all the motions of the celestial bodies, and of our sea.” For Newton, the classical laws he derived were all that was needed to describe and predict any mechanical phenomenon one encountered. In the 18th and 19th centuries electrical and magnetic phenomena were investigated, and Maxwell gave a complete theoretical account of these in the 1860’s. In 1900, German physicist Max Planck brought the happy situation to an end. Planck’s contribution came out of a quest to find a theory for the energy density of a blackbody cavity that yielded values that were consistent with and yielded an explanation of experimental results. The interesting quality of blackbodies, bodies that absorb all of the radiation incident upon them, is that all blackbodies at the same temperature, regardless of their size, shape, and chemical composition, will have the same thermal emission spectrum. Before Planck, no one had been able to theoretically derive a formula that would correctly describe the wavelength or frequency dependence of these spectra. A formula for the energy density of a blackbody cavity derived by Lord Rayleigh and Sir James Jeans which used the classical law of equipartition of energy implied that the emission energy would go to infinity as wavelengths got small in what became known as the ultraviolet catastrophe. Planck’s world shattering claim was that the seemingly unexplainable experimental phenomenon could only be explained by assuming that the blackbody was emitting energy in discrete bundles, or quanta. Planck found that the energy of these bundles was related to the frequency of light by

where Planck’s constant h = 6.626 x 10-34 Js. This implied a violation of the law of equipartion of energy, a result of classical statistical mechanics. The Pythagorean Theorem is an example of a mathematical relation to which there are no exceptions. Before 1900, classical mechanics had this same unquestioned almost axiomatic status. Planck’s theory of cavity radiation was only the beginning of a major paradigm shift in physics.
The photoelectric effect is the phenomenon which is explained today by averring that electrons are ejected from a metal surface by the action of light almost instantaneously. It had been observed as early as 1887 by Heinrich Hertz who noticed it while performing a series of experiments investigating electromagnetic waves. In 1905, German physicist Albert Einstein successfully explained the photoelectric effect by considering the beam of light as a burst of discrete particles known today as photons. He found that for light of a given frequency ν, these particles had a constant energy, . This was quite peculiar considering that Thomas Young had conclusively demonstrated the wave nature of light with his double-slit experiment more than one hundred years before Einstein’s explanation. Despite the revolutionary nature of this discovery, the great scientific minds of the early 1900’s would in no way be anticipating an even greater marvel that was yet to be realized: light was not the only entity that displayed a dual nature—that of both wave-like and particle-like aspects.
The nature of the atom remained a mystery until Danish physicist Niels Bohr utilized the idea of light as a particle and proposed that atomic electrons are also ‘quantized’ in the sense that they can remain at fixed energy levels around the nucleus in his seminal paper on the hydrogen atom in 1913. Much like the experimental paths of blackbody emission spectra, New Zealand-British physicist Ernest Rutherford’s previous model of the atom could not be completely understood classically. According to Maxwell’s theory of classical electrodynamics, a charge moving in a curved path is accelerating and thereby emits radiation and should spiral closer and closer to the nucleus until it eventually crashes into the nucleus. Bohr proposed that this can be resolved by assuming that when electrons, which naturally reside at certain fixed energy levels in an atom, jump between these levels, energy is released as electromagnetic radiation in discrete packets, now known as photons. It was becoming dreadfully apparent that many laws of the macroworld did not apply to the microworld.
In his doctoral dissertation presented in 1924, French physicist Louis de Broglie theoretically proposed that like light, matter exhibits a wave-particle dichotomy. The wave nature of matter was observed experimentally later that year when American physicists C. J. Davisson and L. H. Germer scattered low energy electrons from the surface of a metal crystal and observed peaks that were interpreted by them as the diffraction of the associated electron wave. One remarkable experimental result of particles displaying wavelike properties is the tunneling effect, which was not explained until 1928 by Russian physicist George Gamow. The tunneling effect is that: whereas in classical physics, when a particle meets a potential barrier it lacks sufficient energy to overcome it. However, in the quantum world, it has a nonzero probability of actually tunneling through the barrier.
Soon after de Broglie’s doctoral presentation, two very different theories were introduced as a result. In 1925 German physicist Werner Karl Heisenberg developed a theory commonly called matrix mechanics. With the aid of Max Born and Pascual Jordan, he was able to associate the position and momentum of a particle with matrices in the following way . Let X be an array (or matrix) representing the position of an electron and let P be a similar matrix representing the momentum of the electron. The relation between the two was found to be
.
In 1926, Austrian physicist Erwin Schrödinger came up with his own theory completely independently of Heisenberg’s work. Given a particle and the associated acting force system, the solution to Schrödinger’s wave equation provides both wave function solutions and allowed energies for the system. This famous wave equation is represented as follows
,
where Ψ(x,t) is the wavefunction that describes the state of a given system and V(x,t) is the potential that describes the spatial characteristics that influence and act on the particle. These two ways of approaching the same phenomenon are perhaps as different as night and day, but surprisingly enough they yield the same results. They are different in that Heisenberg’s matrix mechanics emphasized the discontinuity of physical processes and the particle-like behavior of the electron whereas Schrödinger’s wave mechanics emphasized the continuity of physical processes and the wavelike behavior of the electron. Although Heisenberg and Schrödinger took different approaches to explaining quantum mechanical systems, they came up with equivalent explanations. Today, these two theories are considered to be alternative formulations of a single theory known as quantum mechanics. It follows from this that angst and anxiety arose within the scientific community for want of a single unified interpretation of quantum mechanics.
Later that year, German physicist Max Born proposed an interpretation of the wave function with consequences that are raising questions today as much as they did when Born introduced his theory. Born suggested an interpretation of the wave function to be the probability that a particle is located at particular point in space and at a particular time. The position of an electron was not something that could be definitively determined in the way the world was accustomed to seeing classical mechanics provide definitive answers. More puzzling yet, in 1927, Heisenberg presented these ideas in quantitative form through his uncertainty principle, which gives limits to the simultaneous determination of the position and the momentum of a particle. The actual relation between the two quantities can be represented as
,

where the momentum in the x-direction is known to within an uncertainty of and the position in the x-direction x is known to within an uncertainty of . Another form of the uncertainty principle can be represented as

where ΔE is the uncertainty of the energy of a system and Δt is the time interval during which this energy is emitted. Heisenberg argued that this was not merely some experimental flaw, but that this indeterminacy was a result of the nature of the actual particles. He believed it was a fundamental uncertainty unlike a game of roulette which is probabilistic until one knows all of the variables that describe the roulette wheel. It was also in 1927 that Bohr presented his complementarity principle which says that seemingly mutually exclusive characteristics like the wave-particle dualities and certainty in position or momentum are each needed to completely describe a physical system. The complementarity principle is a key aspect of what is called today the Copenhagen Interpretation of quantum mechanics, named after the city where Bohr lived. Bohr and other advocates of the Copenhagen Interpretation would argue that physics cannot answer questions about what an electron or any other entity is; rather physics only answers questions in regards to what can be measured about these entities. The Copenhagen Interpretation is the dominant view of quantum mechanics in the scientific community today. Its popularity can perhaps be associated with the accurate experimental results that the Schrödinger and Heisenberg forms yield, as well as at least partially a result of who was tenured at major universities during that time. However, this statistically indeterministic way of looking at the quantum world has been a source of much controversy for many people. Many paradoxes have been pointed out, and many alternate interpretations have been introduced suggesting that there are actually a number of ways of interpreting quantum mechanics. In fact, the very physicists who laid the ground work for quantum theory disagreed amongst each other in terms of the ultimate meaning of quantum theory.
By the 1930s, three main schools of thought had emerged amongst the physicists whose ground breaking scientific discoveries were the introduction to the quantum world in regards to what seemed to be indeterminacy. The first has already been mentioned—it is what was advocated by Niels Bohr, referred to today as the Copenhagen Interpretation. The uncertainty is an experimental limitation that can never be overcome to get a thorough and complete understanding of the way the quantum world works. This is understood as a consequence of the role the observer plays in determining an outcome at the quantum level. If one measures the position of an electron to increasingly precise positions, the accuracy to which the momentum can be measured decreases. Thus one cannot simultaneously measure the position and momentum of a particle beyond certain accuracy. The main implication of this school of thought was that one can never know whether the world is truly deterministic or indeterministic.
The second view of quantum uncertainty is that it is merely a consequence of our present ignorance. Several physicists, including Albert Einstein and Max Planck believed that our universe is a clockwork deterministic universe, much like the world as described by Isaac Newton. Einstein expressed his reservations in the following way: “Quantum mechanics is certainly imposing, but an inner voice tells me that it is not yet 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 [God] is not playing dice [with the universe].” The main implication of this thinking was that quantum mechanics was incomplete and that evidence of determinism at that level had yet to have been discovered. More recently, David Bohm has taken a similar position and developed the pilot wave theory into a deterministic formulation of quantum mechanics that yields the same results as does the orthodox Copenhagen interpretation.
The main player in the third school of thought was Werner Heisenberg. Heisenberg came to believe that the apparent indeterminacy was a consequence of the nature of the world. Particles have inherent probabilistic characteristics. From this viewpoint, an observer does not disturb the state of a particle; rather an observer causes one of many potentialities to occur. A majority of physicists today do not regard the Heisenberg uncertainty principle as an epistemological limit but rather as an ontological statement about the inherent nature of the quantum world. Heisenberg at first thought the uncertainty principle was an epistemological principle. Later he came to see it as an ontological principle, but this idea was a choice not a consequence of the quantum formalism.
The result of having three disparate ways of understanding quantum indeterminacy has resulted in paradoxes and thought experiments intended to contradict or look further at the different metaphysical suggestions. The most famous of these is Schrödinger’s cat paradox. Some people found quantum indeterminacy unsettling because it results in the coexistence of two possible outcomes resulting from the superposition property of the wave function. In order to illustrate how peculiar this concept is, Schrödinger applied the superposition of the wave function to the macroworld with the following gedanken (thought) experiment in 1935. Suppose there is a cat in an enclosed box which contains a hammer, a vial of cyanide, a Geiger counter, and a small amount of some radioactive alpha active substance. An alpha particle has a finite probability of being emitted at any time, and if it does, the Geiger counter will detect it and trigger the hammer to fall on the vile and kill the cat. To find out whether the cat is alive or dead, an observer must open the box and find out whether the cat is either alive or dead. The question is what is taking place in the box before the lid is opened? Quantum mechanics says that while the cat is in the box and before someone observes the cat, it is neither alive nor dead, but rather is a linear combination of the two possibilities:

Figure 1: Schrödinger’s cat experiment
It is not until an observer opens the box that the wavefunction of the cat, by the act of observing it, is forced into one of the two possible states. James T. Cushing shows that this concept can be clarified by seeing mathematically how the wave function evolves into the superposition of two separate states. Initially, the wave function can be represented as :
,
where ψ represents the eigenstate, or wave function, of the microsystem which in this case is the alpha particle being emitted or not being emitted, and where is the eigenstate of the macrosystem which is the cat being alive or dead. Over time, it is unknown whether the alpha particle has been released or not. The Schrödinger equation evolves the initial wave equation into this entangled state :
.
Thus it seems that while in the box, the cat is both alive and dead at the same time. From this, Born’s statistical interpretation yields the probability the cat will be in either state by squaring the wave function. When an observer opens the box the wave function collapses and the cat is found either alive or dead. The purpose of Schrödinger’s cat paradox was to illustrate that quantum mechanics is incomplete in the sense that if the wavefunction represents one’s knowledge of the cat-alpha particle system, there is a missing link in the sense that nothing physically happens to the cat upon measurement, the state of the cat is just unknown whereas if the wavefunction represents the actual physical state of the system, the baffling consequence is that the act of measurement kills the cat and the is no objective world apart from the observer.
That same year, Einstein together with Nathan Rosen and Boris Podolsky devised a thought experiment also to portray the incompleteness of quantum mechanics. Peter Hodgson [a research physicist and a Fellow of Corpus Christi College, Oxford] explains that the EPR experiment shows how the position and the momentum of a particle can both be determined to an arbitrary degree of accuracy. However not many people agree that the consequences of the EPR experiment are this severe. There are many versions of this experiment. The fairly simple version by David Bohm follows. Suppose a neutral pion at rest decays into an electron and a positron
.
Due to the conservation of angular momentum, when the pion decomposes the electron and the positron will fly off in opposite directions with total spin zero represented by the configuration
.
In theory, one could let the electron and the positron fly hundreds of light years apart and then measure the spin of the electron. If the electron is found to have a spin up the positron will have a spin down and vice versa. By assuming that the electron and the positron are very far apart, one might assume that they are localized in that two entities cannot ‘communicate’ with each other faster than the speed of light. However, it is at the very instant that the spin of the electron is measured that the spin of the positron is known. It follows, then, that the spins of the two entities must have been determined before the measurement was made. Similarly, if a particle at rest explodes into two equal parts, A and B, one could simultaneously measure the momentum of A and the position of B and deduce the position of A and the momentum of B or vice versa by the principle of conservation of momentum. But Heisenberg’s uncertainty principle implies that one cannot simultaneously measure the position and the momentum of a particle with complete accuracy. Thus it seems that Einstein, Podolsky, and Rosen have demonstrated the incompleteness or some incompleteness of quantum mechanics. Many attempts at alternative interpretations to the Copenhagen theory have been formulated to resolve quantum paradoxes and to leave no questions unanswered.
Hidden Variables Theories
Considering the results of the EPR experiment, it would not be illogical for one to suspect a completely deterministic universe. Einstein himself spent much of his life searching for evidence that such was the case. The assumption being made is that there are variables at the quantum level which are affecting the outcome of interactions, but the current [rudimentary] experiments cannot detect the information required for a completely accurate prediction. This ideology is analogous to the Wheel of Fortune. The wheel is a seemingly probabilistic apparatus. However, if one were to consider air resistance, torque, friction, mass, and other detailed workings of the mechanism, it would be possible to determine what value would be the outcome of a given spin. Could the same be true of quantum mechanics? This line of thinking leads to what are called hidden-variables theories. Hidden variables theories assume that there are certain variables or mechanisms that, if known, would give a more complete and deterministic picture of quantum mechanics. John von Neumann presented an impossibility proof of such theories in 1932 that quieted the search for hidden variables for the next twenty years. The proof considers the angular momentum of a particle represented as a linear combination of its angular momentum in all three dimensions
,
where ℓn(t) is the particle’s total angular momentum in the unit vector n direction at time t, ℓx(t), ℓy(t), and ℓz(t) are its angular momentum in the x, y, and z directions at time t, and nx, ny, and nz, are the components of the unit vector in the n direction. The existence of hidden variables would imply that all of the observable quantities in this relation should have a definite value that could be determined with mathematical formalisms. Since n is a unit vector, each of the three components could equal one over the square root of three by the Pythagorean Theorem. Then the total angular momentum could be represented as:
.
This is equivalent to:
.
However, this cannot be true because the quantity on the left is an irrational number while the quantity on the right must be either a positive or negative integer because angular momentum is quantized.
While the math von Neumann used is correct, the proof that all hidden variables theories are impossible is logically inconsistent in that he assumed that all of the theories would possess a common property that he showed to be false. F. J. Belinfante classifies the specific type of theory von Neumann dealt with as hidden variables theories of the zeroth kind, whereas hidden variables theories of the first kind will make the exact same probability prediction as the orthodox interpretation of quantum mechanics, and hidden variables theories of the second kind are local theories that do in fact deviate from ordinary quantum theory, but are disparate from the theories with which von Neumann dealt. In 1952, David Bohm presented a hidden variables theory that like the Copenhagen Interpretation agreed with experimental results.
David Bohm: Causal Interpretation
In 1926 Max Born put forth the pilot wave theory which was later further developed by de Broglie the following year. The theory says that a particle is guided by a pilot wave which acts on it through the quantum potential. According to this theory, the hidden variables missing from the current understanding of the quantum world are very simply the positions of all the particles that constitute a particular physical system. Given enough knowledge about the initial conditions of a particle, its subsequent motion could be determined from the equations.
In 1947, Bohm was working on a book in which it was clear that he adamantly supported Bohr in the Bohr-Einstein debate. While at Princeton, he spent a lot of time discussing quantum theory with Einstein and by 1952 he published two works that revealed Einstein’s influence and his reconsideration of the conceptual basis of quantum theory. Bohm argued that even though our present observations reveal it imperfectly, there is in fact a reality at the microworld. This is where he differed from De Broglie. De Broglie understood the wave-function to be a pilot wave, not a real wave. He believed a second wave would tell the exact location of the particle. Bohm believed the wavefunction acted on a real particle which had an exact position through the quantum potential. Mathematically, Bohm rewrote an equivalent form of the Schrödinger equation similar to Newton’s second law of motion. He started by defining two real functions, let’s say and where:
.
This can be substituted into the Schrödinger equation and separated into its real and imaginary parts yielding

,
where the quantum potential U is defined as
.
If , the equation for the partial derivative of R with respect to time can be written as the continuity equation
,
where we can write
.
If P is the probability density for the distribution of particles and the momentum is the familiar , the equation for the partial derivative of S with respect to time can be written as:
,
where F is the gradient of the classical and quantum potential energy. If one considered many systems described by the same wavefunction, the distribution of the positions of the individual particles would be the same as that predicted by standard quantum mechanics. An advantageous quality of Bohm’s causal interpretation is that for one, there is no measurement problem, but also there is no struggle to connect the different behavior exhibited at the classical and quantum levels: the quantum potential U is negligible at the classical level. Cushing explains that one of the less desirable consequences of this deterministic nonlocal interpretation is that it demotes special relativity from a universal foundational theory to something demanded only of the “observational content of physical theory”. This is not all that bad since Einstein’s postulates for special relativity were based on observational consequences they were not demanded by experiment. However, they would remain postulates that accounted for experimental data that pops up in a particular physical theory. Special relativity could never be more than this—it could never be a general foundational theory that is at the root of everything. Again, this is not all that bad but it is a consequence of accepting Bohm’s interpretation.
Another Deterministic Interpretation of Quantum Mechanics
Stochastic mechanics, or stochastic electrodynamics, is based on the idea that every physical system can be influenced by its surroundings. When applied to quantum physics, the idea is that quantum systems are influenced by the fluctuating background electromagnetic field. The equation of motion for an electron would be the Newtonian equation of motion plus emission and absorption yielding the Braffort-Marshall equation , which is
,
where and F is the field tensor of the zero-point field interpreted classically. However, since the mathematics that comes with stochastic mechanics is difficult to handle, study turned to the mathematically simpler Schrödinger equation.
Although deterministic theories of quantum physics are not the most commonly accepted theories by physicists, there are several prominent physicists who support this view. Hodgson, believes the statistical interpretation of the wavefunction represents the average behavior of several similar systems, not a single system, and that the Heisenberg Uncertainty Principle refers to the relation between the spread of possible values of position and momentum and is therefore consistent with a fully deterministic world. This idea of a deterministic world is often connected to a theistic view of religion—that God is not only supreme over the world but His action in the world suspends natural law. It portrays a transcendent God as opposed to an immanent God who would have to suspend natural law if He were to act in the world. Hodgson says, “It is an impoverished conception of God to suppose that he is bound by his own laws.” This thinking has its origins in Einstein’s belief that the world exists independently of conscious life.
“Many Worlds” Interpretation
In 1957, Hugh Everett proposed the radical “Many Worlds” interpretation of quantum physics. Everett suggested that a totally deterministic universe is described by the Schrödinger equation and that it splits off into a multiplicity of causal sequences when a measurement occurs. According to this interpretation, all possible quantum worlds exist. It is helpful to apply this hypothesis to a concrete example such as Schrödinger’s cat. Quantum mechanics is not able to explain how or why the superposition of the alive/dead cat collapses into one of the possible states. Everett’s hypothesis offers an explanation of this phenomenon. According to the “Many-Worlds” interpretation, when a measurement of the state of the cat is made, the universe splits into two copies: One copy contains the live cat; the other contains the dead cat. Each copy of the universe contains a copy of the individual who made the measurement and who would think of themselves as unique. The consequence of the “Many-Worlds” interpretation is that one must accept the idea that there is an infinite number of parallel universes co-existing with the one we see.
Although it may be likened to science fiction by some, the “Many Worlds” interpretation is actually entirely consistent with the rules of quantum mechanics and it is supported by several leading theoretical physicists (e.g. Bryce DeWitt and David Deutsch). However, there are major criticisms of this hypothesis. One of these criticisms is that it is not testable. This interpretation is not testable because we live in the universe in which the outcome of a quantum event occurs and we have no access to the other universe in which copies of us as the observer experience other outcomes of the quantum event. One cannot confirm or disprove something that is not testable. Paul Davies nicely expresses the other major criticism: “It introduces a preposterous amount of ‘excess metaphysical baggage’ into our description of the physical world.” We only experience one of the infinite universes suggested by this hypothesis. Supposing that there are an infinite number of universes to explain the collapse of the wavefunction may seem like a giant leap of faith to some.
“Many-Minds” Interpretation
In reply to some of the criticism the “Many-Worlds” interpretation received, David Z. Albert and Barry Loewer formulated another interpretation of quantum physics that is generally referred to as the “Many-Minds” interpretation. In this interpretation, there is only one world and one ‘copy’ of every conscious observer in it rather than an infinite number of parallel universes. However, each observer has an infinity of minds each of which perceives one of the possible outcomes of every quantum event. Rather than all possible events taking place as in the “Many-Worlds” interpretation, all possible perceptions take place. The minds of two observers observing the same quantum event must be synchronized in such a way that they experience the same outcome. Returning again to Schrödinger’s cat, all of the observers will have the same consciousness of the state of the cat, i.e. all of the observers will perceive the cat as dead and alive, but they will all have consciousness of only one of these two possible states and it will unanimously be the same state. Like the “Many-Worlds” interpretation, the “Many-Minds” interpretation is not testable and is thus a more philosophical interpretation than some of the other interpretations that include mathematical formalisms.
Bell’s Theorem
In 1965, John Bell proved a very important mathematical theorem while studying the problem of two-particle quantum systems. He explains that he proved that “no local deterministic hidden-variable theory can reproduce all the experimental predictions of quantum mechanics”. In order to understand Bell’s theorem, it is helpful to examine the following apparatus used by David Bohm to portray the EPR experiment:

In the center of the apparatus is a source of particles that emits them to an analyzer on the left and to an analyzer on the right. Each analyzer has two particle detectors that are arbitrarily labeled “up” and “down”. Experiment has shown that if only one analyzer is studied, the outcomes of one of the three angles in combination with an “up” or a “down” detection are completely random, and that if the analyzers are aligned so that θ = φ, the detections are always complementary, i.e. when one reads up, the other reads down. Now suppose the left and right analyzers are randomly oriented at angles 0°, 120°, or 240° and that θ ≠ φ. The frequencies of the four possible outcomes (up-up, up-down, down-up, down-down) have been measured and calculated to be:
Outcomes: up, up up, down down, up down, down
Frequencies: 3/8 1/8 1/8 3/8

This result is somewhat puzzling. One might reason that the four outcomes would each have a probability of 1/4 of occurring. Interestingly, they do not. Bell proved the implications of this result to be very important for quantum theory. To understand Bell’s theorem, the following figure is helpful:

This is a unit square in which the three circular regions represent the probabilities of the analyzers being oriented at angles 0°, 120°, or 240°. It is a priori obvious that examining the three possible ways of getting an up-up detection leads to:
P[up at 0° on left, up at 120° on right] +
P[up at 120° on left, up at 240° on right] +
P[up at 240° on left, up at 0° on right] +
≤ 1

This statement is called “Bell’s Theorem” or “Bell’s inequality”. The trouble arises when the probabilities from the experiment described above are substituted into the inequality. Since P[up, up] = 3/8, the following paradox is unavoidable:
3/8 + 3/8 + 3/8 ≤ 1, but 9/8 > 1.
In words, David Wick explains that Bell’s theorem says that no deterministic, local hidden-variables theory can account for the empirical result of this experiment. Thus a completely deterministic basis for physics does not seem possible , and it seems that there is an inherent uncertainty in nature.
The Case for the Copenhagen Interpretation
These interpretations of quantum physics are all very different from each other. Some of them are more experimentally testable than others. I personally believe that all of these interpretations are worthy of careful consideration. That being said, I believe that one form of the Copenhagen Interpretation is the most satisfactory portrayal of what is occurring at the quantum level. It is John von Neumann’s assertion commonly referred to as orthodox quantum theory that the act of measurement causes the wavefunction of a given quantum mechanical system to collapse into only one of the possible outcomes that formed the initial superposition. Philip Clayton explains that this interpretation of quantum physics is necessary for a theory of quantum divine action because it allows for an ontological indeterminacy. That is, nature itself is inherently indeterminate at the quantum level. This would allow for an openness in the world in which God could act without suspending natural law.
Part II: Divine Action
Defining God
Perhaps the most difficult task of formulating an argument on divine action is defining the concept or view of the God who acts in the world. It is not enough to loosely use the term ‘God’ or even to refer to the God of Christian doctrine. The temporal, geographic, and cultural setting of Christian doctrine has changed so much that there is hardly anything close to a consensus on an interpretation of it. Worse yet, there was never a consensus on the meaning of Christian doctrine even in the first century C.E. Ignoring this fact is not an option—it is a dilemma that absolutely must be addressed. My main criticism of the arguments presented by the proponents of quantum divine action presented in this paper is that they do not adequately address this problem in that they presuppose a particular notion of God that is not fully explained.
There are several terms that are used to describe people’s understanding of who God is and how He relates to the world. These views of God are not necessarily views of the Christian God. However, many of them are often used to describe the Christian God. I define the terms here and will later discuss the view I take in more detail. Theism is the belief that there exists one perfect being who created the cosmos and continues to sustain and providentially guide it but can be distinguished from it. Deism is the belief that God brought the world into existence at the beginning of time and then left it to run on its own according to its inherent natural laws. For the deist, God’s only interaction with the world was during creation; He cannot act in the world. Pantheism is the doctrine that nature and God are identical. Pantheism threatens the idea of God’s transcendence and is therefore not often associated with Christianity. Panentheism as defined in the Oxford Dictionary of the Christian Church is “The belief that the Being of God includes and penetrates the whole universe, so that every part of it exists in Him, but that His Being is more than, and not exhausted by, the universe.” The world is in God but is more than the world. He is both immanent and transcendent. After developing the arguments of four of the major proponents of quantum divine action, I will argue for God’s action in the world at the quantum level from a panentheistic perspective.
The Nature of Approaches to Divine Action
When discussing a concept like divine action, clarity is crucial. It is equally as important to be aware of what the argument is not doing as it is to be aware of what the argument is doing. It is not my intention to present an argument that favors Christianity over other world faith traditions. Nor is it my intention to prove the existence of God. Philip Clayton explains that “the question is not how to prove that God is active in the world at particular moments, but rather how to think about this possibility in a manner that does not conflict with what we know of the world.” It comes down to the fact that one cannot subject God to experiment. The argument is not even that God acts at all. The purpose of these constructions is to show one possible way that God could act in the world without suspending natural law, and that is through the realm of quantum indeterminacy.
Quantum Divine Action
One common approach to divine action is through our understanding of physical processes at the quantum level. The quantum world is attractive for divine action because its possible indeterminacy allows for a way that God could act in the world without suspending natural law. It is helpful to see the range of ways quantum divine action can fit into an all-encompassing spectrum:

This spectrum ranges from atheism where there is no divine action in the world to theism where at its extreme God is essentially a grand puppet master. Within this range, there is a range of views of quantum divine action.
I will examine the arguments for quantum divine action from four of its major proponents: William Pollard, Thomas Tracy, Nancey Murphy, and Robert Russell. It is relevant to note that many of the scholars who discuss scientific perspectives on divine action have a Christian background. Before examining these arguments, I find it necessary to define a few terms and introduce some of the jargon. When people consider the concept of ‘divine action’, many will generally naturally think of a form of intervention, i.e. God’s action in the world that would suspend or intervene with the laws of nature. For example, in the gospel story where Jesus turns five loaves of bread and two fish into enough food to feed five thousand men (which would more accurately be about ten thousand people if one were to include the wives and children who also would have been present) He is scientifically creating matter out of nothing. However, natural law says matter can neither be created nor destroyed so if this story were intended to be historical fact, God would have been intervening with natural law to perform this action in the world. This is not the ideal approach to the understanding of divine action. The goal of this project is to construct a noninterventionist manner through which God can act in the world. When discussing different models of divine action, the idea that something caused a given event is handled in different ways. There are three general descriptions of causation that are used to describe different constructions of divine action. Bottom-up causation is the idea that phenomena can be accounted for by action at a lower level affecting higher levels. Top-down causation is the idea that phenomena can be accounted for by action at a higher level affecting lower levels. Whole-part influence is the idea that the whole determines the coordination of its parts. It is also important to understand what is meant by the term ‘quantum event’. I agree with Robert Russell that it is useful to restrict the term to certain “measurements”: irreversible interactions that are either between elementary particles and classical measuring devices, between elementary particles and microscopic objects, or between elementary particles and other elementary particles. A distinction is continually being made between general and special providence. General providence is the divine creation and sustaining of the orderly world, whereas special providence is God’s particular action within the process of creation. All of these theological constructions of quantum divine action attempt to avoid occasionalism—the concept that God is the only actor in reality and the laws of nature describe divine action instead of independent structures of reality. An understanding of these terms is important to properly analyze the following approaches to quantum divine action.
Part III: Proponents of Quantum Divine Action
William Pollard
William Pollard, a physicist and an ordained Episcopal priest, is generally considered one of the earliest proponents of quantum divine action. The concept of chance is absolutely crucial in Pollard’s understanding of quantum divine action. In fact he argued that the actual nature of the world is chance-based. He says, “Whether we like it or not, it seems to be a world in which indeterminacy, alternative, and chance are real aspects of the fundamental nature of things, and not merely the consequence of our inadequate and provisional understanding.” This ontological indeterminism is called chance within science, but for the religious person it is a place where the providential control of God is manifest. Pollard argues that God is active in all quantum events and that all quantum events display His providential character. This follows from the idea that when probability is introduced in science there are at least two different outcomes of an event and it is beyond the scope of science to decide which outcome is actualized. Pollard explains that if one takes the view of scientific determinism, divine action must occur through intervention. This view makes God and nature alternative causative agents and places them in opposition to one another: if God refrained from intervening in the world natural law would deterministically govern all interactions. However, if one accepts ontological indeterminism, God does not modify natural probabilities or suspend natural law. God can influence events without acting as a physical force. For Pollard, quantum indeterminacy is one, but not the only, branch of science that portrays the chance-based nature of the world.
There are several objectionable consequences of Pollard’s argument. First, Pollard maintains that God has total control over the world and is active in all quantum events. He believes all events have a providential character and he defends the idea of predestination. Insisting that God is active in all events exacerbates the problems of evil and suffering in the world. If God is responsible for all events, that includes the deformation of a single cell that triggers cancer and many other instances of suffering and physical evil in the world. This notion of God’s total control of all events may be understood as incompatible with human freedom. Second, Saunders points out that there is no reason that one would assume God respects the probabilities predicted by quantum theory. In that sense it seems that they are not really probabilities at all. Thirdly, Pollard’s argument is essentially an instance of occasionalism in that it is neither mind nor matter that causes events, it is God. Perhaps the most fundamental problem with Pollard’s argument is that he says God acts to determine every indeterministic quantum event. God is the hidden variable. This is paradoxical because it uses indeterminism to create a view of the world that is essentially deterministic.
Thomas Tracy
Thomas Tracy [a professor of religion at Bates College] argues that while God is not active in every quantum event, He is active in those quantum events that have macroscopic consequences and that God remains true to the bulk probabilities predicted by quantum theory. Tracy also stresses the importance of indeterminacy. He explains that several theologians (Bultmann, Kaufman) who have maintained that the world is governed by deterministic laws have argued that scientific findings are incompatible with the notion that God can act in the world and that in principle, scientific methods rule out divine action. This is where quantum mechanics is of interest. Quantum mechanics could very well be that indeterministic path to true openness in the world. There are two forms of indeterminism that could be implied here. First, it could be “epistemic chance” in which transitions between states are probabilistic, or it could be the case that individuals have free intentional action. Basically, Tracy is arguing that the openness in the world could either be the idea that quantum events are chance-based not pre-determinded or that the world is open in the sense that humankind has free-will and can alter a course of events. Tracy explains that one could argue that God determines the outcome of chance events or that God leaves some or all chance events undetermined. In the second option, God would have determined how chance plays into the course of events and what range of possible outcomes there are for a given interaction when He established the laws of nature. This option also allows for humankind to have free will. Tracy explains that God could give humankind the power to make choices that are not determined by God or anyone else. Tracy views this God-granted free will as a gift that expresses God’s care for the created world. Tracy argues that, “If we affirm that God performs particular actions which affect the course of events in the world, then it certainly appears that there will be gaps in the explanation of these events in the sciences.” For Tracy, this is not the conventional God of the gaps argument in which God is used to fill the gaps of what we do not know about the world. Rather, he argues that there are ontological gaps in the natural world, as opposed to epistemic gaps. This ontological interpretation of nature that integrates chance and law allows for “creative new developments not rigidly prescribed by the past.” Quantum mechanics is one element of the world that provides a necessary ontological gap.
There may not be many strong criticisms of Tracy’s position because he does not present a very strong argument. Tracy is adamantly against the notion that one must choose one approach rather than others. In fact he is very clear about his belief that God does not necessarily only act at the quantum level or even exclusively through causal gaps in nature. I do not necessarily agree that there must be ontological gaps in the world. I believe ontological indeterminacy is a necessity, but I do not consider it a gap in what one can understand about the world. There is a difference between the world being inherently open with an unknowable future, even to God, and there being a gap in that there are things going on that we just cannot understand. This was the difference between Bohr and Heisenberg—Bohr reasoned that our ignorance of a quantum entity’s exact position was an experimental limitation (it has an exact position and momentum but humankind will never be able to simultaneously measure both of these quantities) while Heisenberg argued that it was inherent in the entity (it is the nature of the particle that it does not have an exact position and momentum). It is my understanding that Tracy approaches the indeterminacy from a standpoint like Bohr’s that there is a gap in one can understand about it. My standpoint is like Heisenberg’s in that I believe that it is the very nature of the world to be inclusive of openness and that future is unknowable even to God, it is not merely human ignorance that accounts for our inability to foresee the outcome of quantum events. Using God to fill epistemic gaps is a bad approach because the gaps will eventually be filled with new science. Asserting that there are ontological gaps in what can be understood about the world sounds like a more attractive option but is essentially the argument made in traditional “God of the gaps” arguments that scholars are so careful to avoid. In a sense, if the world is truly open and pure chance does play a role, events would occur without sufficient cause and would violate the principle of sufficient reason. Meeting the requirements of the principle of sufficient reason is in no way a necessity; however, it certainly is an attractive philosophical advantage that events happen for a reason. Moreover, Tracy’s idea of occasional divine action could be understood to lead to interventionism in that God would essentially override pure chance at the quantum level whenever He so desired. While Tracy has criticized Nancey Murphy’s approach which is explained in the following section for exacerbating the problem of evil, his own approach may lead to the same pitfall. Why would God choose not to act in some events if His action would alleviate suffering? Clearly the problems of theodicy and human suffering are difficult to handle.
Nancey Murphy
Nancey Murphy [a professor of Christian philosophy at Fuller Seminary who is also on the board of the Center for Theology and Natural Sciences at Berkeley] maintains that God is active in the outcome of all quantum events. The motivation for Murphy’s argument is that it would be helpful to have a new picture of the “relation of God’s action to the world of natural causes” that represents the idea that God sustains, governs, and cooperates with all things in a manner that would allow one to make sense of revelation, petitionary prayer, human responsibility, and of extraordinary acts, without exacerbating the problem of evil. Her position on divine action is that God acts within the created order in two ways: at the quantum level and through human intelligence. As far as her argument that God acts at the quantum level goes, it is important to understand that she is not suggesting that God solely and directly produces all quantum events. She is arguing that God determines when quantum potentialities are actualized. To illustrate this idea, she offers a useful analogy to Buridian’s ass. Buridian, a medieval philosopher, supposedly hypothesized that a hungry donkey equidistant from two equal piles of hay will starve to death because it would have no incentive to choose one of the piles over the other. Murphy supposes that the entities at the quantum level are essentially Buridian asses. In reality, however, the entities at the quantum level do actualize one of their possible courses of action—something induces them into one outcome over all of the other possible outcomes. The question is: What is the something? Murphy argues that God determines the outcome of a quantum event. “God is the hidden variable.” God actualizes possible outcomes of quantum events while He is voluntarily constrained by the inherent limitations of these entities. She pictorially represents this as:
G
S1→S2,

where S1 is the initial state of a quantum system and G is God’s intentional actualization of one of the possibilities inherent in S1. Murphy reasons that this bottom-up account of divine governance is necessary because all things in the macro-world are made up of these quantum entities and God’s ability to act in every macro-event must encompass His action on that which makes up the macro-world.
While Murphy presents a very meaningful and sound argument, there is a flaw in her starting point. Murphy argues that, “both doctrine and logic suggest that if God acts at all, God is acting in everything that happens.” The meaning of Christian doctrine is something that is widely debated and interpreted in many different ways and it is not reasonable to assume that all people will agree on what it suggests. It is my understanding that Murphy has a theistic view of God. Be that the case, the idea of God acting in every event if He acts at all is not a priori obvious as Murphy suggests. It also seems rather contradictory to say that while God acts in every event, the problems of evil and suffering are not exacerbated because God has self-limited his power. If God has limited His power but still acts in every quantum event, He seems to be playing a role in the evil and suffering in the world. Although Murphy asserts that her aim is to come up with a construction of divine action that does not exacerbate the problem of evil, her argument seems to do just that. For example, it is my understanding that if it is always God who actualizes a particular outcome of a quantum event, then He would ultimately be responsible for the deformation of that single cell that triggers cancer. Even if God were only deciding when an outcome would be actualized, He would be responsible for cancer occurring in children. Further, Nicholas Saunders has argued that with Murphy’s argument, God can only act where there is an observer present to make a measurement. In places where humankind does not exist God cannot act. For example, this implies that God could not act on the Galilean satellite Io where there are no observers present to make measurements. The idea of whether or not the world exists independently of observers has plagued the minds of quantum physicists since the discovery of the strange behavior of the quantum world in the 1900s. However this is strongly dependent on the way the term ‘quantum event’ is defined.
Robert Russell
Robert John Russell [founder and director of the Center for Theology and Natural Sciences at Berkeley. ] is a physicist-theologian who is a contemporary advocate of the view that God can intervene in the world through the frame of quantum indeterminacy. Russell argues that if one interprets quantum mechanics in terms of the ontological indeterminism that is found in one form of the Copenhagen Interpretation: “a bottom-up, noninterventionist, objective approach to mediated direct divine action can be constructed in which God’s indirect acts of general and special providence at the macroscopic level arise, at least in part, from God’s direct action at the quantum level”. God’s action at the quantum level involves sustaining the “time-development of elementary processes as governed by the Schrödinger equation and in acting with nature to bring about irreversible interactions called quantum events”. Russell makes the important point that the presence of “chance” that results from ontological indeterminism implies that God is everywhere present and purposely acting in the world, not that God is absent and the world is meaningless. To further develop his argument, Russell discusses the implications of Boltzmannian statistics, Fermi-Dirac statistics, and Bose-Einstein statistics. The world consists of two types of particles. Those that can share the same state with another particle of the same kind are called bosons (e.g. photons and pions); those that cannot are called fermions (e.g. protons and electrons). The nature of bosons is described by Bose-Einstein statistics. The nature of fermions is described by Fermi-Dirac statistics. At regular temperatures and energies, the distribution of both types of particles approach the Boltzmannian equation that characterizes classical statistics. However at low energies and temperatures, the equations that describe Bose-Einstein and Fermi-Dirac statistics are very different. Russell explains that:
If we are interested in ontology and start with Boltzmannian statistics, we are led in opposite directions: to determinism if we stay within the framework of the classical world in which it originated, and to indeterminism if we move to the quantum world and derive Boltzmannian statistics from FD and BE statistics.

Particles retain their FD and BE properties during quantum events and the time evolution of the Schrödinger equation. The classical properties of bulk matter including classical statistics that are experienced as the everyday world are accounted for by these FD and BE properties. Russell is making a connection between the openness that is evident at the microlevel to the macrolevel. It is important that a connection between these two worlds is made in order to show that a theory of God’s action at the quantum level could affect the macroworld. The everyday world is where people generally attribute divine general providence. Thus, Fermi-Dirac and Bose-Einstein statistics show that God’s general providence arises indirectly from His direct action at the quantum level, according to Russell.
Russell does a nice job addressing the relationship between God and the wavefunction, Ψ. He maintains that in his bottom-up approach, God is active everywhere in relation to Ψ as it progresses through space and changes over time. It is both divine and natural causality that cause the collapse of the wavefunction. He differs from Murphy here in that while he maintains that God causes all of the process of the ordinary world, he argues that few of them genuinely convey special meaning. Russell argues that God was active in all quantum events until there was life and consciousness in the world after which God limited His own action “leaving room for top-down, mind/brain causality”. As God increasingly refrained from determining outcomes, there would be more room for top-down causality in self-conscious creatures. God’s voluntary self-limitation would make the prospect of free will a viable option. Russell reflects on other approaches to quantum divine action that attempt to handle the problem of theodicy and he suggests that it can be responded to from a standpoint of Trinitarian theology better than from theistic theology. With theism, it is easy to fall into this trap where God is like a grand puppet master who controls all events and is responsible for the problem of evil. However with a Trinitarian theology, there is the concept of God incarnate who subjects Himself to the evils of the world. The idea is that through the incarnation and the passion, God redeemed the world. This is stronger than process theology, in which God acts through persuasion and suffers with the world, because Jesus is actually God incarnate who physically suffers and experiences evil with the world.
Out of the four above mentioned approaches to quantum divine action, Russell offers the most compelling argument. He smoothly incorporates the Copenhagen interpretation of quantum mechanics into a construction of mediated noninterventionist divine action. His approach to dealing with the problems of evil and human freedom is very helpful. He assesses the problems associated with quantum divine action and responds to them well. My only critique of Russell’s argument is that he argues that God limited His action in the world with the rise of life and consciousness, but from a framework of evolution, there is a huge gray area as to when this limitation would have occurred.
Part IV: A New Perspective
A Panentheistic Construction
When one proposes an approach to divine action, an explanation of the view of God and His relation to the world is a crucial part of the approach. I take a panentheistic view of God in my approach to divine action. While panentheism is not limited to Christianity, it is certainly compatible with it. A useful portrayal of panentheism is the soul-body analogy: God is to the universe as the soul is to the body. (Also—the mind can be substituted for the soul here) The body is within the mind and the soul but the soul and mind are more than the body. With panentheism, the world is within God but God is more than the world. Panentheism encompasses the central biblical teachings about God’s relationship to the world. Philip Clayton explains that Biblical writers in both the Hebrew Bible and the New Testament resisted the Greek dualism of soul (or mind) and body. The body is not evil. Also in some people’s theology, there is a dualism between the material world and heaven. One will hear rhetoric such as “We are not of this world”. “We are not comfortable here because our soul is supposed to be with God in heaven.” Clayton and many others are saying, no “God need not be defined as spirit in opposition to the world as long as matter is not seen as evil or inferior.” If one embraces the theology of the first creation account that God created the world and thought ‘it was good’, it is not evil for God to be intimate with this world. Also, the idea that humankind was made in the image of God is present throughout the Bible. “Then God said, ‘Let us make humankind in our image, according to our likeness’… So God created humankind in his image, in the image of God he created them.” “Just as we have borne the image of the man of dust, we will also bear the image of the man of heaven.” “And [you] have clothed yourselves with the new self, which is being renewed in knowledge according to the image of its creator.” If the idea that humans are made in the image of God is accepted, it would be natural to envision God working in and through at least some parts of the material world.
Panentheism can be understood in Trinitarian terms in the sense that creation is understood as the free expression of the fruitfulness of the Trinity. A key idea in the notion of trinity is the idea of relation. Rather than focusing on separate and separable substances, beings, or things, the notion of the trinity centers upon the notion of relatedness. A panentheistic, Trinitarian view such as that proposed by Denis Edwards in the article cited here, focuses on the fact that the idea of relationship is inherent in God, and that this relationship is dynamic and extends into the world in a creative way. Although Edward’s discussion is primarily a theological one, he makes some very suggestive arguments about how the idea of relationship is not only a characteristic of the trinity but functions in a way at every level of the universe. Edwards suggests a conceptual convergence of Trinitarian thought and scientific thought insofar as “contemporary science points to the fact that created entities are constituted by relationships.” Similarly, he notes that “contemporary Trinitarian theology points out that God exists only as communion.” Thus the universe, which the panentheistic view asserts is in God, is itself relational, as is the trinity. Yet it is important to note that, in saying that the universe is relational and that it is in God, the panentheist is not simply locating the universe in any ordinary sense. The sense of this statement is much deeper and can be expressed in the words of Luke, “In him we live and move and have our being.”
A given view of God will directly affect the concept of divine causality. The connection between panentheism and divine causality is an important one to consider. Recall that panentheism is the idea that the world is in God. This has particularly helpful implications for approaches to divine causality. Clayton argues that when the world is understood as ontologically outside God as in the classical theistic view, God must intervene from outside the world to take any action in the world. This view poses problems and raises many difficult questions for both believers and nonbelievers. If God completely transcends the world, how would humans be able to discern his interventions? If this transcendent God created a perfect world, why would He need to intervene at all? It seems that it would be far better theologically if inner-worldly causality was understood as a manifestation of divine agency.
A panentheistic view of God has tremendous implications for quantum divine action. God is present in each physical interaction and at each point in space. It follows that God is present in all quantum events. It is impossible to construct an approach to divine action without addressing the concept of consciousness. What is consciousness? This is not an easy question to answer, but it is useful to describe it. It consists of two different aspects: passive manifestations of consciousness which involve awareness of things like color and memory and active manifestations of consciousness which involve concepts like free will. How does free-will fit with this approach to divine action? I think Russell and Tracy handle this question well with the notion that God allowed humankind to have free-will. This works with a panentheistic view of God in that while He is present in all quantum events, His self-limitation allows for free will. This self-limitation also allows for natural and moral evil to occur and not be attributed to God’s direct action. Nature can be held responsible for competition, violence, suffering, and death.
The relationship between a panentheistic view of God and the Copenhagen interpretation of quantum mechanics is worthy of some examination. All of the interpretations of quantum mechanics have positive and negative implications. The most attractive quality of the Copenhagen interpretation is the ontological openness that it offers. However, the measurement problem, the collapse of the wavefunction, and the definition of a quantum event are consequences that must be addressed. The measurement problem and the definition of a quantum event will be addressed in the following section. The collapse of the wavefunction is a rather complex result of the Copenhagen Interpretation. Does God cause the collapse of the wavefunction? Does consciousness? Saunders offers four possible ways God could be connected to the collapse of the wavefunction. God could alter the wavefunction between measurements, He could make His own measurements on a given system, He could alter the probability of obtaining a particular result, or He could control the outcome of measurement. This is a good general overview of the possible connections God could have to the wavefunction.
However, I do not see how Saunders incorporates free will and human consciousness. Also, Saunders views God as outside the world. Arguing that God determines the outcome of every quantum event is an instance of divine over-determination. God’s self-limitation must be incorporated into God’s effect on the collapse of the wavefunction. While God is present in all quantum events, He controls the outcome of some events, allows consciousness to determine the outcome of some events, and allows some events to be determined by natural causality. God’s self-limitation allows consciousness to play a role in causing the collapse of the wavefunction upon measurement. This is important because while the term ‘quantum event’ is not restricted to measurements made in a laboratory setting, it is inclusive of them. Thus it follows that one aspect of divine action should include allowing human consciousness to also cause the collapse of the wavefunction. However, there is far more to consciousness than just human consciousness. It is logical to aver that there are different levels of consciousness, as David Hawkins does. A baby has a different level of consciousness than an adult. Animals also have consciousness. Even plants can be understood to have a level of consciousness higher than say, a rock. Especially when the theory of evolution is considered—when exactly did the evolving creature have a consciousness that could be considered human consciousness? Rather than grappling with these gray areas, I would attribute the collapse of the wavefunction to two overarching causalities: divine and natural. All levels of consciousness are then under the umbrella of natural causality. An obvious follow up question is how can one discern the difference between divine and natural causality? It is an ontological limitation of this argument that exactly who is causing what cannot be known. The important underlying concept is that there are two overarching causes of the wavefunction collapse.
The Trouble with Quantum Divine Action
While divine action at the microscopic level is an attractive idea to many people for the ontological openness of quantum theory, it has been criticized for several reasons. Quantum Divine Action is most often criticized for fear that action at the subatomic level would not be significant enough in general to have macroscopic effects. Nicholas Saunders argues that it is viable that God could affect distance outcomes by altering the parameters of quantum events without violating natural laws, but it seems that He would have to determine the outcome of a huge number of quantum events to achieve any major macroscopic results. Saunders uses an “absurd example” to portray exactly what he means by “distant outcomes”. If an asteroid were naturally going to skim the Earth’s atmosphere and God opted to cause it to collide with the Earth through quantum adjustments, He would have had to start steering the asteroid long before the evolution of the dinosaurs. However there are examples from biology and physics that portray the imminent macroscopic effects quantum events can have. In some species the eye can actually detect individual photons falling on the retina. George Ellis explains that “the photon is absorbed by a molecule of rhodopsin, eventually resulting in a nervous impulse coming out of the opposite end of the cell with an energy at least a million times that contained in the original photon”. Much of the amplification in the initial step is due to a single photon. Another example from biology is the idea that DNA can be mutated by a single photon and have macroscopic consequences like cancer. This kind of mutation could also have more beneficial effects like enhanced cognition. Robert Russell explains that superfluidity and superconductivity are “bulk” quantum states that are phenomena which are found in the ordinary classical world. Russell also explains that most of these biological and physical processes do not rely on chaos theory, which will be discussed in the following section. While the prospects of quantum chaos are attractive, the connection is not a necessity.
The measurement problem has also raised concerns about quantum divine action. Saunders has expressed these concerns. Saunders explains that associating divine action with quantum mechanics results in the idea that divine action could only occur through some kind of measurement interaction. Saunders argues that the problem with this is that, not only does this concept makes God subordinate to creation, but the episodic nature of measurements places limitations on the actions God could take in the world. He further argues that the measurement problem leads to the outlandish conclusion that God could not act in places in the world where there are no observers present to make measurements. It is crucial to realize that the measurement problem has absolutely everything to do with the way a “quantum event” is defined. As mentioned earlier, Robert Russell’s definition is the most useful. If the term “quantum event” is restricted to a measurement (where measurement is defined as an irreversible interaction that is either between elementary particles and classical measuring devices, between elementary particles and microscopic objects, or between elementary particles and other elementary particles), then a large number of opportunities for divine action exist.
John Polkinghorne has also expressed concerns about quantum divine action. He has explained that quantum theory is subject to different interpretations and the attractive ontological openness that comes from the Heisenberg Uncertainty Principle is not the only conclusion that can be drawn from quantum theory. Robert Russell has addressed this question of how one can take quantum physics seriously in discussing a theology of divine action when quantum mechanics is subject to different interpretations. He explains that it is not realistic to reduce this problem to only something that must be dealt with in the quantum realm because every scientific theory is open to competing metaphysical interpretations. Metaphysics is always undetermined by science, but there are some theories that seem to strongly favor one interpretation over others. Even when addressing this question solely from a quantum mechanical standpoint, there are reasons to support an ontological interpretation. Russell explains that none of the interpretations of quantum mechanics portray an entirely classical view of the world; they all require a “reconstruction of our philosophy of nature”. Even David Bohm’s interpretation that seems to offer determinism can be bought at a high price: the interpretation is highly nonlocal and nonmechanical. Thirdly, Russell explains that many of these approaches to divine action are not forms of natural theology (arguing from science alone) but a “theology of nature” (reformulating religious beliefs in light of science), which implies that if the scientific or philosophical interpretation of quantum physics changed, the constructive proposal would indeed be challenged but not the overall viability of a theology of divine action in nature. The primary evidence for the validity of a theology of divine action in nature lies in Scripture, tradition, reason, and experience. Finally, Russell explains that these constructive theologies are important because the strengths and limitations of a particular interpretation of quantum physics are revealed when the implications of noninterventionist approaches to divine action are illuminated. This will lead to more insight and new areas of research which can only be beneficial.
Chaos
An area other than quantum physics where individuals look to find a way that God can act in the world without suspending natural law is chaos. John Polkinghorne is the leading scholar in this line of thinking. There are many classical systems that are extremely sensitive to minute details of their circumstances. Chaotic systems would allow for God’s action to have macroscopic effects because very small perturbations have very large effects on the systems. Polkinghorne argues that it is possible that humankind can exercise free-will and that God can act in the world if one allows the epistemological unpredictabilities of chaotic systems to lead to a hypothesis of ontological openness. He stresses the need for an interaction between bottom-up causality and top-down causality in any valid theological discourse on divine action. Chaos offers an avenue towards a balance between these two types of causality. Chaotic systems are one depiction of the idea that the world is open (causal principles that determine energy exchange among parts (bottom-up) do not completely determine the future), and integrated (additional principles will have a holistic nature (top-down)) in character. This combination of bottom-up and top-down causality frees the world from physical determinism and leads to an inherently unknowable future even to God. For Polkinghorne, chaos theory offers a direct connection to macroscopic phenomena which is where human and divine agency are both expected to manifest themselves. One way to reconcile the disagreement between advocates of chaos as a means of divine action and advocates of quantum physics as a means of divine action would be to explore the possibility of quantum chaos.
Quantum Chaos
Quantum Chaos could imply a few different things about the way the world works. Some who follow Einstein about the incompleteness of quantum mechanics refer to it as “quantum chaology” and see it as a possibility for explaining the observed randomness in what is really a deterministic quantum world. A better approach is to first maintain the ontological openness of chaos as John Polkinghorne does. He then suggests that macroscopic openness could essentially be chaotically amplified quantum openness. The trouble with such a hypothesis is that it is difficult to combine the microscopic and macroscopic worlds in such a way that the interpretation presents only one physical world that is encountered at these two levels. The nature of the compatibility of chaotic dynamics and quantum mechanics has not been established, and there is currently quite a bit of confusion about what correspondence could be established between the two. However, I find it an attractive concept worthy of examination because the substantial macroscopic consequences of chaos would obliterate the largest criticism of quantum divine action—that action at the quantum level is not significant enough to have macroscopic effects. The philosophical connection between the quantum level and chaos is so strong that it is not far fetched to say, “The math will catch up” , and continue seeking the mathematical connection between the two.
Conclusion
This paper has been an attempt to review the theories of quantum divine action and to construct a panentheistic approach to noninterventionist divine action. After reviewing various interpretations of quantum mechanics, I have suggested how the Copenhagen Interpretation is the most fruitful place to focus this discussion because of the ontological openness it incorporates. In order to elucidate the relationship between divine action and quantum theory, it is necessary to consider the different understandings of God that have been presupposed by these discussions. I have examined the arguments of four of the major proponents of quantum divine action. I have argued that the panentheistic understanding of God and God’s relationship to the universe offers the most promising avenue to a noninterventionist account of God’s direct action at the quantum level. After assessing and responding to some of the problems associated with quantum divine action, I have shown that quantum chaos is an attractive prospect since with this proposal it is not necessary for God’s action at the quantum level to have macroscopic effects.

About the Author

Mara Gertrude Block was born in September of 1984 in Chicago, Illinois, to Marlene and Barry Block. She moved to Redlands, California in the summer of 1989 when her father came to work as a physician at Loma Linda University Medical Center. Mara grew up in Redlands where she attended Sacred Heart Academy and she is now a member of Sacred Heart Parish. After graduating from Redlands Senior High School in 2002, she accepted admission to the University of Redlands where she initially anticipated receiving a Bachelor of Science degree in physics. During her sophomore year, she decided to double major in physics and religious studies, with a minor in mathematics. Mara was a member of the University of Redlands Women's Basketball team all four years and received honors such as being named First-Team all SCIAC in 2005 and 2006, being a member of the ESPN CoSida All-American Academic Team in 2006, and being named most valuable player in 2006. After graduating in May of 2006, she will attend Harvard Divinity School in the fall and pursue a Master of Theological Studies Degree. She intends to pursue a doctorate in religious studies and become a college professor.

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Keywords: Quantum Divine Action; Panentheism; Indeterminism; Interpretations of Quantum Theory; Science and Religion; William Pollard; Thomas Tracy; Nancey Murphy; Robert Russell.

A Survey of Interpretations of Quantum Theory: A Panentheistic Approach to Quantum Divine Action