From The Thomist 61 (1997), 455-468. Thomism and the Quantum Enigma William A. Wallace, O.P.

The recent publication of Wolfgang Smith’s The Quantum Enigma: Finding the Hidden Key1 has done more than propose a novel interpretation of quantum theory. It has also reopened a train of thought that has been somewhat muted in recent decades, namely, that of the relevance of the thought of St. Thomas Aquinas to solving problems raised by modern physics. What I have in mind are books published in the 1950s and 1960s by Jesuit professors at the Gregorian University in Rome2 and by Vincent Edward Smith in the United States,3 plus my own writings on the subject before I became heavily involved in the history of science.4 Now, out of the blue, as it were, Aquinas’s name is once again being invoked in the context of modern science, this time as originating concepts that provide a “hidden key” to the solution of the quantum enigma. The author of this startling claim, a professor of mathematics at Oregon State University and apparently no relation to Vincent Edward Smith, surely deserves a hearing in these pages.

Wolfgang Smith’s thesis is set out in six chapters: the first two, “Rediscovering the Corporeal World” and “What is the Physical Universe?,” establish the terms of discourse; the next two, “Microworld and Indeterminacy” and “Materia Signata Quantitate,” propose Smith’s solution, which basically consists in explaining the significance of state vector collapse in quantum theory; and the last two, “On Whether ‘God Plays Dice?’“ and “In the Beginning,” draw out metaphysical implications of this teaching. An appendix provides a brief mathematical introduction to quantum theory so that the reader can appreciate what is meant by state vector collapse and other technical terms. A glossary gives a handy index of such terms and where they occur in the text.

In Smith’s view, the devil that needs to be exorcised from contemporary physics is the bifurcationism that took its origin from René Descartes, then was reinforced by a succession of philosophers from John Locke to Immanuel Kant (chap. 1). This is the split between res extensa and res cogitans, the first denuding the world of sensible qualities and the second creating the impression that all such qualities (and the nature that underlies them, das Ding an sich) are projected into the universe by the observer. The mind-set such bifurcationism puts into physicists is so strong, and has been reinforced in so many ways by their education and culture, that it is almost impossible for them to recognize it, let alone work at eradicating it. But eradicate it they must if they would solve the enigmas of quantum theory. And the only way they can do so, Smith argues, is by rediscovering the corporeal world. What this means is that they must learn what it is to perceive the world as it presents itself in sense experience, to experience in their own lives the “miracle” of sense perception (16).5 The apple is outside us, but we perceive it nonetheless, with its colors and its other attributes, which are as real as we sense them to be (1-20).

What, then, is the actual universe of the physicist? Obviously it is different from the corporeal world (chap. 2). It is accessed, not through perception, but through measurements and the artificial instruments that yield them. But more than measurements are required; they must be complemented by theories and the models these invariably suggest. Such modes of knowing result in “representations” (somewhat analogous to sensible images) through which physicists know what Smith calls “physical objects,” the entities that populate their universe and so are different from the “corporeal objects” of sense experience (23). The precise relationships between the two sorts of “objects” may be understood as follows. Every corporeal object X can be subjected to measuring procedures that will yield an “associated physical object” SX. X and SX are not the same thing, for X is perceptible whereas SX is not (25-26). Yet there is a similarity, a “resemblance,” between the two, and this consists essentially in the likeness of a mathematical form, of an abstract structure.6 Yet an asymmetry is found here also, in that one can always go from a corporeal to a physical object by metrical procedures, whereas one cannot always go the other way round. In the event that one can, the physical object is the SX of a corporeal object X, and X is referred to as a “presentation” of SX. Smith uses this asymmetry to divide “physical objects” into two further classes: physical objects that admit of presentation he refers to as “subcorporeal objects,” whereas those that do not admit of presentation he calls “transcorporeal objects” (27). The requirement of presentation is essential, Smith insists, if there is ever to be intellectual knowledge of entities in the physical world (31, 21-42).

With this language presupposed, Smith moves on to consider problems of the microworld and indeter-minacy (chap. 3). He first clears the ground by dis-tinguishing a “generic physical object” from a “spe-cific physical object,” since it is only the latter with which the physicist actually comes to deal. Its dis-tinguishing note is that some type of observational contact has to already have been made with the object and in this sense can serve to “specify” it.7 Precisely how this specification of a physical object is achieved can be rather complex, but for Smith it usually involves conceiving the object in terms of an abstract or mathematical representation, what he terms a “physical system” (23n., 45). It is this sys-tem that defines the observables, that is, quantities that can in principle be determined by physical means. And it is here that the problem of deter-minacy and indeterminacy in quantum theory has to be addressed.

Can the physical universe be divided into two subdomains, the macroworld and the microworld, and is the microworld really a “strange” world, different from that of ordinary experience? Smith’s answer to the latter question is that the microworld is indeed strange in the sense that it can be neither perceived nor imagined, but it is not “quantum strange” as it is commonly thought to be. “For example,” he goes on, “it is by no means the case that the electron is sometimes a particle and sometimes a wave, or that it is somehow particle and wave at once, or that it ‘jumps’ erratically from point to point, and so on” (48). This kind of talk “results from an uncritical and spurious realism—a realism which in effect confounds the physical and the corporeal planes.” What is happening here is that the microsystem and its observables are being confused, and the observables are being treated as classical attributes of the electron, “which they are not, and cannot be.” But this does not mean that Smith rejects realism itself. He is explicit on this: “the microworld is objectively real—as real, indeed, as the physical world at large, with which in fact it coincides” (49).

What then to do about the Heisenberg uncertainty principle, the common source of talk about indeterminism? In Smith’s view that principle does not refer to the microworld as such. It refers to the result of measurements, and thus to the transition that takes place in passing from the physical to the corporeal plane. In the microworld itself, Smith maintains, there is no such thing as the Heisenberg principle. What is known about the electron, for example, is not its position or its momentum, but rather the state vector of the physical system in which it is being specified. In holding this Smith is not denying that a measurement performed on a physical system can cause the so-called collapse of the state vector (51). His point is rather that quantum mechanical systems still behave in a deterministic way, provided the type of determinism involved is properly understood:

Obviously enough, this quantum mechanical determinism is a far cry from the classical. However, what has been forfeited is not so much determinism as it is reductionism: the classical supposition, namely, that the corporeal world is “nothing but” the physical. It is this axiom that has in effect become out-moded through the quantum mechanical separation of the physical system and its ob-servables. Quantum physics, as we have seen, operates perforce on two planes: the physical and the empirical; or better said, the physical and the corporeal, for it must be re-called that measurement and display ter-minate necessarily on the corporeal plane. There are, then, two ontological planes, and there is a transition from the physical to the corporeal resulting in the collapse of the state vector. The collapse, one could say, be-tokens—not an indeterminism on the physical level—but a discontinuity, precisely, between the physical and the corporeal planes. (52)

The discussion of Heisenberg brings Smith to another aspect of the former’s teaching, one on which he expatiates throughout the rest of the book. This is Heisenberg’s invoking of the Aristotelian notion of potentia when he suggests that micro-physical systems constitute a kind of potency in relation to the actual world. From here on the discussion becomes more technical and is not easily summarized. Since our interests here are more ontological than mathematical, perhaps this brief excerpt from Smith will convey the flavor of the exposition.

Measurement . . . is the actualization of a certain potency. Now the potency in question is represented by the (uncollapsed) state vector, which contains within itself, as we have seen, the full spectrum of possibilities to be realized through measurement. To measure is thus to determine; and this determination, moreover, is realized on the corporeal plane: in the state of a corporeal instrument, to be exact. Below the corporeal level we are dealing with possibilities or potentia, whereas the actualization of these potentiae is achieved on the corporeal plane. We do not know how this transition comes about. Somehow a determination—a choice of one particular outcome from a spectrum of possibilities—is effected. We known not whether this happens by chance or by design; what we know is that somehow the die is cast. And this “casting of the die” constitutes indeed the decisive act: it is thus that the physical system fulfills its role as a potency in relation to the corporeal domain. (56-57.)8

An additional point may now be made on the subject of determinism in relation to the electron. Smith had earlier noted that dynamic attributes such as position and momentum are not attributes of the electron. Now he clarifies his position on the electron’s so-called static attributes, such as mass, charge, and spin. These quantities do belong to the electron as such, and they are measurable with stupendous accuracy. “Of all the things, in fact, with which physics has to deal, there is nothing more sharply defined and accurately known than the electron” (60).

There can be no doubt that Smith takes inspiration from Heisenberg, and yet he is not in agreement with every element of Heisenberg’s teaching. The German physicist obviously considered himself a member of the Copenhagen school, even though he offered a distinctive interpretation of its doctrine. The distinctive element in that teaching, for Smith, was Heisenberg’s realist view of the microworld based on the Aristotelian concept of potency. It was this that allowed Heisenberg to maintain that there are two ontological domains in the discourse of physicists. There is a gap between the two domains, and physicists manage to bridge it by a measurement process. With this much Smith agrees. But he faults Heisenberg for making “no sharp distinction between the physical universe on a macroscopic scale and the corporeal world, properly so called” (63). Smith’s own view is that the “macroscopic objects of classical physics are every bit as ‘potential’ as are atoms and subatomic particles,” (64) a possibility Heisenberg fails to take into account.9

At this point we come upon Aquinas’s famous ex-pression, materia signata quantitate, “matter signed with quantity,” which Smith makes the title of his fourth chapter. Here he uses the concept of nature as invoked by Heisenberg to explain the funda-mentals of hylomorphic doctrine. Heisenberg’s “nature,” for Smith, touches a deeper level of reality than that represented in the corporeal and physical planes, a reality that points beyond the space-time continuum and suggests a way of dealing with “Bell’s interconnectedness theorem” (68-69). The structure of this new reality, which Smith refers to as “meta-physical,”10 is explained by Aristotle and Aquinas in terms of hyle (matter) and morphe (form), whence comes the English term “hylomorphic.” Hyle designates a pure substrate unintelligible in itself; morphe, its correlative knowable principle which ren-ders natures intelligible to the human mind. Aligned with the former, the material principle, is the acci-dent of quantity, and aligned with the latter, the for-mal principle, is the accident of quality. Smith then goes on to explain Heisenberg’s “nature” as a materia secunda in relation to the physical and corporeal planes:

As materia, thus, it stands “beneath” the spatio-temporal domain in an ontological sense, as the carrier or receptacle, that is, of its formal content. And yet it owns a form which it passes on to the universe at large as a universal law or principle of order; as the least common denominator, so to speak, of the sum total of manifested forms. Nature, thus, turns out to be a materia quantitate signata (a materia “marked by quantity”), if it be permitted to adopt this excellent Thomistic phrase. (78)11

Here Smith’s explanation of the role of form is cryptic, but he clarifies it somewhat in his subsequent exposition. Qualities, he maintains, are ubiquitous on the corporeal plane, but they are missing completely on the physical plane. In his view “physical objects prove ultimately to be . . . [only] ‘potencies’ in relation to the corporeal world” (79). It is quality, as opposed to quantity, that betokens the “essence” of a corporeal entity (80). How Smith then sees the two as going together may be gleaned from the following:

Quantity and mathematical structure . . . refer to materia, or more precisely, to the material aspect of things. The concrete object is made up . . . of matter and form; and this ontological polarity is reflected on the plane of manifestation. The existent object bears witness, so to speak, to the principles by which it is constituted; to both the paternal and maternal principles, if you will. And that is the reason, finally, why there are both qualities and quantities in the corporeal domain: the one indicative of essence, the other of the material substrate. (81)

Once one understands this, it is easy to see why “the only thing about a corporeal object that one is able to understand in terms of physics are its quantitative attributes” (82). SX is all that physics perceives.

And that is no doubt the reason why physicists have been able to convince themselves (and the rest of the educated world!) that the corporeal object as such does not exist; or to put it the other way round: that X is “nothing but” SX. It is the reason why corporeal entities are thought to be “made of” atoms or subatomic particles, and why the qualities are held to be “merely subjective.” (82)

These excerpts from The Quantum Enigma, unsatisfying as they may be, will have to suffice for our present purposes. In the penultimate chapter, “On Whether God Plays Dice,” Smith takes up problems of causality and determinism and “hidden variable” theories, and makes use of the concepts of natura naturans and natura naturata to resolve the apparent impasses that are discussed in the literature. In his view, the significance of quantum discontinuity as seen in state vector collapse is that it betokens an action of natura naturans, not natura naturata (85-97). And in the final chapter, “In the Beginning,” he discusses the so-called big-bang theory and shows how it too involves a singularity and thus, like state vector collapse, gives witness to some type of “creative act” that lies well beyond the pale of the physical sciences (112, 99-113).

*****

By a remarkable coincidence The Quantum Enig-ma came into my hands just as I was putting the finishing touches on the manuscript for a book, one that may lay the groundwork for understanding theses such as that advanced by Smith. This work has just been published with the title The Modeling of Nature: Philosophy of Science and Philosophy of Nature in Synthesis.12 In it I give some consideration to the quantum theory of the atom but I do not take up problems associated with quantum anomalies. Since I had the opportunity to insert a reference to Smith’s book before mine went to press, I added a footnote that now appears on p. 414 and reads as follows:

No attempt has been made in this study to ad-dress the subject of quantum anomalies, since these presume technical competence beyond what can reasonably be expected of the general reader. A recent work that takes ac-count of such knowledge and offers solutions that are consonant with the Aristotelian-Thomistic perspective here adopted is that of Wolfgang Smith, The Quantum Enigma: Finding the Hidden Key, Peru, Illinois: Sherwood Sugden & Company, 1995.

Having introduced that note, in the context of this discussion article I now feel it incumbent on me to reflect further on Smith’s work and its relationship to my own.

Although the two books are concerned with differ-ent problems and addressed to different audiences, there are a number of points they have in common and on which they mutually support each other. These are the strong realism both endorse with respect to the corporeal object (X), the unequivocal rejection of Cartesianism and Kantianism (along with the mindset they introduce into modern physics), the need to address the status of the physical object (SX) and how one can make the transit from it to the corporeal world, the endorsement of Heisenberg’s use of the Aristotelian concept of potentia and the hylomorphism this involves, and, in general, the replacement of logical positivism by an Aristotelian Thomism that opens out to a metaphysics for the eventual solution of problems now arising at the frontiers of physics. (The reader is not to think that X and SX and other technical terms introduced by Smith will be found in my book; of course they will not. But their rough equivalents will be found there, although conceptualized in a different way.)

The major difference between our two approaches is that Smith begins with a philosophy of science and works his way to a philosophy of nature at the end, whereas I do the reverse, beginning with the concept of nature and then ending with a philosophy of science based on that concept. His work addresses a very specific problem, the enigma posed by state vector collapse in quantum theory, whereas mine has the broadest possible scope, that of relating all of the modern sciences (physical, life, and human, including even ethics and politics) to the one concept of nature. And whereas Smith uses Aristotle and Aquinas mainly for their teachings on potencies and materia signata quantitate, I expand generally on the way analogia underlies the work of both thinkers, taking analogy as a synonym for “model” and exploiting the use of models in all these areas of inquiry.

Although I nowhere mention this in my book, what is implicit in my treatment is the following idea. Aqui-nas, having been taught by Albert the Great, had an excellent grasp of Aristotle’s science of nature. He upgraded the knowledge this gave him to organize, as it were, a science of supernature (that of revealed theology), making use of analogy and the Aristotelian concept of a “mixed science,” combining propo-sitions established by reason with propositions assented to by faith. My project would be to do something similar: to take knowledge we possess from ordinary experience of nature to organize the special type of knowing we call modern science, making use of analogy or modeling techniques and the “mixed science” of mathematical physics, which combines propositions established through the observation of nature with those of mathematics. Here I rely on a teaching that is distinctive of Thomism, in contrast to other Scholastic systems of thought, namely, that analogical middle terms are sufficient for a valid demonstration, no less in mathematical physics than in the science of sacred theology. Such terms, and the models they frequent-ly employ, can provide us with insights into the microworld and the megacosm that are not unlike those Aquinas offered his contemporaries into the spirit world of the immaterial and the incorporeal.

Another premise I owe to Arthur Fine, who proposed to mediate between “realists” and “anti-realists” by having both sides of their ongoing dispute adopt a “natural ontological attitude,” one that gives scientists the benefit of the doubt.13 This entails taking the certified results of science as knowledge claims on a par with the findings of common sense. Working with the leverage such an attitude provides I explain first the concepts of hyle and morphe, then how both of these were regarded as “nature” by Aristotle, and how they constitute the “inner dimension” of all natural bodies. I go on to instantiate this teaching by modeling, in sequence, inorganic natures, plant natures, animal natures, and human nature, inserting between the last two a treatment of the modeling of mind. In common experience natures are grasped intuitively. My conviction is that, in the present day, people have a quasi-intuitive knowledge of the microworld and the megacosm based on the ways in which these are pictured for them in school and through mass media, particularly television. Indeed, they know more about natures than they give themselves credit for, once they are told what to look for and how to integrate what they see into their existing body of knowledge.

Generally I bypass both quantum and relativity theories because of the mathematics they require for proper understanding. I do make use, however, of the Bohr-Sommerfeld model of the sodium atom, and this in fact is illustrated on the cover of the volume. The point I make is that the quantum “jump” of electrons that can be pictured in that model illustrates very well how “form” (morphe) functions as an energizing and stabilizing principle in an inorganic nature. (Not that electrons really “jump,” as Smith makes clear.) The models I employ are for the most part iconic or pictorial models, and they suffice to give some sense of the “miracles” nature performs not only here but at all levels of being. I steer clear of mathematical models, mainly because they might prove opaque to many readers. Smith, of course, is expert with them. He uses precisely such a model to explain state vector collapse, and that is the strength of his book. Here I would only remark on how well he explains that model in the appendix. He starts with the double-slit experiment; then he gives a carefully crafted exposition of finite-dimensional Hilbert spaces, complex numbers, and state vectors; he next applies this geometry to the Heisenberg uncertainty principle, Schrödinger’s wave equation (having earlier discussed “Schrödinger’s cat,” 58), and the wave function of a particle; and he ends by going back to the double-slit experiment to show how matrix mechanics explains its findings precisely (115-36).

With regard to technical details, there is little I would disagree with in Smith’s thesis. Although I too invoke Heisenberg in defending my models, and despite the fact that the latter has expressed qualified support for my views,14 I endorse Smith’s correctives to Heisenberg’s teaching on the relevance of potency to macroscopic objects as well as to atoms and subatomic particles (64). I also think he is on the right track in his insights employing the concept of esse, but that is an area of Thomistic metaphysics on which much has been written and is beyond the scope of this brief essay.15

Notes

1 (Peru, Ill.: Sherwood Sugden & Company, Publishers, 1995), iii + 140 pp., with an appendix, a glossary, and an index of names.

2 Especially the following, all published by the Gregorian University Press, Rome: Peter Hoenen, S.J., Cosmologia, 5th ed. (1956); idem, De noetica geometriae (1954); Philip Soccorsi, S.J., De physica quantica (1956); idem, De vi cognitionis humanae in scientia physica (1958); idem, De geometriis et spatiis non-Euclideis (1960).

3 Notably his Philosophical Physics (New York: Harper & Brothers, 1950); and Footnotes for the Atom (Milwaukee: Bruce Publishing Co., 1951).

4 See my “Newtonian Antinomies Against the Prima Via,” The Thomist 19 (1956): 151-92; “The Reality of Elementary Particles,” Proceedings of the American Catholic Philosophical Association 38 (1964): 154-66; “St. Thomas and the Pull of Gravity,” in Science and the Liberal Concept (West Hartford, Conn.: St. Joseph College, 1964), 143-65; and “Elementarity and Reality in Particle Physics,” Boston Studies in the Philosophy of Science 3 (1968): 236-71.

5 Numbers in the text refer to the page numbers of The Quantum Enigma.

6 Other connections between the two are that X and SX “occupy exactly the same region of space” and that they are also in “temporal continuity.” Geome-trical continuity, Smith further explains, entails that “every decomposition of a corporeal object X into corporeal parts corresponds to a congruent or geometrically isomorphic decomposition of SX” (31-32).

7 Smith’s example of a generic physical object would be “the electromagnetic field,” which exists only “in some abstract, idealized or purely mathematical sense”; his example of a specific subcorporeal object would be the planet Pluto, with which we already have some type of observational contact. Further-more, there can be specification of a transcorporeal object, such as an elementary particle, but this must come about in two stages: the object must first interact with a subcorporeal entity, and then the latter must be observed (or rendered observable) through presentation as already described (43-44).

8 In this citation a footnote is inserted at the end of the sentence that reads, “We do not know how this transition comes about.” The note states: “We shall return to this question in chapters 5 and 6,” that is, in the last two chapters, which address more metaphysical issues.

9 The precise difficulty is explained in more technical detail on pp. 62-64. This concerns, as I suggest, the problem of where one should situate the “potency” to which Heisenberg refers. Smith sees his distinction between X and SX as crucial in this matter. Smith is explicit that “SX exists as a potency, whereas X exists as a ‘thing or fact.’” Heisenberg, on the other hand, “appears in effect to identify SX and X” (64).

10 By his use of the expression “metaphysical realities” (73) Smith intends to designate realities that lie beneath the appearances, which is a common use of the term “metaphysical” today. This is not St. Thomas’s usage, however, for he reserved the term for a science of “being as such,” which he differ-entiated from “physics,” the science that treats of material or changeable being and whose principles are hyle and morphe.

11 Here Smith adds a footnote in which he disavows any claim that the meaning he assigns to this phrase coincides with its original Thomistic connotation, for obviously “the Angelic Doctor was not thinking of quantum field theory.” Actually St. Thomas uses this expression to explain how natural substances, or “natures,” are individuated within a species, and thus it is commonly referred to as his “principle of individuation.” For Aquinas, forma in the sense of natural form or substantial form is a specifying principle, whereas materia, along with the quantitas that serves to put “part outside of part,” is what differentiates one substance from another, despite their being the same in kind. Precisely how such indi-viduation takes place is difficult to understand, and it is much disputed among Thomistic commentators. For a concise overview of the problem, see J. R. Rosenberg, “Individuation,” The New Catholic Encyclopedia 7:475-78.

12 Washington, D.C.: The Catholic University of America Press, 1996, xx + 450 pp., with illustrations and an index of names. What lies behind the subtitle is the fact that I have spent over forty years teaching both philosophy of science and philosophy of nature at the graduate and undergraduate levels. Much of my interest throughout that period has focused on Aquinas’s commentaries on the Physics and the Posterior Analytics of Aristotle.

13 See Fine’s The Shaky Game: Einstein, Realism, and the Quantum Theory (Chicago and London: The University of Chicago Press, 1986), 112-35.

14 See The Modeling of Nature, 414 and esp. n. 39.

15 I wish to thank Professor Smith for having read this essay in advance of publication and assuring me of the accuracy of my presentation of his thesis.