From The Thomist 61 (1997), 455-468.
Posted May 13, 2010
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.