The universe presents itself as extended in space and changing in time, and its spatio-temporal locus can be represented mathematically in terms of three spatial coordinates and one temporal: the familiar quadruple (x1, x2, x3, t). The “container” is thereby decomposed conceptually into an infinite aggregate of punctual loci, which define a corresponding decomposition of the “content”: and this twofold conceptual atomization constitutes the foundation upon which physics as such is based. The fact that it operates by way of differential equations is thus predetermined, as is presumably a major part of what we normally take to be its “empirical findings.” What needs to be grasped is that physics deals not simply with the universe as such — as almost everyone assumes — but is descriptive rather of the cosmos as “atomized” by way of the aforesaid spatio-temporal fragmentation. It is hardly surprising, therefore, that the manifestations of authentic wholeness — from the simplest to the most profound — prove as a rule to elude its grasp.
Metaphysics, on the other hand, would know that which precedes this fragmentation both ontologically and epistemologically. It is possible of course to suppose that there is no wholeness at all — that the “atomized” universe is all there is — and ontologies of that kind have been enunciated, time and again, beginning perhaps with Heraclitus. Yet the fact remains that the great sapiential traditions, both of the East and the West, have emphatically declared the contrary: i.e., that wholeness precedes division — not temporally, to be sure, but in veritas. What is transcends both space and time: and it is upon this very recognition, precisely, that authentic ontology rests.1For those who respect the Judeo-Christian tradition I would point out that the “ego sum qui sum” of Exodus 3:14 suffices to make this abundantly clear. Moses had asked by what “name” God is to be known, and the answer he received was: “I am who am.” We are not suggesting, to be sure, that the cosmos shares in the eternity of God, but only that, on its highest plane, it likewise transcends the flux of time. This is what, in Scholastic parlance, is referred to as aeviternity.
Given thus that the primary cosmic reality is both supra-temporal and supra-spatial, one might imagine that the spatial and temporal bounds definitive of the cosmos, as it normally presents itself to mankind, are imposed upon that antecedent wholeness “at a single stroke” as it were. There are however cogent grounds to conclude that such is not the case, and that in fact the bound of time precedes the bound of space — not temporally, to be sure — but in a metaphysical sense: the integral cosmos proves thus to be ontologically tripartite. Between the pre-temporal wholeness and the spatio-temporal world, namely, there exists a domain subject to the bound of time but not of space; and let me note that this metaphysical fact has scientific implications, the most evident being that it disqualifies Einsteinian physics at a single stroke. For in thus distinguishing categorically between “time” and “space,” the given trichotomy affirms the existence of a universal temporal “now”: an absolute simultaneity namely, defined throughout the length and breadth of the corporeal universe — which the Einsteinian construct of “space-time” rules out.
I would note2Physics and Vertical Causation: The End of Quantum Reality (Angelico Press, 2019), pp. i-vi. that the concept of a tripartite cosmos is indigenous to the sapiential traditions of mankind, and has apparently received its most explicit formulation in the Vedic, where the cosmos thus conceived is known as the tribhuvana or “triple world.” Inasmuch, moreover, as the discernment of the anthropos as a tripartite microcosm — composed of corpus, anima, and spiritus — was current in Europe right up to the Enlightenment, the conception of a tribhuvana is in a way indigenous to the West as well. This isomorphism between man and cosmos taken in their integrality — which proves likewise to be indigenous to the sapiential traditions — entitles us to designate the primary cosmic domain as the “spiritual,” and the third as the “corporeal.” The second could of course, by the same token, be termed the “animate,” yet for reasons which need not detain us, we shall refer to it as the “intermediary” domain.3This is what, in nineteenth-century occultism, was known as the “astral plane,” and what the Orthodox Church refers to as the “aerial” world. But whereas nowadays this realm is virtually unrecognized and unaccessed in the West, it can in fact be entered and crossed by means which may in principle be termed “scientific”: the catch is that when it comes to sciences of this kind — which have existed in the past, and may still be operative in some forgotten corner of the globe — the “instrument” can ultimately be none other than the man himself, who by certain means can acquire requisite powers of perception in respect to the “inner” world. But whereas the concept of the tribhuvana proves to be well documented in the traditional literature, its specification in terms of spatial and temporal bounds, as given above, seems to be extant neither in ancient nor in contemporary sources. What primarily concerns us, however, is not the historical origin, but the scientific and ontological implications of the given trichotomy.
* * *
The most basic and indeed most obvious conclusion to be drawn is that physics as such is restricted to the lowest of the three cosmic domains: to the corporeal namely — for inasmuch as both ontological domains above the corporeal are no longer subject to the spatial bound, they are “invisible” to the physicist, restricted as he is in his purview to regions within space and time. Or to put it another way: inasmuch as physics deals with functions f(x1, x2, x3, t) defined in terms of spatial and temporal coordinates, it ceases to apply above the corporeal plane.
Having thus recognized its proper domain, we need to take note of the fact that physics entails further restrictions, that in the final count it “has eyes” only for spatio-temporal bounds: for the “container” namely, as distinguished from its “content.” And what is that “unperceived” content? It follows from our conception of the tripartite cosmos that this content pertains ultimately to the spiritual realm: the primary reality from which both the intermediary and the corporeal domains derive. The true “substance” of all entities — be they corporeal or intermediary — pertains thus to the spiritual order. In another sense, however, it can also be said that the “substance” of a corporeal entity pertains to the intermediary domain: the “subtle”4As equivalent to the Sanskrit “sukshma” by which the intermediary region of the tribhuvana is characterized in the Vedic tradition. world which transcends the spatial but not the temporal bound. But inasmuch as the “substance” of a subtle entity pertains evidently to the spiritual domain, there is in fact no contradiction between these respective conceptions.
It has become apparent by now that the “subtle substance” of a corporeal entity corresponds to the Thomistic conception of a substantial form. I say “corresponds,” because the point of view implicit in our conception of “tripartite wholeness” does not coincide with the hylomorphic perspective: what we conceive as the “unbounded,” after all — so far from reducing to the nonentity of materia prima — pertains in fact to the highest level of cosmic reality. Yet it turns out that the tripartite and the Thomistic ontologies prove to be closely related, to the point, as we have said, that the “subtle substance” of a corporeal entity in the tripartite ontology reduces to a substantial form.
* * *
Physics deals ultimately, as we have noted, with functions f(x1, x2, x3, t) which bear reference to corporeal reality, howbeit by way of two stupendous reductions: first, a decomposition of the “container” into an infinite set of infinitesimal fragments, each defined by four coordinates (x1, x2, x3, t); followed by a quantification of the thus-fragmented content, which reduces that “infinitesimalized” constituent in effect to a density of some kind, defined in appropriate units according to the cgs or “centimeter-gram-second” system of standard magnitudes.
At first glance one cannot but be amazed that a strategy so disintegrating — and so “superficial” — can give rise to a science of immense efficacy, let alone to the discovery of so-called “laws of nature”: the laws of nature as we are told, no less! Admittedly there are factors in play which favor the enterprise, the most obvious perhaps being the fact that, under laboratory conditions, the system is prepared to conform to the very criteria of “uniformity” upon which physics as such is based. So too, in applications of physics to natural objects, the effects of nonuniformity may cancel on statistical grounds, as happens for example in the Newtonian calculation of planetary orbits, in which an entire planet, with all that it carries, is conceived as a single “mass point” located at its center. Yet it needs to be understood that considerations of this kind will not suffice to account for the possibility — let alone for the staggering “multi-decimal” accuracy — of a mathematical physics.
This brings us to the question of causality, and the point I wish to make above all is that there exist perforce two kinds: what I term the “horizontal” kind, which operates “in time” by way of a temporal process, and the “vertical,” which does not. But whereas, from our contemporary point of view, it appears that horizontal causation covers the entire ground, the opposite has now come to light: for given that the primal substance is subject neither to space nor to time, the absolute primacy of vertical causation is evident from the start.
It is apparent, first of all, that by virtue of acting “above time,” vertical causation originates in the highest ontological sphere: the one that is not subject to the bound of time. Yet inasmuch as vertical causation may act directly or by way of a substantial form, two possibilities present themselves on the lower planes. As regards the direct mode of action, this corresponds evidently to what St. Thomas Aquinas terms “the act of being,” conceived as “the most intimate element in anything, and the most profound element in all things, because it is like a form in regard to all that is in a thing.”5Summa Theologiae, I.8.1. Yet it must not be supposed that individual beings have no efficacy of their own: the fact is that every corporeal entity, in particular, endowed with a substantial form, does in truth have the capacity to act by way of vertical causation, a power which evidently attains its zenith on the human plane in what are traditionally termed acts of “free will.” And let me add parenthetically that the existence of such “vertical” acts can in fact be established rigorously on the strength of William Dembski’s so-called “design inference” theorem, which affirms, on mathematical grounds, that the production of what is termed “complex specified information” or CSI cannot be effected by way of horizontal causation alone.6See Physics and Vertical Causation, pp. 32-5.
* * *
Given that the primary mode of causality is vertical, horizontal causation cannot but be an effect of that vertical causality. There is thus a hierarchic distinction between the two: the vertical holds primacy. So too their respective modes of action are vastly different, and in a way complementary: the vertical acts instantaneously, as we have said, and over unlimited regions of space, whereas the horizontal operates by way of a temporal progression through a region of space. One might say that the vertical is a causality derived from wholeness, whereas the horizontal is derived from the parts — which brings us back to the issue of primacy: the fact is that, ontologically speaking, the whole has primacy over the parts. And this ontological recognition has scientific implications: it entails namely that horizontal causality applies to the extent that it is not “over-ruled” by the vertical; it applies thus in the limiting case in which effects of wholeness can be neglected. To which I would add that this way of looking at the matter has in fact been pioneered by the physicist David Bohm, who arrived at the realization — so very startling to the Einsteinians — that the breakdown of horizontal causation in the phenomenon known as nonlocality constitutes in truth an effect of what Bohm himself refers to as “wholeness.”7On this issue I refer to my article, “Pondering Bohmian Mechanics.”
To comprehend a science, it is above all needful to perceive its limitations; and it should be clear from the start that in the case of physics, the prime limitation stems from the fact that, by its very modus operandi, it obliterates wholeness in the most drastic manner conceivable. The wholeness of a corporeal entity, however, derives from its substantial form, which makes it incumbent to recognize that there are in fact different kinds of substantial forms. The most basic — and doubtless the most useful — classification is given by the time-honored distinction between mineral or inorganic, vegetative, sentient, and rational substances: we may think of these designations as defining four different degrees or levels of wholeness, and thus by implication, four corresponding “grades” of vertical causation.
A number of corollaries present themselves almost immediately, beginning with the realization that if horizontal causality fails to cover the entire ground in the inorganic domain — as the phenomenon of nonlocality demonstrates — what to speak of even the lowest levels of the organic, in which wholeness plays an incomparably greater role! It is hardly surprising, therefore, that by the time we arrive at the wholeness of homo sapiens, the preponderance of vertical causation stares us in the face, beginning with the prodigious output of CSI characteristic of the anthropos.
This leads quite naturally to the conclusion that horizontal causality applies on the corporeal plane in the limit when the effects of wholeness are sufficiently small to be negligible. Inasmuch, however, as it pertains to the very nature of the organic “whole” to control the structure and functioning of every part, down to a single cell, it is evident that this condition is nowhere met in the organic realm. It follows that physics can in truth be no more than the science of the inanimate — to which one should add that even in the inorganic realm, as we have noted, effects of “wholeness” break the generally assumed hegemony of horizontal or “mechanistic” causality.
* * *
Pre-quantum physics was said to be the science of “matter,” a hybrid notion which proves to be murky in the extreme. What interests us are two key points: first, that one arrives at this idea of “matter” by casting out all that traditional ontology knows as “form” or “substance”; and secondly, that this so-called “matter” is conceived to be inherently “granular,” which is to say that it consists ultimately of minute and indecomposable particles termed atoms. To be sure, there is a certain logic in these suppositions inasmuch as they conform evidently to the modus operandi of physics. Yet from the standpoint of traditional ontology, the conclusion imposes itself that such a proposed reduction of the whole to its “atomic” parts is fundamentally wrong-headed: that, ontologically speaking, the physicist is actually looking “downwards” in the direction of “outer darkness,” where all knowing and being come finally to an end.
It is safe to say that the discovery of the quantum realm in the early decades of the twentieth century came as a complete surprise to both sides: to the physicist, because what he discovered proved to be “sub-existential,” and to the philosopher, because he never expected that a materia signata quantitate8An expression used by St. Thomas Aquinas to designate a “sub-existential” entity defined in purely quantitative terms. could attain even that much “empirical” reality, let alone could give rise to a quasi-magical technology: to “signs and wonders that could deceive even the elect”! Yet even so the philosopher’s conclusion stands, now as before: the physicist is looking “downwards,” in the direction of “outer darkness.” And though it turns out that “between” the corporeal world and that “nothingness” there are atoms composed of protons, neutrons, and electrons — quantum particles which “half-exist” if you will — it has since become clear that, “beneath” this level, there is in effect nothing at all: the recent history of particle physics should suffice to make this abundantly clear.9The best reference on this topic is Sabine Hossenfelder’s Lost in Math: How Beauty Leads Physics Astray. A brief account may also be found in my article, “Lost in Math: The Particle Physics Quandary.”
Yet it cannot be denied that the physicists have made a stupendous discovery: midway between the corporeal world and “outer darkness” — which cannot after all be exorcised — they have detected an ontological domain made up of what the philosopher terms “materia signata quantitate,” entities which seem to attain a kind of weird reality of their own. The catch however, as we have seen, is that this “world” does not in truth exist!10I have dealt with this issue extensively, beginning with The Quantum Enigma: Finding the Hidden Key (Angelico Press, 2008). For a brief introduction I refer to the article, “From Schrödinger’s Cat to Thomistic Ontology.” One finds in the end that the quantum realm consists — not of actual entities — but of potentiae that can be actualized on the corporeal plane in basically three ways: by way of measurement namely, along with what I have elsewhere termed presentation and display.11These are technical terms introduced in The Quantum Enigma, the first of which refers to the corporeal object X represented by a corresponding quantum mechanical system SX, and the second refers to the visible representation of a physical process or entity, as in an oscilloscope or a cloud chamber.
It is to be noted that a discrepancy with our “tripartite” conception of corporeal being has thus come into view, which we need forthwith to clarify: for whereas we have conceived of the corporeal domain as simply the cosmos subject to the bounds of space and time, we are now confronted — within this very space and time — by a “subcorporeal” realm, which in a sense “underlies” the corporeal. We need thus to sharpen our conception of the latter: it no longer suffices to define corporeal being by its subjection to the bounds of time and space. What is it, then, that differentiates a corporeal entity, properly so called, from a conglomerate of so-called quantum particles? And by now the answer to this question is not far to seek: it is — and cannot but be — the fact that corporeal entities own a substantial form — which is tantamount to saying that they exist.
* * *
Long ago Richard Feynman observed that “no one understands quantum theory,” and this may yet prove to be the most profound statement on the subject ever made: how, after all, can one understand a theory which deals with a “world” that only half-exists! There are those, to be sure, for whom it suffices that quantum theory “works.” Yet, now as before, “no one understands.”
What, on the other hand, one can — and should by all means — understand is that the quantum world does not exist “by itself,” in separation from the corporeal: to think that it does would be to ascribe to the quantum realm an actuality which it does not possess. And once again it is Werner Heisenberg who has given us the requisite clue when he observed that “science [meaning physics] no longer stands before Nature as an onlooker, but recognizes itself as part of this interplay between Man and Nature.”12Das Naturbild der heutigen Physik (Hamburg: Rowohlt, 1955), p. 21. One might add that inherently the same conclusion had previously been reached by Sir Arthur Eddington, who went so far as to surmise that “the mathematics isn’t there until we put it there” — to which, in a poetic vein, he adds: “We have discovered a footprint in the sand; and lo, it is our own!”13The Philosophy of Physical Science (Cambridge University Press, 1939), p. 137. Regardless, however, of whether “the mathematics” is or is not there until “we put it there,” my point is that Eddington, no less than Heisenberg, perceives physics as an “interplay between Man and Nature.”
That “interplay,” however, cannot be effected without vertical causation; and the easiest way to recognize this fact is to reflect upon the act of measurement which connects the physical to the corporeal. We have here a transition from the physical to the corporeal plane, and it is self-evident that a transition between two distinct ontological planes cannot but be “instantaneous.” One finds thus that horizontal causality is simply not up to the task. Quantum measurement proves thus to constitute an incurably vertical act — which is of course precisely the reason why the so-called measurement problem proves to be insoluble on the plane of physics. The fact is that the “collapse” of the wave function cannot be understood in terms of the Schrödinger equation, to put it in quantum-mechanical terms: for an instant, that differential equation is superseded, as it were, and this instantaneity constitutes the “hallmark” of the vertical. As the Scholastics might say, vertical causality acts in the nunc stans: in the “now” that stands.
* * *
Having once recognized the necessity for the intervention of “instantaneous” acts, it becomes apparent that vertical causality enters the physical scene in a wide range of phenomena known as quantum entanglement, in which pairs or larger groups of quantum particles are mysteriously connected, so that the results of measurement, applied to individual particles within the group, are “instantaneously” correlated. Entanglement constitutes thus a certain wholeness which cannot be understood in terms of horizontal causality, and must consequently be ascribed to a vertical mode of causation — what Einstein famously ridiculed as spukhafte Fernwirkung: “spooky action at a distance.”
Entanglement ceases of course to be “spooky” above the corporeal plane: for where there is no more distance, there is also of course no “action at a distance” as well. The point is that vertical causation — acting, as it does, from the primary level of the cosmic trichotomy — “sees” no distance, if one may put it so, and can consequently act “across a distance” instantaneously. Entanglement can therefore be understood as a manifestation of vertical causality: in one way or another, thus, the entangled system must have interacted with a corporeal entity in the course of that “interplay between Man and Nature” from which physics as such derives.
What appears however to have puzzled physicists more even than quantum entanglement is its cessation on the corporeal plane. Once one assumes that the cosmos at large reduces to an ensemble of quantum particles, “decoherence” turns into an insoluble mystery: in a universe in which particles multilocate and cats can be both dead and alive, the world as we know it proves in fact to be inexplicable. The customary answer, to be sure — the one that comes instantly to mind — is that the bizarre features of the quantum realm, such as multilocation, cancel out statistically when it comes to ensembles large enough to be actually perceivable — which proves however not to be the case: this is, after all, what Schrödinger proved by way of his famous cat. The truth of the matter is that so long as all things reduce to quantum particles, the weirdness of the quantum realm bleeds inevitably into the macrocosmic domain.
It is thus imperative to realize that “all things” do not in fact reduce to quantum particles. Yet how many physicists will believe you if you were to suggest that there may indeed be “more things in heaven and earth, Horatio, than are dreamt of in your philosophy”! What needs to be grasped is literally “worlds removed” from the inherently mathematical conceptions to which physics has been reduced since the advent of quantum theory. As Sir Arthur Eddington may have been the first to observe, it is at that juncture — that point of transition — that “the concept of substance” disappeared from physics. And it is this “disappearance of substance” that defines the quantum realm, and entails that the latter does not in truth “exist”: that it consists — not of actual particles — but of potentiae “midway between being and nonbeing,” to quote Heisenberg once again.
The attempt to understand how the corporeal world arises from the physical — what is nowadays conceived as “decoherence” — cannot but falter, for the simple reason that the corporeal world does not in fact “emerge” from the physical. It is actually the other way round: for as Heisenberg and Eddington have recognized, it is “the interplay of Man and Nature” — and thus the corporeal world — that gives rise to the quantum realm. Attempts to explain the corporeal domain in terms of physics — and thus in terms of horizontal causation — prove hence to be ill-conceived; and no one among contemporary physicists seems to have grasped this more sharply than Steven Weinberg. “You can very well understand quantum mechanics,” he writes,
in terms of an interaction of the system you are studying with an external environment which includes an observer. But this involves a quantum mechanical system interacting with a macroscopic system that produces the decoherence between different branches of the initial wave function. And where does that come from…? And, strictly speaking, within quantum mechanics itself there is no decoherence.14Quoted by Sabine Hossenfelder, Lost in Math (Basic Books, 2018), p. 126; italics mine.
And the reason, moreover, why “there is no decoherence” in the quantum realm has by now become evident: it resides in the fact that decoherence demands vertical causation, which arises from a substantial form. There is no decoherence therefore within quantum mechanics itself, for the simple reason that in the quantum realm there is no substantial form.
* * *
Let us consider, finally, whether indeed “the mathematics isn’t there until we put it there” as Eddington claims. It is to be noted, first of all, that the quantum realm as such is an effect — not of horizontal — but perforce of vertical causality, for as we have noted in reference to the measurement problem, horizontal causality is restricted to a given ontological plane. Inasmuch as that vertical causality, moreover, arises from “an interplay of Man and Nature,” it arises not simply from Nature alone. The point is that Man — “we” as Eddington has it — have a part to play, and quite clearly it is the active part: it is “we” who ask the questions as it were, and it is Nature that gives the response. And that “response” is in effect the physical.
How, then, do we “ask the question”? We do so, clearly, in the capacity of the experimental physicist: by means of corporeal instrumentation that is. Yet the essential ingredient proves to derive from the theoretician: it is he who — by means of the experimentalist — “poses the question” that elicits the answer, and in so doing “puts the mathematics there” as Eddington has it. Yet it is Heisenberg who has the last word; for it is not actually “we” who “put the mathematics there,” but “Nature” — howbeit in response to our “question.”
This leaves open, of course, whether Eddington’s epistemological and group-theoretic derivations of that “mathematics” prove to be cogent. The fact that he calculates the fine structure constant, for example15Relativity Theory of Protons and Electrons (Cambridge University Press, 1936).— without reference to a single measurement — to be 1/137, which agrees with the empirical value to within three-hundredth of one percent, is of course astounding; yet, to my mind at least, reasonable doubt remains.
But be that as it may, the point is that so long as the quantum realm itself is defined through an “interplay of Man and Nature,” its “mathematics” too cannot but be “put there” by means of that very “interplay.” We are thus confronted, in the final count, by the momentous realization that the “footprint” we have discovered “in the sand” — proves, in the end, to be indeed “our own.”
* * *
A brief postscript, at least, may be in order to convey the fact that the conception of a tripartite cosmos, as here presented, is by no means foreign to the purview of Christianity; and I would make the point by citing the parable of the “leaven” hidden in “three measures of meal.”16Matt. 13:33 As I have argued elsewhere,17Physics and Vertical Causation, pp. 115-22. there is good reason to suppose that — apart from other admissible interpretations — the “three measures of meal” do in fact refer to the respective “tiers” of the tripartite cosmos. Not only, however, does the parable allude thus to a tripartite division of the integral cosmos, but it apprises us at the same time of two supreme truths: of the immanence and transcendence, namely, of God in relation to that tripartite cosmos. For whereas, on the one hand, the “leaven” is “hidden” in each of the three “measures of meal,” the parable itself affirms that it refers in truth to “the kingdom of heaven,” which as such immeasurably transcends the aeviternity of the spiritual or “celestial” realm. That Kingdom, thus, proves to be nothing less than the ultimate End of the spiritual quest, which surpasses the limits of the human intellect, and can therefore be alluded to only in parabolic terms.
The Philos-Sophia Initiative Foundation’s feature documentary chronicling the life and work of Dr. Smith, The End of Quantum Reality, is now available.
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|1.||↑||For those who respect the Judeo-Christian tradition I would point out that the “ego sum qui sum” of Exodus 3:14 suffices to make this abundantly clear. Moses had asked by what “name” God is to be known, and the answer he received was: “I am who am.” We are not suggesting, to be sure, that the cosmos shares in the eternity of God, but only that, on its highest plane, it likewise transcends the flux of time. This is what, in Scholastic parlance, is referred to as aeviternity.|
|2.||↑||Physics and Vertical Causation: The End of Quantum Reality (Angelico Press, 2019), pp. i-vi.|
|3.||↑||This is what, in nineteenth-century occultism, was known as the “astral plane,” and what the Orthodox Church refers to as the “aerial” world. But whereas nowadays this realm is virtually unrecognized and unaccessed in the West, it can in fact be entered and crossed by means which may in principle be termed “scientific”: the catch is that when it comes to sciences of this kind — which have existed in the past, and may still be operative in some forgotten corner of the globe — the “instrument” can ultimately be none other than the man himself, who by certain means can acquire requisite powers of perception in respect to the “inner” world.|
|4.||↑||As equivalent to the Sanskrit “sukshma” by which the intermediary region of the tribhuvana is characterized in the Vedic tradition.|
|5.||↑||Summa Theologiae, I.8.1.|
|6.||↑||See Physics and Vertical Causation, pp. 32-5.|
|7.||↑||On this issue I refer to my article, “Pondering Bohmian Mechanics.”|
|8.||↑||An expression used by St. Thomas Aquinas to designate a “sub-existential” entity defined in purely quantitative terms.|
|9.||↑||The best reference on this topic is Sabine Hossenfelder’s Lost in Math: How Beauty Leads Physics Astray. A brief account may also be found in my article, “Lost in Math: The Particle Physics Quandary.”|
|10.||↑||I have dealt with this issue extensively, beginning with The Quantum Enigma: Finding the Hidden Key (Angelico Press, 2008). For a brief introduction I refer to the article, “From Schrödinger’s Cat to Thomistic Ontology.”|
|11.||↑||These are technical terms introduced in The Quantum Enigma, the first of which refers to the corporeal object X represented by a corresponding quantum mechanical system SX, and the second refers to the visible representation of a physical process or entity, as in an oscilloscope or a cloud chamber.|
|12.||↑||Das Naturbild der heutigen Physik (Hamburg: Rowohlt, 1955), p. 21.|
|13.||↑||The Philosophy of Physical Science (Cambridge University Press, 1939), p. 137.|
|14.||↑||Quoted by Sabine Hossenfelder, Lost in Math (Basic Books, 2018), p. 126; italics mine.|
|15.||↑||Relativity Theory of Protons and Electrons (Cambridge University Press, 1936).|
|17.||↑||Physics and Vertical Causation, pp. 115-22.|