John Taylor, Guest Contributor
The term “being” has taken on a number of competing meanings in contemporary philosophy. Some say that being concerns the essence or definition of a thing; others that it applies only to being of a very peculiar kind (such as human existence); and for some it’s a more or less arbitrary “quantifier” in a logical argument.
The key point for Wolfgang Smith, at any rate, is that being is—as it was for Plato—intimately connected to irreducible wholeness, a wholeness which cannot be reduced to a summation of parts. When one encounters irreducible wholeness (IW), one encounters a plenitude of being itself and therein a manifestation of the fulcrum from which the entire tapestry of cosmic reality emanates.1
This thesis is the bedrock of Dr Smith’s latest opus, Physics: A Science in Quest of an Ontology (PSQ). In the pages of this profound book he convincingly argues that the objects of classical physics are not discrete but rather possess a kind of quantitative version of irreducible wholeness, albeit derivatively:2 a “subcorporeal” object SX is the res extensa of a perceivable, “corporeal” object X.3 Corporeal objects, however, possess substantial form4—i.e., real being—and are therefore IW’s. And so any SX necessarily inherits a “quantitative IW” by its association with X.5
Prof Smith’s conclusions about objects SX thus carry profound implications for what he calls “subcorporeal physics.” But more intriguing still is the latter’s counterpart, “transcorporeal physics,” the physics of a domain situated outside the X–SX cut:6 while SX constitutes the objective quantitative structure of its associated corporeal object X—from which SX derives—the contiguity is disrupted when it comes to the transcorporeal.7 If we may identify the physics of the subcorporeal as classical, the physics of the transcorporeal is quantum-theoretic. Thus transcorporeal physics has a purely quantum mechanical modus operandi and is brought into existence, in a manner of speaking, by the intervention of the physicist.
The latter occurs through a two stage process.8 In the first stage, the physicist poses empirical questions to Nature, employing specialized corporeal instruments—such as Geiger counters or Stern–Gerlach setups—and these do the actual “questioning.” In the second stage, the physicist receives the “response” in the form of measured values registered by the corporeal instruments. Owing directly to this process, an element of IW enters the transcorporeal realm, on pain of not being able to do quantum physics to begin with.9 It is crucial to note, however, that although quantum objects are a product of irreducible wholeness, they are not IW’s of themselves. Instead, they are to be viewed as “mathematical potentiae,” powered or effected by the IW emanating from the corporeal measuring instrument.10
Given this synopsis of Professor Smith’s account, I wish now to see if we might discern some resonance between Smith’s paradigm and the inner workings of certain quantum mechanical phenomena, which I consider a very important angle to pursue. I will begin by giving a brief introductory to quantum theory, and then turn to some preliminary considerations on how irreducible wholeness plays a key explanatory role in quantum physics. I will close with a few thoughts on what I take to be the general character of the “transcorporeal domain”—reflections which will hopefully prompt further development of Wolfgang Smith’s Platonist ontology of physics.
Hermitian operators in quantum theory
Quantum mechanics emerged in the early 20th century in response to the realization that the understanding of particles in classical physics—i.e., as “tiny spheres governed by Newtonian laws”—was fundamentally flawed, and repeated experiments unequivocally demonstrated this inadequacy.11
The ensuing paradigm shift brought about such mathematical constructs as the “wave function” which provided a more precise description of particles. Within the framework of quantum mechanics, every physical space—specified by a Cartesian coordinate system—is associated with a wave function that assigns a complex number to each of its coordinates.12 The wave function can be transformed or “acted upon” using Hermitian operators, which are associated with specific observables, such as position, momentum, or spin. These operations yield probabilities intimately tied to the prospective measurement of observables.13 The position operator, for instance, works by multiplying the wave function by a variable known as an eigenvalue; this manipulation facilitates the derivation of probabilities of the measurement of particular positions, achieved by squaring the modulus of coefficients associated with the wave function (a fundamental concept encapsulated by Born’s rule).14
Technicalities aside—ones which nonetheless needed to be presented in anticipation of the discussion below—the upshot is simply that quantum mechanics has revolutionized our understanding of the fundamental nature of particles and their behaviour, replacing the classical paradigm with a rigorous mathematical formalism employing wave functions and operators to predict the outcomes of quantum measurements. The shift from a deterministic classical physics to a probabilistic quantum physics is no doubt the most stupendous advancement in the history of modern science, with far-reaching implications for our understanding of the universe at levels both empirical and ontological.
The complementarity principle
I’d like to now to explore some of the empirical phenomena wherein we might see how quantum theory stands in relation to Wolfgang Smith’s ontological interpretation.
The first point I would bring to one’s attention is the intriguing fact that the physicist’s choice of experimental apparatus determines his field of measurement (somewhat analogous to the affect of his choice of Hermitian operator). The primary reason for this is exemplified by Niels Bohr’s principle of complementarity. According to this principle, if the physicist chooses to measure a property A, the possibility of simultaneously measuring a counterpart property B is excluded15—at least insofar as he wishes to measure B with any degree of certainty. Indeed, the most celebrated example of Bohr’s principle of complementarity is the Heisenberg uncertainty relation, which stipulates that if one measures the momentum of a particle with precision, one is necessarily foreclosed from measuring or knowing its position with precision, and vice versa;16 neither can be known, with certainty, simultaneously. The complementarity principle is also seen in wave–particle duality, as well as the intrinsic limitations on simultaneous measurement of a particle’s spin along different axes.17
With regard to measuring device and that which is measured, there is a decisive divide between the classical and the quantum: that is to say, the outcomes of quantum measurements depend upon the settings of a classical measuring device—the latter determines which attributes of a quantum system will come within the sphere of empirical observation. In the Stern–Gerlach experiment, for example, the choice of apparatus dictates which of a particle’s spin components will be observed—be it along the x-axis, the y-axis, at a 45 degree angle, etc.18
Given that potential measurement outcomes are contingent upon the arbitrary choices made by the physicist, the ontological implication is that there is an implicit active connection between the classical and quantum domains—in Prof Smith’s nomenclature, between the subcorporeal and transcorporeal, respectively—supporting his assertion that the quantum “realm” comes forth as a direct result of the physicist’s insertion of IW into the transcorporeal.
This connection suggests a novel theorem within the framework of Smith’s philosophy of physics, namely that complementarity is itself an effect of IW, and the proof of this turns out to be quite simple:
P1: In complementarity we see that attempting to measure some observable X precludes us from simultaneously measuring its counterpart observable Y.
P2: This preclusion must be the effect of vertical causation, since it results from a change in the measuring instrument, as opposed to some spatio-temporal interaction between the instrument and the system under investigation.
Consequently, since IW is necessarily the source of all VC, complementarity is an effect of irreducible wholeness.
This “theorem,” if you will, builds upon the ontological framework established in PSQ, insofar as it reaffirms the role that IW is said to play in quantum mechanics, in this case through the lens of complementarity.
Space, time, and Hermitian operators
Further support for Wolfgang Smith’s ontological interpretation of quantum theory is recognizable in the fact that, unlike spatial position, there is no Hermitian operator for time in quantum mechanics. Time is only there as an external parameter, something “in the background.”19 The suspicious absence of a temporal operator in quantum theory is a strong indication that time is more foundational than space. This undoubtedly reinforces Dr Smith’s ontology, which posits an “intermediary” domain subject to time but not to space.20 That is, even as the transcorporeal is ontologically below the subcorporeal, and the subcorporeal below the corporeal, so the corporeal—bound by space and time—is below the intermediary.21
In any case, and on a broader note, Hermitian operators can be viewed as symbolic conduits of the injection of IW into the transcorporeal realm (which gives rise to quantum objects). At its core, the Hermitian operator instigates a top-down transformative process upon the wave function, reshaping it to generate probabilities regarding observables. Such alteration of the wave function arguably reflects the arrival of IW into the transcorporeal realm—a kind of miniature of the grander top-down process within the abstract mathematics of quantum theory. In an experimental context, quantum objects are fashioned through the top-down imposition of IW, and the very essence of quantum mechanics as an abstract theory is solidified by the top-down role that Hermitian operators play in conferring its remarkable predictive prowess.
In sum, much like subcorporeal—i.e., classical—physics, the mathematical fabric of quantum theory possibly harbours quantitative significations of irreducible wholeness, the significations being embedded within the Hermitian operators.
Vertical causation & Irreducible wholeness in quantum entanglement
Something else that speaks in favor of Prof Smith’s position is “entanglement.” As aptly described by Schrödinger, this phenomenon stands as “the defining feature of quantum mechanics that distinguishes it from classical reasoning.”22
In essence, quantum entanglement occurs when two or more wave functions establish a unique connection, giving rise to a state wherein their properties are intertwined, or “entangled.” A textbook example is when two electrons become correlated to the extent that the measurement of one instantaneously determines the state of the other. Consider that electron A is measured as having an “up” spin: this instantaneously determines that its partner, electron B, has a “down” spin—without a transfer of energy or information in space, regardless of the distance between them. The “instantaneity” of entanglement, then, affirms the authenticity of vertical causation.23
An equally intriguing facet of entanglement, which has been somewhat overlooked, lies in its relationship to irreducible wholeness. For when two quantum states or wave functions become entangled, the resulting quantum state cannot be reduced to the mere combination of the original two.24 Imagine, for instance, two wave functions X and Y. When entangled, the resulting wave function Z is not reducible to the combination of X and Y in any way. Instead, Z is in effect a new object, whose time-evolution cannot be modelled through the manipulation of X and Y.25 The fact that entangled states cannot be reduced to the wave functions from which they originated absolutely accords with Smith’s assertion that it is the injection of irreducible wholeness into the transcorporeal realm that makes quantum mechanics possible.
This outcome, however, does not entail that quantum or transcorporeal objects are literally, in and of themselves, irreducible wholes—e.g., the wave function of an entangled state remains reducible to a set of complex numbers associated with a function. The implication, rather, is that quantum objects are effected by the “injection of IW” into the transcorporeal domain by the agency of the physicist. After all, only a force which exceeds a mere combination of components is capable of generating something substantially greater than that of which its initial constituents are capable.
Intimations of Wonderland
Another phenomenon I would mention, recently discovered, is the so-called “quantum Cheshire Cat effect,” which involves not merely the distinction but the separation of certain accidental properties of particles from the particles as such.26
By way of illustration, consider a beam splitter, a device that can split a single particle (like a neutron) along two paths: one path determines the particle’s location, and the other path an accidental property, like spin. From a classical perspective, we’d expect the location and spin values to travel together along the same path. However, in the quantum Cheshire Cat experiment scientists have been able to manipulate conditions so that the particle’s path and the path of its spin are separated.27 It’s as if the grin (spin) of the Cheshire Cat travels down one path, while the rest of its body (location) travels down another!28
In consideration of this effect, we ought not—as some have suggested—introduce a sweeping revision of the long established distinction between substance and accident. Instead what we should reconsider is the assumption of an intrinsic connection between a so-called particle and the properties of that particle. The purported properties actually find their abode within IW, encompassing even what are commonly deemed their “essential” attributes, such as location in space.29 As Smith has asserted repeatedly, the domain of true being transcends temporal bounds—be it pre- or post-measurement30—which dispels the notion of “isolated” particles altogether, introducing the possibility that a particle’s properties actually pertain to irreducible wholeness,31 and this seems to be supported by the quantum Cheshire Cat effect.
Does the transcorporeal stand on its own?
The aim of this article has been to bring to one’s attention the fact that there appears to be compelling evidence, even on strictly empirical grounds, that Wolfgang Smith’s ontological interpretation of physics is right. We have noted, in particular, the corroboration of his assertion that the being of transcorporeal objects are the direct result of intervention by the physicist.
But before closing, there is one further point I’d like to propose: namely, that the ontological status of the transcorporeal sphere possesses an existence, albeit of a unique kind, in its own right. It is clear that the transcorporeal realm harbours quantitative potentiae, epitomized by quantum particles: for this “realm” to contain such potentiae, however, it follows that there must exist a substrate wherein these potentialities reside. The lingering question for me is whether the transcorporeal as such may in fact precede any manipulation—prior to any “injection of IW”—by the physicist.
My proposal is that the transcorporeal realm exists as yet another potentia. That is, the transcorporeal, on its own, stands as an unquantifiable potentiality—reciprocal, if you will, to the capacity to receive forms that gives birth to new quantifiable potentials. Furthermore, the transcorporeal realm also possesses the potentiality for its resultant objects to ultimately merge into a subcorporeal SX. But, unfortunately, the fleshing out of this proposition would require more space than I have left here.
Incidentally, to those acquainted with the categories of Scholasticism, I would address a potential misconception: It may be tempting to equate the transcorporeal with what Thomas Aquinas, for one, refers to as “prime matter”—matter wholly devoid of any form. This would be mistaken, for unlike Aquinas’ prima materia, the transcorporeal actually does exhibit a semblance of structure—indeed of “form”—but form of a strictly quantitative kind. So while the transcorporeal certainly pertains to materia, nonetheless it does not coincide with the notion of materia prima. It can, however, be posited as one step removed from that designation; it may be that the proper category, in the scholastic parlance, would be materia secunda and/or materia quantitate signata.32
In conclusion, I hope these reflections may serve as a foundation for future development of viewing contemporary physics in light of Wolfgang Smith’s Platonist ontology of physics. If my endeavour has been successful it will have yielded a few new insights into these matters and perhaps awakened the reader from the “dogmatic slumber” of mainstream interpretations of quantum theory. Prof Wolfgang Smith has opened up to us new avenues of inquiry and leaves us with much left yet to explore.
—
Acknowledgements
I would like to thank Wolfgang Smith and John Trevor Berger for their helpful insights and advice which aided in the completion of this article.
A recent graduate of University College London, John Taylor is currently studying at London School of Economics’ Department of Philosophy, Logic, and Scientific Method.
Physics: A Science in Quest of an Ontology (Philos-Sophia Initiative, 2023), p. 51.
Ibid., p. 27.
Res extensa, literally meaning “extended thing,” is an object conceived strictly as extended in space—and thus in its quantitative, measurable attributes alone—to the exclusion of all perceivable qualities (e.g. colour, texture, taste, sound). Every sense-perceptible object X is corporeal, and it determines an associated subcorporeal object SX, the latter consisting exclusively of the quantitative attributes of X.
In St Thomas Aquinas’ philosophy, a “substantial form” is a metaphysical entity which organizes the matter of a thing to actually be that which it is—i.e., its essence or nature.
PSQ, pp. 26-7.
The distinction between the subcorporeal and the transcorporeal was first introduced in Smith’s epochal work, The Quantum Enigma (Philos-Sophia Initiative, 2023), p. 35 (originally published in 1995 by Sherwood Sugden & Co.).
PSQ, p. 28.
Ibid., pp. 29-33.
Ibid., pp. 30-1.
Ibid.
Tim Maudlin, Philosophy of Physics: Quantum Theory (Princeton University Press, 2019), pp. 1-6.
Ibid., pp. 37-8.
Ibid., pp. 66-7.
Ibid.
Ibid., p. 17.
Ibid.
Ibid.
Ibid., p. 20.
Ibid., pp. 41-3.
Cf. The Vertical Ascent (Philos-Sophia Initiative, 2021), ch. 2.
In Smith’s philosophical cosmology, time and space are restricting “bounds” on being as such; thus, as one transitions from intermediary to corporeal, from corporeal to subcorporeal, and from subcorporeal to transcorporeal, one is moving further away from pure being and wholeness. Therefore, the absence of a temporal operator in quantum mechanics is not a mark of the ontologic superiority of space, but of the ontologic inferiority of the transcorporeal.
“Discussion of Probability Relations between Separated Systems,” Mathematical Proceedings of the Cambridge Philosophical Society 31:4 (1935), p. 555.
See again The Vertical Ascent, op. cit., ch. 2.
Vassilios Karakostas, “Forms of Quantum Nonseparability and Related Philosophical Consequences,” Journal for General Philosophy of Science / Zeitschrift Für Allgemeine Wissenschaftstheorie 35:2 (2004), pp. 287-9.
Ibid.
Yakir Aharonov, et al., “Quantum Cheshire Cats,” New Journal of Physics 15:113015 (2013), pp. 2-6.
Ibid.
Ibid.
To clarify: For a spatio-temporal particle, while the property of owning a spatial location is indeed essential, nevertheless the specific location it happens to manifest is arbitrary and therefore accidental.
PSQ, p. 51.
Ibid., pp. 37-8.
Wolfgang Smith has made a similar suggestion. Cf. The Quantum Enigma, op. cit., ch. 4.