Reflections on Top-Down Causation

11 September 2020

John Taylor

Recently I penned an article for the Initiative on the phenomenon of “causal emergence” and its connection to vertical causation (VC). Now I would like to address the issue of a similar curiosity called “Top-Down Causation.” A term frequently employed by Dr. George Ellis, top-down causation is an effect where the higher or macro levels of a system direct the outcomes of the system’s lower levels in order to execute a higher-level causal requirement.1George F. R. Ellis, “Top-down causation and quantum physics,” Proceedings of the National Academy of Sciences  115:46 (2018). Evidently, just by definition this phenomenon is patently reminiscent of Aristotelian teleology. Like vertical causation, the examples of top-down causation are ubiquitous, and can be found in areas ranging from heart physiology, superconductivity, the arrow of time, to the quantum measurement process.2Ellis, ibid. It is the latter to which this article will largely devote itself, and examine in relation to vertical causation.

In 2018, a landmark paper entitled “Contextual Wavefunction collapse: an integrated theory of quantum measurement” was published by Drs. Barbara Drossel and George Ellis.3New Journal of Physics  20:11 (2018). Their publication delineates how the measurement procedure in quantum mechanics is intrinsically “top-down.” This manifests itself in a number of ways, one being that “the specific set up of the measuring apparatus determines the possible events which can occur.”4Ibid., pp. 1-2. Additionally, and perhaps more crucially, their work also reveals that these “macro” — or higher up — systems that induce state vector collapse are intrinsically classical.5Ibid., p. 21. Moreover, this principle extends not only to the “experimental measuring apparatus,” but also to its “thermal system” or “heat bath,” which like the former has been shown impossible to describe using a multi-particle wave function.6Ibid., pp. 12-21.

Drossel and Ellis declare that because a measuring device is “macroscopic and at a finite temperature” that it has to include a “heat bath with a macroscopic number of degrees of freedom.”7Ibid., p. 6. A heat bath is essentially a system in thermal equilibrium that emits a “non-zero temperature.”8Ibid., p. 17. Moreover, the detector’s heat bath is a classical entity since it can only be described using statistical mechanics and not by quantum mechanics.9Barbara Drossel, “Ten reasons why a thermalized system cannot be described by a many-particle wave function,” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics  vol. 58 (2017), pp. 12-21. Consequently, Ellis contends that it is the classical nature of the detector’s thermal system that causes collapse.10“Contextual Wavefunction collapse: an integrated theory of quantum measurement,” op. cit. To simplify immensely: this is because when a particle in superposition interacts with a detector’s heat bath, its wave function becomes affiliated with it. In turn this means that the dynamics of a quantum particle are forced to concord with the classical dynamics of the heat bath, which as a result instigates state vector collapse.11Ibid., pp. 15-6.

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However, it must be unequivocally stated that a heat bath is not a corporeal object, but instead a quantity associated with one; or what St. Thomas Aquinas would term an “accident.” This is the case because a heat bath hasn’t any qualitative attributes and typically emerges from a corporeal entity, which in this scenario is a measuring apparatus.  Nevertheless, although a heat bath is a quantity that betokens a substantial form, it still follows from this that a heat bath’s existence would be sustained by an act of vertical causation, by virtue of the fact that it is intimately affiliated with a corporeal object.

In The Quantum Enigma,  Dr. Wolfgang Smith details how, unlike horizontal causation, vertical causation operates “not from some distant past” but in the here and now.12San Rafael, CA: Angelico Press/Sophia Perennis (2011), pp. 109-25. Primarily, what this means is that VC not only brings an object into existence, but also sustains it there. That VC is able to achieve this owes to the fact that it is non-temporal and does not act via a direct sequence of events.13Smith, ibid. Therefore, because a heat bath is an accident of a corporeal  measuring device, it is reasonable to postulate that its existence is also held in place by this mode of causation — and this is precisely what we find!

In their paper on wave function collapse, Drossel and Ellis highlight how the “stochastic nature of a heat bath … allows it to forget the past and to establish an equilibrium state that is determined by nothing more than the macroscopic variables that control it.”14Op. cit., pp. 20-1. In other words, the stochastic dynamics of heat baths have a confined memory of their previous states, which inevitably results in their exerting little influence on the system’s future. Instead, it is principally controlled by factors in the present moment. These factors are “macro-variables” which determine the specific equilibrium state that the heat bath will be in.15Ibid., p. 17. Such a discovery — by Ellis and Drossel — arguably unearths a specific case of VC in action. For here is an example of a phenomenon that isn’t caused by a string of antecedent events — as in the Newtonian “clockwork universe” — but by something which exists in the here and now. Evidently such an effect is identical to the mode of causality Wolfgang Smith identifies as “vertical,” since in both instances the causal action is in the present; nor can either be characterized by a model wherein the system’s previous states are the sole dictators of its future.

Additionally, Ellis’ research employs the use of not only matter,  but also of form,  to explain the quantum measurement process. Aristotle said that physical entities have, in addition to a material cause, a formal cause. A formal cause is basically an object’s shape — or, literally, its “form” — and thus is the particular type of cause that can answer questions such as “why does a lake hold water?”; because of its shape.16Andrea Falcon, “Aristotle on Causality,” Stanford Encyclopedia of Philosophy (2019). Moreover, formal causes are those essential properties that make something to be what it is (e.g., it is the arrangement of DNA in a certain manner which makes a human a human and not a dog).17Falcon, ibid. Now in the case of quantum measurement, it is clear from Ellis’ analysis that material causes alone are not sufficient to explain the measurement process in quantum mechanics. Rather it can only be fully explained with a combination of both matter and form. For instance, Ellis declares that one “common feature” necessary for measurement to take place is for the “apparatus to have a macroscopic structure (i.e. arrangement of atoms) that is sufficiently stable before measurement.”18Op. cit., p. 6. Such an inference employs the use of not only a material cause (i.e. atoms are needed) but also a formal cause: note that Ellis insists it is the particular “arrangement of atoms” (matter) into a certain “macroscopic structure” (form) that allows it to be sufficiently stable. Henceforth, it can be reasoned that Ellis has shown that a combination of matter and form are needed to allow quantum measurements to happen. Primarily this is because he has demonstrated that it is not just “bare matter” at a certain magnitude that is required to make an apparatus “sufficiently stable” but also that this matter is “arranged” into a particular shape or structure. Thus Ellis and Drossel have shown that “form” is also needed because without the atoms being in a particular shape — or, more fundamentally, “what it is to be a measuring apparatus” — measurement would not be possible, as the structure would be unstable.

Ellis also dictates that it is the structure of the macroscopic measuring apparatus that provides “a macroscopic number of internal degrees of freedom that create the local heat bath.”19Ibid., p. 25. Now having just established that Ellis proclaims that both matter and, crucially, form are needed to produce a measuring apparatus capable of carrying out quantum measurements, one can deduce from this that the local heat bath is a product of the measuring apparatus’ structure/shape — which is to say its “form.”  Thus, because the heat bath is the “bridge from the quantum to classical”20Ibid., pp. 25-6. it can be said that it is the form of a measuring device that produces this “bridge,” as it is the structure of the measuring apparatus (consequently meaning its shape/form) which generates the heat bath.

Moreover, quantum mechanical top-down causation vindicates Aristotelian ontology by virtue of confirming his principle that “matter is relative.” Aristotle held that an object counts as “matter” relative to something else — or, more specifically, to the entity that it constructs.21Thomas Ainsworth, “Form vs. Matter,” Stanford Encyclopedia of Philosophy (2020). For instance, letters are the matter of words and words are the matter of sentences. Thus matter can be said to exist relative to “form” or the higher entities that it composes. Similarly, in quantum mechanics this principle can also be found. Particles can be said to exist in order to construct the classical universe. Henceforth, if Aristotle is correct that “matter is relative” it can be reasoned that these particles would only exist as “matter” in relation to the classical universe at large. Amazingly, this is precisely what we find. In a lecture given by Barbara Drossel, she highlights how when a system is “isolated from the rest of the world,” it can be described by a fully deterministic Schrödinger equation.22“How the Laws of Physics Leave Room for God’s Action.” Presented at 2019 International Academy of Philosophy. She goes on to say that the probabilistic “stochastic outcomes,” of wave function collapse to an “authentic particle,” only occur in relation to classical reality: an example of this obviously being the quantum measurement process, where “stochastic outcomes” only happen in relation to a classical measurement apparatus. Moreover, the whole process of deriving the probabilities associated with the wave function has to assume the existence of a classical reality to begin with, since the various probabilities that can be derived from it are always in connection to a classical entity (e.g., a measuring apparatus). Thus it can be said emphatically that the probability — and more crucially the outcomes of “particles” coming into being — is a phenomenon that only happens in relation to the classical world!

Drossel’s observation vindicates Aristotle by showing that matter is relative to form or what it exists to construct. Particles exist for the purpose of constructing the classical world, and here Drossel has shown that these particles can only be said to “come into being” and be probabilized in relation to that classical domain. Moreover, when a quantum system/wave function is not viewed in the context of “the rest of the world” it can be identified as a fully deterministic abstract entity — owing to the fact that it can be described by the Schrödinger equation. This, therefore, supports the notion that matter is relative to what it constructs (its form), because the “idea of particles” exists only in relation to the classical world, which is what they exist to build. Furthermore, this also directly supports Wolfgang Smith’s position that the wave function is quantitative potentiae  in relation to the corporeal domain. For here we have evidence of a system which under the context of isolation from the macro world is a fully deterministic, yet also abstract, wave; but when viewed in relation to the classical realm it can be identified as quantitative potentiae, of particles, relative to it. Thus it seems that top-down causation in quantum theory does indeed provide formidable evidence in favor of the ontologies of Aristotle and Dr. Smith.

Another fascinating phenomenon pertaining to top-down causation is the influence of abstract entities on the material universe. Dr. Ellis cites how computer algorithms, which are abstract, are responsible for impacting the behavior of electrons at the subatomic scale.23G. Ellis & B. Drossel, “How Downwards Causation Occurs in Digital Computers,” Foundations of Physics  49:11 (2019). In tandem with the physical structure of the computer’s hardware, these algorithms control the flow electrons so as to create a type of “structured interaction network.”24George F. R. Ellis, “Recognising Top-Down Causation,” arXiv:1212.2275 (2012), pp. 4-6. In effect abstract entities can therefore create a type of “substance,” with infinitely many virtual parts, that nevertheless acts as a unified whole (an idea championed by Robert Koons).25Robert C. Koons, “Thermal substances: a Neo-Aristotelian ontology of the quantum world,” Synthese  (2019). Now because a computer algorithm is abstract, or immaterial, it follows that it must employ, at least initially, a type of causation which does not propagate through space and time to effect outcomes in the real world. Hence the manner by which top-down causation effects change is in some situations analogous to the way that VC does.

Overall, top-down causation can perhaps be best characterized as an epiphenomenon in relation to a primary mode of causation — that is, vertical causation.  This can be inferred from the fact that although top-down causation shares many of VC’s attributes, it can rarely be reduced to it. Therefore it is possibly best to conclude that top-down causation is a by-product of vertical causation, or a type of “physics of the subcorporeal,” that works to realize the desired outcomes of VC. But although top-down causation is for the most part not synonymous with vertical causation, it does contain many examples where the influence of Aristotelian types of causation are clearly present. Perhaps no more profoundly is this found than in the quantum measurement process. To reiterate, Ellis has shown that it is not just bare matter at a specified magnitude which creates the heat bath or makes the apparatus “sufficiently stable before measurement,” but also the particular structure or shape of the measuring device that yields these effects. Thus because formal causation is essentially just an object’s shape, it can be deduced that Ellis has shown that formal causality is present within the quantum measurement process, by demonstrating that it is the structure/shape which makes the measuring apparatus stable for quantum measurements and also produces the “bridge from quantum to classical.”  Moreover, it can also be concluded that because the structure/shape of a measuring apparatus “creates” the heat bath, the “bridge from quantum to classical,” the form of the measuring device is genuinely responsible for enabling this transition from the quantum to the classical (or at least it is under the scenarios mentioned by Ellis). This in turn provides compelling evidence for the hypothesis that substantial form is responsible for wave function collapse.

With all of that in mind, it seems suitable to close this monologue by declaring that the discovery of top-down causation represents a significant milestone towards the vindication of vertical causation. It seems at last that the jig is now up! It is only a matter of time until physics, and science at large, professes the existence of a mode of causality, and also a worldview, that they have for long schemed to ignore — namely, vertical causation and classical metaphysics.

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John Taylor, a 19 year old student residing in England, hails from a family which includes a number of physicists. He is currently preparing to attend University College London this fall and discerning a vocation to the priesthood.

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The Philos-Sophia Initiative Foundation’s feature documentary chronicling the life and work of Dr. Wolfgang Smith, The End of Quantum Reality,  is now available.

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George F. R. Ellis, “Top-down causation and quantum physics,” Proceedings of the National Academy of Sciences  115:46 (2018).
Ellis, ibid.
New Journal of Physics  20:11 (2018).
Ibid., pp. 1-2.
Ibid., p. 21.
Ibid., pp. 12-21.
Ibid., p. 6.
Ibid., p. 17.
Barbara Drossel, “Ten reasons why a thermalized system cannot be described by a many-particle wave function,” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics  vol. 58 (2017), pp. 12-21.
“Contextual Wavefunction collapse: an integrated theory of quantum measurement,” op. cit.
Ibid., pp. 15-6.
San Rafael, CA: Angelico Press/Sophia Perennis (2011), pp. 109-25.
Smith, ibid.
Op. cit., pp. 20-1.
Andrea Falcon, “Aristotle on Causality,” Stanford Encyclopedia of Philosophy (2019).
Falcon, ibid.
Op. cit., p. 6.
Ibid., p. 25.
Ibid., pp. 25-6.
Thomas Ainsworth, “Form vs. Matter,” Stanford Encyclopedia of Philosophy (2020).
“How the Laws of Physics Leave Room for God’s Action.” Presented at 2019 International Academy of Philosophy.
G. Ellis & B. Drossel, “How Downwards Causation Occurs in Digital Computers,” Foundations of Physics  49:11 (2019).
George F. R. Ellis, “Recognising Top-Down Causation,” arXiv:1212.2275 (2012), pp. 4-6.
Robert C. Koons, “Thermal substances: a Neo-Aristotelian ontology of the quantum world,” Synthese  (2019).