William M. Briggs

Statistician to the Stars!

Quantum Mechanics, Potentiality, Ontology, Epistemology, & Probability

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What is and what is known about what is are two concepts which are often entangled, especially in quantum mechanics (puns intentional). This is one of the subjects which I cover in my upcoming book, incidentally, but which I’d like to expand in a second edition. (I’m assuming it’ll be a best seller.)

Here’s a lump of clay. It exists; it is actual. But also existing, in a sense, is the potential for that lump to be an ashtray (attention young readers: the ashtray was a device to catch cigarette ashes. I miss people smoking.) The ashtray is in the lump; it exists in potentia.

Now at the very top is a being of pure act, which is to say, God; a being (being itself!) in which there is absolutely no potency, i.e. no potential to change (we covered this in our Summa Contra Gentiles series). At the bottom (I use these positional terms metaphorically) is prime matter, stuff which is pure potential and which contains no actuality; you can’t measure or collect a bucketful of it. Everything else (including you) is in between, containing a mixture of act and potency. Some objects are weighted more heavily towards act, others towards potency (but there is no claim to form a numerical measure of this “weight”).

All this is preliminary to follow the paper “Werner Heisenberg and Thomas Aquinas on Natural Indeterminism” in New Blackfriars by Ignacio Silva.

Ed Feser in his must-read Scholastic Metaphysics has collected apt quotations from Heisenberg in describing quantum reality. Here’s one (p. 126, from H’s Physics and Philosophy; ellipsis in quotation):

The probability wave of Bohr, Kramers, Slater…was a quantitative version of the old concept of “potentia” in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of reality just in the middle between possibility and reality. (p. 15)

And, more to our point, this:

The probability function combines objective and subjective elements. It contains statements about possibilities or better tendencies (“potentia” in Aristotelian philosophy), and these statements are completely objective, they do not depend on any observer; and it contains statements about our knowledge of the system, which of course are subjective in so far as they may be different for different observers. (p. 27)

Regular readers recognize this is what I insist is the proper definition of “subjective” probability: people having different premises for the same proposition of interest. (The standard Bayesian view I reject because probability is not “feelings.”)

Finally to Silva, who spends most of his time showing Aquinas anticipated quantum mechanics, as it were, at least as far as causes go. He says, for instance, “Thomas explicitly rejects a rigid determinism in nature, i.e. the position that whenever there is a cause a certain determinate effect necessarily follows”, etc. The reasons for Aquinas advances for this are not quite quantum mechanical, however, but have more to do with unaccounted forces and the presence of multiple causes. Granting all this still does not tell us what actuality (God? our non-material intellects, at least sometimes?) reduces the potentia of a QM wave to actuality.

I can’t do the whole paper, but here’s Silva on what’s pertinent to us:

As we descend the degrees of being, the corresponding reduction in actuality correlates with an increase in potentiality, down to the forms of the elements, which are the closest to prime matter, pure potency…

Greater or lesser actuality comes from the participated esse, received by the essence. Essences which are closer to matter would be those that would have lesser actuality, thus, greater potentiality. The farther the substance is from pure actuality, the greater its potentiality, and thus the greater the possibility of an ineffective action. That is why Thomas says that there are three main spheres of action within reality: 1) that being which is only act [God], operates always without defect; 2) that which is only potency, pure matter, needs an act to actualise it; and 3) that which is a mixture of act and potency, every natural being, which acts perfectly most of the times…

We find, then, in every natural being a passive indetermination, which is essentially an imperfection or — more accurately and absolutely speaking – a lack of perfection in relation to the whole of being. According to the hierarchy of being postulated above, we can say that natural things, as they are farther from Pure Act, they participate less in act: they are less determinate.

Now there are some who argue the QM wave exists, i.e. it is ontic (see Ringbauer et al.). This existence is not specified, at least as far as I can tell, in terms of a mixture of actuality and potentiality; instead, the wave just exists. That means all the potential end states exist actually in some “superposition”. But then, since the wave-as-actuality “collapses” to one point, it must exist at least in potential to these end states. And it also exists in potentia in the sense the entire wave can exist potentially in other localities.

This is why it makes much more sense to go with Heisenberg (and Aquinas) and say the wave exists, like we do, as a mixture of actuality and potentiality. In what portions, I have no idea. A “pure” wave, interacting with nothing, would exist as pure potential, i.e. would be prime matter; though I doubt the QM wave is pure potential. But here is where my ignorance is most glaring. I don’t know enough to see what parts of the QM wave are actual and what part potential. Silva says “it does not sound very implausible to affirm that quantum mechanics is working and describing natural things which are great in potency and low in act.”

Silva also thinks QM waves “cannot be pure potency, as Heisenberg claimed, because they would be primer matter itself, which needs to exist under some kind of formality…For sub-atomic particles to be considered in potency, they need to be under a formal determination, and thus some degree of actuality”

Anyway, the main point (for us) is that our knowledge of the potential end states, which are not actual, is not the wave, even if we have full knowledge of the wave, but is a function of the wave (its “squared modulus”) and other premises. In other words—the exciting conclusion—probability is not actual, nor is it even a potential. It is fully epistemic. Probability doesn’t exist, even if wave functions do as full actualities. Silva (with his spellings):

In particular, matter in these quantum systems can take unpredictable forms, which are only predicted probabilistically by the wave-function included in the Schrödinger equation. Although matter is open to the reception of new forms, it cannot receive any form. The system described by the Schrödinger equation could only receive those forms included probabilistically in that equation.

In other words, not only does probability not exist, epistemically all probability is conditional on the premises fix, here by Schrödinger’s equation. (A QM wave for an electron is potentially, say, a particle and not potentially a Buick.)

15 Comments

  1. Well, I’m not sure what to make of all that, or if I understand it. One thing I’m sure of. This interpretation, like others, is not susceptible to empirical verification. Or is it?
    By the way, there is a book out on a Thomistic interpretation of QM.
    “Quantum Enigma–Finding the Hidden Key”
    (see W.A. Wallace’s review
    http://www.anthonyflood.com/wallacewolfgangsmith.htm)
    which I plan to read but haven’t yet.

  2. Good post. I’m curious about the notion that existing things, which are composites of prime matter and substantial form, may have varying “proportion” of potency and act. Is that what Silva states or implies? If so, on what basis would he be saying that?

  3. Briggs

    May 23, 2016 at 11:56 am

    Michel A,

    Silva gets it from Aquinas. I don’t have time to track it down at the moment (is this the right one?), but the rough idea is that potency implies imperfection. Anyway, it’s obvious enough that things are composites. A vase is potentially a collection of shards. Etc. etc.

  4. Having thought some more about the post, I would like to put the following question. How would one apply the principals in a particular situation, for example, the classical double slit experiment? How does an observer enter into the transition from potentiality to actuality? In other words, if the particle is observed before going through the slit, it behaves classically, i.e. the potential particle nature is activated before it goes through the slit. If it is observed AFTER it goes through the slit, but before it hits a detecting screen, the particle nature is also activated. Is that how it’s supposed to work?

  5. Ye Olde Statistician

    May 23, 2016 at 2:34 pm

    Perfection means “thoroughly made.” A thing is perfect when it lacks nothing required for being that thing. Imperfection is thus automatically a lack of such a such power/attribute, and such a lack necessarily implies a potency toward it.

    The lump of clay is not only in potency toward an ashtray, but also in potency toward a pot, toward a plate, toward a death mask, etc. These are called passive potencies. If they were numerically different rather than qualitatively/categorically different, we might capture all of them by means of a numerical function, which we may call a ‘wave’ function, rather than by simple listing. Once we have determined on a particular outcome, let’s say the ‘pot’, then all these potencies “collapse” onto a single potency and the pot is now an active potency of the lump of clay.

    The change of the clay from lump to pot is called kinesis (or ‘motion’) and is conceptually important to the “Argument from Motion,” which might otherwise be thought erroneously to be a theory in physics. As the motion proceeds, potency is reduced and actuality is increased. The clay becomes more and more actually a pot. It is being perfected in its pottiness.

    The process may terminate in several ways. The potter’s wheel may seize up and the clay ends up as an imperfected pot. Termination is one sort of telos. Or the process may run to completion and the pot is perfected — that is, it contains all the features that had been intended for This Pot. Continued processing will actually degrade the pot and make it less perfected. Perfection is a second sort of telos. (Of course, even such a pot may contain imperfections, called “de-fects,” which are diligently sought out by the QC inspector. If the pot contains too many defects, then it is smashed in the outer darkness.) These collectively comprise the Quality of Execution.

    A third sort of telos we’ve already alluded to: the decision that the clay would become a pot in the first place. This is the telos of intention, or the Quality of Design. The pot itself is the final cause: the intention to mold it is the reason why the lump of clay was thrown on the wheel in the first place.

    An interesting medieval question: as the clay is being molded, is there a first moment when it is a pot? A last moment when it is simply a lump of clay? Are these these the same moment? This led the medievals to the idea of what we now call open sets and to the very brink of the Dedekind cut.

  6. Matt,

    Thanks. I understand that a given thing (vase) has more potentiality in some respect (to become shards) than another. What I don’t really see is that within the realm of composite beings there should be general (in all respects) degrees of potentiality, i.e., that a given composite thing could be closer to prime matter, as it were, than another. And I don’t really see Aquinas arguing that. His hierarchy had to do with the broader classes of beings: pure act, angelic beings, substances, and prime matter, no?

    Michel

  7. Given that matter and energy are the same thing (although one is congealed and the other isn’t at any particular moment), then every thing potentially is (at least part of) any and every thing else. Yes?

  8. Maybe I’m just stupid, but this seems to me (like Godel’s incompleteness and related ramblings) mere quailing in the face of the infinite. Three things to note:

    1 – Heisenberg wrote in German; so what he actually tried to say and what he is interpreted as having said by non physics speaking translators are often quite different. In this case, the principle merely says that measurement affects outcome. As in, duh.

    2 – there is no wave collapse in physics. EM/object propagation is sometimes best modeled as a wave, and sometimes as a particle, a “collapse” marks the “point” ( sure, but, you know: language) at which the usefulness changes – but we need to understand that both methods are approximations that do not describe whatever the thing really is, they only help us describe its behavior (and predict our description of its future behavior) under some rather special circumstances.

    3 – as for the act potential business: it’s a cool intellectual construct but not any more obviously related to reality than the stuff that comes out of the back end of male bovines does. I suppose it’s as a good an analogy as any and it’s certainly consistent with historical thought, but let’s make sure we remember that’s what it is and not run off too far saying it be applied to prove anything until that either happens or it doesn’t.

  9. Sander van der Wal

    May 23, 2016 at 4:36 pm

    The universe is ruled by gravity at a large scale. Gravity gives you stars that make matter that is able to be the clay to turn into an ash tray. So, even if this equivalencing the Schrödinger equation with potentiality and act, you miss out on the big one.

  10. To all those puzzled or bemused by Matt’s insistence on classic act/potency analysis uber alles, take heart.

    For in his apt summary of aspects of ‘perfection’ and ‘potency’ within classic Aristotelianism, YOS remarks > “This led the medievals to the idea of what we now call open sets and to the very brink of the Dedekind cut.”

    Not exactly. More importantly, it led the medievals to nominalism, which is now ascendant, and has been a coruscating influence on rationality, philosophy, and theology, and through them all science, since then.

    It is sadly typical of classic Aristoleians/Thomists –commonplace– that they never see that postmodernists also seriously ask, when does clay become a pot? Postmodernism asks exactly the same questions about identity, and its fixedness, that the classic act/potency paradigm drove the medievalists to ask.

    And classic Aristoleians/Thomists certainly never observe that this “coincidence” of question between inquiries otherwise radically incoherent to each other, may mean that the question itself may be radically ill-formed, indeed, poisonous to inquiry, and may therefore be the very thing that generates the basic trouble. Of course, such thoughts cannot really even be thought, since (to convinced classical Aristoleians/Thomists) the act/potency account, as classically conceived, is coterminous with Reality.

    Far more importantly, beginning prominently with Berengarius in the 11th century, the same medievals, prompted by the same misbegotten hermeneutic, began to ask the identical question of “Hoc est enim Corpus Meum” — “This is My Body”. The dire theological repercussions persist to this day.

    Fr. Donald J. Keefe, SJ, in Vol. II of his Covenantal Theology, points out that St. Thomas is unable to give a coherent account of the Eucharist within the classic act/potency analysis. For one thing, the sacramental signs of bread and wine are indispensable to sacramental efficacy, according to faith; and St. Thomas agrees. But methodologically, within the strictures of Thomas’s act/potency analysis, the bread and wine are not truly significant at all. In fact, they are utterly replaceable. This of course completely contradicts the profession that the bread and wine are indispensable to the sacrament. The Summa Theologiae thus provides no methodologically coherent account of the Eucharist, the heart of the Church, her Source and Summit. One might thus observe a certain failure in the methodology deployed in the Summa, were one not an already-convinced Thomist:

    The matter-form analysis of the Eucharistic sign, as Thomas employs it, places all sacramental efficacy in the words of consecration;i if we take seriously the meaning of form and matter in the Thomist act-potency analysis, it is clear that only by the “form” of the sacramental sign (sacramentum tantum), viz., by the words of consecration, do the bread or the wine signify and cause what they signify. That the bread and wine, as signs, are indispensable to this efficacy must be conceded–and in fact this is insisted upon over and again by St. Thomas, for if the bread or the wine is corrupt, or substituted for by invalid matter, there is no sacrament–but he provides no act-potency explanation for their indispensability. If the words of consecration are truly the formal content of the sacramental sign, the matter upon which they bear cannot but be formally insignificant; as material causes, they can do no more than individuate the sign in space and time, for which purpose any material whatever would suffice. [Covenantal Theology, 2nd ed., p. 422.]

    Speaking of QM, it is interesting that a reader reently alerted Jerry Pournelle to a recent revivification of Bohmian mechanics, over against both the Copenhagen and Many Worlds interpretations.

  11. Matt,

    I found this post interesting but I didn’t quite understand it. There must be a book that’s a good general introduction to philosophy for a curious reader with little exposure to philosophical arguments. Do you have any recommendations?

  12. “In other words, not only does probability not exist, epistemically all probability is conditional on the premises fix, here by Schrödinger’s equation.”

    The same goes for potentiality.

    And you wish people still smoked? Really? 😐 What, are you still hangin on to your old RJ Reynolds stocks? You better hope there’s not a God!

    JMJ

  13. John K,

    “If the words of consecration are truly the formal content of the sacramental sign, the matter upon which they bear cannot but be formally insignificant; as material causes, they can do no more than individuate the sign in space and time, for which purpose any material whatever would suffice.”

    This statement reveals a misunderstanding of what happens during substantial change. Matter (secondary matter, that is) has to be properly disposed to receive a given form.

    “Furthermore, every substantial form requires a proper disposition in matter, without which it is not able to be; whence the way towards generation and
    corruption is alteration. (De Mixt. Elem., n. 17–18)”

    Generation depends on both preexisting matter and form, each making its own distinct metaphysical contribution:

    “Matter is prior to form from the point of view of generation and time because that to which something comes is prior to that which comes to it. But form is prior to matter from the point of view of substance and completeness, because matter has completed existence only through the form. (De Princ. Natur., n. 32)”

  14. beortheold: You might find the book, The Last Superstition, by Edward Feser helpful for an explanation of actuality and potentiality. Personally I found the book’s salty take-down of materialism highly entertaining. He also has a philosophy blog that is anything but dry with its frequent references to popular culture, especially sci-fi works, and much manly intellectual sparring.

  15. Jean: thanks for the recommendation.

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