Philosophy

Quantum Potency & Probability

A note on a complex subject. Ed Feser points us to the paper “An Aristotelian Approach to Quantum Mechanics” by Gil Sanders, and in turn Sanders points us to “Taking Heisenberg’s Potentia Seriously” by Kastner, Kauffman, and Epperson. Feser’s book Scholastic Metaphysics is also not to be missed.

Heisenberg was, of course, brought up when Aristotle’s notions on the distinction between act and potency were still taught. He thought those ideas useful in explaining quantum (= discrete) curiosities that were flooding through physics.

Sander’s paper is a gentle and informative introduction to these topics, while Kastner et al. go a little deeper. Below are some quotes. I believe they are useful in dispelling the recurring idea that probabilities are ontic, i.e. real things. Probability is purely epistemological, a relative measure of evidence, whereas potency is a real feature of objects. I urge you to read the papers themselves; they are not long. If you know about Aristotelian beneathphysics already, then jump to the end about probability.

Sanders (the set up in brief):

A wave function is a complete mathematical description of the properties of particles (represented as state vectors) in a physical system. By itself the wave function is a superposition of all possible state vectors. With Schrödinger evolution, the wave function evolves as a linear superposition of different states. It is deterministic in that the current vector state will physically determine the resulting vector state. If we could know all the proceeding conditions, we could predict with certainty what the resulting state vector would be. The wave function generally evolves in accord to Schrödinger, but once some form of measurement is performed, the wave function collapses in the sense that it no longer operates in accord to Schödinger’s equation but in accord to the collapse postulate. Through a linear combination of these state vectors, the once indefinite superposition of state vectors nondeterministically produces some definite state vector. In other words, the collapse postulate tells us that once a particle is measured, it is no longer in a superposition of different states but collapses into a particle with definite properties and a definite position in a nondeterministic manner.

Sanders (Aristotle is on his way):

The methodology of physics is such that it must use the exceedingly abstract tools of mathematics in order to perform its inquiry. Mathematics is inherently quantitative and structural by nature, thus it is in principle incapable of capturing qualitative aspects of nature in the same way that a metal detector is in principle incapable of detecting plastic. Whatever does not fit this quantifiable method, like immanent teleology and causal powers, must be ignored; only mathematically definable properties are discoverable. The wave function, for example, is a mere abstract equation that is standardly interpreted to be a representation of something concrete, but as to what that is we do not know. At best physics can only give us a partial description of reality (unless abstract structure is all that exists), it fails to tell us what is the inner qualitative nature of the thing that exhibits this mathematical structure.

Sanders (Aristotle has arrived):

According to the world renowned physicist, Heisenberg, the wave function “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 physical reality just in the middle between possibility and reality” (1958, 41)…

A potentia is simply a thing’s potential to have its qualities or substance changed. For example, a piece of glass has the potential to shatter or it has the potential to melt into a fluid. The former kind of change is a change of qualities or accidents, whereas the latter is a change in substance. This stands in contrast to actus, which refers to the way a thing actually is here and now… A potentiality should not be confused with mere possibility. It is possible for a unicorn to exist, but it is not possible for a piece of glass to become a unicorn because it lacks that potential whereas it does have the potential to break. A piece of glass’ actuality limits the potential range of things that can be actualized.

Sanders (Aristotle has filled the room):

[Modern physics restricts] the “real” to actuality because their view of matter is still mechanistic, where material objects are mere forms, which corresponds only to actuality. The Aristotelian conception of matter is decidedly hylomorphic in that all material substances are composed of form and matter. Form (or structure) corresponds to actuality, whereas matter corresponds to the potency that persists through change. This matter is the substrate of a material substance that is receptive to different forms, whereas the form gives definite structure to the matter…Since matter and form are just more specific instances of potency and actuality, we already know that this analysis is plausible given the above argument for Aristotle’s act-potency distinction.

Sanders (skipping over a justification of hylomorphism and a proof that potency has a kind of existence, then this):

Additionally, hylomorphism entails a gradual spectrum of material beings with greater degrees of potentiality to greater degrees of actuality. Something has greater actuality if it has more determinate form (or qualities) and something has higher potency if it is more indeterminate with respect to being more receptacle to various forms. For example, a piece of clay has higher potency insofar as it is more malleable than a rock and thus more receptacle to various forms. A rock can likewise be modified to receive various forms, but it requires a physical entity with greater actuality or power to do so because it has more more determinate form as a solid object… [H]ylormophism predicts that you will find higher levels of potency because you are getting closer to prime matter. This is precisely what we find in QM. The macroscopic world has more actuality, which is why we experience it as more definite or determinate, whereas the microscopic world has far less actuality, thereby creating far less determinate behavioral patterns.

Sanders (finally QM):

Let’s start with the wave function, which if you recall, initially describes several mathematical possibilities (aka superposition) prior to collapse. QM forces forces us to reify the wave function in some way because by itself it would suggest that the quantum world only exists when we are measuring it, which is rather absurd….It’s far more plausible to interpret the wave function as real insofar as it describes a range of potential outcomes for particles that are low in act but great in potency. This view reinterprets superpositions as being the potentials of a thing or state, not as actual states in which all possibilities are realized.

Sanders (more QM):

Thus collapse occurs when there is contact between a perceptible object and a non-perceptible particle whereby contact with the perceptible object actualizes a particular potential (spin-y as opposed to spin-x) of the particle into a definite state. The actualization of certain outcomes at measurement has the result of affecting the range of potential outcomes of some other particle: “actual events can instantaneously and acausally affect what is next possible” (Kastner, 2017)… This problem is resolved if you’re an Aristotelian. Suppose you intended to visit Los Angeles but unbeknownst to you an earthquake sunk that traffic-ridden city into the ocean. This actualized event changed the range of potential places that I (or anyone else) could visit without acting upon other persons. In other words, actuality cannot directly alter a distant actuality without interaction but it can instantaneously and acausally change a distant range of potentials.

Kastner (skipping over the same material discussed in Sanders; the Kastner PDF was built, I’m guessing, from Windows, making it very difficult to cut and paste from; thus my laziness explains why I quote them less):

We thus propose a new kind of ontological duality as an alternative to the dualism of Descartes: in addition to res extensa, we suggest, with Heisenberg, what may be called res potentia. We will argue that admitting the concept of potentia in to our ontology is fruitful, in that it can provide an account of the otherwise mysterious nonlocal phenomena of quantum physics and at least three other related mysteries (‘wave function collapse’; loss of interference on which-way information; ‘null measurement’), without requiring any change to the theory itself…

As indicated by the term ‘res,’ we do conceive of res potentia as an ontological extant in the same sense that res extensa is typically conceived—i.e. as ‘substance,’ but in the more general, Aristotelian sense, where substance does not necessarily entail conflation with the concept of physical matter, but is rather merely “the essence of a thing . . . what it is said to be in respect of itself”.

Of course, “one cannot ‘directly observe’ potentiality, but rather only infer it from the structure of the theory.” If we could measure it directly, it would be actus not potentia. They use the phrase quantum potentia (QP).

Probability

The belief that all things had to be all act, pure actus, and contain no potentia accounts for many of the confusions about QM. One of those confusions was the concepts of probability and “chance”. Physicists were reluctant to throw away the useful idea of cause; there had to be some causal reason “collapse” was happening. That collapse is the movement of a potential to an actual, but they didn’t see it that way, thinking the superposition of waves was all act. How did this happen? Probability was discovered to be indispensable in applying and understanding QM. Thus some thought probability itself was ontic, that chance was an objective feature of the world, and that probability/chance was the causal agent that selected the collapse point.

After all, isn’t QM probability calculated as a mathematical-function of the physical-wave-function? Didn’t that make probability real?

Well, no. It’s true the probability is a mathematical-function, something like the “square of the corresponding amplitude in a wave function”. The probability thus takes as input aspects of reality, a reality (the wave) which contains both act and potential, and spits out a number. But so what? Conditioning on measures of real things doesn’t turn thoughts about things into the things themselves or into causal forces. (This does not rule out the mind-body projecting energy, but I don’t believe it can, and that is not what turning thoughts into causal forces means.)

If I tell you this bag has one black and one white ball and one must be drawn out blind, the probability of drawing a black is a function of reality all right, but your thoughts about that probability isn’t what is causing your hand to grasp a ball. There is no probability in the bag. Or in your hand, or anywhere except in your thought. That’s easy to see in balls-in-bags because, as the two papers emphasize, we are dealing with objects that contain mostly act. That the balls have the potential to be all sorts of places in the bag is what makes the probability calculation non-extreme (not 0 or 1).

This is made even more obvious by recalling two physicists can have different probabilities for the same QM event. Just as two people could have two different probabilities for balls in bags. Person A has the probability 1/2, given just the premise above, but Person B notices the bottom of the bag is transparent; Person B has probability 1 of drawing the black. Physicist A knows everything about the measurement apparatus except for one thing newly learned by B, an additional physical measure. Both have different probabilities. It will turn out, in both cases, B makes better predictions. But in neither case could the probabilities have caused anything to happen. Indeed, Person B has an extreme probability because the cause of selecting black is perfectly known—and obviously isn’t the probability.

Physicist B does not have that advantage Person B has. For in Physicist B’s case, we have a proof that we can never reach extreme probabilities for certain class of correlated (in the physics use of that word) events. It has to be something in act that moves the potential in the wave to act (“collapse”), but what that is is hidden from us. That isn’t “hidden variables”; that’s an understanding our knowledge of cause is necessarily incomplete.

Consider Kastner:

[W]e might plan to meet tomorrow for coffee at the Downtown Coffee Shop. But suppose that, unbeknownst to us, while we are making these plans, the coffee shop (actually) closes. Instantaneously and acausally, it is no longer possible for us (or for anyone no matter where they happen to live) to have coffee at the Downtown Coffee Shop tomorrow. What is possible has been globally and acausally altered by a new actual (token of res extensa). In order for this to occur, no relativity-violating signal had to be sent; no physical law had to be violated. We simply allow that actual events can instantaneously and acausally affect what is next possible…which, in turn, influences what can next become actual, and so on.

They mean causal in the efficient cause sense, of course; and we needn’t agree with them about physical “laws”. The probability, in their minds, ignorant of the closing, that they will meet inside the coffee shop is high (close to or equal to 1 depending on individual circumstances). That they will meet inside won’t happen, though. They did not have the right information upon which to condition. That knowledge was not a hidden variable in any causal sense. Bell lives on.

Now about how all this works in individual experiments, and the relation to probability, we’ll leave for another time.

Categories: Philosophy, Statistics

23 replies »

1. Beautiful. Just beautiful. Thank you for this.

2. Sander van der Wal says:

As far as I understands this, an electron with two different spin states is actually in spin state ‘up’, and potentially in spin state ‘down’. Or the other way around. This is because matter is always in one particular state, and is potentially in other states. Matter is not actually in no state at all, and potentially in all states.

The theory behind the Schroedinger Equation says something else, again, AFAIK. Unless one measures, matter is potentially in all possible states, but not in any actual state. The Schroedinger Eqation lets you compute the chance that a particular piece of quantum matter will be actually in a particular state at the time of measurement.

3. JohnK says:

So, now there are three: the Copenhagen Interpretation, the Many Worlds Interpretation, and now the Act/Potency Interpretation. But why stop at three? Matt has a proof somewhere of how one can multiply post hoc interpretations infinitely. There’s always another possible curve one can fit to a given set of data points. But how to choose among them?

Actually, the very venerability of Aristotelianism is a mark against it in this instance. Act/Potency categories certainly didn’t predict, or even suggest, quantum mechanical effects in advance, to anyone. That’s a pretty big black mark against it, if you ask me.

And Aristotelians must now in effect say, “We knew all along that these effects are perfectly consistent with an Act/Potency analysis” — except, they didn’t know that all along.

As far as I know, the Act/Potency Interpretation is new. So it took — what — a hundred years, before Aristotelian savants noticed that the Act/Potency analysis was obvious here?

Not saying it’s wrong, not saying it’s right. Just saying: there’s a lot of curves that can be fitted to a given set of data points.

4. reighley says:

I do not like the coffee shop analogy. The shop itself is a local hidden variable, perhaps not local to me at the time my coffee potentia is changed, but local to me when I show up to the coffee shop to take a measurement. That’s the important thing. The disturbing thing about the Aspect experiment is not that my coffee potentia and yours are correlated in so far as I will not have coffee with you if you will not have coffee with me. That is not hard to account for. The problem is that this correlation can occur even if we are outside of each others light cone. What if (for reasons which are totally mysterious) whenever I had coffee with my friend you had coffee with yours even though we are far apart. I try to use this phenomenon to send a signal to you faster than light by carefully controlling the timing of my coffee dates, but I find I can’t control the causal variables in my coffee habits tightly enough. I try to randomize my coffee consumption, so as to eliminate the possibility that this is a deterministic phenomenon rooted in the past when our light cones intersected. The phenomenon persists! Whatever the efficient cause of my cup of coffee is, it touches my random number generators also. Surely this is more than a little strange, and it remains strange after the measurement; by which time we might have thought all the potentia would be actualized. Casting the wave function as potency rather than act does no good, because we still need an efficient cause for the events as they turned out and a potency can’t be it. I definitely look forward to an analysis of a particular experiment in Aristotle.

5. John B() says:

As long as Schroedinger has been mentioned, I have an issue with the conclusions drawn from his cat in-the-box thought experiment.

From elementary logic, to draw the conclusion that the cat is both dead AND alive is wrong.

If we cannot say that the cat is alive or dead (Ca V Cd) then … we have ~(Ca V Cd)
Distributing the not (~) through the expression yields ~Ca ^ ~Cd

The most we can say is that the cat is NOT dead AND that the cat is NOT alive.

Throughout literature we have ideas of “the un~dead” … an accident victim is more dead than alive … or may as well be dead … Doctors deciding when to pull the plug or when to remove the feeding tube.

Of course there is the whole Living Dead thing …

6. Ye Olde Statistician says:

@JohnK: You have neglected to mention Bahm’s Standing Wave interpretation and Cramer’s Transactional interpretation. But you correctly note that modern inductive science is inherently underdetermined and through any number of data points one may draw innumerable theories.
###
Back in 2014, I described Aristotelian motion using these terms:
The motion of a thing is always toward something which that thing has in potential, and a motion consists in some sense of being what-it-is-now and what-it-is-going-to-be. The original potency is made actual in two ways.

A set of building materials has the potential to become a house. It also has the potential to become a barn for storing grain, a scaffold for dealing with impertinent comm boxers, a grandstand for others to watch the aforesaid entertainment, or it may remain a set of building materials. It does not have the potential to become an aardvark, so it’s not Heraclitus’ “Anything Goes.”

When construction begins, the “wave function” of all those various potentialities collapses to a particular potential aimed at the one particular end, let’s say a house. This is the first act: the potency becomes an “actual potency.” The second act is when the kinesis reaches its equilibrium state (final cause): the house is actually finished. Between the first and second act … is what Aristotle called ‘motion’ or kinesis.

“Building” in either sense [participle or noun] is not the actualization of the house. It is the actualization of the building materials.

7. Ye Olde Statistician says:

Bohm, not Bahm.

8. BB says:

There are several reasons why the Aristotelian’s didn’t jump from their own knowledge of the Act/potency distinction and start developing quantum mechanics. I would like to mention a few of them. Firstly, Aristotle didn’t think that physics should be explained mathematically. This was one of the most important distinctions between Aristotle’s and Plato’s thoughts. This led to a prejudice against the early mathematical physicists of the fourteenth century among the Aristotelians, and an even stronger prejudice against Aristotle in those who took that medieval work and developed it into modern science. A second reason is that the required mathematics was unavailable to them. Modern quantum physics relies not only on calculus, but also differential geometry, group theory, topology, vector spaces, complex analysis and probability, none of which reached the necessary maturity before the nineteenth and twentieth centuries, well after the heyday of scholasticism. Thirdly, they didn’t know enough physics. A strong knowledge of optics and electromagnetism at the very least is a necessary pre-requisite to quantum physics, and those subjects were only just starting to be studied systematically in the early fourteenth century when scholasticism was at its peak. Fourthly, the analogy between act/potency and quantum eigenstates is not perfect; for example Aristotle’s philosophy had no knowledge of the ideas of superposition or that you could have different bases representing the same thing. One of the comments above mentioned an electron being either spin up or spin down, and if it was actually spin up it would be potentially spin down. Aristotle would have understood that well. The complication is that one also has to think about the direction or basis. Spin up in one direction would in another direction be a superposition of spin up/spin down states — if its spin in one direction is defined, then in any other direction it must be undefined. Fifthly, the experimental motivation for quantum physics needed twentieth century technology. Quantum physics is weird; there are aspects of it which defy common sense (for the Aristotelian as much as the mechanist) — not least the idea that uncertainty should be primarily parametrized in terms of amplitudes rather than probabilities, and without experiment to kick you in the right direction its difficult to see how anybody would go there.

Thus the Aristotelians weren’t motivated to develop a mathematical theory of act/potency, didn’t have the required mathematics or physics to do so even if they were, and would need to be prepared to make some minor departures from Aristotle, and think in ways which defy common sense. And even if they surmounted all of that, they would still have no evidence for their new physics, since the experimental data was over half a millennium away.

But that doesn’t mean that we can’t look back now we have everything we need, and see a distinct similarity between the direction modern physics has gone and Aristotle’s philosophy. This interpretation is not new; for example Heisenberg was onto it as he was developing his formulation of quantum mechanics. It is certainly uncommon (at the moment). The problem is that the few philosophers of the early twentieth century who really knew Aristotle didn’t pay much attention to theoretical physics (or have much training or skill in mathematical physics), while most physicists from the mid twentieth century onwards (the generation following Heisenberg, Dirac, Einstein and so on) have cared little for philosophy, and what philosophy they do know is largely the mechanical world-view they were taught as they studied Newtonian mechanics. The philosophers of physics have been somewhere in the middle, neither fully understanding the physics, nor knowing enough of Aristotle’s philosophy beyond the caricature they picked up in their quick skim over classical philosophy as first year undergraduates.

It’s clear that the mechanical philosophy, which historically supplanted Aristotle, has failed, and failed in pretty much in pretty much exactly the areas that the Aristotelian would have predicted. The analogue between quantum physics and Aristotle’s philosophy goes considerably further than just the act/potency distinction.

I have outlined my own views on the matter, which are somewhat more detailed than Gil Sander’s, at
https://www.amazon.com/What-physics-defence-classical-theism/dp/1974401650
You even get a bonus reference to Uncertainty in the introductory chapters.

9. JohnK says:

So everybody takes the point that post hoc interpretations are not very impressive of themselves, though how devastating that is to the OP remains a matter of judgment.

Very amusing commentary today. My favorite so far is the idea that Aristotelians of the fourteenth century would have come round to developing or at least anticipating quantum mechanics, had they been actually interested, had the proper mathematics, had the proper scientific foundation, and had found just the few minor tweaks in the Aristotelian system that were needed.

10. This all reminds me of books like the *Dancing Wu Li Masters* and the tiresome claims made in physics texts about Democritus. The former finds rhetorical parallels in Taoist and early Buddhist writings to some things that physicists say about QM and quantum field theory, and suggests that the two traditions are, in some meaningful sense, saying the same thing. And, of course, Democritus is given credit for launching atomic theory because he mumbled something about matter being made of atoms. Neither claim withstands much critical scrutiny, although both impressed me as an undergraduate.

11. Ye Olde Statistician says:

Not only that, but had they maintained an Aristotelian outlook, they might have avoided the paradoxes and absurdities inherent in the modern interpretations of the mathematical formalism of the mechanics.

12. John B(): What is left out of the Schroedinger’s Cat story is that he proposed it as an argument ad absurdum, to show that the Copenhagen interpretation was bunk. He was later bullied into going along with the cool kids and not rocking the boat.

The only thing we know for sure about how quantum mechanics “really” works is that it’s not along the lines of the Copenhagen interpretation. The observer paradox has thoroughly broken it. It was all scientific hubris and ‘woo-hoo’ from the beginning, anyways. (It did serve the purpose of getting the scientists of the day to change their way of thinking. It just ossified again into this, also incorrect, pattern. “Science advances one funeral at a time.”)

13. Blast and double blast….my comment was deleted as spam!!! Presumably because of the link???
OK, once again into the breach.
I’m not sure how much the original posters or other commentators actually know about quantum mechanics (with the usual exception of YOS, who knows about Cramer’s transactional interpretation.) I’ll state my own credentials: A and A+ in Schwinger’s QM and advanced QM courses; papers involving density matrix theory (QM and stat mech). The quoted authors use of the term “wave-function” rather than “state-function” inclines me to believe their knowledge of quantum mechanics is superficial, whatever their background in philosophy might be. The wave-function is only one of many possible representations of the state function. And I’ll give the quote attributed to Richard Feynman:
“If you meet someone at a party who tells you he understands quantum mechanics, then he’s either drunk or a liar.”
I’m surprised that the most remarkable feature of quantum mechanics, quantum logic–the violation of the distribution law of Boolean logic–was not mentioned in the post or comments.
I’ve posted on this but won’t give the link (spam??)–Google “Last Days and the Resurrection of the Dead I.
Finally, I’m with Bernard d’Espagnat, a theoretical physicist and philosopher who worked with Aspect on the experiments showing the violation of Bell’s Theorem, that there is a “veiled reality” inherent in quantum mechanics, which “veiled reality” reinforces our belief in God.

14. Joy says:

Between Roger Penrose and Keith Ward I start to understand what is intended, what is concluded, what is and is not understood about Quantum mechanics and where physics is really at. If you can trust the numbers are correct, which one can only hope happens at the pointy end then there’s conclusions drawn from physics and theories proved or disproved or whatever. Those things don’t require an advanced understanding of mathematics.

Once I knew a man with a first class degree in physics, finished his QM exam early so that his mates thought he’d got a problem. He said it was a load of rubbish. (In not so polite terms that the maths was not pristine) as it is declared by important mathematicians. It was from he where I first heard the word axiom! You don’t need these things in real life, thought. Like you don’t know you need an organ until it stops working.

If serious physicists want people to believe that a thing, which isn’t a thing, can only be in existence if it is being observed if you’re looking at them then Berkeley was/is nearer to truth than people, including churchmen, who change with the wind, gave him credit.

15. Joy, I agree with you about a neo-Berkeleyan interpretation of QM. Google “Quantum Divine Action via God, the Berkeleyan Observer: the Delayed Choice Experiment.” (Spam control won’t let me post a direct link.)

A lot of other physicists would not agree, however.

16. I should add, the delayed choice experiment is the basis for Wheeler’s “It from Bit,” “The Participatory Universe,” the notion that we create both present and past by observation.

17. Sander van der Wal says:

@Bob Kurland

I had a semester on Quantum Mechanics, but we only did the maths. not a word on Interpretations. Schroedingers Cat was not mentioned at all. A bit disappointing, really, given the hoopla that existed about the Interpretations in the popular physics literature.

I also believe that there is some kind of Measurement Interpretation, i.e. measuring where bits of matter are by bouncing other bits of matter off them is is bound to have some uncertaincies. The name of Landau comes to mind.

18. Sander, what you may be thinking of is the “consistent histories” approach of Griffiths that uses decoherence of phase relations by which a state vector consisting of a superposition of basis states goes to an ensemble of state vectors, that is to say, to a classical situation. To quote the Wikipedia article on this:

“The interpretation based on consistent histories is used in combination with the insights about quantum decoherence. Quantum decoherence implies that irreversible macroscopic phenomena (hence, all classical measurements) render histories automatically consistent, which allows one to recover classical reasoning and “common sense” when applied to the outcomes of these measurements. More precise analysis of decoherence allows (in principle) a quantitative calculation of the boundary between the classical domain and the quantum domain covariance.

It is the phase relation between component states (dead and live cats) that gives a superposition; interactions of systems that are larger than an atomic sizes (roughly) with their environment destroys such phase relations.

19. Chao Feng says:

Reading this because I am reading your “Uncertainty” and in which you argue that probability is purely epistemiological. So I wonder what about the uncertainty in quantum mechanics.