The Quantum Thomist

Musings about quantum physics, classical philosophy, and the connection between the two.
Why is quantum physics so weird (Part 2)?


Aristotelian Potentia and the measurement problem.
Last modified on Sun Dec 31 18:33:48 2017


Introduction.

In my previous post, I discussed the idea of regarding quantum states as representations of Aristotelian potentia. The idea of potentia was introduced by Aristotle to allow for the possibility for change. Before him, people regarded being (or actual existence) or non-being (actual non-existence) as the only options. Aristotle added a third category, potential existence. Every being has numerous potentia which describe what changes are possible for that being, and change is simply potential existence becoming actual existence and vice versa. If we just treat being and non-being as the only options, then there is a problem when considering change; we have to say that being becomes non-being and non-being becomes being.

If this were the case, there is no justification for saying that something has changed. Rather something would have gone out of existence and something else come into existence to replace it. I would not be the same person as the one sitting at my desk who wrote that last sentence; an infinite number of different mes would have flickered in and out of existence between these two full stops. This contradicts our every day experience. It is solved, and to my knowledge no other valid solution has been found, by Aristotle's proposal of potential existence.

The idea is that something endures throughout all these changes. Aristotle called this something prime matter, which is pure potentiality. When united with form by an act, prime matter takes on a particular shape; but all the potentials in some sense continue to exist within the object. One of these potentia is actual at any given moment, and that is what we see and touch. But the matter doesn't have to be in that state; it has the potential to adopt many different shapes, and so those different possible states exist potentially within the matter. The matter itself changes, in that there is a movement between potential and actual existence within it. So change doesn't involve movement from non-being to being; it involves the movement from one type of being to another; from potential being to actual being.

A corollary of this is that there are two aspects to a substance; matter, which represents potentiality, which is constant but can take on different shapes, and form, which represents actuality, which describes which shape happens to be adopted by the matter in any given moment, as well as the other possible potentia it could adopt while remaining the same being.

As is well known, in the early modern period, Aristotle's metaphysics was overthrown. Aristotle got things wrong, and one of his biggest mistakes was to reject Pythagoras' and Plato's suggestion that physics ought to be understood geometrically. When geometrical physics was resurrected in high medieval Europe, the early pioneers in Oxford and Paris thus needed to go beyond Aristotle to find some analogy to explain what they were doing. They turned to the newly invented and exciting clockwork clocks, with their dependence on intricate and finely engineered moving parts.

When the work of these pioneers was given new impetus in the early modern period (with medieval philosophy and Aristotelian basis now generally spurned in favour other classical traditions, nominalism and empiricism), this analogy was taken as reality, and the mechanical philosophy was born.

Key Aristotelian principles, such as form and finality (which I believe are also necessary to understand quantum physics; but that's not today's topic) were chucked out of the window. With them went Aristotle's notion of potential existence. Unable to describe change in this way, modern philosophers have in effect been reduced to either saying that change is impossible or constancy is impossible; or by mixing the two proposals in some way. For example, the mechanical philosophy denies the possibility of change in (fundamental) substances as impossible, and denies the possibility of constancy in location (indeed, it cannot even define what constancy in motion means, given the identity between different reference frames).

What replaced Aristotle was the mechanical philosophy. In this philosophy, matter could be reduced to its constituent and most fundamental parts, which some writers called atoms and others corpuscles. There is a subtle difference between the two in the technical literature of the period, but I'll ignore that distinction and just use the word corpuscle, since atom has come to have a very different meaning in modern science. These corpuscles are the most fundamental objects in nature. So I will use the less familiar word (at the risk of using it in a slightly different sense to how it was used in the sixteenth and seventeenth century literature) to avoid confusion with the modern concept.

In the mechanical world view, corpuscles have a limited number of primary properties: location, velocity, dimension, mass, and maybe a few others. They are basically just localised lumps of matter, which interact solely through collisions. These properties are seen as being inherent to the corpuscles. There were also secondary predicates, such as colour, texture, sound, and others, which were added to objects when filtered by our senses. The diverse array of different objects we see around us just come from different arrangements of these corpuscles. Change just comes from movement of corpuscles from one arrangement to another. The corpuscles themselves are unchanging, except in their location and velocity. They cannot come into or out of existence; they cannot morph from one form to another. There is only actual existence. Moreover, their motions are completely deterministic. Know everything about the universe at one moment of time, apply the correct laws of motion, and with enough computing power you can correctly calculate the state of the universe at any future or past moment of time.

There are philosophical issues with the mechanical world view (particularly related to the philosophy of mind and ethics), but these were either ignored and neglected because it seemed to work so well in describing physics, or people tried to modify the mechanical picture to solve these problems (for example Cartesian dualism, or Kantian idealism), and just created new ones in their place. Scientific problems with the picture also emerged. The action at a distance implied by Newton's gravity caused some headaches; more importantly the demonstration of the reality of extended fields in electromagnetism by Faraday, Maxwell and others also confused the picture. The mechanical philosophy had to be adapted to accommodate this. But it continued to have its successes, and physics inspired by this philosophy continued to make progress, culminating in Einstein's theory of general relativity.

But then came quantum physics, the principle of superposition, and the Pauli exclusion principle. This is a headache to the mechanist, because there are properties of a being which can't be held simultaneously. We like things to be nicely defined; but suddenly we find, for example, that particles don't have definite spin in one particular direction. Everything we can measure must have actual existence. Everything that exists must be either spin up or spin down along every possible axis. (The only alternative to existence is that it doesn't exist, and if a property can be measured then it must be an actual predicate of the object.) So far there is no problem with the mechanical philosophy. But then we add the final ingredient: if the spin is defined along one axis, then it is undetermined along every other axis, until someone measures it when it has a definite value. We find a particle which exists but is not spin up on a particular axis, nor is it spin down, but is perhaps neither of them or both of them at once. To the mechanist, this is a contradiction. Something that exists must be in a definite state, and yet this particle isn't in a definite state. Something could be in a indefinite state if it doesn't exist, and yet this particle certainly exists because we can measure it. It therefore has some of the properties we expect of being, but not all of them, and some of the properties we expect of non-being, but not all of them. It is in a half-way house between being and non-being, not really fitting in either category.

The Aristotelian, however, has things easier. He has one more option: potential being. Something in actual existence can't exist simultaneously in contradictory states; but its potentia can be, and usually are, mutually exclusive states. The Aristotelian would phrase it as follows: Everything we can measure must have either actual or potential existence. Everything that exists must be potentially either spin up or spin down along every axis. One of those states is actual, and the rest are potential. The particle exists actually in a spin up or spin down state along a particular axis. It also has potential existence, and these potentia include the spin-up and spin-down states in the direction we are studying. It be potentially spin-up and spin-down at the same time; there is no difficulty in two of the potentia being in contradictory states. Thus for the Aristotelian, qualities such as this (superposition of states) are no problem at all. Because the Aristotelian also allows for things to have potential existence, he finds himself at home in situations which the mechanist, indeed all modern philosophers, can't cope with.

I am not the first person, nor the only one, to identify quantum mechanical states with Aristotelian potentia. In particular, a work by Gil Sanders has recently come to my attention. In the rest of this post, I want to briefly comment of the strengths and weaknesses of that article.

Summary of article

One thing I haven't dwelt on much in my own work is the measurement problem in quantum mechanics. I'll explain why I don't tend to dwell on it much a little later.

There are different forms of the measurement problem in quantum mechanics (QM), but the most important (in my view) can be phrased as follows. In QM, the particle's state is governed by the wavefunction, which can be regarded as a superposition of the fundamental states. It basically describes the likelihood (using the terminology I use here) or amplitude (using more conventional terminology) that each state is occupied by the particle is at any given time. There is a separate wavefunction for each particle in QM; QM borrows from classical mechanics the premise that the fundamental building blocks of matter are indestructible. This wavefunction evolves according to a differential equation, and is therefore deterministic. This equation is the Schroedinger equation in non-relativistic quantum mechanics, or the Klein-Gordon or Dirac equations in relativistic quantum mechanics. However, when we take a measurement, there is indeterminacy: the particle magically drops into one state or another. The wavefunction is affected by the act of measurement. It no longer evolves deterministically, but is suddenly forced into a particular state. Which state is chosen is unpredictable, and occurs according to the distribution computed in the likelihoods in the wavefunction.

The dichotomy about the deterministic evolution of the wavefunction and the unpredictable nature of measurement is this form of the measurement problem. What is it about the problem of measurement that causes this collapse of the wavefunction? Is consciousness somehow involved? The separation of scales between the microscopic and microscopic?

The article lists four basic problems involved in the measurement problem.

  1. What does the wavefunction represent?
  2. What constitutes a measurement?
  3. When does the wavefunction collapse?
  4. What happens with entangled particles?
The article next considers some of the most popular philosophies of QM, focussing on the Copenhagen interpretation, the Bohm interpretation, and Everett's many worlds interpretation.
  1. Does the wavefunction collapse when there is a measurement? This leaves the notion of measurement vague and undefined. Also, it seems problematic and counter-intuitive to say that no object exists until we observe it. What about other observers? Does my wife exist when I can't see her? (It would be interesting to see someone use that argument in a courtroom in defence of their adultery.) Do I exist when my wife can't see me?
  2. Does the wavefunction collapse at the level of consciousness. But then how do we define consciousness?
  3. Does the wavefunction collapse when a microscopic system comes into contact with a macroscopic system? But then, how do we draw a line between the two? After all, QM is meant to describe both the microscopic and macroscopic worlds.
  4. Can we use an empirical definition? Wavefunctions collapse when wavefunctions collapse. But this circularity doesn't allow a theoretical understanding. We can't predict wavefunction collapse in the equations of QM.
  5. Could the wavefunction describe some real entity? This would imply that there are real entities without definite properties. On the other hand, if it doesn't, how is the wavefunction linked to the real object of scientific study?
  6. The de Broglie-Bohm interpretation posits a deterministic wavefunction spreading over all space. This wavefunction really exists, but comes at the cost of locality. It guides particles with definite trajectories. By creating the two levels of wavefunction (which we don't observe, but is represented by the equations of QM) and particle (which we do observe, but is absent in the equations), it denies that the collapse of the wavefunction occurs. Properties are not intrinsic to the particles but are contextual, depending on the circumstances at the time of its measurement. But then we encounter the issue of how the unobservable guiding wave is linked and can affect the observable particle.
  7. The many worlds interpretation treats the wavefunction as the universe. Rather than a collapse of the wavefunction, the universe splits into different branches. We only see one of these branches (which one is "random"), so it appears to us as though the universe is indeterminate; however as a whole the universe is determinate, and still largely mechanical. But to talk about probability requires a basis to describe the range of measurement outcomes, which can only be determined through a decoherence process. But this decoherence can only occur if the universe is indeterminate.

This provides a good summary of the major interpretations, and why none of them are especially appealing. I have a few quibbles about the discussion of the many-worlds interpretation and how probabilities emerge from it. I personally feel that this interpretation is stronger in this regard than the author of the article gave credit to it. (I still don't agree with this interpretation, but it is harder to pick apart than the rest of the modern and post-modern interpretations.)

There then follows in the article a discussion of mathematics in physics, and how things such as causal powers and teleology were left on the wayside because they don't really fit in with the mathematical description. However, metaphysics is important. Physics only partially describes reality. If some aspects of metaphysics can't be (easily) treated mathematically, then we might expect the mathematical to create various paradoxes as we get down to the more fundamental level. This is especially true if we adopt an incorrect metaphysics. Since the time of Galileo and Newton, the primary way of thinking about the world has been mechanical, which worked well up to the time of Maxwell. They insisted that the physical world should display a precise mathematical structure. The success of classical physics seemed to render Aristotle's more intricate metaphysics, with its numerous non-mathematical elements, redundant.

There are, however, significant philosophical problems inherent in the mechanical world view. The mind-body problem is one of them. This states that

excluding qualities from the world is wrought with problems. If matter is essentially quantitative and devoid of any qualitative features, then it is impossible to reduce a mind that is essentially qualitative to something that is essentially non-qualitative. At best something quantitative can be correlated to some quality insofar as it has a power to produce a quality, but this power is not itself a quality (unless we accept Aristotle’s qualitative account of causal powers) so it can only produce a quality in something that is already essentially qualitative.

Equally, there are issues with causality and causal powers. The denial of final causality (that beings have an inherent tendency towards particular effects) leads to the denial of any inherent rationality in our understanding of nature at all, as Hume most clearly expressed. Even the concept of "laws of nature" is not clearly defined in a mechanical point of view. If the laws of nature are a description of physical regularities, then they do not explain them.

However, that quantum mechanics seems weird means that the paradox is almost certainly not in QM itself, but in the link between QM and the metaphysics used to interpret it. Thus we should not trust any mechanical metaphysics. Even though most of the world regards these philosophies as "scientific", they are contradicted by the best science.

The article then proceeds to give a good account of the Aristotelian account of potentia, and how modern interpretation of physics has created problems for itself by denying it. It raises one important point missing from my discussion above: that, in an Aristotelian metaphysics, complex substances are substances in their own right. They are not simply the sum of their parts. Water is not hydrogen plus oxygen; but has its own structure and energy levels. The hydrogen and oxygen lose their own independent actual existence when they join together into a water molecule. Instead they can be said to exist virtually within the water. This virtual existence is actualised, for example, when the water is split by an electrical current. This is in contrast to the mechanical philosophy, which states that matter is no more than the sum of its parts.

This hylomorphic construction of nature allows a gradual spectrum of material beings, ranging from pure potency (prime matter) to pure actuality (God). It has greater actuality if it has a more determinate form. The closer one gets to prime matter, the more one would expect something to be dominated by potency. The less the potentia are obvious, the more definite an being will seem to be. As we come closer to pure potency, then we would expect things to become less determinate and fixed.

As Aristotle noted, matter is "universal and indefinite" (Metaphysics) so when you destroy a substance to break it down to its smaller parts, hylormophism 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 behavioural patterns.

Aristotle's prescription accounts naturally for the counter-intuitive aspects of QM. For example, the wave-function naturally needs to be linked to some physical reality; otherwise there is no good reason why it should be able to make such successful predictions. Neither should we give the states that it describes an actual existence. All the common interpretations of QM interpretations implicitly suppose an anti-Aristotelian metaphysics so they are left to choose between giving the wavefunction actual existence or denying that it exists at all. But this is a false dilemma, because potency is also a real feature of reality.

This view reinterprets superpositions as being the potentials of a thing or state, not as actual states in which all possibilities are realized. Unlike its rivals, Aristotelianism does not posit new entities to solve a very specific empirical problem. The act-potency distinction is something that permeates throughout all levels of reality already, it is not something conveniently used to fit into the facts but is necessary to account for the facts. So when Aristotelians appeal to potencies to account for QM, it is not ad hoc or lavish but has a natural explanatory advantage over competing interpretations.

Three issues remain: defining measurement; describing wavefunction collapse; and entanglement.

Aristotle's world-view thus provides a very plausible reply to the metaphysical problems raised by the measurement problem. If the microscopic world is indefinite, then so should the macroscopic world be. In a mechanical conception of matter, all macroscopic devices are reducible to their microscopic particles. If all microscopic particles are equally actual, then we would either have to say that all things are determinate (many world) or all things indeterminate (quantum idealism). The first of these posits unobservable entities, the second is subject to Descartes' problem of linking the mental and physical worlds. But if Aristotle's conception is true, then the combination of indeterminacy and determinacy we observe is roughly correct.

Criticisms

I think that the article raises many good points; I agree with its overall conclusion that many of the difficulties in QM disappear once we adopt an Aristotelian metaphysic. I have a few minor quibbles here and there, but two major concerns with the paper.

The article makes frequent mention of Bell's theorem. This is not surprising, since it is very relevant to the topic. Bell's theorem is related to entangled particles. These are two particles whose properties are linked together, for example the results of some decay process which must have opposite spin. We don't know the spin until we measure one of them; when we do so the spin of the other particle is determined, even if it is at the other end of the universe. Both wave-functions must collapse simultaneously. The obvious way around this is to posit that each particle has various hidden variables; the unpredictability of measurement is because we don't know what these variables are. Bell's theorem creates a series of inequalities based on a number of assumptions, including:

If Bell's inequalities fail, then at least one of the axioms must be false. Since the other axioms are also necessary for quantum mechanics as a whole, the focus falls on these two. The first of these is often called scientific realism; the idea that the wave-functions represent particles with real and determined properties, and a given number of particles have definite spin in each direction. From this frequency distribution we can reconstruct the probabilities. In other words, the idea is that there is an underlying classical mechanical (or similar wholly deterministic) system, and the apparent indeterminacy is simply caused by us not knowing all the details of the underlying system.

Bell's inequality is experimentally violated, which means (according to the standard interpretation) either realism or locality must be false. Neither are very appetising: a breakdown in locality seems to violate special relativity; a break down in realism leads us with no clue at all as to what is going on.

The article, however, classes this as a dichotomy between determinism and locality.

For example, Bell’s theorem showed that no interpretation can have both locality and determinism as classically conceived. If locality is abandoned then particles can causally affect another particle at a distance without any intermediary contact between particles (aka spooky action at a distance). But if we reject determinism for locality, then the world is indeterministic and it defies a full scientific explanation.

I think that there might be a confusion between two senses of the word determinate here. Bell's theorem strictly refers to objects with determinate properties, i.e. all the properties of an object are specified. However, determinism by itself is the belief that events are predictable (if we knew the starting conditions to enough precision).

Indeterminate in the sense of unpredictable is not inconsistent with a full scientific explanation or even with causality. Modern descriptions of causality (excluding Hume's nonsense), based on the mechanical philosophy, generally adopt the position that every change in motion is caused by an event; while every event is caused by the interaction between different particles. For example, we might have two particles colliding (an event) and then moving off in a different direction (change in motion). This has a problem in QM because it is no longer true that every event has a cause. Some events (such as spontaneous emission) seemingly have no explanation.

However, the classical position of efficient causality is that every substance in a particular state has as its cause another substance (or substances). So, for example, when an up quark spontaneously decays into a W+ Boson, and down quark (beta radioactive decay), the efficient cause of the down quark is the up quark in whichever potentia it happened to be in. Classical causality thus skips the middle-man of the event; it does not require that events need to be caused. Obviously we can extend the theory to also describe the circumstances when actualisation of potentia could occur, which would cover the use of events in the mechanical philosophy, but need not bring in the extra philosophical baggage of mechanism such as determinism.

To my mind, the solution to Bell's theorem is straight forward. In the derivation of his inequalities, Bell assumed that uncertainty concerning the hidden real substratum of matter should be parametrised using classical probability; assuming that all the predicates of the particle have actual values in the hidden substratum, and we can just counting how many particles of each type there are. If, however, classical probability doesn't apply to the hidden substratum, then Bell's derivation breaks down. The issue is not with realism, but in treating uncertainty classically. If a quantum particle needs to be described both in terms of which state it is in and in which basis that state exists, and the possible bases are not unique and not orthogonal, then the axioms of classical probability break down. Bell has a hidden assumption (not usually stated): that uncertainty in a physical process should be parametrised using probabilities, and it is this assumption rather than locality or realism which is violated.

The second major problem I have with the article is more fundamental. It is based on outdated physics.

Whenever I read a philosophy of physics article which discusses the Schroedinger equation, except to say that it is irrelevant, I throw my hands up in the air and run around screaming. Quantum mechanics is wrong. It is usefully wrong, because it led us to quantum field theory, and many of its concepts are carried onto into field theory, but it is still wrong. Although many people I have read regard quantum field theory (QFT) as little more than QM updated to handle fields, this view certainly understates the differences. For one thing, the objects modelled in QFT are not classical fields; nor are they classical particles; they are something wholly different.

Quantum mechanics removes some assumptions of mechanism, but retains some others. It adopts the idea of potential and actual states, contrary to mechanism. But it retains various other mechanistic premises. The most important of these is the assumption that the fundamental building blocks of matter are indestructible. Each wavefunction in QM describes the states in which a single particle could exist in an external potential energy. There is no possibility for that particle to come into or out of existence. Decay processes, absorption processes, annihilation processes and so on cannot occur in quantum mechanics. Yet these are observed constantly and unpredictably.

A differential equation, such as the Schroedinger equation, also cannot cope with discontinuous events such as particle creation or annihilation. The true theory of nature thus cannot be reduced to any differential equation; it is not merely a case of fine tuning the Schroedinger equation until we get something that works.

Quantum mechanics is known as first quantisation. It expresses observables in terms of the eigenvalues of operators. The eigenstates of those operators describe the possible potentia of particles, and particles move between those states, with amplitudes given by the wavefunction. But this is not enough. If particles can be created and destroyed, then we need operators describing the creation and annihilation of particles. Particles are now represented by these creation operators rather than probability amplitudes. The operators act on a space which basically counts how many particles we have of each type at any given moment of time.

The time evolution operator is constructed from these creation and annihilation operators. It acts on the state vector, but there is no deterministic evolution of the state at all. Rather, any "path" to get from A to B is possible. Each path consists of the creation of annihilation of different particles. Each decay, emission or absorption in this process is an unpredictable event, although it still has an efficient cause (in that each new particle emerges from something else). To calculate the total amplitude for the final result, we need to sum over the likelihood for each possible path weighted by the appropriate factor.

The measurement problem is thus drastically changed. There is no deterministically evolving wavefunction coupled with an indeterminate measurement process. Rather, everything is indeterminate. There is no collapse of the wavefunction because there is no wavefunction, at least not in the sense that there is in QM. What we have in its place is a Fock state, which describes everything in the universe; and it does not evolve deterministically as the QM wavefunction does. I have seen proposals that collapse occurs with the creation or annihilation event. If the notion of collapse still makes sense, then this proposal is plausible to me, and it is not something relevant in QM because QM does not allow for creation or annihilation events.

However, I am not convinced that we need collapse of quantum states in QFT at all. I would rather say that the Fock state represents our knowledge of the system. The system evolves in one of the many possible ways allowed in the path integral. We cannot say which one, so there is uncertainty about future states, which we express in terms of an amplitude. There is no anomaly in saying that our knowledge changes when we take a measurement. This explanation again is not really possible in quantum mechanics, but makes more sense in QFT.

In QFT, we are given an initial state (which is best expressed as a momentum eigenstate). What we calculate in QFT is the likelihood that the system will finish in a particular final state. We calculate this amplitude by counting how many ways or paths the system can evolve from the initial to final state (weighting each path by an appropriate factor). We cannot know what route the system took to get from A to B. When we want to calculate the expected value for some property, we multiply the eigenvalue times the likelihood for the corresponding eigenstate, and sum over all the options.

When we take a measurement, therefore, what we are asking is `Is there a particle, when expressed in this basis, in this particular state at the given time, given that it was in the initial state and the laws of QFT?' This is a different question than in QM, where what we compute and compare against experiment are the properties directly, rather than using the states or potentia as the chief objects of our consideration.

If the question we ask in QFT is `What is the likelihood that this particle will be in a particular state given what we already know about the system', then QFT primarily asks about our knowledge of the system, and our degree of uncertainty of various outcomes occurring. When we perform a measurement, our knowledge changes. In this way, what remains of wavefunction collapse is easy to understand. As is entanglement; for example, the decay products (say of a spin 0 particle) emerge in some particular eigenstates (of opposite spin) of some particular basis; and using the laws of how we compute likelihoods in QFT we can say that for each state in whatever basis that the first particle could be in, the chance that the other particle is in the same state is zero. Behind the scenes, the states are determined at the moment of decay; there is no need to postulate communication at a distance.

The indeterminacy of QFT means that we can never be sure how a system will evolve. This means that we can compute certain results, only varying degrees of uncertainty. The weirdness of quantum physics arises from that uncertainty is parametrised using amplitudes rather than the more familiar probabilities.

There are differences between QM and QFT; and these differences have important philosophical consequences. QM takes some ideas (such as the intermediate state between being and non-being) from Aristotelian metaphysics, and other ideas (such as event causality, or the indestructibility of matter, or deterministic evolution of a wavefunction) from the mechanical philosophy. QFT is more like what we would expect in a pure Aristotelian system. Now, it might be that some philosophical idea translates directly from QM to QFT. But that need not be the case. It might also be that the solution to a QM "paradox" is apparent in QFT but doesn't fit into QM. It thus seems to me foolish to worry about the philosophy of Quantum Mechanics, since there is no guarantee that whatever you conclude will carry over to the more advanced theory. Start with field theory, and build your philosophy on that.



Are fundamental particles of matter indestructible?


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