Quantum Physics, the Wavefunction and Realism


Interview by Richard Marshall


'... most scientific realists believe that the incompatibility between quantum theory and scientific realism is expressed by this problem, and that by solving it one can make quantum theory compatible with a realist interpretation. I disagree: the measurement problem does not necessarily capture what the incompatibility between quantum theory and realism really is.'

'... what about the wavefunction? Its name comes from the fact that it is a function obeying an equation whose form is typical of waves, so it is just natural to think of it as representing something vibrating. The view that the wavefunction represents something physical in this way goes under the name of ‘wavefunction realism’, and in this sense is very natural and straightforward.'

'I think that problem of incompatibility between quantum theory and realism is not how the wavefunction evolves in time. The problem is thus not the cat problem, namely that there are unobserved macroscopic superpositions. Rather the problem lies in the space the wavefunction is defined on, as it is not defined on three-dimensional space. If one wishes to provide a theory that does not provide such counterintuitive consequences as wavefunction realism, then one has to postulate an ontology in ‘regular’ three-dimensional space….'

'... in my schema if you understand how Lego brick works, you also understand how quantum mechanics work, as long as you allow for the Lego bricks to connect in ways that classically were not possible.' 

'One of the reasons to motivate wavefunction realism is that it seems to be the most suitable way of ‘interpreting the formalism’. But why do we need to start with the formalism? This amounts to try to force an ontology on the formalism. Namely to force some meaning into the symbols. Shouldn’t we instead propose an ontology first, and then an equation for it, so that we can reproduce the formalism and the experimental data?'

'What is it in the nature of the wavefunction that makes it change so radically depending on whether we look at it in the forward or in the backward movie? It is like saying that when we watch “Back to the Future” projected forward Mary McFly is played by Michael J. Fox, while when we watch it projected backwards he is played by Keanu Reeves. Why does it happen? Does it even makes sense?'

'Quantum nonlocality is indeed THE mystery physics needs to solve. We have the idea that things can affect one another only if they are in direct or indirect contact. This is the concept of locality. We take it so much for granted that we do not even think about that. Newton, after repeated failed attempts to provide a local account of gravitational interaction, had to postulate the existence of a force which instantaneously acts at a distance. He disliked it so much that he regarded this nonlocality as a symptom of the inadequacy of his theory.'

Valia Allori is interested in philosophy of science, philosophy of physics, and metaphysics. She studies our best physical theories to understand how they can give us new insight in metaphysical issues such as the nature of time, space and matter. Here she talks about quantum physics and realism, the realist view of the wave function, primitive ontology, the wave function as projected ray, whether quantum physics is a Kuhnian paradigm shift, the Copenhagen interpretation, David Wallace, interpretation, physics and freewill, the direction of time, spooky causality at a distance, and the relationship between physics and philosophy.

3:16: What made you become a philosopher?

VA: I apologize in advance, as this is going to be a long story. However, it is going to serve nicely as background for the other questions, so I will simply go ahead. I was born and raised in Italy, and the type of high school I attended had a fixed curriculum, which included philosophy classes for the last three years. I thus started reading philosophy when I was 16 years old and I immediately loved it! The questions that philosophy asks are the questions that teenagers ask every day, or at least they were the questions what we, my friends and I, asked ourselves all the time: who am I? How do I fit? Is life worth living? Do I have a value? Do we survive death? What are thoughts, feelings and sensations? What is my relationship with the rest of world? What is the nature of reality? I could go on and on, telling you about all the discussions I had with my best friend almost every afternoon in front of a cup of tea. Anyway even if I knew just then, when I was 16 years old, that I wanted to explore at least some of these questions, I did not go straight to them. In fact, my undergraduate degree is in physics, and also my (first) graduate degree is in physics as well. Only after many years I came back to vindicate my 16 year-old self and earned a doctorate in philosophy. 

But why? I did not get crazy, if that’s what you are thinking. I simply had a crazy plan, those plans that make perfect sense to bold 16 year-olds and pretty much to no one else. Anyway, in the last year of high school our philosophy professor had us do presentations. I got stuck with something on positivism and modern physics. I was not particularly thrilled, as I was not very fond of physics in itself. Until then, I could not understand why one would ever be interested in studying physics: I could not see the point, so dry, removed and abstract. However, I quickly changed my mind after reading Albert Einstein and Neils Bohr: finally, something clicked, and all the pieces of the puzzle started to come together. The two physicists, among the founding fathers of modern physics, were debating about what physics is, and I finally saw how close it was to philosophy. I immediately sympathized with Einstein, who was a scientific realist and thus thought that physics can tell us about the nature of reality. This is it! Physics is just philosophy ‘made precise’! It may not provide a response to some of the questions listed above, but it will tell us something about the nature of reality. And it will do so in a reliable way through the scientific method: theories that do not match with experiments are substituted by better theories, and that is how our image of the world gets closer and closer to the truth. However, I was also fascinated by Bohr, who thought that quantum theory made this enterprise not difficult but really impossible. I did not understand the physics enough to understand why (or whether) it was the case, and thus I resolved to do my undergraduate studies in physics to figure things out. The idea was: I can read and understand philosophy on my own, but I can’t master a physics book all by myself, so the choice was obvious. I could always come back to philosophy when I mastered the physics.

3:16: You are interested in philosophical questions regarding science and physics in particular. So let’s start with some of the big questions that rumble around in this area. Quantum mechanics seems to pose a big problem for scientific realists, understood as those who think theories should inform metaphysics, contrasting with the scientific anti-realists who think theories need be just empirically adequate without answering anything metaphysical. Can you sketch for us why quantum mechanics seems to be so problematic for the realists, and whether you agree with the realists that mere empirical adequacy isn’t good enough? Is the problem the wave function (and is it possible for you to say what this object of the theory does?)

VA: The incompatibility between quantum theory and scientific realism is what brought me to physics in the first place. With much surprise and enormous disappointment, I learned that we, as physics undergraduates, were discouraged to ask questions, especially about this incompatibility. We were told that quantum mechanics forces us to instrumentalism, that theories are merely good instruments for making predictions, not for learning about the nature of the world, and that we had to learn to live with it. Full stop, period, end of story. But I was stubborn, and I could not accept this verdict so uncritically, also because it would have defeated my whole plan. After a lot of hesitation, I decided to go to graduate school in physics to further explore the question of how quantum theory and scientific realism fit together. After that, and after a Ph. D. in philosophy, I have to say that the reason behind this incompatibility is still controversial. I think this may come as a surprise for many philosophers of physics, as the standard response to your question would be to introduce the (infamous) measurement problem, sometimes called the problem of the Schrödinger cat. In other words, most scientific realists believe that the incompatibility between quantum theory and scientific realism is expressed by this problem, and that by solving it one can make quantum theory compatible with a realist interpretation. I disagree: the measurement problem does not necessarily capture what the incompatibility between quantum theory and realism really is. 

But I am jumping ahead too much; let me explain the cat problem first. The fundamental object of quantum theory is called the wavefunction, and it evolves in time according to an equation called the Schrödinger equation, because it was Erwin Schrödinger who proposed it first in 1926. Assuming one is being a scientific realist, the solution of this equation describes possible ways the world, or any object in it, can be. This equation has the mathematical property of being linear: sums of solutions are also solutions. This creates a problem. In fact, take a cat and put her in a room where there is a device hooked up to a vial of poison and a radioactive source. When the nucleus decays, the device breaks the vial, and the poison kills the cat. When the nucleus has not decayed, nothing happens and the cat remains alive. These two are solutions of the equation, they describe possible ways the cat can be in a 'superposition' of being alive or dead. But then, because of linearity, the cat can also be ‘alive and dead’ at the same time. However, when we open the door of the room, we always see the cat either dead or alive, never in this ‘superposition’ of states. So, the theory is empirically inadequate: it does not match our observations. The ‘orthodox’ way to deal with this, namely the way one finds in physics books (most of which introduce this rule without even mentioning the cat problem), is to postulate that when a measurement is performed, like when one measures the state of the cat by opening the door, the wavefunction no longer evolves according to the Schrödinger equation. Rather, it ‘collapses’ or ‘jumps’ in one of the terms of the superposition. That is, by opening the door and observing the cat, I change the evolution of the wavefunction, and that effectively makes one of the possibilities (‘dead’ or ‘alive’) to become actual: the cat transforms from being in a 'superposition' state of ‘alive and dead’ (whatever that means) into being either ’dead’ or ‘alive’. This makes the theory intrinsically probabilistic, as there is a fixed probability for the wavefunction to collapse into each one of the various terms of the superpositions. In this way one has made the theory empirically adequate, and this is going to be enough for an instrumentalist, who only care or reproducing experimental results without explaining where they come from. Instead the scientific realist will be very unhappy: what kind of theory is one in which the notion of ‘measurement’ or ‘observation’ is in the very formulation of the theory? Isn’t a measurement just another physical process? What is required from someone to be an observer? Is consciousness involved? What does it mean for the cat to be in a ‘superposition’ state? What if it is me in the room? What would I feel before someone ‘observes’ me? What would I feel after? Bottom line: the problem of the cat is that: if 1) the wavefunction provides the complete description of any physical system, and 2) it evolves according to the Schrödinger equation, then 3) there would be unobserved macroscopic superpositions. 

As I said, the standard way to fix this it to invoke the observer or measurement, but this is totally unsatisfactory for the realist, because of the vagueness due to referring to imprecise concepts such as observer and measurement. The challenge is to eliminate these unobserved macroscopic superpositions in a precise way. One, indeed can do this by rejecting (at least) one of the premises 1, 2 of the argument above, or its conclusion 3: either the wavefunction does not provide a complete description, or it does not evolve according to the Schrödinger equation, or macroscopic superpositions are real. This is the trilemma that, according to the realist, will allow for a reconciliation of quantum theory with scientific realism. The most famous solutions of this problem are the three most famous so-called ‘interpretations’ of quantum mechanics (however, they are actually better be thought as different theories, as they do more than just provide significance to the formalism of the theory). First, the pilot-wave theory, also known as Bohmian mechanics or de Broglie-Bohm theory because they both contributed to construct this theory, assumes that the complete description of physical systems is not given by the wavefunction, as one also needs to specify particles’ position. The spontaneous collapse theory, also known as spontaneous localization theory, dynamical reduction theory or GRW theory from the initials of the physicists Ghirardi, Rimini and Weber who proposed it, makes precise the standard story. In fact, in this theory the wavefunction suitably ‘collapses into’ (or is ‘reduced to’ or ‘localizes into’ or ‘jumps into’) one of the terms of the superpositions because that is what the modified equation which governs its motion prescribes. So, there is no need of any special observer. Finally, the many-worlds theory, or Everettian mechanics from its creator, assumes that superpositions are physically real: whatever happen, actually happen, somewhere. Every term of the superposition has a distinct reality, and since these different ‘worlds’ practically do not interact among one another we are not aware of the fact that they exist. These are the solutions of the measurement problem, which was taken by most realists to be the one to solve to fix the problem of incompatibility between realism and quantum theory. As anticipated, I disagree. The measurement problem is the problem of eliminating or making sense of macroscopic superpositions, while I think instead that this is not enough: the problem is rooted in the wavefunction, regardless of whether it is in superposition or not.

3:16: Can the wave function be understood in terms acceptable to the realist? Is it possible to give a material interpretation of this weird thing and if not isn’t that the end of realism?

VA: Short answer: yes, this is not the end of realism. Longer story: the way this is usually done does not really ‘smell’ like it is the right thing to do, however. Let me try to explain that. By solving the measurement problem, one obtains quantum theories that are amenable of a realist interpretation. That is, the pilot-wave theory, the spontaneous collapse theory and the many-worlds theory are all possible candidates to tell us about the nature of reality because there is no mention of ‘measurement’ or ‘observer’ in their formulation. Each will paint a different picture for us, but what exactly is it? In the pilot-wave theory there are particles and there is the wavefunction, while both in GRW and Everett there is only the wavefunction. They all have in common the wavefunction. So, if the realist project so understood (which I ultimately disagree upon, but let us just assume it for a little more) has some chance of succeeding we need to suitably figure out what the wavefunction, which is a mathematical entity, represents in the physical world. Points in Euclidean space usually are taken to suitably represent particles, functions of three-dimensional coordinates usually are taken to represents fields, like the electric and magnetic fields, which propagate through space as waves. 

So, what about the wavefunction? Its name comes from the fact that it is a function obeying an equation whose form is typical of waves, so it is just natural to think of it as representing something vibrating. The view that the wavefunction represents something physical in this way goes under the name of ‘wavefunction realism’, and in this sense is very natural and straightforward. The defenders of this position also have other arguments for the view, like the desire of keeping the theory local, but this characterization will suffice for now. The problem to solve if one goes in this direction is that the wavefunction, contrarily to the functions describing electromagnetic fields, is not a function of three-dimensional coordinates. Rather, it is a function of 3N of them: three coordinates for each of the N ‘particles’ in the physical object under consideration. Thus, if we want to think of the wavefunction as representing something material, it will have to represent something vibrating in this high-dimensional space, not in three-dimensional space. This suggests that the ‘real’ physical space is not three-dimensional, as we perceive, but rather 3N-dimensional. However, how can we ‘recover’ our experience of three-dimensionality from the true space? This 3N-dimensional space is called configuration space, and the corresponding problem is called configuration space problem or macro-object problem: how do we recover the characteristics macroscopic objects appear to have, such as localization in three-dimensional space, or being distinct from one another, in term of something which exists in a high dimensional space? Wavefunction realist such as David Z. Albert and Alyssa Ney have both alternative strategies to solve this problem. Albert argues that macroscopic objects can be composed of microscopic entities which are three-dimensional but not fundamental: they are functionally defined in terms of the wavefunction. That is, he shows that three-dimensional microscopic objects are what they are in virtue of the function they play, and this functional role can be played by the wavefunction. So, effectively, one can ‘read-off’ these objects from the wavefunction: they are derivative or emergent in this sense. Instead Ney does not attempt to reconstruct microscopic three-dimensional objects from the wavefunction but she wishes to recover the macroscopic world more directly. She proposes that symmetries can pick out, among all the possibilities, the three-dimensional world as privileged, from which the three-dimensional picture we experience emerges. 

I do not subscribe to this position: I rather think that the wavefunction does not represent physical entities at all. The main reason for this is that it is a function on configuration space, and as such it is not the right kind of object to represent something which is physically vibrating. This was the reason why people like Albert Einstein and Schrödinger himself who were initially sympathetic with this view ultimately rejected it: “a field in configuration space does not smell like something real”, said Einstein. Indeed, Werner Heisenberg, another key figure in the development of quantum theory, was partially driven to instrumentalism discouraged by the fact that the alternative committed him to think that physical space is high dimensional: “the sky is blue, and birds fly through it” he said to a colleague. I think that if wavefunction realism leads us to this radical and counterintuitive conclusion, then wavefunction realism should be rejected, and something else needs to be modified. What’s left to modify? In short: the ontology of the theory, not necessarily its evolution. If I want to be a scientific realist, and if quantum theory is a theory about the behavior of the wavefunction, then quantum theory is incomplete: otherwise I would have to accept that physical space is configuration space. Therefore, I think that problem of incompatibility between quantum theory and realism is not how the wavefunction evolves in time. The problem is thus not the cat problem, namely that there are unobserved macroscopic superpositions. Rather the problem lies in the space the wavefunction is defined on, as it is not defined on three-dimensional space. If one wishes to provide a theory that does not provide such counterintuitive consequences as wavefunction realism, then one has to postulate an ontology in ‘regular’ three-dimensional space….

3:16: So you offer what you call a ‘primitive ontology’ approach to the realist requirement to speak to metaphysics. So what is this approach and what does it say the wave function is if not a material thing representing material objects? Am I right in thinking that it’s your view that the realism pertains to the primitive ontology and not to the wave function?

VA: I think that the wavefunction does not represent material entities. I already sketched above the main idea behind this. The reason why I think we should ‘get rid’ of the wavefunction as something material has also to do with the kind of realism I think should be adopted, which goes hand in hand with the type of explanation of the phenomena I find satisfactory, which is also connected with the fact that I think that we should stop focusing on the measurement problem as the realism problem. Let me try to elaborate a little more on that. I am not entirely convinced that the wavefunction realist strategies for recovering the appearances of three-dimensionality do actually work. However, I think that even if these accounts formally succeeded, they still would be unsatisfactory. I am not satisfied with the recovering of the appearances: I want to explain them. An instrumentalist, not a realist, cares about the appearances. I want to know how these appearances come about. Of course, wavefunction realist would immediately object to this, as they do not think of themselves as instrumentalists, and that they do provide an explanation of the phenomena in terms either of functionalism or symmetries. Still, I want more. I think that one should look for a microscopic, constructive, dynamical explanation of the phenomena: in a classical picture a macroscopic object such as a table is made of microscopic entities which interact with one another so that they give rise to the properties of the table. This is more than just providing some principles, either based on functionalism or symmetries, to suitably constrain the physical phenomena, as the wavefunction realists are doing. That is too weak. Scientific realists ended up in thinking that weaker forms of realism such as this are acceptable because they looked at solving the measurement problem. In other words, some people started endorsing wavefunction realism because they thought they had to make realist sense of what the wavefunction is, and this is because all the solutions of the measurement problem have in common the wavefunction. 

However, one should take a step back: the reason why we no longer have a constructive, dynamical, microscopic explanation of the phenomena (which was familiar in classical physics) is that the wavefunction is not in three-dimensional space. So, I will say this: just get rid of it! Just think quantum theory is incomplete, just like Einstein unsuccessfully tried to prove. Reality is described by something else, rather than the wavefunction. The trilemma in the measurement problem (either the wavefunction is not complete or it does not evolve according to the Schrödinger equation or macroscopic superpositions are real) is a false trilemma: the wavefunction is never complete, not even if it evolves according to the Schrödinger equation. The real problem of incompatibility between quantum theory and realism, in my opinion, boils down to the problem of how to complete quantum theory so that we can get rid of the wavefunction, and not merely of its macroscopic superpositions, like focusing on the measurement problem would suggest. The wavefunction does not represent anything ‘material’ so if a quantum theory mentions only the wavefunction, then the theory is not complete. Full stop, period, end of story. Forget about the wavefunction or other mathematical objects defined in abstract spaces, and focus on mathematical entities that can describe stuff moving or vibrating in three-dimensional space. That is what represents what matter is made of, that is what the so-called primitive ontology is. My position takes seriously a position briefly discussed in the work of physicists Detlef Dürr, Sheldon Goldstein and Nino Zanghì, with whom I have also written some papers. However, they do not discuss this view in many details and do not fully embrace some of its natural consequences as I instead do. Anyway, the qualifier ‘primitive’ is supposed to be in contrast with ‘nomological’ ontology: while the former specifies the nature of matter, the other specified the nature of the law which constrains the behavior of matter. 

The wavefunction is part of the nomological ontology. Or, more straightforwardly, it is part of the law of nature which governs the behavior of matter. The primitive ontology tells us what matter is, the wavefunction tells matter how to move. The wavefunction can play this role, regardless of a precise understanding of what laws of nature are: either real, objective, mind independent entities that govern the motion of physical objects, or convenient, informative, simple generalizations which effectively systematize the phenomena. In other words, the wavefunction is real, but not material. This should be contrasted with another view, which takes the wavefunction to be not material too, namely the so-called epistemic position. According to this approach, the wavefunction does not represent matter but rather our knowledge of the state matter is in. In my view instead, the wavefunction represent an objective feature of reality, which has to do with laws of nature, and not our knowledge of it. Anyway, going back to the primitive ontology: matter can be made of particles, fields or whatever. The important thing is that these components are in three-dimensional space, just like Newtonian particles and electromagnetic fields.

3:16: You argue that a good way to understand the wave function is as a ‘projective ray’ – at first glance a ray seems material but this is a maths object right? Can you say something about this and how it leads you to conclude that the wave function is a nomological rather than an ontological entity.

VA: As I pointed out earlier, wavefunction realists think of the wavefunction as a function on a high dimensional space, which can be interpreted as a field or a wave. Instead I argue that it is better seen as a more abstract object, namely a projective ray, which is even less suitable to represent physical objects. The reason for thinking the wave function is a projective ray is that if one thinks of the wavefunction as field in configuration space then quantum theory loses important symmetries, such as the Galilean symmetry. In other words, the theory is no longer Galilei invariant, as commonly thought: if wavefunction realism is true then it is no longer the case that one cannot distinguish between a system at rest and a system which is moving with uniform velocity with respect to it. The reason for this is that in order for the theory to be Galilei invariant, one would need, mathematically, the wavefunction to transform in a particular way which seems to be in contrast with assuming that its nature is to be a field. It is as if someone who has always been honest mannered would now have to be considered to be responsible of the greatest crime in human history: it does not fit. The same can be said for the wavefunction: it does not fit with the wavefunction being a field that it transforms as Galilei invariance would require. Instead, if one assumes that the wavefunction is, contra wavefunction realism, a projective ray, then the theory regains Galilei invariance. A projective ray turns out to be the kind of object whose nature fits well with Galilean transformation so that one can save Galilean symmetry. The wavefunction realist could deny that symmetries are a desiderata for a theory. However, this seems to run against much of the contemporary science practice in which symmetries are used as a guide to theory construction and theory evaluation: one finds new theories imposing symmetry constraints, and one judges theories to be better or worse than other theories by looking at how many symmetries it preserves. On another point, a projective ray is a purely mathematical thing and has not much in common with something like a ray of sunshine. Indeed, it is not even a single mathematical object but an equivalence class of objects, namely a set of objects that differ only by a multiplication constant. That is, and y, where 𝑐  is a constant, are in a sense the same thing. Thus, if I am right and the wavefunction is a projective ray and not a high dimensional field, it is going to be more difficult for the wavefunction realist to find a way to interpret the wavefunction as something material, reinforcing my suggestion that one should ‘get rid’ of the wavefunction when talking about the ontology of matter. I think this also brings support to the idea that the wavefunction is nomological in that it is the type of mathematical object that describes how matter moves, preserving the symmetries of the theory.

3:16: So what’s the connection between the microscopic description of reality provided by quantum theories in your PO framework and the macroscopic, classical world of our everyday experience?

VA: The motivation of taking this approach, namely getting rid of ontologies which are unnecessarily distant from our everyday experience of the world and stay as close to space-time as possible, is that if one does that, then the explanatory schema used in classical theory, namely macroscopic stuff being composed of microscopic stuff and explain macroscopic properties in terms of the microscopic components, remains substantially unchanged. That is, classically one explains the solidity of a table in terms of the chemical bonding of the molecules composing the table. Quantum mechanically one does basically the same, provided that one changes the fundamental laws: macroscopic objects are ‘made up’ of microscopic three-dimensional entities described by the primitive ontology. So, contrary to wavefunction realism, I do not have to invoke new concepts such as functionalism or privileged decompositions based on symmetry considerations. Rather, I simply use compositionality: in my schema if you understand how Lego brick works, you also understand how quantum mechanics work, as long as you allow for the Lego bricks to connect in ways that classically were not possible.

3:16: Do you think the quantum paradigms constitute a radical departure from the classical paradigm in the sense that Kuhnian paradigm shifting requires?

Thomas Kuhn has argued that science proceeds through revolutions. He was an anti-realist, he believed that science does not track truth, that there is no slow but constant scientific progress towards a more accurate picture of the world. Rather, he thought that science proceeds in a non-uniform manner, through long periods of normal science and then few sudden but radical revolutions. During the periods of normal science, scientists work within a paradigm: a certain view of the world, which specifies which methods of investigations are acceptable, and what counts as good science. Their job is to ‘solve puzzles’, namely to try to figure out clever ways to eliminate small anomalies, data that seem not to fit in the general framework. Then slowly but constantly the number of unsolved puzzles begin to increase until one reaches a breaking point and the whole paradigm collapses and is replaced by a new one: a new view of the world, a new set of tools, methods, and evaluation criteria. The two paradigms are mutually exclusive but equally valid: there is no true paradigm. Kuhn makes even more radical claims, such as that paradigms are incommensurable, they cannot even be compared, as they speak different languages that cannot be translated into one another. 

Aside from that, which is implausible, many think that there is something true in the main idea behind this view, namely that there are big fractures in the history of science, revolutions that dramatically change our ways of understanding nature. The passage from the Ptolemaic system, according to which the Earth is at the center of the universe, to the Copernican system, according to which the Earth rotates around the Sun, entailed a change in perspective, a new way of thinking about ourselves and our place in the universe. Sometimes people make the same claim about the passage from the classical to the quantum description of the world, as usually presented: while classically we can picture the microscopic world and we can imagine the macroscopic objects as composed of microscopic constituents, instead we cannot do anything of the sort in a quantum world. So, if orthodox quantum theory is correct we seem to have a revolution. But we have said that the orthodox view is at best vague. What about the solutions of the measurement problem? Indeed, there seems to be a revolution also in this case, if one endorses wavefunction realism: it is no longer true that this table is made of microscopic stuff in three-dimensional space; now I have to make sense of the table as being made of a wavefunction which is neither microscopic nor in three-dimensional space. This is a big fracture with the classical understanding. However, this is not the case in my account, as the table is still made of three-dimensional microscopic stuff described by the primitive ontology. So, since there is no other reason to go radical, one should not. Rather, one should endorse my view to avoid the quantum revolution. Actually, there would be a good reason to go radical as wavefunction realism suggests if one could show that only wavefunction realism makes quantum theory local. I will take this up later.

3:16: According to Hugh Everett ‘… the Copenhagen Interpretation is hopelessly incomplete because of its a priori reliance on classical physics . . . as well as a philosophic monstrosity with a “reality” concept for the macroscopic world and denial of the same for the microcosm.’ His many words interpretation is supposed to solve this vague division between the macroscopic and the microscopic – so according to your approach, is the many worlds claim an ontological commitment or nomological, and if nomological how would that solve the division?

VA: The Copenhagen interpretation Everett is mentioning in the quote above was Bohr’s favorite way of reading quantum theory. His idea was that there is a macroscopic world governed by Newton’s equation and in which objects have definite properties, and a microscopic world governed by Schrödinger’s equation and in which it does not make sense to assign properties to anything. The wavefunction does evolve into superpositions at the microscopic level, due to the Schrödinger evolution. However they never turn into macroscopic superposition because in the moment the object becomes macroscopic the quantum laws cease to be valid and classical mechanics kicks in. By definition classically objects are never in macroscopic superpositions, and that is the reason why we never see them. Take the case of the Schrödinger cat: the radioactive nucleus is quantum, so it can be in superposition, namely, of ‘decayed' and 'not decayed’. If it decays it triggers the breaking of the vial of poison. This is macroscopic, so it cannot be in superposition, so it is either broken or not. Classical mechanics has taken over the Schrödinger evolution. Consequently, the cat can be either dead or alive. This is the sense in which quantum theory needs classical theory: they both need to be applied in order to get the correct results. This is at best, suboptimal: two theories valid at the same time?! And also hopelessly vague: when does an object count as macroscopic? This is why many people, including Everett, found this view extremely unsatisfactory. Everett’s own theory, which slightly differs from more modern varieties of the many-worlds theory, asserts that the Schrödinger evolution is universal and that the wavefunction is complete, but each term of the superposition describes the state of a system relative to a possible observer. This is why it was called ‘relative state formulation of quantum theory’. In this theory the wavefunction is the ontology, as it is the only thing there is in the theory. There is no in principle distinction between the macroscopic and the microscopic, it is a universal theory, in contrast with the Copenhagen interpretation, which is not even that.

3:16: David Wallace, for one, has shown that the many worlds interpretation flushes out more clearly than is usually the case some problems with understanding the metaphysics of probability. Does your approach help us to grasp the relevant metaphysics?

VA: Both the pilot-wave theory and the many-worlds theory have a problem with accounting for quantum probabilities: both theories have deterministic evolutions equations (in contrast with the spontaneous collapse theory, which is instead indeterministic and stochastic), so where are the quantum mechanics probabilities coming from? In the case of the pilot-wave theory, cutting a long story very short, the theory provides probabilistic predictions because there are fundamental limitations in our ability to know the initial conditions of the particles. In the case of the many-worlds theory instead the problem is that everything that can happen does indeed happen. So, how can we understand that there is a ½ probability of the nucleus to decay, given that it will decay for sure in one universe? Wallace proposes that we understand the probability talk we use in terms of a theory of rationality: he proves that a rational agent who believes in the theory would assign to each world a probability compatible with the one prescribed by the quantum rule. I do not find these approaches very convincing, as they wish to explain the appearance of probabilities rather than explaining why the branching is what it is. In any case, I do not think my approach is of any help in understanding Wallace’s approach to the many-worlds theory, as it is in direct contrast with it. Wallace is not a wavefunction realist, but he thinks the wavefunction represents matter nonetheless. He is a state-space realist, together with Christopher Timpson, and he thinks that the wavefunction should be understood as describing abstract features of spacetime regions. I am not convinced by this approach, as the wavefunction is no longer in configuration space but it is still abstract and difficult to understand ‘visually’. So, all things being equal, I would rather go with the primitive ontology approach.

3:16: For physics idiots like me the fact that physics needs interpretations and these seem to be part of the theory suggests a problem. Why am I wrong?

VA: No, you are not wrong in the least! I think that interpreting the formalism a posteriori is misguided, as the formalism comes from something. Why did we end up with Newton’s equation? Because Newton postulated first that the world is made of particles, whose positions in space can be suitably mathematically modelled in terms of points in three-dimensional Euclidean space. That’s why Newton’s equation is what it is, namely an equation which describes the temporal evolution of these points. It is the fact that Newton already had in mind a clear hypothesis about the ontology of the world that we do not have to interpret Newton’s formalism: he gave us an interpretation to start with. He told us what the symbol in the equations meant from the start. The case of quantum theory is instead different because of how it was born: there was no single scientist behind it, and different people had different ideas about what needed to be done. Heisenberg, for one, developed matrix mechanics as a mathematical tool to systematize experimental data, without thinking that the matrices he introduced actually represented something about the world. Schrödinger instead wanted something to visualize, he wanted an equation that would reproduce the data but that also could be seen as describing the fundamental entities in the world. He proposed his wave equation, an equation for something that he thought he could be interpreted as something vibrating. At the end, given that the wavefunction has to be on configuration space, he came to believe that one could not think of the wavefunction in realist terms, and basically abandoned research on quantum theory. Others instead were not convinced by this objection, and tried to develop wavefunction realism in full. 

One of the reason for to motivate wavefunction realism is that it seems to be the most suitable way of ‘interpreting the formalism’. But why do we need to start with the formalism? This amounts to try to force an ontology on the formalism. Namely to force some meaning into the symbols. Shouldn’t we instead propose an ontology first, and then an equation for it, so that we can reproduce the formalism and the experimental data? I think the latter attitude makes more sense, and this is what is done in my approach: one chooses the primitive ontology first (that is, the ontology of matter), then she chooses the mathematical entity that best represent it (for instance, if the ontology is particles then use three-dimensional points in Euclidean space), then one tries to figure out what equations one needs to assume in order to recover the data. In this way the formalism does not need any further interpretation: it is already given from the start, just like in Newtonian mechanics. If you are a mathematically inclined person, think of the situation in this alternative way. Saying that one needs to interpret the formalism of quantum theory is just like saying that one needs to interpret the symbols in the simple harmonic oscillator equation : ,𝑥.+𝑘𝑥=0. Now, interpret the equation; try to read off the meaning of the symbols from the symbols. How do you even start to read it? What is 𝑘? What is 𝑥? How can you possibly know? You need context, also because this equation describes many unrelated and vastly different phenomena, from the motion of a pendulum to economic simulations, given that it approximates the behavior of almost any system near equilibrium. 

You cannot go blind and read a formalism without assuming that the mathematical symbols already mean something. And when you assume that, you fix the context and you do not interpret the symbols anymore: you already know what they mean. When you look at the Schrödinger equation, you see an equation of a wave, so naturally, as the wavefunction realists do, you think the wave is real. Indeed, presumably the reason why wavefunction realism focus on Schrödinger’s wave mechanics is that it is easier and most straightforward to imagine a possible physical meaning of the symbols in that theory rather than in Heisenberg’s matrix mechanics. However, I think wavefunction realists should go back on their steps when they realize that the wavefunction cannot be interpret like vibrating in space time. If they took the Schrödinger equation more ontologically seriously than matrix mechanics because the formalism looked more suitable to ‘read off’ the ontology from it, then now that the situation is not as straightforward and unquestionable as originally thought (because they end up with a wave in configuration space), what is their justification in preferring it? Why do they think the Schrödinger formalism is so untouchable? I think that the whole situation is better understood if one just abandons the idea of ‘reading off’ the ontology from the formalism, and is more open to the possibility that the formalism is not immutable and can be revised, if required by our preferred choice of the (primitive) ontology.

3:16: Does a quantum world help those who argue for free will? Why is it supposed by some to do so?

VA: Quantum theory, being so vague (what is a measurement?), is commonly invoked to explain all kinds of things, including free will and consciousness. Certain people, first of all famous physicist Eugene Wigner, have suggested that quantum theory needs a theory of consciousness to make sense. In fact, one could think that the wavefunction collapses in one of the terms of the superposition not necessarily when a measurement is performed but when a conscious observer interacts with the physical system under consideration. People like physicist Henry Stapp have argued that the holistic character of quantum nonlocality, namely the existence of strong intrinsic correlations between certain types of objects that do not fade away regardless of how distant these objects are, is at the root of the holistic character of the stream of consciousness. Moreover, quantum theory is intrinsically probabilistic rather than deterministic, and people have taken this to be an indication that quantum theory can help us solve the riddle of free will. In fact, John Conway and Simon Kochen, two prominent mathematicians, have recently published what they called ‘the free will theorem.’ They wish to argue many things, but one of their points is that quantum randomness can help with free will. 

A deterministic theory is one in which the initial conditions and the laws of nature at one time determine how a physical system will evolve at any other time. Given the present, there is a unique future, which will happen with certainty. This is incompatible with free will, if the deterministic theory is universal, namely also includes us in its description. In fact we think that we are free if we have control over our actions. But if determinism is true our actions are beyond our control, as they are determined by the initial conditions and the laws. So, free will is an illusion. Instead in an intrinsic probabilistic theory the future is open in the sense that there are different possible futures, each with a particular probability of happening. For instance, a single radioactive nucleus has ½ probability of decaying within a given time, and it cannot be predicted that it will decay for sure. Some, Conway and Kochen included, have thought that the fact that there is an open future can help with free will because the future is not determined. However, this is not enough, as the randomness introduced in such an intrinsic probabilistic theory has not much in common with what we think free will is: if free will has to do with having control over what we do, then in an indeterministic theory we have no control at all, regardless of how many possible futures are open to us. We do not choose what will happen, the laws will, even if this time are probabilistic laws.

3:16: Does your thinking about the wave function alter our thinking about the direction of time, in fact, the nature of time itself? Perhaps to start you could sketch for us the different ideas flying around at the moment about this before saying where you stand?

VA: Recently, David Z. Albert and Craig Callender have argued that quantum theory may indicate that time has a preferred direction. Time has a preferred direction if you can tell which one is the past and which one is the future. Instead if one cannot distinguish between the two by looking at the relevant equation of the theory, then it is said that the theory is time reversal invariant. Newtonian mechanics is like that: if you film the motion of a ball on a billiard table and project it to someone (without the beginning, when someone hit the ball, and the end, when the ball stops) they will not be able to tell you whether they are watching the movie projected forward or backwards. What about quantum mechanics? It is a mathematical fact that, in order for the forward and backward movies to be time reversal invariant, the wavefunction should be, pictorially, ‘red’ in the forward movie and ‘blue’ in the backward one. The reason for this is that if the wavefunction remains unchanged when one reverses the direction of time then solution of the time-reversed equation fails to represent reality. To understand this, think one more time about billiard balls. Imagine two balls directed towards one another, which then collide, and then bounce back. Now, think about the movie of this collision but projected backwards. What will you see? You will see the balls coming back together, bounce and then move apart. 

However, think a little harder. The backward movie first snapshot is the last snapshot of the forward movie, so it would be one in which the balls are moving apart. But that does not make any sense: haven’t we just said that they come together also in the backward movie? In order to fix this, when passing from one movie to the time-reversed one, we need to reverse the direction of the velocities in the snapshots as well. That is, the backward movie first snapshot is the last snapshot of the forward movie with the reversed velocities, the backward movie second snapshot is the penultimate snapshot of the forward movie with the reversed velocities, and so on. In the case of quantum theory, in addition of doing that, we also need to transform the wavefunction in the way I pictorially described as transforming the wavefunction from ‘red’ to ‘blue’ (if you really want to know: if you flip time, the wavefunction needs to be transformed into its complex conjugate). All right. Now think about that. In the case of velocity it makes some sense that its direction changes (as velocity is defined as change of position in time, and while positions do not change, time does), what about the wavefunction? Why would the wavefunction transform like that? What is it in the nature of the wavefunction that makes it change so radically depending on whether we look at it in the forward or in the backward movie? It is like saying that when we watch “Back to the Future” projected forward Mary McFly is played by Michael J. Fox, while when we watch it projected backwards he is played by Keanu Reeves. Why does it happen? Does it even makes sense? Albert and Callender argue that it does not: there is no reason the wavefunction changes this way, so they conclude that it does not change at all. And that means that the backward movie will be different from the forward movie, and the fact that they can be distinguished induces a directionality in time: the theory is no longer time-reversal invariant. That is, the theory loses a symmetry, namely time-reversal symmetry, and time has a preferred direction. 

Even if this argument is very compelling, I do not think one should conclude that time has a preferred direction. Instead I take this argument to be additional evidence that wavefunction realism is mistaken. In fact, this argument assumes that the wavefunction is part of the material constitution of the world. Namely it assumes that the wavefunction is something that is pictured in the snapshots of the movies of the phenomena. Only if we assume this we find ourselves to solve the problem of justifying why the wavefunction does funny things like the ones we have seen. And to get out of this problem wavefunction realists have to accept the loss of time-reversal symmetry. This is not cost-free: as I already mentioned when discussing Galilei invariance, scientist usually think of symmetries as important desiderata a theory should have. So, one will naturally wonder whether there is a way out of this, whether one could preserve the symmetry while remaining a scientific realist. And I think one could, very straightforwardly, in my approach: if one assumes that the wavefunction is not material, then it is not pictured in the snapshot, and nothing really changes about matter from one movie to the other. The wavefunction is more like a director in a movie, rather than the actor. The director of the movie may change, but she will direct the same story, with the same actors. In this case the argument does not have force and there is no reason to assume that time has a preferred direction.

3:16: So you argue that it’s premature to conclude that time has a preferred direction but why do you do that – and if time didn’t go from the past to the future wouldn’t the very ability to do empirical science be screwed given that it starts with a hypothesis and tests follow (in time)?

VA: Indeed, one could be very puzzled of why I (together with many others) want to keep something like time-reversal invariance while it seems to contradict what we experience everyday: we know that there is a direction of time, don’t we? We know what has happened in the past, not what is going to happen in the future; we have lived in the past, but not yet in the future; we assume time directedness almost always, both in science as you point out and in everyday life. So it may seem very unclear why I keep insisting in denying that this directionality is a real feature of the world: didn’t I just say that we should not unnecessarily depart too much from our experience? It is indeed true that macroscopic phenomena are time directed: coffee gets cold, not hot; people get old, not young; ice melts, does not solidify. This is usually characterized in terms of entropy, which always increases. So, the direction of time is the direction of entropy increase. One would want to be able to account for these phenomena in terms of the fundamental physical theory. If this theory is classical mechanics, then the theory is time reversal invariant, as I stated below, that is, it does not distinguish the past from the future. So it goes against what we perceive every day. How is it possible that macroscopic time-directness we experience every day comes from its absence in the fundamental dynamics? This has been explained by Ludwig Boltzmann, who proved that time does not have a preferred direction but, assuming that the universe started off in a particular circumstance, entropy increasing phenomena happen much more often than entropy decreasing ones. So it is not impossible for entropy to decrease, but it is very ‘unlikely’. This makes the macroscopic time directedness a sort of illusion, as at the fundamental level there is not any. The question addressed in the previous question was: does quantum theory change that? I argued that there is no reason to believe time has a fundamentally preferred direction, especially if one has already reasons to think the wavefunction is not material.

3:16: Wasn’t spooky causality at a distance thought to be a problem for physics not just for the layman but for people like Einstein too because it seemed to require signals of information travelling too fast. But it’s not a problem is it? So how should we understand what’s happening – and what kind of metaphysics could allow for it? It looks like magic!

VA: Quantum nonlocality is indeed THE mystery physics needs to solve. We have the idea that things can affect one another only if they are in direct or indirect contact. This is the concept of locality. We take it so much for granted that we do not even think about that. Newton, after repeated failed attempts to provide a local account of gravitational interaction, had to postulate the existence of a force which instantaneously acts at a distance. He disliked it so much that he regarded this nonlocality as a symptom of the inadequacy of his theory. Later, James Clerk Maxwell introduced the concepts of field, something which permeates space between the particles, which then allowed to understand the particles interaction locally. In 1925, Einstein, together with Boris Podolsky and Nathan Rosen, published a paper in which he argued that quantum theory had to be incomplete because otherwise would imply nonlocal action at a distance. The feature of quantum theory that makes it problematic in this respect is entanglement. The theory predicts that, for instance, certain pairs of particles which are 2 meters apart do not have in themselves a definite position, or that two particle which together are blue and yellow do not have an individual color. Assume that a source keeps producing pairs of these particles, and emits them in opposite directions. Then, have two people go at these opposite sides and then measure the color of the particle that comes to them. It turns out that, experimentally, if the person on the right measures that their particle is yellow, then the person on the right will measure their particle being blue, and the other way around. That is, the results of the color measurements of the two experimenters are always anti-correlated. 

But this is strange: the theory does not assign any color to each particle before the measurement, so it has to be that when the person on the right measure the color of their particle and finds it blue, say, then this information is immediately transmitted to the other particle, regardless of the distance, so that the person on the left always finds their particle of the opposite color. This is a sort of nonlocal correlation. Einstein thought that it was unacceptable, because, like everyone else at the time (at least), thought that we have to assume local interactions Thus, the only other explanation of the observed perfect anti-correlations is that we are missing a piece of information: both particles have been of a given color at all times, so that the perfect anti-correlations in the measurement results simply reveal the perfect anti-correlation at the production. That is, if you know that one particle is blue and one yellow, but you don’t know which one yours is, and your friend measures theirs to be blue, then you will immediately know that yours is yellow. There is no nonlocal action at a distance, just incomplete information. Einstein took the nonlocality of (present) quantum theory as an artifact of it being incomplete, and that once the theory will be suitably supplemented by the relevant information, then this (future) quantum theory will no longer be nonlocal. On the other hand, Bohr embraced the fact that (present) quantum theory is nonlocal, and took it as an indication that the theory cannot be interpreted in a realist way. For a variety of reasons the question of whether nonlocality is an artifact of the theory or a real feature of reality remained untouched for three decades until in 1964 physicist John Bell tried to provide an answer. He asked whether or not it was possible to make the nonlocality present in quantum theory go away. So he constructed a completion of quantum theory as Einstein wanted, and showed that it makes different predictions from (present) quantum theory. This disagreement could serve as a sort of crucial test, and in the 1980s experiments were performed to assess which theory is correct: is quantum mechanics genuinely nonlocal, or can one find some way of completing it avoiding nonlocality? Bell could show that there cannot be any way of completing quantum theory as Einstein wanted so that it would reproduce the experimental results. Thus, since the only assumption made was that the world is local, we have to accept the fact that, contrary to our intuitions, the world is instead nonlocal. 

This creates a problem of compatibility between quantum theory and relativity because the kind of nonlocality quantum theory requires needs some sort of absolute simultaneity, which relativity rejects. How to solve this? It is going to depend in the theory. The pilot-wave theory is such that thevelocity of a given particle in general depends on the instantaneous positions of all the other particles. Thus, the theory needs an extra physical structure, called a preferred foliation, to define a notion of absolute simultaneity, which relativity instead prohibits. One could make the theory relativistic, by substituting the Schrödinger equation to its relativistic counterpart, but one would still need the preferred foliation. The only way out is to make this absolute reference frame in principle undetectable, but this would make the theory only ‘effectively’ and not ‘truly’ relativistic. The complaint here is that doing this looks like cheating, as there are no other reason for the absolute frame to be undetectable other than that it is necessary to make the theory compatible with relativity. Progress has been made recently when researchers have proposed theories in which the existence of the foliation is, one way or another, more natural, For instance, a proposal is that the foliation could be extracted from the wavefunction. This seems particularly interesting to me because one could argue that if the preferred foliation is extracted from the wavefunction, since the wavefunction is common to all quantum theories, then the foliation is present in all of them. Thus one cannot object that the pilot-wave theory is particularly in bad shape because it has a preferred foliation, given that all quantum theories have one as well. 

However, I still have my doubts: the fact that some weird object, such as the preferred foliation, can be extracted from the wavefunction does not mean that this object necessarily has some sort of ontological significance! While the pilot-wave theory needs the foliation to have physical significance, in the other theories it could merely be some mathematical construction. Moving on to the many-worlds theory, the situation is more controversial. In fact when he formulated his theorem Bell assumed that there are not multiple universes, so it is unclear how this theorem applies to the many-worlds theory. In the case of the spontaneous collapse theories the situation seems more interesting, at least in some respects. Roderich Tumulka, a German mathematician and physicist, has recently developed a relativistic extension of a GRW-type theory which is manifestly nonlocal. In this theory the ontology is not the wavefunction, but rather it is collections of events in spacetime, called ‘flashes’, whose probability distribution is governed by a relativistic invariant wavefunction. This was a great success, as this theory is relativistic and quantum but requires no preferred foliation. Nonetheless, if you ask me the path is still long and difficult because, even if one has a theory which combines quantum nonlocality and relativity, it is very difficult to understand what it means for the world to be nonlocal. As you say, it is just like magic! Wavefunction realists like Alyssa Ney are driven by this concern in their conviction that the strongest argument for wavefunction realism is that it restores locality: since the wavefunction is in the high dimensional configuration space and in it all interactions are local. Unfortunately, I do not find this very convincing: what needs an explanation, in my opinion, is that we observe nonlocal quantum correlations, while what Ney explains is that ‘true’ reality, the one in configuration space, is local. However, I still find mysterious why and how three-dimensional nonlocality comes out of high-dimensional locality.

3:16: Birds might be better off if they knew their ornithology. Would physics be better off knowing its philosophy?

VA: Yes, physics would be better off with philosophy, despite of the flawed analogy: ornithology is the classification of birds, philosophy is not the classification of physics. In short, physics needs philosophy otherwise it is blind: you do things, compute values, but you do not know what they mean, and you do not know why you are doing it. If you don’t care about ontology, and you only care about getting experimental results right, then tell me why you find the activity of collecting and systematizing experimental results important. Why do you care about experimental results being suitably reproduced? A possible answer would be because if they are correctly reproduced then the theory is more likely to be correct. But what does ‘correct’ even mean, if you do not think the theory is about the reality? You cannot say that ‘correct’ means that ‘the experimental results are correctly reproduced’ because that would make your reasoning circular: you wanted to give me a reason why getting results correctly is important, and now our reason is that it is important to get them correctly because they get results correctly! If instead you care about the reality the theory describes, then you care about getting the results correctly because this is evidence that your theory is on the right path of being true.

3:16: And for the readers here at 3:16, are there five books you can recommend that will take us further into your philosophical world?

VA: There are many books that have influenced me, so five will not even come close! Anyway, aside from recommending you to read Schrödinger, Einstein and all the physicists who contributed to the development of quantum physics in the 1920s, I would suggest some more recent books that deal more specifically with issues I am interested in. First, there is a forthcoming book by Alyssa Ney entitled “Finding the World in the Wavefunction”, in which she ingeniously defends wavefunction realism. 

Then I suggest ‘The Emergent Multiverse” by David Wallace, where he thoroughly argues for the many-worlds theory and for his space-state realism. 

Also, Tim Maudlin’s book ‘Quantum Nonlocality and Relativity’ provides a thorough discussion of the tension between the two theories, which I believe poses the greatest challenge to physics at the moment. 

Among all the books that David Z. Albert has written, “Time and Chance” is a great illustration of Boltzmann’s explanation of macroscopic behavior in terms of the microscopic Newtonian dynamics, and expresses interesting views about ontology and symmetries. 

Finally I would recommend “Quantum Ontology” by Peter J. Lewis, as it discusses in general the metaphysical implications of quantum theory in a clear and straightforward language.

ABOUT THE INTERVIEWER

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