Traditional physics works within the “Laplacian paradigm”: you give me the state of the universe (or some closed system), some equations of motion, then I use those equations to evolve the system through time. Constructor theory proposes an alternative paradigm: to think of physical systems in terms of counterfactuals — the set of rules governing what can and cannot happen. Originally proposed by David Deutsch, constructor theory has been developed by today’s guest, Chiara Marletto, and others. It might shed new light on quantum gravity and fundamental physics, as well as having applications to higher-level processes of thermodynamics and biology.
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Chiara Marletto received her DPhil in physics from the University of Oxford. She is currently a research fellow at Wolfson College, University of Oxford. Her new book is The Science of Can and Can’t: A Physicist’s Journey Through the Land of Counterfactuals.
- Web site
- Oxford web page
- Google Scholar publications
- Wikipedia
- “How to Rewrite the Laws of Physics in the Language of Impossibility,” Quanta
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0:00:00.1 Sean Carroll: Hello, everyone and welcome to the Mindscape Podcast. I’m your host, Sean Carroll. Very often here on the podcast, we talk about the laws of physics, right? Both what they are and what they might be. We don’t have all of the laws of physics completely settled yet, so one of the ongoing things that physicists try to do is suggest different kinds of laws of physics. But there’s different kinds in different kinds, there are specific laws of physics, like the Standard Model of Particle Physics is a very, very specific set of laws, or Einstein’s Theory of General Relativity is a specific set of laws.
0:00:33.8 SC: But then there are broader frameworks within which we can think about proposing laws. The obvious ones would be quantum mechanics is a broad framework, classical mechanics is also a broad framework. But even those two broad frameworks of classical and quantum mechanics, they share a certain underlying paradigm, what in other contexts I’ve called the Laplacian paradigm for doing physics. And the Laplacian paradigm is basically, you give me the state of a system, either now or in the far past as initial conditions, there’s something we call the state of the system that has all the information you need, and then there are dynamical laws. The dynamical laws say, starting from that state, where does the system evolve to, and you can evolve it forward in time, or if the theory is reversible, both forward and backward in time, if you like.
0:01:23.1 SC: And that kind of paradigm is broader even than the ideas, the frameworks of classical mechanics and quantum mechanics. So what if that paradigm isn’t right, what if it’s not the best way to think about physics in either some contexts or even all contexts? That’s the suggestion made by something called the constructor theory, which was first proposed by David Deutsch at Oxford and has been picked up by some people, most notably by today’s guest, Chiara Marletto, who’s both a collaborator of Deutsch’s and also has moved the field forward herself and with other collaborators quite a bit.
0:02:01.9 SC: So the idea of constructor theory, very, very roughly, you’ll hear more about it later, is that rather than being given conditions for the system and how they evolve, you tell me the complete set of things that can be done and things that cannot be done within the laws of physics, whatever they are. And somehow the set of things that can happen and cannot happen, so factual and counterfactual possibilities, are enough to either, hopefully, maybe ideally, completely tell you the laws of physics or at least shed some explanatory light on what actually happens in the world. And this is potentially very interesting. As we’ll talk near the end of the podcast, Chiara has come up with some ways to use this perspective to propose things you might not have proposed by doing physics the more conventional way, like possible experimental tests of quantum gravity. But also, a completely new perspective says that you change what you think of are the interesting and relevant puzzles and problems in your field. Potentially, you think about connections, for example, between fundamental physics and emergent higher levels in different ways.
0:03:18.6 SC: So it’s clear why you might want to do something like this. It’s very, very ambitious. You’re trying to do big things. It also is hopefully clear what the drawbacks of something like this is. The more ambitious you are, the harder it is to get things right. I mean, the Laplacian paradigm has been around for a lot of years. It was implicit in the work of Galileo and Newton and Pierre-Simon Laplace circa the year 1800 put it down quite explicitly. That’s a long track record of success. To try to start with physics on a completely different footing, it’s hard, because you’ll probably fail. Most ways of doing physics are going to be wrong, and you have some success in the current system, so why not just stick with that and try to improve it?
0:04:02.9 SC: But it’s good that some people try to jump out of the current way of doing things and look at things from a brand new angle. The burden on them is to sort of come up with some useful sign posts along the way that correspond to real advances that we can all agree on are solving some puzzles. So I will try to, or rather we, ’cause I really don’t understand this stuff very well, we, I and Chiara, will try to explain what constructor theory is, and why it might be useful, why it has things to say, not about just fundamental physics like quantum gravity and quantum mechanics itself, but also real world stuff: Heat engines, thermodynamics, the physics of life and biology and so forth. So I think it’s one of these fascinating conversations that goes a lot of places.
0:04:50.3 SC: I will remind you, as I occasionally do, that you can support the Mindscape Podcast on Patreon. If you go to patreon.com/SeanMCarroll, you can post a little pledge, rather, a little donation, once per episode, a dollar or a euro or even more, if you’d like to do that. Mostly, I think the reason to do this is just to express appreciation, but you also get ad-free versions of the podcast. And once a month, as you know, I do Ask Me Anything episodes, and it’s the Patreon supporters that get to ask the questions that are answered on the Ask Me Anything episodes, but mostly it’s a little community of people who like the Mindscape Podcast and support it, and for whom I am extremely grateful. It really helps keep me going podcast-wise, which I hope everyone is enjoying. So with that, let’s let Chiara take over and expand our minds a little bit, let’s go.
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0:06:00.4 SC: Chiara Marletto, welcome to the Mindscape Podcast.
0:06:01.7 Chiara Marletto: Glad to be here.
0:06:03.1 SC: So, one thing that strikes me about what you’re trying to do is it’s super ambitious, right? [chuckle] You’re sort of rewriting the rules for how physics should be done. So before we get into the actual ways in which you’re doing that, let me just ask the sort of a more personal question. I mean, if one of my graduate students said, “Yeah, I’m going to work on completely changing the way that we do physics,” I would say, “Don’t do that,” or at least don’t do that until you’re a little bit older, right? It’s good to be ambitious, but it’s also hard to get things right, when you’re that ambitious right from the start. So how do you think about that? Do you think, “Well, screw it, I’m just going to be ambitious,” and we’ll see what happens, or is it a matter of going back and forth between being super ambitious and being more down to earth?
0:06:50.0 CM: Yes, so I think… As I said initially, when I started working on this, this was during my PhD in Oxford, and what happened is that I attended this very interesting talk that David Deutsch gave on sketching or outlining what this program of constructor theory was about and how he envisioned this as being a generalization of the quantum theory of computation. And so in a way, because my PhD was on the quantum theory of computation, I was very intrigued by this idea that there could be something more, something beyond that, and since then, my main question, the thing that interested me beside this, of course, bold vision of reformulating the laws of physics in a different way and so on was, is there a way that we can find problems that are currently open and tractable that we can address with this approach?
0:07:58.6 CM: And so in a sense, my focus so far has been to find these problems and solve them in a way that this… In a way of convincing my own self that it is actually a worthwhile, good working approach. And I’m completely open to the fact that this may not work to the degree that in a way the whole program hopes, but I think so far the results are promising enough that they entice me to work more on it. And more broadly, I think there’s one more point I wanted to make, but I think in general, any work in foundational physics is about working out these bold questions. So even though, yes, the kind of advice to students is to try to find tractable problems, I think it’s the case that what physics is about is to address these questions, and so in that sense, I don’t see what I’m doing as particularly unusual or a different thing from what all physicists that are interested in foundations are really doing, it’s just one of the various things that we’re trying to move a step forward and try to find new ways of solving these open problems.
0:09:21.5 SC: Yeah, that sounds perfectly fair to me, but I have noticed in my own writing papers, giving talks and getting responses to them, that there’s always a difficulty when you have to both convince the audience that there exists a problem and that you’re making progress solving it, right? Everyone has a list of actual existing problems in their head, and if you say you’re solving those, like, “Why is there more matter than antimatter?” People go, “Oh, yes, that’s a good problem to be working on,” but is this the situation you find yourself in where you have to convince people that there is an issue to be addressed or are people more or less sympathetic to that?
0:10:00.0 CM: Well, it depends on the particular kind of problem. I think I do recall having to elaborate on why there is a problem with the quantum theory of computation itself. So, I think this is because most people who are currently working in the field are somewhat focused on the technological developments that stem from the field, but they are not, perhaps, focusing on the more foundational aspect that are actually the ones… The reasons why the quantum theory of computation in a way came about in the first place, and so in that sense, yes, sometimes you have to point out that there are these new problems, but in broader terms I think some of the other issues I’ve been working on, which have to do with this issue of making predictions in cases where the dynamical laws that we have either fail or we don’t quite know which particular dynamical law we could apply, this is a problem that’s recognized by most people who work in foundations of physics in the sense that both in the… An example is the quantum gravity community, where of course, this is a known issue.
0:11:19.4 CM: And likewise, problems with the foundation of thermodynamics have some kind of open problems that I don’t have to argue about because they’re already somehow understood. So yeah, I think it’s… The most challenging thing I’ve found myself tackling so far is really the… So showing that there is a kind of advantage in appealing to these principles that constructor theory has, which can lead us to somehow supplement the dynamical laws as we currently know them. So in that sense, this is more like kind of challenging, finding specific problems where this approach makes a difference rather than in explaining why the problems are important, which I think in a way it’s understood at least in the foundational community.
0:12:16.0 SC: Right, and so, I’m getting the impression that this grew out of thinking about quantum mechanics, quantum foundations and quantum computation and information in particular. So, that’s a pretty easy sell. These days, everyone agrees that quantum computing is something interesting, so maybe if you are presenting a framework that will help us understand that, that’s a relatively tangible thing that people can hold on to.
0:12:41.8 CM: Yes, and I think perhaps the less widely known thing is that when you look at the quantum theory of computation… So, you open a textbook where they are proving some theorems about channel capacity or other things, most of what’s proven there is rooted completely in the formalism of quantum theory, of known relativistic quantum mechanics, really. And this is a plus, of course, in the sense that, it’s great that we can prove these theorems. But somehow, if you look at it from a purist point of view, from the point of view of a person who’s interested in information theory, you would consider this as a slight deficiency, in fact an important deficiency, I would say, of the approach, because as a theory of information, if you compare it to, say, Turing’s theory of classical information, it really relies a lot on the formalism of a particular theory, which we know will somehow have to be modified one way or another by the next dynamical law that will match quantum theory and GR and general relativity.
0:14:00.0 CM: So in that sense, I think one of the aims of this program that I’m developing is to find a way of emancipating these results from the specific details of quantum theory, while still retaining all of the information theoretic reach of the results themselves. So in a way, still being able to talk about things like entanglement and superpositions and exponential speed up due to quantum effects without there being a specific formalism, which is the one of… The formalism quantum theory. So this is one way in which the theory of computation needs to be generalized. And it’s quite important, I think, because in a way, we haven’t quite completed the program of formulating the quantum theory of computation in this more general way, and constructor theory is attempting this generalization.
0:15:02.5 SC: Yeah, I want to get to the details of constructor theory, but you keep saying interesting things that I need to follow up on. And the interesting you just said was the possibility or the prospect that standard quantum theory itself might need to be modified in some way. Of course, that’s always a possibility. But I and I think a lot of other physicists would say there’s no evidence that we need that kind of thing, except maybe if you say that the fact that we havn’t quantized gravity yet should make us skeptical. But you seem more open to the fact that quantum theory itself is going to not be up to the task of describing physics in the years to come.
0:15:44.2 CM: Yeah, I think there are a number of reasons why I think this. So on the one hand, there is what you said; there is the fact that we have a number of very well-crafted proposals for quantum gravity, both in the perturbative regime and in the non-perturbative regime and so on. But, there is no somehow consensus on which one of these is the right one, and there are some considerable issues with some of them, and difficulty in finding obvious predictions that stem out of them and so on. So in that sense, I think in the absence of this one candidate, it’s quite important, I think, to emancipate the results that we have about the universality of computation and various other things that pertain to the quantum theory of computation from the specific formal aspects of quantum theory, because some of them may stay and some of them may not stay in the future.
0:16:51.9 CM: But whatever happens, I think my bet is that the information theoretic structure of quantum theory will be maintained, so things like the quantum multiverse, the idea that the quantum computing mechanism will still be viable, and the possibility of proving that the universal quantum computer has modes of computations that are more general than those accessible to a classical universal computer. All of these things will still be true and we need a way of expressing them without necessarily rooting them into quantum theory.
0:17:25.1 CM: The other reason why I think quantum theory is somewhat problematic or has some kind of things that are not so satisfactory about it, is that there is this field, which is called quantum field theory, which is something that we effectively use whenever we have to make a… Perform a calculation to perform some kind of predictive statement about what happens in a laboratory and so on. So in that sense, it’s a very successful thing, formalism, but quantum field theory itself was at least conceived by those who proposed it, especially in regard to the theory of electromagnetism, a kind of work-in-progress. So it wasn’t really supposed to stay as a fundamental theory of nature, and it has issues, so it has various issues, mathematical issues, and it also has conceptual issues to do with continuum and things of that kind. So in a way, I also find that not such a satisfactory theoretical device from the foundational point of view.
0:18:43.2 CM: Of course, it’s very successful, and it’s great that we can use it to make predictions about things that we can test right now and so on. But the question is, we need a better theory, and so in all these cases, I’d like to be able to build a more robust foundation for the edifice of quantum theory of computation so that it will survive no matter what the new dynamical law will be.
0:19:11.8 SC: Okay, that is a good set of motivations. So now that we’re motivated, maybe… I want to ask about what exactly constructor theory says, but is it first helpful to compare it to the standard paradigm, if we have people listening in the audiences who are not professional physicists. What is it about the standard way of doing physics that is there that you’re considering either altering or presenting an alternative to?
0:19:41.7 CM: Yeah, so first, let me just say one thing that is perhaps slightly related to the former question, but it kind of prepares the answer to this one. So the name constructor theory might make the people wonder why constructor, what is that? I think von Neumann, so this is a term that was coined by von Neumann, so he was wondering whether there could be a more general device that can somehow supplement the notion of a computer. So he was trying to find ways of saying that, the way in which Turing had devised its universal computer was too limited. And so, in a way, while a universal Turing machine can simulate anything that is permitted by the dynamical model on which it runs, it may not be able to perform all the physically allowed transformations, not just computation, so more general transformations.
0:20:53.4 CM: And the classic example that von Neumann gave in one of his brilliant lectures in the ’50s was that there is this task, which is the task of self-reproduction, which of course, cells can implement very easily. Now, this is a task that requires the device in question to create a replica of itself. And while a universal Turing machine can simulate in its workspace an ecosystem with cells, self-reproducing and undergoing natural selection, and so on, it cannot itself be programmed to create a replica of itself. So that’s one slight kind of drawback of Turing’s construction. Unfortunately, I can’t kind of create a replica of my computer just by programming it in a suitable way.
0:21:43.2 CM: But so in that sense von Neumann thought we need to treat more general programmable machines, and constructors, that’s the term he coined, were precisely used to kind of label this more general class of programmable machines, which include programmable computers, but also this more universal set of objects that can perform general physical transformations, not just computations. And the universal constructor is a machine that can perform any transformation that’s physically allowed. So it’s a kind of ultimate generalization of Turing’s universal machine.
0:22:29.6 SC: Good. So… Yes.
0:22:34.3 CM: Now… Yes, so the reason why we use the term constructor is because the key new step in constructor theory is that we would like to focus laws of physics, and the fundamental laws of physics, not just on what traditionally is considered to be the most fundamental way of formulating the laws of physics, which is to use a dynamical law with some boundary condition or initial condition, however you want to call it. But we’d like to enlarge the set of fundamental statements to include statements about what physical transformations are impossible and what are possible, and also why. And I think when we talk about a possible transformation, there is where the notion of constructor is hidden. Because the statement that the transformation is possible means that given a set of laws of physics, the performing that task to that transformation to arbitrarily high accuracy with a device that works like a constructor, so it can perform the task and work in a cycle, so it retains the ability of causing it again. So this phenomenon that leads to the tasks being performed by this constructor, is allowed to arbitrarily high accuracy. That’s what possible means.
0:24:17.7 CM: And the fact that the task is impossible, on the other hand, means that there is a fundamental limitation to how well you can approximate the behavior of a constructor for a given transformation. And the constructor is in this case an even more general notion than the one that was proposed by von Neumann, because it’s really any system that can enact, enable a transformation on a different system, and then retain the ability of causing it again. So it’s in a way, it’s something that can work in a cycle. So you can think of it as a generalization of things like enzymes or thermal engines or computers. And of course, it can be programmed as well, and so on. But I think it doesn’t have to be programmable. And in a way, the fact that it works in a cycle allows you to remove it from the statement about the laws of physics, and the laws of physics are just then about what’s possible and what’s impossible without having to deal with the complexity of each particular constructor.
0:25:23.6 CM: So that’s perhaps the key step that distinguishes this approach from the traditional approach. So these statements are supposed to be now the most fundamental statements, and things like dynamical laws and boundary conditions should be explained in terms of them. So that’s the fundamental switch that you need to take when you try to formulate the laws in this way that we are proposing.
0:25:49.8 SC: So good. So I think this is actually helpful, to me anyway, I hope to the rest of the audience. But so to restate that, yeah, the… Bringing up von Neumann is very, very helpful here. Can I think about it as saying that the point that Turing made was that regardless of any individual computer you might build, I can imagine this universal computer, and asking what it can and cannot do sheds light on the very idea of computation and the limits of that in the physical world, and likewise with von Neumann’s constructors, you and David Deutsch and your collaborators are saying that if we knew the whole set of things that could or could not be performed, the whole set of tasks that could or could not be performed by the universal constructor or individual constructors, that would be equivalent to what most physicists think of as knowing the full laws of physics, is that the idea?
0:26:50.2 CM: Yes, indeed. And I think it would be, that’s a very nice way of putting it, and so here there are a few really exciting insights. The first insight is what you said, that it’s really implicit in the quantum theory of computation, that by studying limitations of programmable machines, which seem to be emergent and they’re supposed to be something that isn’t really at the foundation of physics, according to the traditional way of looking at physics, you can actually understand better the foundations of a very deep theory, which in the case of quantum theory of computation is quantum theory, and in the case of constructor theory we are hoping can be a more general set of laws, dynamical laws that include quantum theory, but possibly its successors and so on. And the other insight is that by switching to the study of the statements about possible and impossible transformations, you are liberating, you’re trying to… You manage to escape this set of philosophically problematic issues that the traditional conception of physics runs into.
0:28:08.4 CM: For example, the fact that we put a lot of emphasis in the traditional way of doing physics on dynamical laws, but somehow we always have, and you have written very eloquently about this, that we always had this issue of setting the theory of what are the boundaries, what are the initial supplementary conditions for these laws. And this is an issue that is still open in a sense, because there are very many theories that are proposed about cosmology and also there are issues about how to test them, and the explanatory statements they make are somehow perhaps less established than those that you can make with purely pure set of dynamical laws, and by appealing to this additional set of principles, we are trying also to explain, to provide an explanatory foundations for theory of cosmology. So in a sense we’re trying to solve this issue of, okay, we’ve got the dynamical laws, now we have to fix the initial conditions, and theories about those seem to be a bit arbitrary or hard to pin down. We want general principles that can help us understanding also, what those theories could be. So in that sense, this is an additional bonus that comes from expanding the set of statements that you take as fundamental in your physical picture of the universe.
0:29:39.7 SC: Yeah, I mean, that would be great if we shed some light on the problem that from the traditional point of view is, what are the initial conditions for the universe. And it’s very often true that if you change perspectives, even if the formalism that you invent is completely equivalent, problems that seemed hard in the original formalism become more illuminated and even easy in the new formalism. So is your… Is constructor theory supposed to be in principle equivalent to the standard way of having initial conditions plus dynamical laws, or do you think that it’s possible the laws of physics ultimately just can’t be expressed in terms of initial conditions and dynamical laws and constructor theory will give you something better, bigger, different than that?
0:30:29.1 CM: So this is something that will become clear in the future, so we don’t have results yet that can help us understand which one of these two options is the true one, but the hope is that this approach can enlarge the set of things we can say about the universe. So in a way, dynamical laws and initial conditions, if this approach works would still be true in some approximate domain in a way, but they would be like emergent consequences of these deeper principles. And I think you can understand, perhaps, in what sense this could be true by considering a principle that one of the principles that is most well-known in a sense in physics, which is this principle of conservation of energy, which I know also you’re quite interested in.
0:31:29.5 CM: So if you take the principle of conservation of energy as a statement about the universe, you can perhaps think of it in two different ways. So one is to say, well, I have these particular set of dynamical laws and I’ve got a quantity that I call energy, or even a more general quantity, it doesn’t have to be energy, and then I can derive by using the symmetries of these laws that actually this quantity is conserved, so it’s one way of understanding what the law says. But there is a different way of thinking about it, which is to say that the law says that in all true laws of nature, those that we already know and those that we may actually come up with in the future, there must be a quantity called something, energy, or a more general quantity that has to be conserved.
0:32:24.4 CM: Now, this latter statement, if you consider it, is more general than the former, in the sense that the former statement is always particular to a specific formalism of a particular dynamical law, and it doesn’t really take a view on what we might want to conjecture tomorrow about a better dynamical law. But the latter statement, really, is like a draconian constraint on any law that we might come up with in the future, really has to conform to this idea that the task of creating energy out of no energy is really impossible. And so in this latter statement, you could say any particular symmetry of a particular dynamical law that happens to conform to this principle, is in a way, explainable in terms of this more general way of formulating the conservation law in question. And so this is the sense in which we expect that these principles of constructive theory should play a role in deriving or explaining features of dynamics, in a deeper way than just saying, well, the dynamics is like this, there are these symmetries, and we expect these things to be conserved.
0:33:41.0 CM: So that’s somehow the switch in perspective, and this is why we expect that constructive theory statements should be somehow more general than any particular statement you can make within a specific law of motion that you happen to know.
0:33:54.4 SC: Okay, I think this is all very helpful, but maybe I’m cheating because I know a little bit ’cause you wrote a book and I read much of the book, etcetera, but the audience hasn’t, so let’s bring it really down to earth. A traditional paradigmatic thing that physicists do, physics problem that we explain, is the motion of planets around the Sun, Kepler’s laws. Kepler came up with the laws, there’s ellipses, and then Newton explained them using this paradigm, this old-fashioned paradigm of dynamical equations plus initial conditions. How would I explain Kepler’s laws from a constructor theory point of view, is that even a fair question? Is that the kind of thing that you would think about addressing?
0:34:40.9 CM: Yes, I think in a way, this is a very interesting example because it’s specifically… So this is exactly one of those cases where you could explain the phenomenon in question in two different ways. So one is to say, well, I have these laws, Newton’s laws, and I’ve got some initial conditions, and I know that for certain initial conditions, I will end up having certain kinds of trajectories for these objects, and then I can put in the values for masses and various other constants and find out exactly something that matches the structure of the solar system as we know it right now. But there is a different way, which is to say, let’s now list all the constraints about quantities that are conserved, and things that are impossible to create out of nothing, and so on. And now, you wouldn’t quite get the prediction, the quantitative prediction about how a particular feature of the orbit of a given planet should be, so you wouldn’t get the quantitative aspects of the dynamical predictions, but you would narrow down the set of allowed dynamical laws and initial conditions that are compatible with these general constraints.
0:36:28.1 CM: And now, within these laws, there would be Newton’s laws, but also of course, Einstein’s general relativity equations and perhaps future laws that will also be able to describe by taking appropriate limits the current structure of the solar system. And of course, to make quantitative predictions, you would need those dynamical laws, but to explain all of their features, you would have to appeal to these more general statements about what’s conserved and what are the things that you can’t change and what are the transformation you cannot, or can perform. So that’s the idea. So the bet is that just by confining yourself to the dynamical laws, you can’t express all of the reasons why, say, the solar system is the way it is. And most importantly, you can’t capture all of the other possible dynamical laws that you could use in order to describe it. And so you need to somehow enlarge the set of statements that you appeal to in order to explain a certain dynamical motion that you happen to be able to verify in your vicinity in the universe. And perhaps a good example here has also to do with the information principles that you can construct within constructor theory. So in a way, maybe we can discuss this in… Maybe in the next question or a bit later.
0:37:48.8 SC: Yeah, no, we can be… I want to dig into this one a little bit more, because I may or may not have understood what you said, but are you saying that knowing all of the principles of what can and cannot happen, so energy is conserved, angular momentum is conserved, etcetera, this is not enough to derive Kepler’s laws. Is that true? We need something else?
0:38:13.0 CM: Well, you wouldn’t be able to derive the exact quantitative statements about the, for example, the… Certain geometry of a particular orbit, and the… Given, let’s say, all the features of the Sun and of the planets and of the things that are orbiting around the Sun and so on. So in that sense, the dynamical laws are, in this specific case, Newton’s laws are quantitative about some of these predictions. And this is something that you can’t get just by stating a set of possible and impossible transformations, because that is a qualitative set of statements. So in that sense, I think the predictions you would get out of a set of statements about possible and impossible transformations are compatible with Newton’s laws and Kepler’s laws, but also with other laws that are more general and then we may not have conjectured yet. And also include, of course, Einstein’s general relativity, which is a kind of improvement on those laws.
0:39:30.2 CM: So in this sense, I think it’s not enough to just concentrate on the statements about… On statements that say what transformations are possible and impossible to derive all the statements that you can derive from, say, things like Newton’s laws. But the statement I’m making, and we are kind of making in general in this research program, is that there are things in the reality that you can describe with dynamical laws, such as Newton’s, that can’t be explained within just Newton’s laws. And therefore, to have a complete picture, you need both the dynamical law approach supplemented with these more general principles. And then we make the statement that we believe that these more general principles are actually in a way, you can think of them as more fundamental because in a sense, they are more general than any specific law of motion. So that… These are the two logical steps involved in thinking about the principles and their relations to dynamical laws.
0:40:37.0 SC: Okay, so good. I think this is helping me out, but let me just check that I have not fooled myself into thinking I understand what’s going on. So in the standard picture, when we have Newton’s laws, we can derive the fact that energy is conserved and momentum is conserved, etcetera, but they seem a little bit parasitic on the underlying dynamical laws. And you’re making the case that it would be better to consider them as at least on an equal footing, if not a more fundamental footing than those dynamical laws for reasons of explanatory power. Is that fair?
0:41:16.1 CM: Yes.
0:41:17.9 SC: Okay.
0:41:18.3 CM: Yes, correct. And in general, as I said, once you have derived the conservation of energy within a specific law of motion, that isn’t very explanatory about possible other laws of motion. So in a way in this framework where you’re considering the fact that this law of motion may be modified and you want to use these principles, actually guidelines, to help you out in guessing future laws, which is actually what we do in physics ultimately, because that’s how we use principles. The thinking of the conservation of, as certain quantity as being just an implication of a particular law of motion isn’t very helpful. So in a way, this logic I’m advocating isn’t that new, because it’s something that we have been informally using for quite a bit in physics. So principles are helpful when we want to conjecture the future laws of physics.
0:42:14.0 CM: It’s just that here, we were pointing out that there are some phenomena which are described by some of these dynamical laws that we know that can’t quite be exactly captured within just those laws, so you kind of need these other additional set of statements to fully explain them. And so conservation laws are an example, there are other examples. And so I think this is kind of… But what you said is exactly it, so.
0:42:41.3 SC: Good. That’s very helpful. I’m just going to keep hitting on this one example a couple of more times, ’cause I’m really… This is very, very helpful to me, and it is… Putting it in these concrete terms is making me understand, but if I understood what you said, then… Newton says that the force due to gravity obeys an inverse square law, right, the force fades away as the inverse of the square of the distance between the objects.
0:43:05.5 CM: Yes.
0:43:06.2 SC: I could imagine other possible worlds in which it obeyed an inverse cube law or something like that, and…
0:43:13.5 CM: Indeed.
0:43:13.5 SC: Energy would still be conserved and angular momentum would still be conserved. So what I’m guessing, and you’ll correct me if I’m wrong, is that constructor theory is sort of silent on which one is right, and the full theory of the world would include, in your view, both these general principles and some specific addendum that says they’re instantiated in the following way in the actual world. Is that correct, or did I go too far?
0:43:43.6 CM: Yes, I think this is correct. There is one interesting thought there that one could explore, and this is to do with, could one then explain even the particular scaling of a particular dynamical law in terms of some other counterfactual principle which we don’t perhaps yet know. Likewise, this is similar in the… There’s a similar question, let’s say, in quantum theory, where we have this certain rule that, what we call the Born rule, which has to do with how to compute probabilities from given, say, the quantum state of a given object, and there are other assignments, there could be in principle other assignments for computing this kind of probability rule.
0:44:33.3 CM: And the question is, well, in this case, we’re just postulating that the rule has to be like that, and at least this is what you do in textbook quantum mechanics, so there could be more general principles that you can conjecture, which would then pin down the exact scaling of the Born rule conjectures for the probability law in quantum theory. So this is a similar question, this is a similar issue to the one you pointed out, and I think this can be said about, for example, constants of nature that are also currently unexplained in general, in even a specific dynamical law, so why a given value and not another?
0:45:13.9 CM: So if the program works in the way we expect, you could then link all of these apparently accidental features of laws that we currently use in order to predict things successfully, to actually, a more explanatory principle that ultimately can be expressed about… In terms of these statements about what’s possible and what’s impossible on a given subsystem of the universe, when you’re trying to perform a transformation on it. But of course, it’s a conjecture, so it’s a kind of work in progress proving all of this. And it’s certainly true that just from the conservation laws, you can’t, of course, pin down some of these features alone, but there should be more general principles.
0:45:55.9 SC: No, that makes a lot of sense. So it seems as if there is sort of a weaker claim that taking these principles as more fundamental than the dynamical laws provides insight and helps us explain things, and the stronger claim that maybe there’s sort of a maximal set of these principles that we don’t know yet, about what can be constructed, what cannot be constructed, that would suffice to pin down the exact laws of nature perfectly.
0:46:26.2 CM: Yes, quite. Or rather, I would say explain them.
0:46:30.7 SC: Explain.
0:46:31.4 CM: So I prefer to use that statement in the sense that it may not be the case that this pins on one specific single law. In fact, my guess is that, as I said, this would at best explain the features of a number of viable dynamical laws that are compatible with these assignments or principles. And of course, the bold conjecture is to say, well, any relevant feature of those laws, if we note it as physicists, in a way that this is the kind of relevant thing that we want to explain, ultimately can be explained in terms of these statements about what possible and impossible transformations you have. And that’s something that may or may not be true, and it will become clear in the future whether it is. That’s kind of an interesting question.
0:47:17.1 SC: Okay, final question about the solar system before we move on to other topics. Just… And this is like the dumbest question, just for clarifying purposes. When I first heard about constructor theory… It’s not that old, right? It was just a few years ago, I guess my question was, what is the constructor that picks up the Earth and moves it to another point in its orbit? But I think, from everything you’ve said and I’ve read subsequently, the point is not that there is a constructor that is making this happen, but that by contemplating the set of all constructors that could do different things, you can figure out how things happen. Yeah?
0:47:57.0 CM: Yes, yes, exactly. So this is a very nice question. When you’re thinking, well, in the traditional way that we all use when we approach physics, as you said, the question is, okay, I see a kind of change in the universe, somewhere, a movement of sorts, and I want to explain this in terms of some… Ultimately, some law of motion and some kind of initial set of conditions for that law of motion. But… So in this sense, the question of… One could say, well, okay, the question in the case of constructive theory is to say, let’s identify the constructor that does this or that, that implements this or that transformation.
0:48:37.6 CM: But as you said, this is not the logic. Here, the logic is to state a kind of constraint about what are the features of the possible allowed constructors for this particular motion that I’m considering. And of course, if you think of the orbits and the planets, you could think of much better constructors than just the laws of physics as they are, because you could think of having a robot that corrects the trajectory of a given planet every so often, and makes it even closer to a specific geometry that you desire. And of course, this is actually allowed by the laws of physics, so it’s a permitted kind of constructor, it’s just we haven’t implemented one yet. We may in the future, I don’t know.
0:49:34.2 CM: And so, for the moment, we just are stuck with this particular shape of the solar system, which is the one that is naturally implemented by the underlying elementary symmetries of the dynamical laws we have. So they are… In a way, you can think of them as the approximate constructors that are at work there, because they, in a way, are unchanged after they have implemented one rotation of the given planet around its orbit. But of course, there are better constructors for the task of letting a given planet move around a specific orbit with a given shape, and we can think of ways in which in principle these constructors could be allowed and could be built.
0:50:17.9 CM: But that’s not what you see in the conservation law. The conservation law just says, well, out of all these constructors that you might think to implement this transformation, surely you can’t use those that violate this particular thing, and they create, say, a given quantity out of something that doesn’t have that.
0:50:32.9 SC: Good. Alright, I will let you go for the solar system now. I think I understand it a lot better.
0:50:40.3 CM: Great.
0:50:41.2 SC: And I want an opportunity to talk a little bit about… Because we are shifting viewpoint, right? That’s a big aspect of this whole program. Sorry, it seems to me right now that in the current state of the program, a shift of viewpoint is the more obvious thing than a particular new view on the theory of everything or anything like that. And part of that viewpoint shift is this emphasis on counterfactuals. Your book is literally called The Science of Can and Can’t… What is the title of your book?
0:51:15.2 CM: Yeah, that’s right, yeah, The Science of Can and Can’t.
0:51:17.3 SC: The Science of Can and Can’t. What is the role the counterfactuals play? Because in some trivial sense, any time you have a law of physics, there are counterfactuals implicit there, because the law of physics says, here are things that can happen and there are things that can’t. ” [chuckle] So things that can happen obey the laws of physics and those other things can’t, but you are putting a slightly different spin on it, I think.
0:51:39.1 CM: Yes, the term counterfactual is used in the book in a very specific way, so it’s really referring to these statements that I already mentioned earlier, the statements about what transformations are, say, possible or impossible on a given system in the sense that we discussed a bit earlier. In this sense, it’s a perhaps narrower sense than what you find in mathematics or philosophy, but it’s… In common with those other notions it has the fact that these statements are more general than a particular statement that you make when you say, well, I have these particular dynamical laws in the describable universe and these are the boundary conditions, and this is what happens in the universe, and that’s all there is to it.
0:52:34.1 CM: This could be regarded as in a way a kind of caricature version of the traditional way of formulating physics, but ultimately, I would say, this is the ultimate goal of the traditional physics program in a way that… We are all hoping, as physicists, let’s say, that we will find this ultimate dynamical law and this ultimate theory of the initial conditions, and this will tell us everything we want to know about what’s going on in the universe. And the idea here is to say that this specific statement, the one [0:53:14.8] ____ this is the dynamical laws and the initial conditions in a given universe, so it cuts out all of the other counterfactuals, because they’re not happening, so there are other possibilities that haven’t been realized, and therefore they’re not of interest in a sense.
0:53:34.4 CM: And here we are saying something different, so we’re trying to say that, first, that statement in itself wouldn’t exhaust all the explanatory things that you can say about the universe. For example, it would miss out, for example, on these conservation law statements that we mentioned earlier because, of course, in a given universe, you may not find a particular perpetual motion machine, but that doesn’t mean that it’s not allowed, it doesn’t happen, but whether it’s allowed or not, with different perhaps initial conditions or different dynamical laws, we wouldn’t know. Whereas the law that says that isn’t allowed, that’s not possible and there is an explanation for why that is, rules out all such counterfactual worlds and leaves us with a set of other possible worlds that are in principle permitted.
0:54:38.2 CM: I think the emphasis on counterfactuals is to say that, among the things that we need to appeal to in order to explain particular features of objects that we encounter in the universe are these counterfactual features and, just like with all laws of physics, they appeal to things that are not directly observable, in the sense that the explanatory part of quantum theory or general relativity is far from what we directly see, but nonetheless is the best part of the explanatory set of statements that the theories can make and likewise in this case, the counterintuitive fact is to say, well, a factual thing, something to do with what happens in the universe as we can observe it, is actually due to these counterfactual principles.
0:55:33.4 CM: And so in that sense, it’s like adding or emphasizing, let’s say, a set of these unseen things in terms of which we explain what we see, in a more systematic and general way than it’s been done so far, because in a way, counterfactuals have been used in thermodynamics and in other branches of physics in an informal or implicit way, and now we want to do it in a proper way. And also including counterfactuals from, say, information theory and other branches of what we now think of physics.
0:56:09.2 SC: [0:56:09.2] ____ obviously you’ve thought about counterfactuals quite a bit. David Lewis had a whole metaphysics of possible worlds and so forth. Is that work of any use to you or do you read about it, or are you just more pragmatic about your counterfactuals?
0:56:26.4 CM: I think these works are useful to understand… Philosophical works are usually useful to categorize things in a very proper and clear way. In that sense, they are very useful to that degree, and they’ve been useful for me as far as… You can tell what kinds of counterfactuals I’m interested in with this theory versus a more general sense of counterfactuals that could be of interest or of use within philosophy or mathematics and so on.
0:57:02.7 CM: I think for the level of predictions and statements that we’re making at this stage within constructor theory, we don’t necessarily need to appeal to the subtleties that are mentioned in these works, but they could be useful in the future. In general, I quite like the work that some philosophers do in clarifying some of these categories, that perhaps in physics we are slightly misusing, and I find it kind of illuminating sometimes to read about those things. I’m not sure I find directly an application for those yet in what I do, so in a way I’m kind of on the pragmatic side, I would say, I’m but open to sort of refining my notions, if I need to.
0:57:48.2 SC: I think it’s a good place to be. I didn’t actually know what the answer was going to be to that question, so I thought I would throw it out there, but… So here’s something maybe more up your alley. It’s very interesting to me, and I think to a lot of people who are physics-minded, who first hear presentations about constructor theory, that we have a standard conventional view of what fundamental physics is like, quantum mechanics, quantum field theory, even a few hundred years ago, Maxwell’s equations, Newton’s laws. And many of your examples when you talk about constructor theory are already at the macroscopic emergent level, enzymes or thermodynamic engines or something like that.
0:58:33.8 SC: And I get the impression that you treat these, what I would think of as an emergent level of physics, a sort of macroscopic approximation to what’s going on, with equal dignity [chuckle] to the more fundamental things that are going on. Is that a fair reading or is there something new and special about the relationship between these different levels from the constructor theory point of view?
0:58:58.9 CM: Yes, I think that’s a great question. I’m… It’s a very important thing that I think is already implicit in this work on the quantum theory of information. So, the divide between what’s macroscopic and non-fundamental and what’s considered as microscopic and fundamental is something that, well, I would say is somewhat blurred, or at least arbitrary in a way, because we can for sure tell what’s clearly macroscopic and what’s clearly microscopic. But then there are all of these things in between that… To be like the question what constitutes something that’s alive. Clearly, a bacterium is, an electron isn’t, but there are lots of things in between, and one might put the dividing line in various places.
1:00:00.7 CM: Now, the laws that we are talking about in constructor theory try to capture regularities that are true, independent of the scale. So they would be true within, say, a set of objects that we would label as microscopic, like a bunch of atoms, let’s say, not particularly aggregating in any specific way. But also it could be true of a more macroscopic object which, for example, displays some information-theoretic regularities such as a flag, which can instantiate some bit of information or something like that.
1:00:41.5 CM: And this is not an unusual thing in the sense that, although I think, as you said, most traditional physics wouldn’t think of laws of this kind as fundamental, in the case of quantum computing, we already encountered these kinds of things because when we talk about a qubit and what a qubit does and what are the laws that kind of underlie its behavior and so on, we’re not really worried about which specific system is embodying… Embodies the qubit.
1:01:13.7 CM: Of course, we can think of an electron spin, which is pretty microscopic, but then of course, as Schrödinger did, we could think of a cat being dead or alive, that if we were able to manipulate the cat in a quantum mechanical way, the relevant degrees of freedom of it would also behave according to the laws of qubits. And so in that sense, the examples I’m referring to bring in possible instances of both microscopic and macroscopic objects, all of which conform to these general principles because the principles are scale-independent.
1:01:53.5 CM: This is something that doesn’t quite… So this is maybe an element of the novelty, if you like, and the principles are not about saying what is the most probable behavior of a given aggregate of atoms above a certain scale, let’s say in the thermodynamic limit. They’re really about just stating that a certain transformation is impossible, and then it’s up to you, in a sense, to work out what this implies for a given aggregate of atom with a given specification, which could be approximating the behavior of an enzyme or a heat engine or something else.
1:02:29.3 CM: So in that sense, I think it challenges the idea, the approach that we are pursuing, it challenges the classic divide between macroscopic and microscopic and tries to find these principles that are not rooted in either of the domains, so it’s not just… They’re not just macroscopic or microscopic, but somehow they are valid across scales, and in a sense it… We’re hoping that this unifies our understanding of objects that we regard as emergent and objects that we traditionally regard as fundamental and more elementary.
1:03:03.2 SC: Yeah, let’s continue in that vein a little bit, because I am a little bit confused about what is approximate and what is exact, and even if that’s a sensible notion in some way. Because you make some provocative statements about the arrow of time and irreversibility, and the sort of standard way of thinking about that, by standard, I mean, what I wrote in my book about the arrow of time, is to say that at the microscopic level, all processes are reversible. The laws of physics do not tell the difference between forward and backward in time, but at the macroscopic level, when you add in some past initial condition of low entropy, you find that certain things happen and certain things don’t, so the world looks irreversible.
1:03:47.2 SC: A classic example is the Carnot cycle back in the 19th century. This is probably one of the first examples of one of what you’re thinking of, stating that certain things are impossible, an engine that has a certain efficiency is impossible. But I take that to be a purely macroscopic statement, and you’re sort of shifting the ground underneath our feet, a little bit to, I don’t know, undo the connection, I guess, between, in my mind anyway, between that kind of macroscopic statement and the idea that it’s an approximation of a more exact microscopic statement. You’re sort of putting it on equal footing, is that fair?
1:04:32.0 CM: Yes, I think this is a very nice way of expressing what we’re trying to do. Okay, this is a very interesting topic.
1:04:41.2 SC: Yes. It is.
1:04:42.7 CM: So the first thing I want to say is that I see the statements about irreversibility to do with, say, the second law, and the issue of arrow of time as different or distinct. So in a way, what I’m going to say has to do a lot with irreversibility and less so with the arrow of time, which is something that I see as a separate problem. And so in regard to irreversibility and what, say, the second law says, the second law of thermodynamics says, I think I agree with the general view that the second law of thermodynamics is a law that, in the current formulations, at least, holds in… Just in approximate… In approximate sense, so in a way, we know that it holds for certain systems that we call macroscopic.
1:05:41.3 CM: What that exactly means, we don’t want to go into, really, because when asked for a specific characterization of what are the systems for which the second law holds, even philosophers have quite an issue there. So it’s very hard to say, to pin down exactly what the exact boundary of applicability, domain of applicability of the second laws as we know them, is, but let’s say we are fairly happy pragmatically that they work in certain cases and not in others.
1:06:15.5 CM: And then we take the dynamical laws as the fundamental things, they are reversible, and then there are some ways in which we can make an argument that typically involves quite ingenious ideas that were pioneered by Boltzmann and others to connect the general… The general sort of statement that the second laws make with the particular dynamical laws, which are not irreversible. Now, this is a general view. And what we think can happen with this new approach in terms of counterfactuals is that there could be a way of reformulating the second law in a way that doesn’t rely on these approximation schemes, so in a sense, it’s no longer scale-dependent, and it would be about certain transformations being possible in one direction and not in the reverse direction.
1:07:31.6 CM: And by this, I mean not that a given dynamical trajectory is allowed in one direction, not in the other, otherwise this would just say that we are thinking that dynamic laws are irreversible, which isn’t what we expect. But I’m saying a transformation is possible in one direction and not in the other, which means the constructor, if you like, is allowed in one direction, not in the other, and this is a much more plausible statement in a sense, and if you think about it, it could actually hold at all scales, because it’s not a surprise that if you want to perform a certain transformation to arbitrarily high accuracy in one direction, you can use a given constructor that has certain features and operates according to some means.
1:08:17.4 CM: But then if you try to use the same machine to perform the opposite transformation, it may actually stop working altogether in the sense that there’s no guarantee that a machine that performs a task in one direction should actually be able to perform the transposed task, the reverse task. So in this sense, we expect that by taking these statements about possible and impossible as fundamental, you can somehow see a possible resolution between this conflict between the laws that are microscopic and reversible and these general statements that hold in thermodynamics and other domains, which prescribe the kind of irreversibility, because you can think of this irreversibility as regarding constructors and their usability in one direction or another, rather than trajectories, dynamical trajectories of isolated systems not being reversible, which are obviously in conflict with the understanding of the microscopic physics that we currently have at the moment, because all of the dynamical laws we know that are fundamental are expected to be time reversal symmetric.
1:09:34.9 CM: So in this sense we are somehow proposing a third way out from this notorious clash, so we would like not to use statistical mechanics methods because this leads to an emergent set of laws, which is somehow only approximate and not really fundamental, I would say, but we’re still leaving the possibility open for the fact that the second law and like similar laws could be fundamental and exact, just that they have to be formulated in terms of these other statements. And there you can see that there is a compatibility between those statements and the fact that the dynamical trajectories of elementary constituents of the objects that obey these general laws are time reversal symmetric.
1:10:31.4 SC: Okay. Yeah, this sounds worth trying to do, but still a little aspirational, we don’t have the full story yet played out, but I do want to give you an opportunity, because I think that there are examples where you have used this kind of way of thinking about things to sort of be specific and make some claims about physics that you might not otherwise have reached, for example, in the case of hybrid quantum classical systems and maybe even quantum gravity and experimental tests. Is this too dramatic? Or is that a fair way of putting it?
1:11:10.8 CM: No. I think that’s correct and it’s quite exciting, I think it’s another thing that currently I’m focused on. So this is… Well, it ties in well with what we said earlier at the start of the conversation about why would you want to have more general principles. After all, you go in the lab, you just want a dynamical order conjecture to describe something and then maybe a rival law, and then you’d kind of test them against each other, and that’s how we do physics.
1:11:51.2 CM: Now, the specific situation you’re referring to is this situation where this logic doesn’t seem to work as straightforwardly as it usually does, and this is the case of systems that one way or another have dynamical laws that are either intractable or worse, they are not even completely settled. In the case of gravity and interaction with a probe that is quantum mechanical, fits the second scenario. So in the sense that we’ve got many suggested proposals to describe what’s going on, I think this goes back to kind of Feynman and kind of other scientists who already at the time, were wondering about how do we describe this kind of system.
1:12:42.8 CM: But we don’t really have a watertight way of just making predictions in these domains that are then testable and at least can help us rule out a class of models for gravity. So it would be nice, at least from my point of view as well, because I’m one of those people who expects gravity to be more defined in a way, that will become quantum rather than quantum theory becoming classical. It would be nice to be able to rule out a class of classical models for gravity, and we haven’t been able to do this yet in terms of just an experiment. So in this domain, even though we don’t have specific dynamical models that can unambiguously work for making predictions, we can use principles.
1:13:32.0 CM: So in the same way that we could in the past use thermodynamic principles to, for example, conjecture the existence of new particles that were not known yet and so on, here too, we can appeal to these general principles that are about counterfactuals and specifically about information, which is one of the works I’ve been developing also with David and others, to set up a kind of witness for testing whether a given system is classical or not. Now, this is a very binary choice, so we’re not really trying to say what is the dynamical law that gravity obeys. That’s not the kind of the question we’re asking. We’re asking a much, much kind of more modest question, which is, can we just say if gravity has some non-classical elements. So something that makes it completely impossible for a classical theory, one that doesn’t have a multiverse, in a sense, a quantum multiverse, to describe this object, to describe gravity. Not just gravity, it could be any object, but gravity is the most exciting application, I would say.
1:14:57.3 CM: And with these general principles, you can set up a theorem, kind of a theoretical argument that says that if you can use gravity to generate entanglement between two quantum masses, in some kind of laboratory setting, and you can rule out other forces, other means of interaction between these two masses, then gravity has to be non-classical. And note that while this is in a way obvious and trivial within quantum theory, because if you have three systems, then you can use one of them to entangle the other two, then in a way, it’s kind of an obvious consequence of the quantum theory of information to say that this system that you use to entangle the other two should be quantum.
1:15:45.5 CM: In the case where you cannot assume that this mediator is… Obeys a given dynamical law, this statement is non-trivial at all. And it’s very interesting that you can still make this very strong statement by just assuming that this system that mediates the entanglement obeys these general principles. And this is something that I developed with Vlatko Vedral. We were both really excited that you could make this general claim, because also it reminded us a bit of the generality that you have in these theorems like Bell’s theorem in quantum information, where you can use this theorem to just rule out if certain correlations are observed on given systems, a whole class of dynamical models for a quantum system… Sorry, for the system in question, so you can rule out the local hidden variable models.
1:16:41.2 CM: And likewise, in this case, if you can set up an experiment where you’re really sure, and this hard, but in principle, where you can argue that the only mediator is gravity between these two masses and they become entangled through it, no matter what dynamical law specifically you want to use in order to describe this mediator, then you can rule out a whole class of classical theories for it, which obey these general principles. One being locality, in the sense of the locality of quantum field theory, if you like, and the other one being the interoperability of information, which is this constructor theoretic information principle, that somewhat captures some intuitive properties of information-like systems that we expect to be true of bits and similar systems.
1:17:36.2 CM: So that’s quite exciting, and I think it’s one of the… It’s kind of maybe the first example of a theorem that goes beyond quantum information in a genuine way. So it’s sort of fulfilling this expectation I was mentioning earlier that it would be nice to have this general set of theorems that are actually more general than quantum information theory, in the sense that they don’t assume quantum theory specifically, or any other dynamical theory, just these general principles.
1:18:00.8 SC: Good, so let me… I think I understood everything you just said, but just to check, let me try to say it back and you can tell me whether I got it. There’s a long-standing worry about quantizing gravity, we haven’t been able to do it, right? People don’t understand the full theory of quantum gravity. And so some people have said, well, maybe it’s because gravity still is classical while everything else is quantum. And one of the problems with testing that proposal experimentally is that nobody knows what it means. Like no one has a theory really where gravity is classical and everything else is quantum. So what you’re saying is that even in the absence of a specific theory of classical gravity quantum everything else, you can still test the idea based on these general principles, and again, in principle, even if in practice it’s very hard, you’ve actually proposed a scenario in which it could be done.
1:18:55.3 CM: Yes, exactly, and I think that’s the… You emphasize the right things. That it’s precisely because there is such skepticism about the fact that the laws that can describe gravity must be quantum or classical, that it’s important that we don’t make any commitment to a specific dynamical model to make a prediction. Or at least, make this general statement. Then, of course, to make a specific prediction about the particular masses that you need in such an experiment, and so on, you can use a number of models. But you would like your conclusions that you, by observing entanglement, you are witnessing some non-classical effects in gravity to be as independent of these specific assumptions as possible.
1:19:39.9 CM: And I think we got quite far in terms of how general these principles are, because locality is a pretty general principle, swayed by both with quantum theory and by general relativity and other theories that we might expect plausibly to describe nature, and then the interoperability of information is really obeyed by any theory that allows us for observables and we surely want a theory to be testable to allow for observables, so in a sense, that’s also a general kind of principle that we hold quite dear.
1:20:12.8 SC: And you were honest about this, but just in case people didn’t catch it, the particular experiment that you’re proposing, you’re not necessarily saying is feasible in the short term, but it’s a in principle thing that maybe some clever experimentalist can figure out a better way to do something analogous to it.
1:20:31.3 CM: Yes, I think so. This is about the particularization of this experiment. There have been a number of proposals in addition to ours, there’s this proposal that was put forward by [1:20:45.0] ____ and his team in London. And now, a number of others are being investigated. So in that sense, it’s a non-trivial enterprise. And in a way, it’s exciting for that reason, so the experimentalists are kind of now taking it seriously and really trying to think hard of ways in which this could be brought into being feasible. But the encouraging thing is, which was also something that excited people in the quantum gravity community, is that the masses that you need for this… To display disentanglement are smaller than Planck’s mass, which is the usual scale at which which we expect quantum effects on gravity to become relevant and so, in a way that was a surprise.
1:21:40.0 CM: So it’s 10 to minus 12 kilograms, which is a bit smaller than Planck’s mass. Not that small, but still quite close to the current threshold of what’s the size of objects that we can put in quantum superpositions. So in a sense, it’s tantalizing, and I think this might require a long-term effort, but it’s somewhat within reach, and that’s very exciting to me.
1:22:06.3 SC: Yes, no, absolutely. I’m like a big believer in trying to figure out what is possible when it comes to quantum gravity in principle first experimentally, but any kind of experiments that we can even contemplate are worth taking seriously and trying to improve. And then I want to ask about one other domain of application to these ideas, which is more macroscopic, this thermodynamics and information and work extraction story. This is one I’m very interested in, the idea that there are fluctuations on the microscopic scale and somehow, I don’t think we’ve talked about it in detail on the podcast, and maybe this is not the place to get into it, but there’s a set of claims going back to Maxwell’s demon that you can sort of interchange information for work or extracting energy from a system or for doing something useful. And I apologize for not having a better understanding of what you’ve said about this, but I have the vague impression that constructor theory is relevant here somehow.
1:23:11.3 CM: Yes, so this is related to this generalization of the second law that I mentioned earlier. So the general statement that’s usually made when talking about the connection between information theory and thermodynamics is, as you said, through the idea of Maxwell’s demon, or more recently, Szilard engine and the work by Bennett and Landauer. So the idea would be that when you want to delete or erase information, there has to be some fundamental thermodynamic cost to that task, which is a logically irreversible task, because you want to send all possible states into one blank state, and this particular step is actually fundamental in creating a thermodynamic cycle within things like the Maxwell’s demon set-up or the Szilard engine set-up.
1:24:16.8 CM: And so somehow it was conjectured by Landauer and then more accurately proven by Bennett that there is indeed a irreducible thermodynamic cost to the task of erasing a bit. Now, this goes through, it’s a connection that somehow implies the number of assumptions, and these assumptions could be spelt out in various ways. And now there is a sense in which, on the one hand, if you describe everything in a completely reversible way, so if you have a fully detailed dynamical model of the Szilard engine or of Maxwell’s demon, then the statement… Of course, if the dynamic laws are time reversal symmetric, which usually are as far as quantum theory is concerned, and you’re not adding any other irreversibility in, then the statement almost follows from the simple fact that the laws are time reversal symmetric.
1:25:20.5 CM: So in that sense, when you’re not putting heat anywhere by hand in this, when you make an account of what’s going on in these kind of cycles, then perhaps you don’t need to appeal to Landauer’s principle to claim that this connection between erasure and universability is like an additional principle on top of whatever else we have. And at the same time, if you then assume that you are in a microscopic domain where there is some fuzziness about your knowledge of the dynamical laws, and you have some heat source at any point during this cycle in the Szilard engine, then you just apply the second law and it seems like you can obtain the same conclusion as Landauer’s principle. So in a way, although this idea of connecting information theory and thermodynamic been discussed a lot, there’s still a lot of controversy there about how fundamental it is and whether it’s even useful, because if we know all the dynamics, we don’t need it, and if we know the second law, and we think it applies, we also don’t need it.
1:26:23.3 CM: Now, in the case of this work that I’ve been doing, you can connect information theory and thermodynamics in a different way, and it remains to be understood whether this other way that Landauer and Bennett were proposing could somehow be derived or understood in terms of this other way that I’m suggesting, so it’s kind of an interesting open question. So the way that I’m suggesting there is a connection is that if you define a task, which is to extract thermodynamic work out of a given system prepared in a number of possible states, so you got like, I don’t know, a fly wheel and it’s got different possible dynamical states, and these are your possible states out of which you want to extract work, or alternatively, you’ve got an atom with different energy levels and you want to extract work out of those, or more generally, a different system that we don’t have to specify necessarily.
1:27:29.2 CM: Then you can prove by using these general principles of constructor theory an interesting statement, which is that these states out of which you can extract work must be perfectly distinguishable. So distinguishable in the sense of single-shot distinguishability or quantum theory, so they must be… For those who like quantum jargon, they must be orthogonal or orthogonal subspaces or things like that. And this has to do with the fact that when you talk about work extraction in the way that I’m envisaging here, you’re thinking of the work exaction to happen reliably, so there’s a key element in the proof, which is that you’re thinking that the task of extracting work out of these possible set of states of a given system is actually possible, which means that there is a constructor which can be presented repeatedly with the substrate and do this task reliably.
1:28:26.6 CM: And so there is an interesting connection between a set of states that you can use to perform what informally is called useful work in thermodynamics and a set of states that you can distinguish perfectly. So any set of states that you can extract work from in this deterministic reliable way must also be a set of distinguishable states. So that’s another connection, and it’s interesting that it doesn’t… To prove this results, you don’t have to appeal to any entropy-like consideration or any scale-related consideration, so your… It seems like the statement is free of the problems, let’s say, that the other connection between information and thermodynamics has. And perhaps, as I said, it would be interesting to investigate whether the second law connection could be somehow rooted into this other connection. And this is an open problem, which I’m kind of thinking about right now, so it’s kind of exciting.
1:29:25.4 SC: Well, we like open problems, we like being able to inspire the young kids in the audience to take all of their physics, and not just physics, but all of their academic projects, inspired by the Mindscape podcast. And the other thing, the other reason why I like this whole connection, one of the reasons why I like this whole connection between thermodynamics and information theory and work extraction is that there are at least claims or hopes that something like this happens in living cells, right, in living beings. Like there’s many attempts, including recent podcasts I’ve done, to link physics principles to how life works, and this might be an example. Is that too crazy or are you on that train also?
1:30:13.6 CM: No, this is not crazy at all, at least from my point of view. Well, this was, I think, the original motivation of von Neumann, so the view of envisaging a theory of universal constructors or more special purpose constructors was indeed to define a set of principles that in the same way as thermodynamic principles can set limitations to thermal engines could also set limitations to biological systems, so and explain to us what both natural selection and artificial section can do when exploring the possibilities of organisms that are fit for a specific environment. And so we don’t have a theory of that kind yet, and it’s a shame, I think, because there is a lot of physics… Physics assumptions and physics considerations to be made within the theoretical biology studies that we’ve been, as a scientific community in general, advancing so far.
1:31:40.5 CM: And in a way, this is, I would say it’s the next step to merge together the theory of information as we know it, quantum and classical, with the theory of thermodynamics, would be like the next step in this program of building an overarching general theory for biological entities, which you can regard in the most general way as programmable machines that happen to have been produced by natural selection. But of course, the forms of things that we see in a given biosphere right now are by no means exhaustive of what can be done. And so the question is, it would be very, very, very important for technological developments to have a set of principles that can tell us exactly what are the limitations for machines that we might be able to synthesize artificially, and so this kind of goes in the direction of artificial life and all of these other things that are very interesting, and although they’re not my direct concern, I’m hoping that some of these principles that we are conjecturing now could be used for kind of a scope of this kind, which was ultimately what von Neumann envisaged, so I’m hoping that he’d be happy if he could see this.
1:33:01.8 SC: Well, I’m glad you’re not being too ambitious, just trying to understand quantum gravity and the origin of life. You know, that’s something to keep ourselves busy during our off hours. [laughter] No, this is great. I think it’s wonderful to… When we’re faced with these big problems, sometimes you solve them just by being… Just by persevering, just by putting your nose down and moving forward step by step. But sometimes you solve them by trying to take a big leap sideways, and looking at things from a very different angle, and maybe some new insights come out of that and you have to try it, so you don’t know it until you give it a shot.
1:33:40.9 CM: Yes, and on this note, I think although some of these problems we mentioned, they do sound as being very different from each other and perhaps going in different directions, there is a sense in which the way I see them, they all stem from the same perhaps misconception or deficiency of the current way in which we look at things. So in a way, it’s one example if this thing that we are doing succeeds, of finding how there is a common root to a number of problems that appear different. And once you shift, as you said, the perspective, the logic of the solution is always the same, it just happens to be applied in different sub-fields. And it’s not the first time that this has happened, I think… Again, the quantum theory of computation is always my reference because it’s kind of the thing I know best, it’s true that methods of proof within the quantum theory of computation often refer to this universality of qubits.
1:34:47.9 CM: So you have very different systems, maybe one is a many body system in condensed quantum physics, that’s a different system which involves photons and so on, but once you reduce all of these different systems into a system of qubits, you can then solve the problem there, and then imply this has very far-reaching implications for all these different fields. And you may not even know about the details of those fields, but you can still make statements that are useful and quite far-reaching. And I think in this case, we are noticing a similar pattern here, and so counterfactuals are helping us in a way in identifying commonalities between open problems and hoping to solve them in a way of… Just by switching to this different mode of looking at things.
1:35:31.0 SC: Well, I think that’s an inspirational place to wind up the conversation, with the prospects of really making progress on some big problems. So Chiara Marletto, thanks so much for being on the Mindscape Podcast.
1:35:43.6 CM: Yeah, thank you so much for having me.
[music][/accordion-item][/accordion]
Hello to you. Im just wondering if any Research Scientists within the fields of Quantum mechanics and sub atomic particles within the atom and 3 possible new forces along with the other known 4 are exploring the possibilities of how the humble photon is constructed and the 3 additional forces could play out in the future. IVE been doing conceptual research on how all light was created for several years now. But as a senior citizen haven t had much luck getting connected on this theory as of late. So ill probably just keep to myself since no partys are interested. So hope your research is successful. Thanks
Just wanted to say this was a very interesting podcast.
Thank you Sean and Chiara. I will list to this again as I found it needing more in depth thought.
Best regards
Phil
Since Turing machines can (just as Von Nuemman machines) be written to access their own code and copy it to the output of do whatever else they want with it (by fixed point theorem) I presume you (Chiara) have something else in mind.
As a mathematician studying computability theory I’m quite interested in what other sense you have in mind but is nevertheless something you could understand as being a theory of computation. Do you have a paper you would recommend that explains this? Preferably one which does do in as mathematical (as opposed to assuming knowledge of physics) way as possible?
Constructor Theory (as I understand it) attempts to express physical laws exclusively in terms of which physical transformations, or task, are possible versus which are impossible, and why.
In many ways it reminds me of the debate between rationalism and empiricism. Rationalism is the philosophy that knowledge can be discovered by thinking. Empiricism is the philosophy that knowledge can only be discovered by observation and measurement.
In practice, both rationalism and empiricism play a complementary role. For example, a physicist may develop a model of the relationship between space and time using a thought experiment. With peer review and validation this may eventually be viewed by rationalist as a well-accepted theory. Many decades later, this theory may be confirmed with empirical evidence. It is unlikely such a theory could be developed without a thought experiment as it is a leap forward in thinking that is not obvious from the numbers. As such, many theories that are now accepted by empiricists were first introduced by rationalists. Generally speaking, rationalism is a far more powerful tool of discovery and empiricism plays a role in creating greater certainty that knowledge is indeed correct.
Ref: Rationalism vs Empiricism
John Spacey, January 26, 2020
A hint: If you study the necessary & choice mechanics, logic & geometry, of the minds eye, itself, all will become clear, much easier.
As Wittgenstein mentioned; If we can’t see it, it doesn’t exist.
One of the main goals of theoretical physics is to incorporate the force of gravity into the standard model of particle physics, and to use that modified standard model to, among other things, explain the so called ‘dark matter’ and ‘dark energy’ that make up approximately 95% of the matter and energy in the Universe. While constructor theory may not give the answer, it could, at some future date, provide valuable clues on how to go about achieving that goal.
Happy Birthday😊
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Um episódio muito interessante desenvolvido por Chiara Marletto, e, como habitualmente, super bem conduzido por Sean Carroll.
Consegui, sem dúvida, (começar a) compreender melhor a Teoria do Construtor.
Obrigada a ambos pelo tempo que dedicam a partilhar conhecimento, Ciência.
Hello. IVE got more than conceptual evidence about this so called new theory or an arrangement about several new forces IVE described. The theory is also based on a logical arrangement of the 4 known forces and the hypothetical 3 new ones which of course must be proved with scientific evidence. Also the structure of the sub particles that are in the parameters of all light would have to coincide with how the forces (now 7) are arranged in ways that give the needed spin in each photon direction. Either in the up.mode or the down mode. Of course this also must coincide with the quarks which these photons make them up in my theory. The problem lies not in my conceptual interpretation of what may or may not happen but the difficulty of calculating the point charge of a quark or a muon or any type of quark or photon. Now the photon is a 4 point vector x y z to the t time. But if this is true for all photons WOULDNT it be true for all quarks. But my problems begin with but don’t end with the quantum calculations of doing this type of connective potentiality if each force and particle I refer to. I think the strong force and the electromagnetic force along with the spin force and derective force are very important. But using just quantum math calculations does not work. Im still evolving of what can or can’t work on this entire theory. But when you work a line like me it can be difficult to really get there. Thanks. Eric