Fallible Animals Episode 6: Interview with Physicist Chiara Marletto
Constructor theory is a newly proposed theory in fundamental physics that proposes to underlie all other currently known theories, and hopefully those yet to be known, and to solve problems across a host of fields in science. I spoke with one of its leading researchers, Chiara Marletto, for an in-depth discussion about constructor theory.
Chipkin: Before I ask about your own involvement, just what is constructor theory?
Marletto: Constructor Theory was originally proposed as a programme by David Deutsch in 2012, when he wrote a paper where he laid out the philosophical foundations of the theory. The program was to try to recast the whole of physics in different terms. So, instead of using the ‘dynamical laws + initial conditions’ type of approach, David suggested to use an approach which is rooted in the quantum theory of computation, but extended to the rest of physics. The approach is to use statements about what tasks are forbidden/impossible, and what tasks are possible, and why. At the time, David outlined various applications, but since then, when we started working together, we realized that the theory actually had a much wider applicability than it had originally seemed. I came in by applying constructor theory to various open problems in quantum information, in quantum thermodynamics, in the foundations of quantum physics, and so on.
Since David proposed the constructor theory programme, a number of problems have been addressed, and as we were going along, a number of new problems emerged. So I think now, the programme has been revived and become even more ambitious. Researchers in world-leading groups are getting interested in our work, and largely thanks to developing the theory and applying it to various things, it turns out that there are practical experimental demonstrations that can be realized, and that’s one of the things we are working on at the moment. At least, that is part of a number of proposals that I am putting forward to continue this research. So I think it’s growing in momentum, and there is lots of excitement around these ideas. We’re also trying to bridge ideas from constructor theory with ideas from current efforts in quantum thermodynamics and quantum information. We are building these connections, and hopefully this is going to provide some more powerful tools even for those fields. So there is growing interchange between the tools of constructor theory and those of more mainstream fields, and that is also quite exciting.
Chipkin: Where are you currently located, and how did you get involved with constructor theory?
Marletto: I’m located in Oxford, England. When David published his 2012 paper, I was doing my PhD in Oxford, mainly working on quantum information applications. At some point, I came across David’s proposal, and it actually turned out to be something that I identified as a very promising tool to solve some problems that I’d been stuck with for a while. For instance, I was interested in von Neumann’s theory of the universal constructor, which was connected to issues in both theoretical biology and quantum information. Von Neumann wrote extensively about these more computational issues, about what it would mean to have a universal machine that exceeds the powers of a universal computer, and this would be what he called a universal constructor. It’s a generalization of the universal computer as Turing envisaged it: a universal constructor must be capable not only of performing all of the computationsthat are physically allowed, but also all of the tasks that are physically allowed; in particular, it would be capable of self-reproducing. So its repertoire would include not just computations, but general tasks, like cooling down a mass of water from a certain temperature to another with given resources, and so on. I was reading some writings from Von Neumann at the time, and as soon as I came across constructor theory, I noticed that it would allow me to connect these issues that I was interested in with foundations of quantum information and also with the foundations of thermodynamics, which were other issues that I have been interested in for a long time.
So I approached David, we started discussing, and in the end we decided to write a paper together. My PhD ended up being maybe one-third about standard quantum information, and the rest was on constructor theory. It turned out that there were more problems than I had anticipated in the theory, and so I suggested we put it on more solid ground first, and try to apply this to some open problems. Solving problems — this is how one can show the community that constructor theory is works. To this end, I opened up some new, independent lines of research, and they grew following this trail of constructor theory, and that’s what I’m doing at the moment; in addition to collaborating with David on the constructor theory of time.
Chipkin: What are the motivations underlying constructor theory’s development?
Marletto: If you look at physics, you will see a very successful enterprise, with universal theories being conjectured such as, first, Newton’s laws of gravitation, which was the first kind of universal theory that was ever proposed. By ‘universal,’ I mean that it applies to everything there is in the universe. Einstein and the founders of quantum physics proposed improvements to Newton’s theory that explained phenomena that Newton’s theory didn’t explain. This happened at the start of the 20thcentury. There is one thing that all of these theories have in common, which is that they try to explain the whole of what is going on in terms of dynamical laws, which describe trajectories. These laws predict where an object goes in space and time, given what the initial conditions of the object are. This mode of description applies to the whole universe.
However, there are also other kinds of principles and laws that have been conjectured which seem very powerful. These don’t have the character of a dynamical law of motion — consider the law of conservation of energy, or the principles of thermodynamics, and, more recently, the laws of quantum information. These are formulated in terms of statements about which transformations are possible and which are not, given certain resources. For example, the law of conservation of energy says that energy can’t be modified for an isolated object — you can only increase or decrease it if you couple it to a source or sink of energy, because overall energy must be conserved. This is a statement that doesn’t mention dynamical laws, although you can prove it given a dynamical law, and we know that all viable dynamical laws satisfy this principle, and hopefully future laws will, too. With thermodynamics, you have the second law, for instance, which is very powerful and successful for macroscopic objects such as heat engines. But if you try to extend this law to microscopic systems, such as in trying to define a heat cycle for a single molecule, then you run into all sorts of problems, because the laws of thermodynamics are not suited for these microscopic objects. It’s unclear what they say about microscopic systems. Even the statistical mechanics, started by Boltzmann, holds only in certain limits. Thus no matter which form you choose, there are all sorts of approximations you have to make in order for the second law to apply, and if those approximations are not satisfied by the physical system of interest, you cannot make predictions. This is a deep problem. Constructor theory has the potential to solve this, by putting some of these laws that only seem to apply to macroscopic entities — and these are very successful in their domain — on firmer ground, stating them in such a way that they are scale-independent. This is because its mode of explanation does not take microscopic dynamical laws as the primitive entitites, but statements about possible/impossible tasks.
Another goal of Constructor Theory is to formulate new laws in terms of entities that have so far been useful in understanding the physical world, but that don’t have a unified theory about them. Information is one such entity. At some point we realized that information is not independent from physics, such that which entities are able to carry information is decided by the laws of physics. So if you have an object and you want to decide whether or not it can carry some bit of information, that depends on what interactions it can have with its surroundings — for instance, whether or not it can be put into two states that are distinguishable. Whether or not a system has these properties — such as distinguishability, whether it’s possible to permute the states of the object, etc. — is decided by the laws of physics. So there is an intimate connection between the fact that information can be instantiated in the physical world, and the physical laws. However, the theory of information that currently we are using to, for example, design the quantum computer, is not as general as it should be, because it is based on various details of quantum theory. Quantum theory is a dynamical law, and it is only specifically applicable to quantum systems. However, one would like a quantum theory of information that is more generally applicable, in such a way that concepts like entanglement, copying operations, cloning, etc., can be defined and explained irrespective of the particular model that you have for your system.
Why is that? This is useful because quantum theory is expected not the ultimate theory, because we know that it clashes with general relativity, so there will be a better theory behind quantum theory. However, it’s also possible and likely that this new theory will still allow phenomena like entanglement of particles, quantum computation, and so on. If we don’t have information-theoretic notions for those that can be applied to systems that may not be quantum, how will we ever be able to have a theory of information for such systems? The second aim of constructor theory is to put on solid grounds a theory of information which can define all of these concepts, and the laws that information follow, irrespective of the dynamics of the physical systems in consideration, but only based on general principles such as locality, others to do with the interoperability of information, and so on.
Finally, and this is a very long-term kind of ambition, can we show how dynamical laws and initial conditions follow from these constructor theoretic principles? Suppose that constructor theory works, and we have this set of principles that augment the theory of thermodynamics, the theory of information that we currently have, and so on, is it possible to change the way we formulate laws of physics in such a way that the dynamical laws followfrom these principles? We don’t know the answer, but one of the aims of constructor theory is to show how dynamics and time can emerge out of these timeless principles and constraints. This would address an open problem at the heart of fundamental physics, which is to explain the initial conditions of the universe. Let’s say I want to explain what I see now in the universe by giving an initial condition and some laws of motion for the whole universe, following current cosmological approaches. This would not be enough! One must explain why we see these initial conditions and not others. It’s not good to say, ‘I have to choose this set of initial conditions because this is the only set that predicts what I see now,’ because that’s a circular explanation. By the same logic, you may as well ‘explain’ the initial conditions of the universe in terms of its current conditions. Even inflation, one of the most prominent theories of cosmology, cannot address this problem. It’s possible that constructor theory provides a way out of this problem, because it does not take dynamical laws and initial conditions as the primitive elements. The first step towards this goal is to provide a theory of dynamics in constructor theory, which is one of the new lines of my proposed research.
Chipkin: What are the main theoretical objects in constructor theory?
Marletto: There are two main concepts in constructor theory — tasksand constructors. However, the fundamental entitites of constructor theory are tasks, and constructors are mentioned only to be abstracted away from the laws, as I’ll explain. A taskis a set of ordered pairs of input/output attributes of a physical substrate, and a substrateis anything that can be changed by appropriate action of the environment. Familiar examples of tasks are a bit flip in computation, cooling down a certain mass of fluid, lifting a weight in a gravitational field, creating entanglement out of no entanglement, and so on. A task is just specifying a putative transformation, and this transformation is either be possibleor impossible. By impossible, we mean that the laws of physics impose a fundamental limitation on how accurately this task can be realized with systems in physical reality. For example, changing the energy of an object from one value to another value is an impossible task because of the conservation of energy. So, if you tried to do that without ever using anything from the environment, this is clearly impossible because there isn’t any energy source or sink there. However, you can achieve the net effect of changing the energy of the system by having some side effects on the environment, so the overall task of transferring the energy of, say, the weight of an object in a gravitational field to, say, a flywheel, is a possible task because it can be achieved with arbitrarily high accuracy with some appropriate setup.
So impossiblemeans we can’t achieve it with arbitrarily high accuracy and no other side effects in the universe. Possiblemeans that we can do that. So the fact that you can achieve a transformation on a system with arbitrarily high accuracy without side effects on the universe means that somewhere in the environment there is an entity, a constructor, which acts like a cycle. The constructor for a task gets the input — the substrate in the input state — , acts on it, produces in output the desired output state as specified by the task, and it remains unchanged. So, it operates in a cycle, like a catalist. However, to say that a task is possible, you don’t have to enumerate all of the possible constructors that could perform the task. The idea is to avoid talking about the constructor’s its explicit designs, but just take the laws as requiring that a certain task is either possible or impossible, and working out the consequences of that, without ever having to specify the particular design of the constructor when we’re talking about a possible task. This is important because, for most tasks that are performed in the universe, the constructor is highly complex. Just think of a computer, which is as close as it gets to an accurate performer of, say, a NOT gate: it’s very complex. The more accurate it is, the more complex it is. The fact that we can abstract constructors from the laws of physics and just talk about the possibility of tasks and working out the consequences is one of the powerful switches in constructor theory.
Tasks, both possible and impossible, have an algebra, and at the moment, there is a mathematician (Dr Paul Raymond-Robichaud) who is working on formalizing constructor theory properly, in a way that is even more mathematically grounded. The algebra of tasks is the recipe to combine tasks in parallel and in series. If two tasks are possible and you take the parallel composition, what happens? There is a law in constructor theory that says that the composition of two possible tasks must be a possible task. The algebra of tasks has to mirror such constraints. Most of the theorems we’ve proven so far have been based on set theory and these basic definitions of tasks as ordered sets of attributes, but we’re hoping that the collaboration with mathematicians will yield an even more sophisticated way of talking about tasks, perhaps using category theory or some other kind of algebraic structure. This should make the theorems even more powerful.
Chipkin: What have been some early successes of the theory?
Marletto: One early success was the combined action of the paper that David and I wrote on the constructor theory of information, and my paper on the constructor theory of probability. The information theoretic structure that emerges out of quantum theory is very rich, and it is something that is independent of certain details of quantum theory. For instance, when we talk of the quantum phenomenon of entangled particles, the fact that two things are entangled is a purely information theoretic concept, and that means that it’s independent of a vast majority of details of the two entangled systems. For instance, you can entangle a photon with another photon, or you can entangle a photon with another atom, and they will be entangled irrespective of the fact that one is a photon and the other is an atom. Likewise for other physical systems. This suggests that it’s possible to free the quantum theory of information of the reference to specific quantum dynamics, and this is something that hasn’t been done yet in the literature, because most of the theorems in quantum information theory are using the dynamical laws of quantum theory. For example, if you talk about the channel capacity in quantum theory, you do need the quantum dynamical laws to show what the channel capacity is. So, the work with David planted some seeds in defining a unified theory of classical information and quantum information. This does not use any specific reference to the dynamics of the system(s) involved.
This is cool because we expect that the future theories that will come after quantum theory — and there must be such theories because quantum theory does not mesh with general relativity, so both probably are going to be improved into a better theory — may still conform to the unified constructor theory of information that underlies both classical and quantum systems, and potentially other systems that don’t obey quantum theory but have the same information theoretic properties. Then we may answer questions such as, is there a different type of dynamical law that supports the same quantum information processing power as quantum theory, but is not itself quantum theory?
That is important because it seems to point into the direction of where to look for the successor to quantum theory. That’s one important application of this theory that we are developing. In the paper with David, we came up with a number of results that show under what conditions you can get all of the qualitative properties of quantum information out of principles that are not based on the particular details of the system’s dynamics, so they are very general information theoretic principles. In particular, the interoperability law of information formalizes the informal idea that information can be copied from any system that can embody information to any other such system, irrespective of the details. Constructor theory expresses this law very elegantly. These are qualitative properties, so we can talk about, say, entanglement, in a rudimentary way, we can say whether systems are entangled or not, but we can’t say to what degree they are entangled, which is very important for making predictions.
The constructor theory of probability defines a set of conditions for dynamical theories that guarantees the fact that they display the same probabilistic structure as quantum theory. This doesn’t mean that I worked out any particular such theory — I just defined the space of such theories by giving some sufficient conditions. So you can imagine a space of possible theories in which there is the successor to quantum theory. This theory will have the same quantitative structure of quantum theory but will be a different theory.
These two papers combined give a framework for future deterministic theories which could in principle generalize quantum theory. And that’s nice because — and this is what I’m working on now — this is useful in many situations, which all have in common the problem that you’d like to make predictions about a physical system whose dynamical laws are not known in detail. This happens a lot in both theoretical and experimental physics because experiments are getting to the point where we can test the claim that in some regimes, quantum theory does not apply. This is because the objects that we can manipulate in the lab are approaching a mesoscale that is beyond the scale of neutrons and electrons but is closer to molecules and even viruses. Some eminent physicists like Ghirardi and Penrose claim that quantum theory should stop applying at a certain scale, and so the famous collapse of the wavefunction should occur. This is the case in which the laws of reversible quantum theory stop applying, the superposition principle stops applying, and you do see a classical world after all. We are getting close to the domain where we can test this claim, and there you have something like a quantum probe, like an elementary particle, interacting with a large object, which could be a large molecule, and you really don’t know whether or not the combined system will obey quantum theory. So if you want to make a prediction for an experiment, you can’t quite use quantum theory to describe the whole thing, because you want to see whether quantum theory applies or not.
However, what you can do is still apply general principles which don’t assume dynamics to be fixed, and these principles that we came up with are applicable in this case. This is the basis for a number of recent articles I’ve been writing with Oxford quantum physicist Vlatko Vedral, where we were looking at ways of saying, ‘Ok, we have a system A with a fully-fledged quantum dynamics and another system B whose dynamics we don’t know. But we know, let’s say, that the latter has some information variable. What can we say about the composite system, and can we infer anything about whether or not system B has some quantum features or not?’ This led us to propose an experiment to test whether or not gravity has quantum features. So this is the endpoint of one of the applications that came out of these two initial constructor theory papers. This test for quantum effects of gravity was also proposed along independent lines by a team in London, led by Sougato Bose. These experiments would tell us whether a classical theory of gravity is viable or not. If it’s not viable, that would be the first experimental confirmation of the fact that Einstein’s general relativity and all other classical theories of gravity do not work when coupled with a quantum system.
Another thing that I’m developing is to try to come up with a quantitative generalization of all these concepts that are prevalent in quantum information theory using this more general framework in which we don’t even use the dynamical laws of quantum theory. This is likely to provide structure for proposed possible candidates for a theory that will be the successor to quantum theory. These are big aspirations and I expect them to be realized in the long term.
Chipkin: Constructor theory brings emergent concepts into fundamental physics, such as life and computation. What would you say to critics who argue that fundamental science should explain ‘large’ objects in terms of ‘small’ objects, or ‘the whole’ in terms of ‘its parts’?
Marletto: The best way to counter this criticism is to show that constructor theory can address some problems that the reductionist approach, such as the one you refer to, cannot address. In fact, constructor theory was proposed precisely because we wanted to try a new way of addressing these problems that purely reductionist approaches seem to struggle with. One example is the initial conditions problem. Another is how to incorporate the laws of thermodynamics into the rest of physics, given that they are successful but are not exactly compatible with the underlying dynamics as they are formulated now.
Of course, reductionists could always say that these laws are only approximate, but not fundamental: they would ultimately not be interested in aspects of reality, such as the laws of thermodynamics, that are not possible to cast exactly in terms of dynamics and initial conditions. I think physics should on the other hand be very opportunistic and not have preconceived ideas about what it should and should not apply to. A more productive approach is more inclusive than the reductionist approach. It goes something like this: ‘Okay, we have this interesting problem, and it seems like the dynamical laws approach can’t quite address it. Can we find a better way of addressing it? If there is such a way, let’s go ahead with that irrespective of whether is satisfies the reductionist take on things.’
Of course constructor theory may not be the way to go. It may not work after all. If it doesn’t work, this will teach us a lot about physics, because it won’t work for a certain reason. That reason will be interesting, because most of the principles that constructor theory is based on underlie our current dynamical laws, and therefore, if constructor theory fails, there is a deep bug into the whole of physics.
One example where the reductionist, purely dynamical law approach can’t quite provide predictions is the domain where quantum theory and general relativity clash. These two theories have been confirmed experimentally so far in their respective domains. However, they don’t seem to agree on fundamental aspects of reality. For example, quantum theory says that there is an absolute time — it’s very Newtonian in this sense — whereas general relativity, and even special relativity, says that there isn’t such a thing. So in this sense, the two theories are profoundly incompatible. In addition, quantum theory says that observables are not all measurable with the same accuracy by the same machine, whereas general relativity is a classical theory that says that you can measure all observables by a single machine — in classical phyiscs, there is no Heisenberg uncertainty principle.
We don’t yet have experiments that can probe the domains where the two theories clash directly, because of current technological limitations. Nor do we have safe ways of modifying the theories by making small variations — for example, by adding a term to Einstein’s equations. Therefore, one way to proceed to make predictions in those domains is to use principles — those of thermodynamics, those of information theory, and these new principles that we are hoping to provide now via constructor theory. These principles would be applicable to systems that are at the interface between quantum theory and general relativity, without committing to a particular dynamical law. This is an important gap in the current approach, which constructor theory can already help with.
Finally, there are a number of phenomena such as life and consciousness which are bound to be compatible with a reductionist view of reality, but not fully explained in terms of dynamics and initial conditions. The fact that my brain is thinking now is perfectly compatible with the fact that my brain is made out of atoms and that my thoughts are a configuration of those atoms at a certain point in space and time. However, we don’t really know what consciousness is — this is what needs explanation. There are all sorts of proposals, but we don’t yet have a theory of how knowledge is created in the brain, how we can emulate that process — this is the enterprise of artificial intelligence — and so on. I feel that if theoretical physics keeps dismissing this problem because it’s anthropocentric, we will miss out on explaining an interesting phenomenon in nature. Brains in humans and in other forms of intelligent life in the universe are an interesting phenomenon which is happening because it produces a number of things that have characteristic properties like resiliency, capacity to modify the environment in ways that are unpredictable and robust, and so on. I think physics has to come up with a theory about all this — a theory that, for instance, answers these questions: what are the physical limitations of this process? Is it a process that has laws, such as how it should increase in time or not? Can we understand why some types of brains can come up with far more creative thoughts than others? The apes’ brains are also thinking in a certain sense, but are not producing the same level of technology and development that our civilization has reached. Clearly, these differences cannot be due to hardware, since all of our brains are quite similar, so what is the additional thing in our brains? Constructor theory certainly doesn’t have an answer to that yet, but it provides some tools to address the question in an objective, scientific way. I think that’s what physics should be doing. I think physicists should try to understand/explain the emergence of consciousness and of knowledge, instead of saying, ‘No, I’m not going to look into that because it’s an anthropocentric problem’ The point is that these phenomena are not about humans — the issue of creativity and knowledge happensto be relevant to explain some human activity, but it’s primarily a physicalphenomenon. A physicist should be interested in explaining it. Refusing to do so is like saying: ‘I’m not going to look into optics because it’s about a thing that happens in human eyes.’ That’s not a good argument from the point of view of a physicist.
However, if reductionists are taking the stance that they don’t want to look into these problems, that’s also fine, I understand that view. But in my opinion, they’re missing out. I’m for an objective, rational approach to problems, and if there is something I can’t explain or understand, I want to use any intellectual tool at my disposal to address the problem. And if the tool comes from reductionism, or not reductionism, or a different approach that I’ve never seen before but is shown to work, I’m going to go for it. I think that that’s what constructor theory is about — suggesting a new set of tools which may or may not work, but they seem to be working to some degree at this stage, and we want to give it a full-go.
Chipkin: Constructor theory has provided elegant, exact definitions of some concepts that were previously thought of as philosophical, such as knowledge. Do you think that there are other such definitions for concepts such as life, free will, or consciousness waiting to be discovered in a constructor theoretic framework?
Marletto: I think it’s not going to be constructor theory by itself, but perhaps constructor theory merged with other tools, certainly from epistemology, certainly from theoretical biology, and also from neuroscience. But the thing that seems to me to be important is that constructor theory might provide the foundation for a theory of knowledge rooted in physics. And the promising thing about the tools is that they provide an objective handle on these concepts. One thing that I feel repels physicists at this stage is that, when you discuss consciousness, you enter a territory where words are very fuzzy, so people don’t know exactly what they mean. The fact that there are so many words to define what people mean by consciousness or creativity or whatnot is a sign of the fact that we are very confused about this. A physicist doesn’t like this. A physicist is into laws that are exact, precise, mathematically formulated in a way that they make absolutely tight the concepts that they refer to. Of course, we don’t yet have that for consciousness, but if we could use some of these notions in constructor theory, let’s say the notion of knowledge, to create such a theory, this would be a great step forward, because we would be talking about something that at least is objective, and doesn’t necessarily refer to sanctioned beings, knowing subjects, things that seem, to be fair, not very scientific at times. So I think, at the moment, constructor theory does not solve any of these problems, but what it does is to provide the conceptual basis for a theory of these concepts to be created.
And this is relevant, going back to the issue that von Neumann was trying to address, for the universal constructor. David Deutsch has some writings about this, and I’ve been thinking about it as well in various ways. It seems that the laws of physics as they are currently known permit the existence of a universal computer. We don’t know of any impediment to the construction of a machine which can perform all of the computations that are physically allowed, and this is the famous ‘universal quantum computer’. There is this race between Google, IBM, Microsoft, who are all trying to crack the construction of this machine. Now, the fact that there can be universal computation is a very peculiar fact about the laws of physics. But now you can also think, instead of building a machine that can perform all permitted computations, of a machine that I can program to perform all permitted tasks. That’s the universal constructor. This is a programmable object, so you can still write a program in it, but basically instead of just doing computations, it can harness all of the materials and resources to also perform tasks that transform physical systems into other physical systems. So it will, for instance, include all of the repertoires of heat engines, of refrigerators, of nanotechnological devices that can deliver drugs in the body, and other types of machines that we are currently using. This machine, this universal constructor, should incorporate the repertoires of all of those into itself, and it should have this other property which is very important, which is what von Neumann was struggling with: it should be capable of recreating itself out of raw materials, so it should be able to self-reproduce. Therefore, it should contain a recipe that would allow itself to reconstruct the whole of the universal constructor, and then put this recipe inside that universal constructor, just like living systems do, to self-reproduce. We have a very rough understanding of how this object should operate. Von Neumann tried to lay some foundations, but he didn’t ultimately succeed because he tried to embed this into cellular automata, but he did not provide general principles.
I think constructor theory will provide a set of principles under which we could, for instance, show whether or not the universal constructor can exist. This would be very interesting because it would at least put the universal constructor on equal footing with the universal computer, and at the moment, we don’t even have that. That’s a very promising direction because the universal constructor is much more general than a universal computer. There is this phenomenon that is happening with intelligent life, with humans and possibly other creatures in the universe, and one fruitful question is: how is a human being different from the universal constructor? Is it more powerful? Well, yes, it should be, because it can come up with new ideas, and a universal constructor can’t, because it can only produce things which you program it to produce. I think that a theory of a universal constructor would be a very important underlying conceptual tool to tackle an understanding consciousness and so on. I think that this is all the more reason to try and deliver general principles that hold irrespective of the scale and dynamics of the system of interest. Then, these principles will be able to underlie even a theory of consciousness. Hopefully constructor theory can provide those principles.
Chipkin: What problem are you currently trying to solve with constructor theory?
Marletto: I wrote a paper where I generalize some of the ideas of existing thermodynamics, called the axiomatic approach to thermodynamics, where you state the second law as requiring that the task of changing the state of an object from A to B is possible, but the task of changing the state from B to A is impossible. In that way, the second law is more easily reconcilable with laws of thermodynamics that are time-reversibly symmetric.
To explain with an example, one can consider Joule and his work on thermodynamics. If you have a glass of water which is perfectly isolated from its environment, and you want to heat it up by stirring it, you can put a stirrer inside it and start stirring mechanically, thus heating the water up. So that’s a possible task. However, if you would like to cool the water by the same mechanical means, by stirring only, this is impossible. You can cool it by putting it in touch with a larger environment which is colder and stirring it, which would allow molecules of air to bounce off the surface of the liquid and thus cool down the liquid. But if you have a perfectly isolated object which is only interacting with the environment through the stirrer, you won’t be able to cool it down. This was already known at the time of Joule’s, but I generalized this statement of the axiomatic second law in constructor theory: as a result, it doesn’t mention stirrers, liquids, volumes of water, or temperature, but it amounts to generalizing the second law to being scale-independent and applying to systems that don’t necessarily have a temperature, etc.
Now I’m trying to work out the consequences of this, because in parallel in physics there is quantum thermodynamics. This is an enterprise where people have tried to generalize the laws of thermodynamics to quantum systems, so they put together the second law and quantum dynamics, and they try to see what happens. They did it very nicely, but I think they still assume a specific dynamics. So what they came up with is not as general as you would like a theory of thermodynamics to be, because you would like it to apply to a reasonably wide set of dynamics, not just those of quantum systems. In collaboration with Benjamin Yadin, I’m now trying to merge this approach from quantum thermodynamics with the approach from constructor theory.
I’m also planning some experimental demonstrations with some groups in Turin, Sheffield and in CQT Singapore to show what the difference is, if any, that constructor theory provides for the existing laws in terms of defining work and heat. This is quite exciting and hopefully will allow us to connect constructor theory to existing enterprises which should be fruitful for both constructor theory and these other existing efforts, making both more powerful.
Chipkin: It seems that not many scientists are yet working on the theory. Are you actively recruiting, or do you think more scientists will flock to the theory after further successes?
Marletto: There are certainly all sorts of open problems that we have have found as we tried to apply constructor theory to various things. These open problems — thermodynamics, post-quantum theories, quantum information, and possibly even theoretical biology — are waiting for people who are interested in working on them, so yes — we’re currently recruiting. At Oxford there are a couple of students who are already working on Constructor-theory related topics. I’m expecting that with these experimental demonstrations there will be even more interest. The enterprise seems to be growing momentum. Time will tell.
Chipkin: Professor Marletto, thank you for your time.
You can learn more about Marletto’s work on constructor theory and related topics at http://constructortheory.org.