Even our most successful and advanced theories of foundational physics – general relativity and quantum theory – have so far been unable to give a complete account of the universe. Meanwhile, philosophy continues to wrestle with questions of knowledge and consciousness. Might constructor theory provide an answer to both?

Constructor theory is a relatively nascent idea in fundamental physics that proposes to underlie all other currently known theories, not to mention those yet to be known, and to solve problems across a host of fields in science and beyond.

Logan Chipkin joins Oxford physicist and constructor theorist Chiara Marletto to discuss what constructor theory is, how it might point the way to a successor to quantum theory, and how it might allow physics to tackle some of philosophy’s most perplexing puzzles.

Chipkin: What is constructor theory?

Marletto: Constructor Theory was originally proposed by David Deutsch in 2012. The program was to try to recast the whole of physics in different terms. Instead of using the ‘dynamical laws + initial conditions’ approach, David suggested 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. 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.

Chipkin: How did you get involved with constructor theory?

Marletto: 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 computations that are physically allowed, but also all of the tasks that are physically allowed; in particular, it would be capable of self-reproducing. As soon as I came across constructor theory, I noticed that it would allow me to connect the 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.

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. They all 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.

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.

Quantum theory is expected not to be the ultimate theory, because we know that it clashes with general relativity, so there will be a better theory behind quantum theory.

The second law of thermodynamics is very powerful and successful for macroscopic objects such as heat engines. But if you try to extend this law to microscopic systems, then you run into all sorts of problems, because the laws of thermodynamics are not suited for these microscopic objects. Constructor theory has the potential to solve this, by putting some of these laws that only seem to apply to macroscopic entities 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 entities, 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. However, the theory of information that currently we are using to 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 expected not to be the ultimate theory, because we know that it clashes with general relativity, so there will be a better theory behind quantum theory. If we don’t have information-theoretic notions 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, the interoperability of information, and so on.

Finally, can we show how dynamical laws and initial conditions follow from these constructor theoretic principles? This would address an open problem at the heart of fundamental physics, which is to explain the initial conditions of the universe. 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.

Chipkin: What are the main theoretical objects in constructor theory?

Marletto: There are two main concepts in constructor theory — tasks and constructors. A task is a set of ordered pairs of input/output attributes of a physical substrate, and a substrate is 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 possible or 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.

So impossible means we can’t achieve it with arbitrarily high accuracy and no other side effects in the universe. Possible means 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 catalyst.

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 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.

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: 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.

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.’

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.

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 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. 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 physics, 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.

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 happen because they produce 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 should be very opportunistic and not have preconceived ideas about what it should and should not apply to.

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. that’s what physics should be doing. 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 happens to be relevant to explain some human activity, but it’s primarily a physical phenomenon. 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.

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 is that, when you discuss consciousness, you enter a territory where words are very fuzzy, so people don’t know exactly what they mean. 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. 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.

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. 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: it should be capable of recreating itself out of raw materials, so it should be able to self-reproduce. 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.