Constructor Theory: Basics, Theory, & Experiment

Note—this is a modified version of an article I published with Gizmodo.

You may think of physics as a way to explain the behaviors of things like black holes, colliding particles, falling apples, and quantum computers. But a small group of physicists today is working on a theory that doesn’t just study individual phenomena; it’s an entirely new way to describe the universe itself. This theory has solved wide-ranging problems such as why biological evolution is possible and how abstract things like ideas and information seem to possess properties that are independent of any physical system. It’s called constructor theory.

Origins

As a young physics researcher in the 2010s, Chiara Marletto had been interested in problems regarding biological processes. The laws of physics do not say anything about the possibility of life—yet even a slight tweak of any of the constants of physics would render life as we know it impossible. So why is evolution by natural selection possible in the first place? No matter how long you stared at the equations of physics, it would never dawn on you that they allow for biological evolution—and yet, apparently, they do.

Marletto was dissatisfied by this paradox. She wanted to explain why the emergence and evolution of life is possible when the laws of physics contain no hints that it should be. She came across a 2013 paper written by Oxford physicist and quantum computing pioneer David Deutsch, in which he laid the foundation for constructor theory, the fundamental principle of which is:

“All other laws of physics are expressible entirely in terms of statements about which physical transformations are possible and which are impossible, and why.”

Marletto said she suspected that “constructor theory had a useful set of tools to address this problem” of why evolution is possible despite the laws of physics not explicitly encoding the design of biological adaptations. Intrigued by the possibilities, Marletto soon shifted the focus of her PhD research to constructor theory.

Motivations

While many theories are concerned with what does happen, constructor theory is about what can possibly happen. In the current paradigm of physics, one seeks to predict the trajectory of, say, a wandering comet, given its initial state and general relativity’s equations of motion. Constructor theory, meanwhile, is more general and seeks to explain which trajectories of said comet are possible in principle. For instance, no trajectory in which the comet’s velocity exceeds the speed of light is possible, but trajectories in which its velocity remains below this limit are possible, provided that they are also consistent with the laws of relativity.

The prevailing theories of physics today can explain things as titanically violent as the collision of two black holes, but they struggle to explain how and why a tree exists. Because constructor theory is concerned with what can possibly happen, it can explain regularities—any patterns that warrant explanation—in domains that are inherently unpredictable, such as evolution.

Constructor theory can also capture properties of information, which do not depend on the physical system in which they exist: The same song lyrics can be sent over radio waves, conjured in one’s mind, or written on a piece of paper, for example. The constructor theory of information also proposes new principles that explain which transformations of information are possible and impossible, and why.

The laws of thermodynamics, too, have been expressed exactly in constructor theory; previously, they’d only been stated as approximations that would only apply at certain scales. For example, in attempting to capture the Second Law of Thermodynamics—that the entropy of isolated systems can never decrease over time—some models show that a physical system will reach eventual equilibrium (maximum entropy) because that is the “most probable” configuration of the system. But the scale at which these configurations are measured has traditionally been arbitrary. Would such models work for systems at the nanoscale, or for systems that are composed of merely one particle? By recasting the laws of thermodynamics in terms of possible and impossible transformations, rather than in terms of the time evolution of a physical system, constructor theory has expressed these laws in exact, scale-independent statements: It describes the Second Law of Thermodynamics as allowing some transformation from X to Y to be possible, but not its inverse—work can be entirely converted into heat, but heat can never be entirely converted into work without side effects.

Physics has come a long way since the days of the Scientific Revolution. In 1687, Isaac Newton proposed his universal physical theory in his magnum opus, “Principia Mathematica.” Newton’s theory, called classical mechanics, was founded on his famous three laws of motion. Newton’s theory implies that if one knows both the force acting on a system for some time interval as well as the system’s initial velocity and position, then one could use classical mechanics’ equations of motion to predict the system’s velocity and position at any subsequent moment in that time interval. In the first few decades of the 20th century, classical mechanics was shown to be wrong from two directions. Quantum mechanics overturned Newton in explaining the physics of the microscopic world. Einstein’s general relativity superseded classical mechanics and deepened our understanding of gravity and the nature of mass, space, and time. Although the details differ between the three theories—classical mechanics, quantum mechanics, and general relativity—they are all nevertheless expressible in terms of initial conditions and dynamical laws of motion that allow one to predict the state of a system’s trajectory across time. This general framework is known as the prevailing conception.

But there are many domains in which our best theories are simply not expressible in terms of the prevailing conception of initial conditions plus laws of motion. For instance, quantum computation’s laws are not fundamentally about what happens in a quantum system following some initial state but rather about what transformations of information are possible and impossible. The problem of whether or not a so-called universal quantum computer—a quantum computer that is capable of simulating any physical system to arbitrary accuracy—can possibly be built is utterly foreign to the ‘initial conditions plus laws of motion’ framework. Even in cosmology, the well-known problem of explaining the initial conditions of the universe is difficult in the prevailing conception: We can work backward to understand what happened in the moments after the Big Bang, but we have no explanation for why the universe was in its particular initial state rather than any other. Constructor theory, though, may be able to show that the initial conditions of our universe—at the moment of the Big Bang—can be deduced from the theory’s principles. If you only think of physics in terms of the prevailing conception, problems in quantum computation, biology, and the creation of the universe can seem impossible to solve.

The Basics

The basic ingredients of constructor theory are the constructor, the input substrate, and the output substrate. The constructor is any object that is capable of causing a particular physical transformation and retains its ability to do so again. The input substrate is the physical system that is presented to the constructor, and the output substrate is the physical system that results from the constructor’s transformation of the input.

For a simple example of how constructor theory might describe a system, consider a smoothie blender. This device takes in ingredients such as milk, fruits, and sugar and outputs a drink in completed, homogenized form. The blender is a constructor, as it is capable of repeating this transformation again and again. The input substrate is the set of ingredients, and the output substrate is the smoothie.

A more cosmic example is our Sun. The Sun acts as a nuclear fusion reactor that takes hydrogen as its input substrate and converts it into helium and light as its output substrate. The Sun itself is the constructor, as it retains its ability to cause another such conversion.

In the prevailing conception, one might take the Sun’s initial state and run it through the appropriate algorithm, which would yield a prediction of the Sun’s ending once it has run out of fuel. In constructor theory, one instead expresses that the transformation of hydrogen into helium and light is possible. Once it’s known that the transformation from hydrogen to helium and light is possible, it follows that a constructor that can cause such a transformation is also possible.

Constructor theory’s fundamental principle implies that all laws of physics—those of general relativity, thermodynamics, quantum mechanics, and even information—can be expressed as which physical transformations are possible in principle and which are not.

This setup is, perhaps counterintuitively, extremely general. It includes a chemical reaction in the presence of a catalyst: the chemical catalyst is the constructor, while the reactants are the input substrate and the products are the output substrate. The operation of a computer is also a kind of construction: the computer (and its program) is a constructor, and the informational input and output correspond to constructor theory’s input substrate and output substrate. A heat engine is yet another kind of constructor, and so are all forms of self-reproducing life. Think of a bacterium with some genetic code. The cell along with its code are a kind of constructor whose output is an offspring cell with a copy of the parent cell’s genetic code.

Because explaining which transformations are possible and which are impossible never relies on the particular form that a constructor takes, it can be abstracted away, leaving statements about transformations as the main focus of constructor theory. This is already extremely advantageous, since, for instance, one could express which computer programs or simulations are realizable and which are not in principle, without having to worry about the details of the computer itself.

Why is Life Possible?

How could one show that the evolution of life, with all of its elegant adaptations and appearance of design, is compatible with the laws of physics, which seem to contain no design whatsoever? No amount of inspection of the equations of general relativity and quantum mechanics would result in a eureka moment—they show no hint of the possibility of life. Darwin’s theory of evolution by natural selection explains the appearance of design in the biosphere, but it fails to explain why such a process is possible in the first place.

Biological evolution is understood today as a process whereby genes propagate over generations by replicating themselves at the expense of rival, alternative genes called alleles. Furthermore, genes have evolved complex “vehicles” for themselves that they use to reproduce, such as cells and organisms, including you. The biologist Richard Dawkins is famous for, among other things, popularizing this view of evolution: Genes are the fundamental unit of natural selection, and they “strive” for immortality by copying themselves as strands of DNA, using temporary, protective vehicles to proliferate from generation to generation. Copying is imperfect, which results in genetic mutations and therefore variation in the ability of genes to spread in this great competition with their rivals. The environment of the genes is the arbiter that determines which genes are best able to spread and which are unfit to do so—and therefore, is the source of natural selection.

With this replicator-vehicle logic in mind, one can state the problem more precisely: The laws of physics do not make explicit that the transformations required by evolution and by biological adaptations are possible. Given this, what properties must the laws of physics possess to allow for such a process that demands self-reproduction, the appearance of design, and natural selection?

Note that this question cannot be answered in the prevailing conception, which would force us to try to predict the emergence of life following, say, the initial conditions of the universe. Constructor theory allows us to reframe the problem and consider why and under what conditions life is possible. As Marletto put it in a 2014 paper: “…the prevailing conception could at most predict the exact number of goats that will (or will probably) appear on Earth given certain initial conditions. In constructor theory, one states instead whether goats are possible and why.”

Marletto’s paper, Constructor Theory of Life, was published just two years after Deutsch’s initial paper. In it, she shows that the evolution of life is compatible with laws of physics that themselves contain no design, provided that they allow for the embodiment of digital information (on Earth, this takes the form of DNA). She also shows that an accurate replicator, such as survivable genes, must use vehicles in order to evolve. In this sense, if constructor theory is true, then temporary vehicles are not merely a contingency of life on our planet but rather mandated by the laws of nature. One interesting prediction that bears on the search for extraterrestrial life is that wherever you find life in the universe, it will necessarily rely on replicators and vehicles. Of course, these may not be the DNA, cells, and organisms with which we are familiar, but replicators and vehicles will be present in some arrangement.

Testing a Meta-Level Theory

You can think of constructor theory as a theory about theories. By contrast, general relativity explains and predicts the motions of objects as they interact with each other and the arena of space-time. Such a theory can be called an “object-level” theory. Constructor theory, on the other hand, is a “meta-level” theory—its statements are laws about laws. So while general relativity mandates the behavior of all stars, both those we’ve observed and those that we’ve never seen, constructor theory mandates that all object-level theories, both current and future, conform to its meta-level laws, also called principles. With hindsight, we can see that scientists have already taken such principles seriously, even before the dawn of constructor theory. For example, physicists expect that all as-yet unknown physical theories will conform to the principle of conservation of energy.

General relativity can be tested by observing the motions of stars and galaxies; quantum mechanics can be tested in laboratories like the Large Hadron Collider. But since constructor theory principles do not make direct predictions about the motion of physical systems, how could one test them? Vlatko Vedral, Oxford physicist and professor of quantum information science, has been collaborating with Marletto to do exactly that, by imagining laboratory experiments in which quantum mechanical systems could interact with gravity.

One of the greatest outstanding problems in modern physics is that general relativity and quantum mechanics are incompatible with each other—general relativity does not explain the tiny motions and interactions of atoms, while quantum mechanics does not explain gravity nor its effects on massive objects. All sorts of proposals have been formulated that might unify the two pillars under a deeper theory that contains both of them, but these are notoriously difficult to test experimentally. However, one could go around directly testing such theories by instead considering the principles to which they should conform.

In 2014, Marletto and Deutsch published a paper outlining the constructor theory of information, in which they expressed quantities such as information, computation, measurement, and distinguishability in terms of possible and impossible transformations. Importantly, they also showed that all of the accepted features of quantum information follow from their proposed constructor theoretic principles. An information medium is a physical system in which information is substantiated, such as a computer or a brain. An observable is any physical quantity that can be measured. They defined a “superinformation medium” as an information medium with at least two information observables whose union is not an information observable. For example, in quantum theory, one can measure exactly a particle’s velocity or its position, but never both simultaneously. Quantum information is an example of superinformation. But crucially, the constructor theoretic concept of superinformation is more general and is expected to hold for any theories that supersede quantum theory and general relativity as well.

In a 2020 paper, Marletto and Vedral showed that if the constructor theoretic principles of information are correct, then if two quantum systems, such as two masses, become entangled with each other via a third system, such as a gravitational field, then this third system must itself be quantum (one of their earlier publications on the problem can be found here). So, if one could construct an experiment in which a gravitational field can locally generate entanglement between, say, two qubits, then gravity must be non-classical—it would have two observables that cannot simultaneously be measured with the same precision, as is the case in quantum theory. If such an experiment were to show no entanglement between the qubits, then constructor theory would require an overhaul, or it may be outright false.

Should the experiment show entanglement between the two masses, all current attempts to unify general relativity and quantum mechanics that assume that gravity is classical would be ruled out.

“There are three versions of how gravity could be made consistent with quantum physics,” said Vedral. “One of them is to have a fully quantum gravity.” Theories that propose fully quantum gravity include loop quantum gravity, the idea that space is composed of loops of gravitational fields, and string theory, the idea that particles are made up of strings, which move through space and some of whose vibrations correspond to quantum mechanical particles that carry gravitational force.

“These would be consistent with a positive outcome of our proposed experiment,” said Vedral. “The ones that would be refuted are the so-called semi-classical theories, such as what’s called quantum theory in curved space-time. There is a whole range of these theories. All of them would be ruled out—it would be inconsistent to think of space-time as classical if it’s really capable of producing entanglement between two massive particles.”

Marletto and Vedral’s proposed experiment, unfortunately, faces some major practical challenges.

“I think our experiment is still five or six orders of magnitude away from current technological capabilities,” said Vedral. “One issue is that we need to eliminate any sources of noise, like induced electromagnetic interaction... The other issue is that it’s very hard to create a near-perfect vacuum. If you have a background bunch of molecules around objects that you want to entangle, even a single collision between one of the background molecules and one of the objects you wish to entangle, this could be detrimental and cause decoherence. The vacuum has to be so close to perfect as to guarantee that not a single atomic collision happens during the experiment.”

The Road Ahead

Vedral came to constructor theory as an interested outsider, having focused primarily on issues of quantum information. He sometimes thinks about the so-called universal constructor, a theoretical device that is capable of performing all possible tasks that the laws of physics allow.

“While we have models of the universal computer”—meaning ideas of how to make a computer that can simulate any physical system—“we have no such thing for the universal constructor. A breakthrough might be a set of axioms that capture what it means to be a universal constructor. This is a big open problem. What kind of machine would that be? This excites me a lot. It’s a wide-open field. If I was a young researcher, I would jump on that now. It feels like the next revolution.”

Samuel Kuypers, a physics graduate student at the University of Oxford who works in the field of quantum information, said that constructor theory “has unequivocally achieved great successes already, such as grounding concepts of information in exact physical terms and rigorously explaining the difference between heat and work in thermodynamics, but it should be judged as an ongoing project with a set of aims and problems.” Thinking of potential future achievements, Kuypers hopes that “general relativity can be reformulated in constructor theoretic terms, which I think would be extremely fruitful for trying to unify general relativity and quantum mechanics.”

Time will tell whether or not constructor theory is a revolution in the making. In the few years since its inception, only a handful of physicists, primarily at Oxford University, have been working on it. Constructor theory is of a different character than other speculative theories, like string theory. It is an entirely different way of thinking about the nature of reality, and its ambitions are perhaps even bolder than those of the more mainstream speculations. If constructor theory continues to solve problems, then physicists may come to adopt a revolutionary new worldview. They will think of reality not as a machine that behaves predictably according to laws of motion, but as a cosmic ocean full of resources capable of being transformed by an appropriate constructor. It would be a reality defined by possibility rather than destiny.

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