Reconstructing Physics

What could be more romantic than developing a new fundamental physical theory, uniting the notoriously incompatible branches of physics into something beautifully simple? Nothing, if you ask Chiara Marletto and Vlatko Vedral, both quantum physicists at the University of Oxford, UK, who fell in love while working on such an approach known as constructor theory.

"I called her a philosopher and she called me an instrumentalist," says Vedral. "But we turned out to be a good combination."

While constructor theory has a mathematical basis, it is largely considered ’philosophical’ in the sense that it had never been been demonstrated experimentally—at least until now. With the help of an FQXi grant of over US$100,000, a new experiment designed by the couple and carried out by Marco Genovese, an expert on quantum optics at Italy’s national metrology institute in Turin, and his colleagues, gives the first indication that the new framework holds up. The experiment could also help solve the puzzle of whether the classical physical rules governing heat—the laws of thermodynamics—apply to the microscopic world of atoms and molecules that is ruled by quantum mechanics.

Laws of physics generally describe what happens to physical systems given some initial conditions. This works well in practice, as long as you restrict yourself to the realm in which particular laws apply. However physics is famously full of inconsistencies, with some theories applying on certain scales only. For instance, quantum theory is tremendously successful, but only describes the behavior of small systems, while Newton’s classical laws of motion are all we need to understand the motion of objects in our everyday world, and Einstein’s theory of gravity, general relativity, reigns over cosmic objects. Thermodynamics is usually applied to macroscopic engines, and it is an open question how well it applies on tiny scales.

Meta-Theory

Constructor theory has been formulated as a meta-theory that can encompass all others, reconciling them by using a surprisingly pragmatic approach. The framework, which was first proposed in 2012 by David Deutsch, also a quantum physicist at Oxford, takes into account that we live in the real world where resources are finite. A "constructor" is defined to be any entity that can carry out a transformation, over and over again, given some energy. For example, a fridge connected to power is a constructor that can carry out the transformation of cooling food (D. Deutsch, arXiv:1210.7439 (2012)). Constructor theory then re-frames the known laws of physics only in terms of which transformations are possible, which are not—and why.

Marletto has spent years developing constructor theory, first in collaboration with Deutsch and then independently. The framework was born out of the information theory developed by the American mathematician and cryptographer Claude Shannon in the 1940s and of the mathematician John von Neumann’s generalisation of Alan Turing’s universal computer—the universal constructor. As a result, information lies at its very heart. Rather than viewing information as an abstract, mathematical concept, constructor theory takes it to be fundamentally physical—a property determined by physical laws that can be described and copied.

"What I like about physics is that whenever there is a gap…if you look at history, a better theory tends to come along that connects things into a deeper theory," says Marletto, who recently published a popular book on the subject, The Science of Can and Can’t. And constructor theory has proven successful at doing just that by exploiting this concept that information is physical to formulate exact laws about entities that have historically been difficult to describe in precise terms. The theory has already enabled Deutsch and Marletto to describe information processing in a way that unifies the classical world of macroscopic objects and the quirky world of quantum mechanics. These realms have so far remained impossible to describe with one theory. But, in 2014, Marletto and Deutsch used the framework to come up with a more clear definition of ’quantum information,’ and then used that to calculate how entanglement—the spooky property linking distant particles—arises in quantum systems (D. Deutsch & C. Marletto, Proc. R. Soc. A. 471 20140540 (2015)).

Constructor theory has also been used to explain the theory of evolution in terms of physics (C. Marletto, J. R. Soc. Interface. 12 20141226 (2015)). This is helping to solve the conundrum of how living systems, which display purpose and agency, can arise from the non-purposeful physical laws that govern inanimate matter (see "Constructing a Theory of Life"). If that were not enough, constructor theory could also help uncover new laws of physics, argues Vedral. "We could discover that there are things that ought to be possible, but that quantum mechanics doesn’t allow us to do," he says.

Nano Engines

Constructor theory may have a practical impact on one area of physics, thermodynamics, that is under increased focus at the moment, thanks to advances in building nano engines and mini motors that could be housed on chips, or even injected into the body. The laws of thermodynamics were originally sketched out in the nineteenth century to describe work, heat and energy transfer, in steam engines and other macroscopic devices. Its rules are based on how large numbers of particles behave. But this means that concepts like "work," "heat," and "temperature," are fuzzy, because they are best described in terms of statistics. For instance, the temperature of a box of gas is related to the average speed of particles in the box, with faster speeds leading to an overall hotter temperature. But it does not make sense to ask what the temperature of any one single particle is, only to talk of the temperature of the whole ensemble. While that wasn’t much of a problem in the past, researchers who are trying to build nano systems need to know whether thermodynamic rules are different in the quantum realm, where the behavior of individual particles becomes important.

The second law of thermodynamics famously states that physical systems tend to become messier and more disordered as time passes—something we describe using a physical property called ’entropy.’ Imagine putting a cup of hot tea on a table in your garden on a cold day (an ordered state). As its molecules interact with the atoms in the air, the cup of tea would eventually cool down to the same temperature as its surroundings (a disordered state). This is irreversible; you never see this process spontaneously going in the opposite direction, with the hot cup of tea randomly heating up further. In that sense, entropy gives us an arrow of time.

We can take a glass of water and raise its temperature by mechanical means, such as by stirring. What happens in this example is that the work carried out by the stirrer gets converted into heat. The reverse isn’t possible with mechanical means only, however; heat can never be completely converted into work.

Here there appears to be something of a clash with quantum mechanics. In quantum theory, all dynamical laws are reversible in time. Anything that can go in one time direction can go in the opposite one. It seems to be completely at odds with thermodynamics and its arrow of time. Yet quantum mechanics has been tested extensively, so there’s no reason to believe there’s anything wrong with its assertion about reversible processes. How can quantum theory and thermodynamics be squared?

Luckily, constructor theory has come to the rescue (C. Marletto, arXiv:1608.02625 (2016)). While thermodynamics describes the laws of physics in terms of processes occurring or not, with some probability, constructor theory can provide exact formulations about possible and impossible tasks. The theory’s exact definitions of information and distinguishability help give precise descriptions of concepts like work, heat and mechanical means. "I take the tradition of thermodynamics and I make it more general because I unpack the concept of mechanical means," explains Marletto. A stirrer for instance is described as a constructor that can raise the temperature of a liquid, but cannot lower its temperature.

It turns out that when you start expressing things in this way, the clash between the irreversible processes of thermodynamics and the time symmetrical laws of quantum mechanics completely disappears. That’s because all constructors must obey time-reversible laws of physics. If the reverse of a process can’t happen, that just means there’s no constructor in the real world that can do it perfectly without error—not that it is an impossible process per se. We could one day invent or discover more sophisticated constructors that may be able to do it to arbitrarily high accuracy.

Sarang Gopalakrishnan, an assistant professor of theoretical physics at the City University of New York in Staten Island, thinks constructor theory is a "promising approach" to understanding thermodynamics better. "Thermodynamics has historically been a bit ad-hoc about what’s work and what’s heat," he says. "It’s nice to try to be more systematic and axiomatic about it." He notes that constructor theory is also able to precisely define the meaning of an "agent"—a somewhat fuzzy concept in consciousness studies—as a thing that does actual work.

Quantum Simulation

But aspiring theories of everything ultimately need to be tested. Working with Genovese, Marletto and Vedral have come up with a clever quantum simulation and demonstrated one of its predictions: that there could be irreversible processes on the quantum scale too.

"This experiment is for visualizing constructor theory—to see how it could work," explains Genovese. The test uses a source of single particles of light, or photons. His team has homed in on one particular photon process and shown that, as predicted by constructor theory, a photon can go from being in one state to being in another through a certain interaction—but that the reverse of this process can’t happen by the same means (C. Marletto et al., arXiv:1608.02625 (2020)).

Here is how the table-top test works: According to quantum mechanics, a photon can be in a mix, or "superposition," of many different states at the same time. For instance, it can be prepared in such a way that it takes multiple paths round the apparatus on a table in a lab, simultaneously. Genovese’s team prepared the main photon under study to be in a pure state A—meaning it follows a single specific path. They also prepared a separate beam containing multiple photons in state B, which corresponds to some superposition of multiple paths. When the main photon interacted with the photons in the beam, it changed paths. These interactions happened when the photon hit a series of devices called beam splitters (see diagram, above). At these points, photon A could swap paths with that of another photon in the beam, one at a time. This is much like the cup of tea cooling down by interacting with a lots of particles in the surrounding air. The probability that a swap happens can be calculated using quantum equations.

At the end of the experiment, the team reconstructed the state of the photons using a method called quantum state tomography, in order to reveal how close to state B the main photon got. The prediction from constructor theory was that it should be very close—and the more photons the main photon interacted with, the closer it should be. This was confirmed by Genovese’s team. But the crucial part of the test came when the team repeated the experiment backwards, starting with the main photon prepared so that it was in state B—a superposition of multiple paths—while the photons in the beam are in state A, following a single path. The team carried out a series of reverse interactions to try to get the main photon to change from state B to state A—a single path. According to constructor theory that task cannot be performed with the same accuracy by the same means—and this is indeed what Genovese found.

So the experiment successfully demonstrated that the fact of irreversibility—that state A can become state B, but not the opposite—is compatible with quantum theory’s symmetric time-reversible laws. There is no contradiction when viewed through the lens of constructor theory.

Mario Rasetti, a theoretical physicist at the Politecnico di Torino in Italy, says it is a huge deal that the team managed to pull off the experiment. "This should convince the community of physicists that there is real value in constructor theory," he says.

In the future, Marletto, Vedral and Genovese hope to scale up the experiment to test organic molecules and larger systems like living bacteria—demonstrating that the theory is truly scale-independent. This may also help solve the mystery of why life, unlike inanimate matter, seems to contradict the second law of thermodynamics by constantly forming highly ordered systems, in which entropy appears to decrease. "The thermodynamic cycles that operate within living cells work with finite resources, they only operate a certain number of times before they have to be wound up again if you like," says Vedral, adding an experiment could probe the origin of this entropy change. "It could be that any irreversibility that we discover is somehow linked to constructors and finiteness of resources—I think that would be cool."

Discovering a theory of physics that can explain the living would be a major breakthrough. With its clear definition of agency, constructor theory may ultimately be what we need if we are to ever crack the huge mystery of human consciousness. And what could be more important? Without consciousness, nobody would come with new theories of physics—and nobody would fall in love.