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FQXI ARTICLE

February 6, 2023

Reconstructing Physics

A photon experiment gives new meta-framework, ’constructor theory,’ a boost.

FQXi Awardees: Chiara Marletto, Vlatko Vedral

September 24, 2021

Vlatko Vedral and Chiara Marletto

Oxford University

"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.

I called her a

philosopher and

she called me an

instrumentalist.

philosopher and

she called me an

instrumentalist.

- Vlatko Vedral

Constructor theory has also been used to explain the theory of evolution in terms of physics (C. Marletto,

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.

Breaking Time Symmetry

Table-top photon experiment demonstrates that some quantum processes can be irreversible.

Credit: Marco Genovese

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)).

Credit: arXiv:1608.02625

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.

This should convince the

community of physicists

that there is real value

in constructor theory.

community of physicists

that there is real value

in constructor theory.

- Mario Rasetti

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.

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OLIVIER DENIS wrote on September 1, 2022

""your quantum gravitation is not renormalised simply""

The ultraviolet divergences can be avoided by taking differences between quantities computed in an excited state and the same quantities computed in the vacuum state;

The black holes entropic information formula is equal to the universal bound originally found by Jacob Bekenstein. Which is equal by Casini’s work to the difference between the expectation value of the modular Hamiltonian in the excited state and the vacuum...

""your quantum gravitation is not renormalised simply""

The ultraviolet divergences can be avoided by taking differences between quantities computed in an excited state and the same quantities computed in the vacuum state;

The black holes entropic information formula is equal to the universal bound originally found by Jacob Bekenstein. Which is equal by Casini’s work to the difference between the expectation value of the modular Hamiltonian in the excited state and the vacuum...

OLIVIER DENIS wrote on September 1, 2022

""The mass energy informations equivalence principle is a pure assumption not proved""

take perhaps a look into the "Experimental protocol for testing the mass–energy–information equivalence principle"" article from Vopson

https://doi.org/10.1063/5.0087175

""The mass energy informations equivalence principle is a pure assumption not proved""

take perhaps a look into the "Experimental protocol for testing the mass–energy–information equivalence principle"" article from Vopson

https://doi.org/10.1063/5.0087175

STEVE DUFOURNY wrote on August 31, 2022

I can understand that you are fan of Dr Melvin Vobson and also Hawking, Landau and Bekenstein, but let s be serious please. The mass energy informations equivalence principle is a pure assumption not proved, and your quantum gravitation is not renormalised simply .

I can understand that you are fan of Dr Melvin Vobson and also Hawking, Landau and Bekenstein, but let s be serious please. The mass energy informations equivalence principle is a pure assumption not proved, and your quantum gravitation is not renormalised simply .

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