Constructor theory might be revolutionary but what can you do with it?
Three reasons why it falls short.
Isaac Newton invented physics as we know it. And one of the ways he did so was that he formalized the initial condition problem into calculus — the mathematics of change.
An initial condition problem is simply a problem where, knowing the initial condition of any system, whether a ball dropped from a tower or the moon in orbit, and the way that condition is transformed in time by forces, and you can predict the system’s state at any time in the future or the past.
The initial condition problem has been the backbone of physics ever since.
In 2012, Oxford professor David Deutsch, famous for his championing of quantum information theory and the Many Worlds Interpretation of quantum physics, introduced Constructor Theory with the intent of tearing down Newton’s hegemony. Chiara Marletto, also of Oxford, has been the main champion and developer of the theory in the physics world since then while Deutsch has addressed some of the philosophical aspects.
Constructor theory claims that the initial condition problem is not fundamental to physics at all but an emergent property of constructor tasks. Constructor tasks are transformations that take in an input (called a substrate) and turn it into an output (also a substrate).
While a reductionist approach to physics based on differential equations and initial conditions, which goes back to Newton, proposes that the state of a system and its dynamics are fundamental, constructor theory proposes that it is what is possible or impossible and why that is fundamental.
Constructor theory proponents argue that, while dynamical descriptions are all well and good for footballs and rockets and planets, they make no sense when talking about living things, information, and heat, all of which are emergent from dynamics but which dynamics give no insight into. Dynamics, on the other hand, are perfectly describable with constructor theory since they involve transformations from one moment to the next. Indeed, this is exactly what a differential equation is.
Furthermore, constructor theory proposes that dynamics fail to consider counter-factuals, essentially all the things that could have happened other than what did happen. Constructor theory, by proposing that the universe is a set of constructors capable of performing tasks to transform substrates, suggests that it encompasses all possibility, including counter-factuals.
From an information theoretic point of view, the theory is interesting because it seems to capture something essential about how people think about the laws of physics. Physics is often presented as a set of equations that are considered fundamental laws. Yet, these equations are simply predictive models. Many laws of physics such as general relativity were derived from intuitions that could be formalized by constructors. Could it be that the equations that we think of as fundamental are simply outgrowths of constructors?
I think that is possible but it has some flaws that, I think, will fail to overcome the reductionist, initial condition dynamics that we have come to know and (maybe) love.
1 Physics already has ways to reconcile dynamics with possibility
It’s called probability theory or, more specifically, statistical mechanics. The goal of statistical mechanics was to provide a reductionist, Newtonian underpinning of thermodynamic laws. In his initial paper, Deutsch suggests those laws are themselves flawed because they are emergent from the notion of an engine. The engine rather contains properties that imply the constructors involved.
One of the problems I see with constructor theory attempts to “redesign” thermodynamics is that statistical physicists have already done this. The “laws” of thermodynamics are two centuries old, and everyone knows what the problems with them are. Fluctuation theorems, non-equilibrium statistical mechanics, and Markov processes predate the constructor theory. So, nobody working in the field needs a new theory to fix problems that have already been fixed and would be unlikely to want to replace common mathematical tools with unfamiliar terminology.
Understanding counter-factuals and the realm of the possible is what probability theory and statistics is all about. Every statistical ensemble contains huge numbers of states that virtually never happen and yet are “possible”. Every stage of a Markov chain has many possibilities encoded in its probability distribution.
Statistical mechanics has been extremely successful at explaining the connection between Newtonian dynamics and macroscopic observations like temperature, pressure, and phase transitions like melting or freezing. It does so by determining not only what is possible or impossible but how probable those things are.
Constructor theorists argue that statistical mechanics is vague about what constitutes a “macroscopic scale” but that isn’t really true. While classical statistical theories are subject to the law of large numbers, meaning that they get more accurate the more atoms or molecules you have, more recent statistical mechanical theories have focused on state transitions for arbitrary numbers of molecules. A state transition is, of course, much like a constructor task but has a more definite relationship to dynamics in a probabilistic form. These theories have enabled the study of very small statistical systems composed of only handfuls of molecules. Notions common in classical statistical mechanics like “equilibrium” vanish at these scales of course. These ideas are a lot like constructor theory but were invented much earlier.
Could constructor theory be a generalization? Perhaps but in generalizing much utility is lost.
Statistical mechanics may, in its non-equilibrium form, tell us how life occurs and how it stays alive, perhaps even providing a definition for what life is (or more likely provide some measure of how “alive” something is).
2 Physics is mainly useful in as far as it can make predictions
Newton developed his physics the way he did because he was able to make predictions about many things from a few simple laws. Yet, predictions go far beyond initial condition problems.
Many problems in physics cannot be described as initial condition problems. For example, boundary condition problems are common in fluid dynamics where the behavior of anything from an ocean to rocket fuel in a pipe requires a complete description of its boundaries. In these cases, the initial conditions are less important than the boundaries that contain and constrain the fluid.
Constructor theory, so far, has not yielded much predictive ability. That may change as more work is done, but it is hard to figure out exactly how it would then differ from ordinary physics.
Most people who use physics on a day-to-day basis are interested in predicting things, not in understanding the complete realm of possibility within the universe. If I want to get a rocket to the moon, I am going to use Newton’s laws.
Yet, suppose I want to predict something that is not easily reductionist, like how a bacterium or a mouse will behave. Would constructor theory give me that power? I wouldn’t think so.
Thus, constructor theory does not appear to add much to the everyday physics user’s toolbelt.
3 Constructor theory does not solve the problems it claims to solve
Despite claims that it solves a number of problems in physics such as the connection between quantum and classical systems (hybrid systems) and irreversibility in thermodynamics, it isn’t clear that it solves any of these problems better than reductionist solutions that are more specific to those subfields.
While there are interpretations of quantum physics that certainly muddy hybrid systems, there are others (superdeterminism for example) that make no distinction between quantum and classical. A reductionist approach would assume that macroscopic classical behavior emerges from quantum physics in some way (e.g., by decoherence). How to interpret that should, ideally, not make some fundamental distinction between the two.
Meanwhile, irreversibility is a problem that certainly causes problems in physics because it requires some definition of why time moves forward but not backward. Some believe that this is just an artifact of information storage mechanisms like the brain and that time moving forward is actually an illusion of information growth. This would mean that time could and does move backwards from time to time. This phenomenon has been observed in small statistical systems (the size of large molecules) in clear violation of the 2nd law of thermodynamics.
Constructor theory attempts to resolve the problem (for quantum thermodynamics) using constructor tasks and making their reverse impossible. I would suggest that you would just have to have many more forward-time tasks than reverse time tasks, since that is compatible with existing theory using, say, phase space path probability theory. Again, it isn’t clear what constructor theory is adding to work that has already been done for non-equilibrium systems in quantum mechanics.
Conclusion
Philosophically constructor theory is interesting because it points out that perhaps we are too focused on equations and should rely instead on more intuitive statements about the universe from which those equations derive. Perhaps that would help us steer clear of theories of everything that seem to be nothing but equations.
Yet, constructor theory seems to be attempting to do what quantum non-equilibrium statistical theory is achieving. They are somewhat similar in that they are focused on state transitions, distributions of possible transitions, and less focused on initial conditions. But unlike constructor theory, that theory fits well within the traditional reductionist paradigm of initial conditions to which it reduces. I would be interested to see constructor theory move more in that direction and become a more rigorous theory. But I do not see it overturning reductionism any time soon.