An important case where traditional dynamical laws break down is that of what I call hybrid systems: where a quantum system (for instance, a qubit) interacts with another system that may not fully obey quantum theory, or whose dynamical trajectories are so complicated that they cannot be computed exactly.

A notorious example of the former case is gravity: we have several inequivalent formulations of a quantum theory of gravity, but the best theory of gravity that we possess at present is still Einstein’s general relativity, which is not quantum at all.

Another example (of the second kind of hybrid systems) is a macroscopic system with lots of degrees of freedom (e.g. a living cell or even a cat!) interacting with a qubit. Such systems have been key to thought experiments like Schrödinger cat, but their dynamics may be intractable.

So how do we make predictions in these cases? Theories of principles, such as constructor theory, come to the rescue. This is because they do not rely on specific laws of motion, but they are more general: they constrain laws of motion, those that are known and those that are yet to be known.

Constructor theory’s principles are formidable tools to deal with hybrid systems – this research programme explores their applications to various qubit systems, to design experiments that probe the physics of hybrid systems.