Counterfactuals do appear in existing laws, but these laws are regarded as second class. They are not incorporated wholeheartedly. Constructor theory puts counterfactuals at the very foundation of physics, so that the most fundamental laws can be formulated in these terms. Concepts like work and heat can’t be captured fully with trajectories and laws of motion, because in the standard conception they are considered emergent and approximate. In constructor theory we can talk about them using exact statements about possible and impossible transformations.

2023-05-04: Assembly theory is an intellectual cousin

Assembly theory started when Cronin asked why, given the astronomical number of ways to combine different atoms, nature makes some molecules and not others. It’s one thing to say that an object is possible according to the laws of physics; it’s another to say there’s an actual pathway for making it from its component parts. “Assembly theory was developed to capture my intuition that complex molecules can’t just emerge into existence because the combinatorial space is too vast”.
Assembly theory makes the seemingly uncontroversial assumption that complex objects arise from combining many simpler objects. The theory says it’s possible to objectively measure an object’s complexity by considering how it got made. That’s done by calculating the minimum number of steps needed to make the object from its ingredients, which is quantified as the assembly index (AI).
Complex mixtures of molecules made by living systems — a culture of E. coli bacteria, natural products like taxol (a metabolite of the Pacific yew tree with anti-cancer properties), beer, and yeast cells — typically had significantly higher average AIs than minerals or simple organics.

The analysis is susceptible to false negatives — some products of living systems, such as Ardbeg single malt scotch, have AIs suggesting a nonliving origin. But perhaps more importantly, the experiment produced no false positives: Abiotic systems can’t muster sufficiently high AIs to mimic biology. If a sample with a high molecular AI is measured on another world, it is likely to have been made by an entity we could call living.
Cronin and Walker hope that assembly theory will ultimately address very broad questions in physics, such as the nature of time and the origin of the second law of thermodynamics. But those goals are still distant.