Frequently Asked Questions

Constructor theory is a ‘theory of principles’. A principle in this sense is a law about laws, not directly about physical objects. Familiar examples in current physics are the principle of equivalence in relativity, the principle of locality, and the principle of conservation of mass in pre-relativistic physics.

Testing a theory always needs there to be at least one rival theory, otherwise the best explanation for the failure of a test is simply ‘experimental error’ etc. When there are rival theories making different predictions about measurable quantities, a crucial test can be performed and the ones making false predictions can be tentatively discarded.

Testing a principle is similar, but at one step removed: again at least two rival principles are needed. The way one tests them is to first deduce predictions from rival laws conforming to each of them. Then, one tests that prediction. For example: the principle of energy conservation has important implications for models describing a skier sliding down a mountain slope.  One can then take two models that describe the skier’s motion: one, e.g. Newton’s laws, obeys the principle of conservation of energy. The other, does not: for instance, it predicts that the skier ends up having more kinetic energy at the bottom of the slope than it had potential energy at the top.  Then, one performs an experiment with an actual skier, to test one model against the other. So far, all experiments testing models that predict spontaneous creation of energy have been refuted.

Principles in constructor theory are tested in the same way. For instance: the principle of interoperability of information requires that the composite system of two information media is also an information medium.  This implies that certain transformations are possible on the composite system, irrespective of the details of their dynamical laws. As in the previous example, for the test we need two rival models describing the composite system of two information media. One model could predict that the principle is not obeyed, for instance because the two systems can only imperfectly interact with each other, in a way that for example perfect copy-like operations are not allowed. Confirming the prediction of one or the other model would test the interoperability principle of information. The same holds for the other constructor-theoretic principles.

No – and there are a number of reasons. The main one is that (despite the name) constructor theory’s laws are NOT about constructors. They are about stating what tasks are possible and what are impossible. A task is impossible if it cannot be performed to arbitrarily high accuracy, with no other side-effects; it is possible otherwise. These are counterfactual statements – about what could or could not be made to happen on a physical system.

So when is the idea of a constructor needed? We need to appeal to a ‘constructor’ in order to explain what it means for a task to be possible, in the traditional conception. An approximate constructor for the task T to be performed to accuracy epsilon refers to the part of the environment of a given physical system that is necessary and sufficient for the task to be performed to that accuracy. When the task is possible, one can find approximate constructors for any arbitrarily high accuracy. In the limit of perfect accuracy, or zero errors, the constructor works in a perfect cycle: it delivers the task and retains the ability to cause it again. It is important to say that constructors are not necessarily machines made by humans:  chemical catalysts and enzymes are examples of constructors as much as heat engines and computers are. But, as we said, constructor theory isn’t about describing the behaviours of these entities.

The logic to formulate the laws in constructor theory is the same as in thermodynamics: for instance, the law of conservation of energy states that certain constructors are impossible (e.g. specifically: perpetual motion machines of the first kind). Out of this statement one can then derive a number of predictions, without ever referring to any specific perpetual motion machine. Likewise, in constructor theory we don’t need to specify the details of the constructors that are associated with a possible task. We only state that the task is possible (or impossible) and derive consequences from that statement. So in that sense constructors are not at all at the foundations of the laws, not any more than they are in quantum computation or in thermodynamics. Constructor theory, however, aims at generalising the logic of these two branches of physics to other fields, at the same time also improving on the laws in those two fields themselves.

An unexpected bonus of switching to counterfactuals is that in constructor theory we can talk objectively about additional entities (such as knowledge or information) that traditionally are considered anthropocentric or subjective. This is because for example information is defined implicitly by the concept of information medium – a system with a set of states on which all permutations and also the copy-like task are possible. Likewise, knowledge is information that is capable of remaining embodied in physical systems. Nothing in these definitions appeals to an observer or a knowing subject. In this sense, constructor theory is superior to the traditional conception of physics because it can handle these concepts on objective grounds, while the traditional conception cannot.