Constructor TheoryConstructor theory is a research program holding that it is possible to state all scientific theories as statements about which physical transformations are possible, impossible, and why. At the core, it introduces a new mode of explanation to the natural sciences, aiming to do away with the 'prevailing view' that expresses everything in terms of initial conditions and deterministic laws of motion.
The research program has provided some promising results, with the most remarkable ones (in my opinion) being the unification of quantum and classical information, as well as the formulation of a scale-independent second law of thermodynamics.
That said, I want to bring attention to the notion of 'possible' that constructor theory invokes, for I suspect that the way it has been presented could lead to misinterpretations.
More precisely, I wish to clarify that being possible under constructor theory is, strictly speaking, not necessarily equivalent to being in fact physically achievable. To understand why, two sources of limits on what is possible must be recognized:
- The laws of physics
- Initial conditions
The former, known as 'subsidiary theories' under constructor theory, are the particular laws that satisfy constructor-theoretic principles. An example of a subsidiary theory is quantum mechanics. Evidently, under this subsidiary theory, some tasks (e.g., those embodying non-unitary processes) are forbidden regardless of the initial conditions that are postulated; meaning it does not matter if every possible initial condition is evaluated, for none of them will result in the enacting of a non-unitary process.
The second source of actual constraints on realizability comes from initial conditions. Constructor theory argues that there is no law of what the initial conditions have to be (which is why it rejects formulations of the second law of thermodynamics that depend on very particular initial conditions). Nevertheless, constructor theory does not deny the existence of initial conditions.
That initial conditions can forbid certain processes from ever happening follows straightforwardly from the axioms of quantum theory, which assert that the state of the universe can be faithfully represented by a vector in Hilbert space. Given that all vectors in Hilbert space have some vector that is orthogonal to them, it follows that there are conceivable states of the world that simply cannot follow from the initial state of the universe.
This definition of possibility, however, ignores the second source of impossibility; namely, initial conditions. Thus, what constructor theory provides is simply a subset of all impossible tasks. This raises the question of why constructor theory should characterize the tasks it deems possible as being genuinely possible.
David Deutsch, the proponent of the theory, has recently hinted that in the light of this objection, constructor-theoretic possibility could be regarded as a FAPP (for all practical purposes) type of possibility. In what follows, I will try to sketch Deutsch's explanation of FAPP possibility (errors are my own).
According to Deutsch, even if particular instances of a task were somehow forbidden by the initial conditions of the universe (for instance, even if a timeline in which a planet-sized bust of Napoleon was not compatible with the initial conditions), given the staggering multiplicity of timelines implied by unitary quantum theory, it must follow that a very close approximation to the task in question is possible in some timeline.
One might object by stating that there is no need to hold the possibility of an approximately similar task to be necessary - it is perfectly conceivable that all planet-sized busts are forbidden by the initial conditions. To this criticism, Deutsch replies with a philosophical argument: although it is conceivable that initial conditions indeed conspire to prevent a class of tasks from being realizable, stating that they in fact do is tantamount to identifying a regularity in nature - thus, if we are to assert that initial conditions indeed conspire to forbid a class of particular tasks that are not prohibited by any subsidiary law, we must be ready to point at some problem that gets solved by postulating the existence of such a regularity.
To this, I present the following question: Is the idea that initial conditions allow for an approximate variant of all tasks regarded to be 'possible' under constructor theory not a regularity in itself? I wonder if there is any way to introduce a notion of expectations of possibility that could distinguish between non-conspiring and conspiring initial conditions...