Do initial conditions conspire?
A note on constructor-theoretic ‘possibility’
Constructor theory is a research program holding that it is possible to formulate all scientific theories as statements about which physical transformations are possible, which are 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', which 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 an exact and 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 some confusion. More precisely, I wish to clarify that the constructor-theoretic notion of ‘possible’ comes with a very substantial philosophical assumption.
Two Sources of Impossibility
To understand why, two sources of limits on what is possible must be recognized:
The laws of physics
Initial conditions
Under constructor theory, there are two types of physical laws: the traditional laws that we are familiar with, and constructor-theoretic principles. Examples of the former include the laws postulated by quantum mechanics and general relativity. Under the constructor-theoretic framework, the theories under which laws of this kind can be found are called ‘subsidiary theories’.
Constructor-theoretic principles, on the other hand, are meta-laws that place constraints on what the subsidiary theories can be. An example of a constructor-theoretic principle is the ‘principle of the computability of nature’, which translates into a requirement stating that all laws of physics must be friendly to being faithfully represented by a universal computer.
Evidently, both types of physical laws can forbid some tasks from being possible. For example, according to quantum mechanics, tasks embodying non-unitary processes are forbidden regardless of the initial conditions of the universe. Similarly, the principle of the computability of nature prohibits any physical object from enacting behaviors that could not be modeled by a universal computer.
The second source of actual constraints on realizability comes from initial conditions. That initial conditions can forbid certain processes from ever happening follows straightforwardly from the fact that in quantum theory, the initial state of the universe can be encoded in a vector - vectors orthogonal to it will represent forbidden states of the world.
Constructor-Theoretic ‘Possibility’
Constructor theory seems to imply that transformations not forbidden by the laws of physics are genuinely possible. The paper introducing the theory states that “when they [constructor-theoretic principles] call a task possible, that rules out the existence of insuperable obstacles to performing it”.
This definition of possibility, however, seems to ignore the second source of impossibility: initial conditions. In my view, constructor theory’s way of avoiding this issue is where the ambiguity on what ‘possible’ actually means arises.
The seminal paper seems to suggest that constructor theory resolves this conflict by postulating that initial conditions are not fundamental - meaning the laws of physics place “draconian constraints on the initial state [of the universe]”. This in turn implies that if the laws of physics specify that some task X is possible, then the initial state of the universe must be capable of evolving into a future state that includes task X.
That said, a more detailed reading reveals that under constructor theory, it might be the case that some tasks remain impossible due to the initial conditions. For instance, Section 3.2 of the paper states that nothing ever performing task A is not incompatible with the assertion that A is a possible task. Given the staggering multiplicity of timelines implied by unitary quantum theory (note that David Deutsch, the proponent of constructor theory, is also an avid defender of unitarity), the previous assertion can be interpreted in one of two ways:
A is not performed in any timeline: This is equivalent to saying that no time-evolution of the initial state will ever lead to A being performed. In other words, it grants initial conditions the ability to forbid some tasks from ever happening - even if the laws of physics do not prohibit them.
A is not performed in some timelines: This interpretation holds that when Section 3.2 talks about nothing ever performing task A, it is talking about a particular timeline. In other words, if the laws of physics do not forbid A from being possible, A must be performed in some timeline.
Given that for tasks deemed to be ‘possible’ under constructor theory, no insuperable obstacle to perform it could exist (as explicitly stated above), the correct interpretation seems to be the second one: task A must be performed in some timeline.
In short, constructor theory requires all tasks not forbidden by the laws of physics to be genuinely possible, which amounts to an assertion that the initial state must be such that everything not forbidden by these laws actually happens.
(Note: Those skeptical of whether that is what Deutsch means with ‘possible’ are invited to read Chapter 14 of his book The Fabric of Reality, where he asserts that the Turing Principle - the assertion that it is possible to build a Universal Turing Machine - requires the machine to actually be built in some timeline).
The Philosophical Assumption
As I expressed at the beginning, I believe the constructor-theoretic notion of ‘possibility’ comes with a substantial philosophical assumption. In what follows, I want to make this assumption explicit.
The constructor-theoretic assumption: The observation of regularities in nature is better explained by laws both causing the regularity and necessitating their observation than by laws causing the regularity while merely allowing their observation.
The question now is: Why does constructor theory adopt such an assumption? Does it resolve some previously problematic controversy?
Deutsch, in the light of this skepticism, seems to have provided a line of argument in defense of the assumption. In what follows, I will try to sketch my interpretation of his view. As always, errors (which will most likely plague the rest of this blog) are my own.
Expectedly, his argument is philosophical in nature, and it goes as follows: Stating that initial conditions conspire to prevent some class of tasks not explicitly forbidden by any law of nature (for instance, the task of building planet-size busts of Napoleon) from being realizable is equivalent to identifying a regularity in nature. Thus, if we are to assert that initial conditions indeed forbid a particular class of tasks that are not prohibited by any known law or principle, we must be ready to point at some problem that gets solved by postulating the existence of such a regularity.
Embedded in Deutsch’s line of argument is an additional assumption that I shall refer to as the regularity assumption: our ability to observe regularities is a regularity in itself that needs to be explained.
I believe we should view Deutsch as holding this assumption because doing so would explain why he believes it is necessary for all things not explicitly forbidden by the laws of physics to be genuinely possible: If the observation of regularities was indeed an unexplained regularity in itself, then it follows that some physical law is behind this - and given that such a physical ‘law’ cannot be a fundamental law about what the initial state had to be (for that would imply that initial conditions conspire, leading to an insertion of an accidental law by fiat), it must be the case that actual physical laws mandate possibility - in the not forbidden by any law of nature sense - to mean actuality in at least one timeline.
Admittedly, I am skeptical of the regularity assumption. I believe I am missing some fundamental insight on why we should consider our ability to observe regularities as a regularity in itself. I wonder if there is any way to introduce a notion of expectations of observability that could reveal whether this ability is in fact crying for an explanation, or if it is simply an unremarkable accident.