Physics

What is Constructor Theory? (# 37)

Constructor Theory (CT) was developed by David Deutsch who was one of the originators of the idea of a quantum computer. In the context of explaining the origin of our universe, CT is interpreted in a slightly different perspective to that explained by Deutsch. According to Deutsch:

Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations — those that can be caused to happen and those that cannot. This is a departure from the prevailing conception of fundamental physics which is to predict what will happen from initial conditions and laws of motion.

Deutsch aims to formulate/deduce CT through analyzing existing physical laws and phenomena. The approach outlined here sets out a context for CT and then suggests the physical laws of our universe would be expressions of that context. Ultimately, while the same CT could emerge from both approaches, this approach starts with what CT could be.

Constructor Theory

CT is a theory about which transformations i.e. input state of substrates into an output state of substrates, can be caused and which cannot, and why. The idea is that all the fundamental questions of physics can be expressed in terms of transformations. The answers do not depend on what the constructor is.

A construction task specifies only intrinsic attributes of its substrates, not extrinsic ones such as the name or location of a particular instance. The laws of constructor theory are all principles that are obeyed by all other laws of physics. When these principles call a task possible, those principles rule out the existence of insuperable obstacles to performing it, even from unknown laws.

Chiara Marletto who works with David Deutsch proposes in Constructor Theory of Life that the neo-Darwinian theory of evolution does not fully achieve its purpose of explaining the appearance of design. She applies CT’s mode of explanation to express exactly within physics the appearance of design, no-design laws, and the logic of self-reproduction and natural selection. She concludes that self-reproduction, replication, and natural selection are possible under no-design laws, the only non-trivial condition being that they allow digital information to be physically instantiated. Under no-design laws, an accurate replicator requires the existence of a ‘vehicle’ constituting, together with the replicator, a self-reproducer.

Self-reproduction is a construction where the self-reproducer, S, is a constructor for constructing another instance of itself given raw materials, N, containing neither S nor constructors for S. For example, when S is combined with raw materials, N, a self-reproducer is transformed into producing two S objects plus some waste, W. The whole system could be isolated. The only condition is that information must be ‘copiable’ from one information medium to another. Whether or not information media exist, i.e. whether or not information can be instantiated in physical systems, depends on the laws of physics.

Constructor Theory and Efimov effects

The contribution of CT to the explanation of the origin of our universe is in connection with the Efimov effect. The Efimov effect has been shown to exist in laboratories. In brief, the Efimov effect shows what happens when certain initial conditions are associated with certain physical laws. What CT proposes is that there are principles that allow this task or transformation.

According to Wikipedia, an Efimov state exists when three bosons (elementary particles) are bound together even if the two-particle attraction is too weak to allow two bosons to form a pair. Expressed differently, the bonds between three bosons are more complex than between any two bosons. Under the Efimov effect, complexity has increased.

The Efimov effect was first discovered theoretically, it was deduced from mathematics and did not need to be created. The Efimov effect arises because of the mathematical configuration associated with a boundary inside a black hole in Anti-de Sitter space. The mathematical formulation of CT must also arise from this configuration because it is associated with describing an Efimov effect. Analogously, CT may also be deduced from mathematics and does not need to be created.

While the emergence of CT may be synonymous with the emergence of the Efimov effect, the framework or principles of CT apply more widely than just to Efimov effects. According to Marletto’s Constructor Theory of Life, self-reproduction can occur when a self-reproducer combines with raw materials. In a finite system like the inside of a black hole, the supply of raw materials may be finite. The Efimov effect, however, is potentially infinite i.e. complexity could keep on increasing as more and more complex content bonds together.

As CT allows for an Efimov effect, the principles of CT must also allow for potentially infinite complexity to arise. In other words, an appropriate formulation for CT would not only allow for complexity but also the identification of laws allowing continuing increases in complexity.

Many of our laws of physics may be explained in the context of CT allowing more complexity to arise. As discussed in Article 11 - What is Quantum Computational Complexity? - the concept of entropy is related to the concept of complexity. CT could allow the second law of thermodynamics to measure how other emerging features increase complexity. The graph below shows a relationship between complexity and entropy.

Efimov effects exist because mathematical descriptions of matter are part of the configuration of content inside a black hole. Information can be instantiated in this matter. The configuration of content inside a black hole provides the necessary conditions for CT, as CT allows for evolution without the need for a designer.

Our universe is a giant computation

CT is about the principles used to create our universe. These principles are not to be found in our universe but deduced from information in our universe. The raw materials used to construct self-reproducers are content in the bulk of space-time inside a black hole. The laws of physics describe the appearance of content inside a boundary. In his discussion of CT, David Deutsch states:

[W]e are not taking computation to be an a priori concept and seeking necessary and sufficient conditions for a physical process to instantiate it. We are conjecturing objective regularities in nature: principles of physics. These happen to be conveniently expressed in terms of the tasks we have called ‘computations’ and the property that we shall call ‘information’.

The question for this article is:

Could our universe be an ongoing computation without there being a final design?

To view the headings of all the articles to be published in this series please click on https://michaeledalton.medium.com/orbiting-stars-and-origin-of-our-universe-338906930f51

To obtain a copy of the book ‘Orbiting Stars’ which contains the first drafts of all these articles, please visit https://www.amazon.com