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Constructor Theory

[Claude Shannon]

Update - 2014-05-28

I found a much better article on this subject on the fantastic Physics Arxiv Blog entitled Deeper Than Quantum Mechanics—David Deutsch’s New Theory of Reality! Instead of removing my original post below, I’ll expand on the insights provided by this article.

This article does a much better job explaining constructor theory, and giving a motivating example. Put simply, “all laws of physics are expressible entirely in terms of the physical transformations that are possible and those that are impossible. In other words, the laws of physics do not tell you what is possible and impossible, they are the result of what is possible and impossible” (emphasis mine). The conservation of energy is provided as an example, saying its not really a law of physics, but a “principle” that all laws must follow, even unknown/yet-to-be-discovered ones. Constructor theory is “deeper” then the laws of physics in this way: “It is a principle, namely a law of physics that expresses and explains constraints on other laws rather than on the behavior of physical objects directly”.

The main focus of the paper is on placing “Information” within this framework. Information has long been studied thanks to Shannon’s seminal 1948 paper. However, quantum information is inherently different (QM superpositions, entanglement, no-holograms, etc. - things I don’t really understand) and physicists want to tie them (conceptually) together in one coherent theory.

I’m finding myself increasingly enthralled by the physical meaning/interpretation of information and the article puts it rather nicely: “Information is similar to energy in this respect. It can be encoded using light, chemistry, electronics, smoke signals and so on, and all these things obey different laws of physics. However, the information itself is somehow separate from all this. It is substrate-independent. But the information itself is preserved, regardless of the laws in play.” I highly recommend a second, third and even fourth reread of that statement. Shannon created a framework for us to abstract the “information” quantity away from that in which its carried. This not only gave birth to the digital age, but is slowly revolutionizing physics in ways I have yet to understand! I once read that the conceptual revolution Information inspires in physics can be compared to the discovery of “energy”!

Heres where I get confused: The authors say: “Previous attempts to incorporate information at a fundamental level into physics or at least into quantum theory have regarded information as being an a priori mathematical or logical concept. Our approach is the opposite.” They then define nine principles based on constructor theory and apply them to what we know is possible and impossible when it comes to information. These principles express the concepts of computation, measurement and classical information. They define something called superinformation that restricts the kind of things information can do and qm information pops on out.

What I’m confused about is: Isn’t constructing a system by what we know (have observed) to be possible/impossible ultimately using knowledge a priori (eg. the laws of physics) anyway? For otherwise, how do we know whats possible/impossible? It feels like we’ve observed the universe for thousands of years, built a set of tools to reason about what we think are possible/impossible (lets call those the laws of physics) and then along comes constructor theory and wants to create a big rule book (computer program) of things we know are possible and impossible, and then say “look! the laws of physics obey these!”. Well, of course they do, we’ve built constructor theory to be that way!

Ill repeat my original word of warning to myself that I did below: David Deutsch is one of the most creative, deep-thinking scientists alive and has made countless contributions to fundamental physics and quantum information theory. All of my objections above are probably-without-a-doubt a direct result of my lack of understanding! I jot them down here only as an insight into my thought process so I can refer back and see how it developed over time!

Things to think about

  • “physical” interpretation of information
  • quantum mechanics
  • how does this tie into epistemology?
  • how does something like Noether’s Theorem play into this?

Original Post

Came across a very interesting Scientific American article: A Meta-Law to Rule Them All: Physicists Devise a “Theory of Everything” on constructor theory. Its the first I’ve ever heard of it, but not the first I’ve heard of the famous David Deutsch! The SA article described a new paper that shows how constructor theory can unite both classical and quantum information processing in one framework.

It briefly explains the basics of constructor theory, where the most fundamental components (of reality) are “constructors”. Accompanying these constructors are a set of laws that define which tasks are actually possible for a constructor to carry out. One example given in the post is: “a kettle with a power supply can serve as a constructor that can perform the task of heating water”. Interesting, but I would probably benefit from a deeper explanation (linked below).

The authors define a “classical information processing system” as one which is capable of perfectly replicating all states. This is a key property missing from quantum information and they use this as the defining characteristic of a classical system. They then define tasks that are already in line with Shannon’s familiar theory. Surprisingly they recover quantum information processing properties on systems that do not have this copy ability.

I definitely need to look more into quantum mechanics, quantum information theory, and constructor theory to fully understand whats going on, but its interesting nonetheless! At this point with my (very) limited information, CT seems to be able to define constructors/tasks almost arbitrarily? Probably not, will look into further.

Further Resources

Note: This post (and most of the ones to follow) is a combination of paraphrasing, copy/pasting, and my own thoughts/questions.

Image Credit: Flickr/thierry ehrmann

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