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My limited understanding of quantum theory is that a quantum system is completely described by its wave function, which deterministically evolves according to Schrödinger's equation until wave function collapse.

Schrödinger's equation is essentially just a differential equation, which means (as far as I can see) that the state at every point in space changes depending only on its surroundings (i.e local rules). Correct me if I'm wrong but it's at the point of wave function collapse that the non-locality comes in, which is what cellular autonoma (CA) models can't deal with very well.

I'm not hypothesizing or suggesting that the universe IS a cellular autonoma (as Wolfram has suggested), but what would a CA model of Schrödinger's equation be like? (Ignoring wave function collapse for the minute)

Providing my understanding described above isn't wrong, I want to know, for the CA model:

  1. What values describe the state at a given point? (i.e. what information would be in each CA cell?)
  2. What rules are followed every discrete time tick to progress these values?

I ask because I've gained a good intuition (an "understanding" that I'm happy with at least!) of heat flow, wave propagation and the rules of fluid dynamics through interpreting their differential equations as local cellular automata rules, and writing little toy simulation programs to see how they behave and look. I'm a computer science/mathematics undergraduate and I've always said that I don't understand something until I can write a program that simulates it, so being a little too ambitious for my own good I want to write a simulation for a QM system! My background is I've read a few Penrose/Feynman books, and I've got the complete Feynman lectures on physics (not read them yet...), and physics has always been a side hobby, but I'm not too hot yet on the mathematical language that is used for QM.

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What do you mean by a cellular autonoma model? Aren't you describing essentially numerical solution to a differential equation using some sort of finite difference method? –  user758556 Aug 10 '12 at 1:20
Probably he's referring to Gerard 't Hooft series of papers on cellular automata and quantum mechanics. –  linello Aug 16 '12 at 10:19
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