The Cellular Automaton Interpretation of Quantum Mechanics

Gerard ’t Hooft

Why I looked at this book

None of the popular interpretations of quantum mechanics appeal to me, and, as a fan of Cellular Automata, I've wondered whether these could play their part in understanding quantum theory. I've been aware of the work of ’t Hooft, and am rather surprised that this book has been published for nearly a year without me noticing - of course I have to read it as soon as possible. There are problems with this approach to quantum mechanics though. The naive approach of making the universe a cellular automaton tends not to agree with what is observed, and even if that is dealt with there is the problem of non-locality. I'm interested to see how well ’t Hooft deals with these problems.

First impressions

Note: There isn't a preview on Google or Amazon, but the whole book can be read for free.

When I started to read this book, I thought that it seemed rather dismissive of the significant problem of nonlocality. It seems that this is dealt with via superdeterminism, which I don't find very satisfactory, but I'm still intrigued as to how a cellular automaton model of quantum theory might work. I'm a bit worried though that the author claims that the first part of the book is non-technical, but this isn't really true, so towards the end the book may become too difficult even to skim.

Main review

I found this book somewhat disappointing. One of the advantages of expressing an idea in terms of cellular automata is that it can make it accessible to a non-technical readership. Toy models can be discussed in the text and more complex examples can be made available online. Unfortunately ’t Hooft doesn't do this at all. I understand that this is written as a monograph rather than a book for general readership, but I do feel it is a lost opportunity.

I also felt that whilst the author talked about cellular automata, the formulae were very quantumish.. Maybe experts who examine the work deeply could tell the difference, but not me. So when he highlights that he can reproduce the predictions of quantum theory it's not that surprising.

The model is based on lattice of Planck volume cells, with a few bits in each, transforming in accordance with a cellular automaton rule. (Although the model is never made explicit). ’t Hooft explains that this means that eventually the model won't match the exponential increase of possibilities of standard quantum theory, and so there will be problems with quantum computers. To me this suggests that there is a way to test these ideas experimentally, but he doesn't mention this. In addition superdeterminism involves a lot of correlations between different parts of the universe. Even using Planck volume cells there is a question of whether enough information can be held locally to express the necessary correlations. This issue is not addressed in the book.

I understand ’t Hooft's desire to show that it's possible to create an underlying model for quantum theory which avoids the weirdness that is usually associated with it,but I feel that this is done better elsewhere. Gaussian quantum theory is deterministic and reproduces the predictions of standard quantum theory apart from nonlocality. Palmer's Invariant Set Theory gives a deterministic (but chaotic) model of quantum theory, and includes nonlocality via superdeterminism. These are technical, but it is possible to get an intuitive view of what is going on in the underlying model. I feel that ’t Hooft's model, where trying to get an intuitive view of what is going on just gives something that looks like standard quantum theory, doesn't really measure up.