I’m going to take another hiatus from blogging, until at least August 1, 2006. I was hoping to come back to my blog properly, but realize that I have too many other things going on. I do hope to blog again one day, and have some ideas for large project into which the blog would be integrated. (I rather like the way Kevin Kelley is using a blog to test out ideas for a book, and could potentially see myself doing the same thing.)

For now, I’ll leave you to ponder a provocative recent comment posted by John Sidles. I haven’t yet read the paper in question, but the authors, Conway and Kochen, are top-notch mathematicians, and I’m looking forward to reading it at some point.

Boy, is it quiet, both here and on Bacon’s Quantum Pontiff. Just to stir things up, what do people think of the preprint on the arxiv server this morning:

The Free Will Theorem” http://www.arxiv.org/abs/quant-ph/0604079

Such titles are often associated with fringe physics — except that these particular nutjobs are the mathematicians John Conway and Simon Kochen!

These guys may be nutjobs, but they are high-power nutjobs, and I enjoyed their preprint very much.

In engineering, we tend to think of every quantum problem as an exercise in model order reduction (MOR). But our MOR colleagues (and there are a lot of them — there are more academic articles by far on MOR than on open quantum systems!) always complain that simulation algorithms for open quantum systems are stochastic. “Can’t you eliminate the stochasticity, and make your open quantum system model deterministic?” they complain.

The Conway/Kochen Free Will Theorem answers that question pretty crisply, by showing that open quantum systems have properties that *no* (locallyrealistic) deterministic simulation can exhibit. And, they prove it in a fun way.

Also, it’s just not right to ignore an article that begins “Do we really have free will, or, as a few determined folk maintain, is it all an illusion? We dont know, but will prove in this paper that if indeed there exist any experimenters with a modicum of free will, then elementary

particles must have their own share of this valuable commodity.”All the above is just to stimulate some comment!

Hmm… I had a look at this paper. The title sounds a bit crackpot, but given the status of the authors I was willing to give it a chance.

First of all the name “Free Will Theorem” opens a whole can of worms, which we probably don’t want to get into. Suffice to say, what they actually prove is an “indeterminism theorem”, i.e. they use a Bell-type argument + a no-signalling requirement to prove that nature must be indeterministic. I have heard similar arguments before, in particular from Y. Aharonov and D. Rohlich mention it in their book, although I’ve never seen it written down formally before.

To call this a “free will theorem” one has to get into the debates about whether free will is compatible with determinism and, if not, whether indeterminism even solves the problem. Most contemporary philosophers seem to answer yes and no respectively, so I don’t think this theorem has much to do with free will, although it would take a lot more space to go through the arguments for and against thoroughly.

However, what I did think was interesting about the paper was the “hexagon universe” toy-model that they introduced in the second half of the paper. Given the current interest in understanding aspects of QM via simpler toy theories, e.g. nonlocal boxes and Spekkens toy theory, this might be a useful addition to the canon. I haven’t managed to decipher all the details of this model yet, so I’ll have to defer judgement on that.

Shameless plug: I have included the text of my previous comment on my blog http://mattleifer.wordpress.com . The blog is about the foundations of quantum theory, and if any foundations oriented people want to help out with it then let me know because I don’t have too much time to write posts myself.

What, no comments? Hmmm … maybe the post was insufficiently “provocative”?

In Seattle, we think that the Conway-Kochen Free Will Theorem is not all that provocative … but it is a wonderfully interesting theorem, and a beautifully written article.

Is it provocative to say “there are more academic articles by far on MOR than on open quantum systems” Well, to be polite, we hasten to mention that there are more *books* by far written on open quantum systems than on MOR, so the academic scales are roughly equally balanced. Why is the book-to-article ratio is so much largerin the open quantum system literature? It’s a mystery to us!

For our QSE Group in Seattle, the most provocative idea is that “open quantum systems have properties that no (locally realistic) deterministic simulation can exhibit.” A more clear understanding of why this is true might help us better understand fundamental questions llike “What makes problems in NP harder than problems in P”?

Engineers appreciate that many of the questions that arise naturally in large-scale classical simulation and control—arguably even *most* of the natural questions—are NP-hard to answer:

http://web.mit.edu/jnt/www/complex.html

This is why books on control engineering often seem unsatisfactory to physicists; engineers are attacking NP-hard problems by methods that necessarily are heuristic.

In a wonderful lecture Mike gave last summer at Caltech, he suggested that these algorithmic complexity issues might be easier to understand if they were generalized to the quantum domain. Perhaps Mike will be able to tell us something new about this, in August!

Meanwhile, in Seattle, we still need help with the “sparsification problem” mentioned in an earlier post …

http://www.qinfo.org/people/nielsen/blog/?p=249#comment-1991

The literature on NP-hardness is *very* tough.

Cowabunga to all … John Sidles