## The Free Will Theorem

Michael Nielsen recently posted a comment by John Sidles about a preprint by Kochen and Conway that was posted on the quant-ph arXiv yesterday. It's called "The Free Will Theorem", which is certainly a provocative title. Here's my comment on the paper that I left on Mike's blog.

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 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.

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6th June 2006 at 4:17 pm

Hi Matt, a paper which predates Kochen&Conway’s and has similar ideas is this one by Yurtsever:

http://arxiv.org/abs/quant-ph/9806059

6th June 2006 at 4:44 pm

I think there’s an even earlier paper that contains similar ideas by some philosophers (Redhead and co.). I’ll try and dig up the reference.