brainwagon

On a mailing list I subscribe to, Tom Duff pointed me at Conway’s Proof of the Free Will Theorem.

From the background:

In mid-2004, John Conway and Simon Kochen of Princeton University proved the Free-will Theorem. This theorem states “If there exist experimenters with (some) free will, then elementary particles also have (some) free will.” In other words, if some experimenters are able to behave in a way that is not completely predetermined, then the behavior of elementary particles is also not a function of their prior history. This is a very strong “no hidden variable” theorem.

I’m not sure I can wrap my head around this, being a Friday, but it is very, very strange. The idea of free will is something which I had decided was more or less unassailable by the methods of science (it wasn’t even clear to me that the phenomena had any real meaning whatsoever) but apparently someone with the intellect of Conway thought that it was worthy of study, so perhaps I was mistaken.

One of my personal regrets is that I didn’t drop in on John Conway while I was working in the Applied Math department at Princeton. I have little doubt that if I had, I’d have met the smartest person I’ve ever encountered so far.

Need a fun book by Conway? Try ::amazon(“038797993X”, “The Book of Numbers“):: that he coauthored with Richard Guy. Very entertaining, and quite accessable.

Note: “entertaining” here is used in the usual brainwagon sense of the word.

Addendum: Here is Tom’s take on it:

The proof, of course, depends on the underlying physics. What is remarkable is that they only require three physical axioms, which, in typical Conway style, they call SPIN, FIN and TWIN.

SPIN:

spins have the 101 property, i.e. the measured (squared) spins of a spin-1 particle in 3 perpendicular directions will be two 1’s and a zero in some order.

FIN:

there is a finite upper bound on the speed at which information travels.

TWIN:

if a pair of particles has total angular momentum 0 then one has
angular momentum s and the other -s.

SPIN and TWIN are fairly well-confirmed experimentally, and while most physicists believe FIN, it’s not the sort of statement that experiments can confirm. (Conway says: “We do not know if some unknown method allows for instantaneous transfer of information, almost by definition.”)

It’s interesting to me that SPIN and TWIN are quantum-mechanical statements and FIN is true in General Relativity. It’s fairly widely held that QM and GR are inconsistent, which might lead you to believe that Conway and Kochen are skating on thin ice. But there may be other SPIN/FIN/TWIN models that aren’t as problematic.

My head hurts.