[FOM] The Strong Free Will Theorem

Timothy Y. Chow tchow at alum.mit.edu
Sun Jan 25 14:56:46 EST 2009

The latest issue of the Notices of the AMS has an article by Kochen and 
Conway about their free will theorem.

Despite being written by two mathematicians and having the word "theorem" 
in the title, the paper is written in a "physics style," meaning that not 
all the assumptions are made explicit.  For example, "relativistic 
invariance" is not explicitly asserted as an axiom (although it is 
implicit since the term "spacelike separation" is used in one of their 
explicit axioms).

One specific assertion they make which interests me is that "no 
relativistic version of a hidden variable theory such as Bohm's well-known 
theory can exist."  But I can't tell whether they're saying anything new 
here.  Is "relativistic" different from "local"?

More generally, what exactly is new about the Strong Free Will Theorem?  
Superficially, its conclusions are not surprising to physicists, so it 
must be that the hypotheses are weaker than previously suspected.  But 
the hypotheses aren't stated with the degree of precision that 
mathematicians are accustomed to, so it's hard (for me anyway) to assess 
the mathematical content of their theorem.  The Kochen-Specker paradox is 
easily comprehended mathematically, but the free will theorem is supposed 
to go beyond that.

I'm hoping that someone here---perhaps Nemeti or others interested in the 
formalization of special relativity---can help clarify.


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