It says that given three assumptions, if particles' behavior is truly predetermined, then people cannot have free will. In other words, if the behavior of a particle is fully determined by its past, so too are all the so-called decisions people believe they are making.
Conversely, if even one experimenter in the universe can make decisions that are not fully determined by the past, then every particle in the universe must be indeterminate as well, the theorem states.
Best make that four assumptions - it sounds like these researchers have never heard of compatibilism.
The most controversial aspect of the new theorem is likely to be the use of the term "free will" to describe a particular choice an experimenter can make. To many, the term belongs more to philosophy than to physics.
"If you bring up free will [in this context] in certain societies, people will say, 'Oh, you're a nut' straight away," Conway said. "Many will prefer a more mealymouthed term, like 'indeterminacy.'"
Well, there's a good reason for that. Namely, 'free will' and 'indeterminacy' are not the same thing. Treating them as if they were is an open invitation to conceptual confusion - as we see when the article starts talking about the "free will" of particles! (I take it they were being metaphorical, but still...)
Terminological quibbles aside, I'm not too sure what the big deal is here. (Perhaps a reader can explain it to me?) Isn't it generally accepted that if determinism is true of particles then it is also true of our brains? After all, the former constitute the latter. That could hardly amount to an "unexpected link" between physics and human decisions.
Rather, I take it that the interesting claim here is that the indeterminacy of a single decision requires the indeterminacy of "every particle in the universe". That's quite unexpected (to me, anyway). I would have thought that an indeterminate decision would merely require some indeterminate particles among those which constitute the person's brain. If this isn't so, then I guess that's of some (academic) interest.
But is it of any real significance to the free will debate? Has anybody ever suggested the indeterminacy of some particles but not others? Because that seems to be the only scenario that this theorem sheds any new light on. If I've understood it correctly, the theorem shows that partial particle indeterminacy is insufficient to produce indeterminate decisions. And that's the only new finding here (I take it everyone agrees about scenarios involving determinism or universal indeterminacy). So if nobody was suggesting partial indeterminacy to begin with, it all seems a bit irrelevant.
So, as I see it, framing the theorem as a breakthrough in the "free will" debate serves only to distract attention from its actual point of interest.
Have I missed something here? (It's entirely possible that I've misunderstood the article, in which case I'd very much appreciate any corrections!)