I've never seen a coherent definition of "free will", but I don't see how someone whose decision is random has any more or less of it than someone whose decision is nonrandom, so IMO it doesn't really have anything to do with free will one way or another.
In one of the lectures Conway goes in depth into the philosophy of free will, which he believed in at a time when it was (and still is) almost universally unfashionable.
That's a distinction without a difference - how would you tell whether the particle is magically looking up its results in the universe's big book of random numbers or deciding for itself? It's true that quantum-mechanical randomness is localised, in a provable sense, but there's no contradiction between that and what "randomness" is usually understood to mean.
> One implication is that our brains, being composed of particles, derive their free will from the sum of the particles' free will.
This is unfounded speculation.
one of the points the theorem makes is that you can't get the behaviour of fundamental particles by injecting randomness into an otherwise determinstic system. Free Will is different from randomness.
Have you watched the lectures ?
What is the distinction you're drawing, concretely? There simply isn't one unless you're using some very non-standard definition of randomness.
> Have you watched the lectures ?
I attended the 2005 version IRL.
AFAIUI by noting that the dice could have been thrown ahead of time and then looked up, we can treat it as a function of time and then it becomes as though another part of the information in the past light cone which doesn't explain the behaviour of particles, as exemplified by FIN, MIN & TWIN
I assert that this is not terribly surprising, and Conway is actually just doing a sleight of hand around the definition of "random". We would normally expect a truly random event to be (by definition) uncorrelated with anything else, in this case including counterfactual versions of itself - the random measurement you get from a given axis must not be correlated with the measurement you would have got if you'd measured a different combination of axes. That's maybe a little odd, but I don't think it contradicts people's normal notion of "randomness", particularly in a QM context. It's like how in early online poker games people would cheat by figuring out the "random seed" and know all the cards - because that's not real randomness.
Well, per everything that Conway's said, it does make a difference - if the experimenter is somehow able to choose which axes to measure after all dice rolls have been fixed, and the mapping of dice roll to measurement result is fixed (and does not depend on which axes the experimenter measures), then that creates a contradiction.
To my mind that's normal quantum behaviour - we see the same thing in the double slit experiment or Bell's inequalities (which this is just a variation on). Quantum behaviour cannot be explained by rolling dice ahead of time, because random results in different possible universes/branches must be uncorrelated with each other, even though we tend to assume that only one of those branches "actually happens". And this result is a cool demonstration of that. But there's no contradiction between that and most people's normal notion of "randomness", IMO.
The most frustrating part is that this is a cool, exciting result; while it doesn't really prove anything that we didn't already know from the Bell inequalities, the fact that everything's discrete makes for a much clearer contradiction. It shows that quantum-mechanical randomness is very fundamental and genuine: it's not just reading dice rolls off some list that was decided ahead of time, unless we want to commit to the idea that the whole universe works that way. But talking about "free will" just obscures and confuses everything.
[1] IMO that part doesn't add anything new or relevant to the result; it's just stapling the existing EPR paradox onto this new paradox.
Strictly speaking, the whole discussion of determinism vs free will suffers from this defect.
Any system will appear unsystematic until the precise rules governing it are known.
Since we can’t ever demonstrate that we’ve exhausted all possible theories of a system, the possibility always remains that tomorrow we would discover a perfectly effective one, and from that point the system would be as plainly deterministic as anything else.
In other words: we lack the capability to definitively distinguish between our own lacking knowledge and a system’s (potential) intrinsic non-determinism.
We might instead interpret the Free Will Theorem as demolishing a position otherwise claimed: People have free will, but people are special; most other things don't have free will, and certainly particles don't! But the Free Will Theorem explicitly contradicts this position.
In terms of philosophy, there are several nuances to consider. There's Kochen-Specker itself [1], its untestability and its applications. There's free will itself [2], including whether free will is definable, is useful for ethics, and indeed whether free will exists. I think it's interesting that [2] has no mention whatsoever of [1] or the Free Will Theorem more generally.
[0] https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experime...