My understanding is that it says if anyone anywhere has free will, then so do some elementary particles. It doesn't say anything about if anyone or if any elementary particles actually have free will right? Does it lend support either way to if free will exists?
It shows that to whatever extent an experimenter can behave nondeterministically, so can an elementary particle. So it's useful as a simple way to convince people that quantum mechanical randomness is a true fundamental phenomenon (in particular, that hidden variable theories are all inherently invalid).
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.
Conway distinguishes Free Will from randomness by showing that randomness is just a special case of determinism. The random numbers could have been written down before the big bang and looked up when needed, which is still predetermined.
What makes Free Will free is that it's the selection of some future state independently from the information in a particle's past light cone. Only the particle determines that part of its state. One implication is that our brains, being composed of particles, derive their free will from the sum of the particles' free will. This doesn't imply that particles are conscious or aware, it only means that certain degrees of freedom evolve according to computations performed by the particles independently.
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.
> Conway distinguishes Free Will from randomness by showing that randomness is just a special case of determinism. The random numbers could have been written down before the big bang and looked up when needed, which is still predetermined. What makes Free Will free is that it's the selection of some future state independently from the information in a particle's past light cone. Only the particle determines that part of its state.
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.
> 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 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.
> 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.
What is the distinction you're drawing, concretely? There simply isn't one unless you're using some very non-standard definition of randomness.
> What is the distinction you're drawing, concretely? There simply isn't one unless you're using some very non-standard definition of randomness.
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
Right, so if you had a fixed dice roll in the past and translated that into the measurement results on each axis in a static way, that wouldn't work. You have to make a fresh random dice roll after the experimenter chooses which axis to measure - or you have to translate the past dice role into the result for the axis in a way that depends on which other axes the experimenter chose to measure.
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.
and I reply that I just record the "fresh" random roll ahead of time and you look that up. Doesn't make any difference. I think you're confusing random with pseudorandom.
> and I reply that I just record the "fresh" random roll ahead of time and you look that up. Doesn't make any difference.
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.
aren't you mixing models of reality here ? You're describing a universe in which there's free will and determinism, somehow combined with many-worlds. It's hard to follow such hypercounterfactual logic
Well, the theorem pretty fundamentally relies on some kind of counterfactual reasoning - many-worlds is my preferred model, but you can use whichever you like. Ignoring the twin/spatially separated part[1], the meat of the theorem is that there is no possible fixed combination of spin along different axes that has the property that we always observe experimentally (that if we simultaneously measure along three axes at right angles to each other, we'll see two of one type of result and one of the other). So if the results we were going to observe were somehow fixed ahead of time, then there must be a contradiction: for some particular counterfactual combination of axes that we could have picked to measure, we would not have seen the two-and-one pattern that we always see.
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.
I hate to criticise him under these circumstances, and I'm going to leave out the more personal side of things, but: The impression I got was that he was playing up the "free will" angle to appeal to a popular audience, at the expense of the physics. Most academics with a book to sell do that to a certain extent, but I felt that he went past what's reasonable. I won't speculate as to whether that was insincerity as such or belief in his own hype.
He devoted a whole lecture to explaining his belief in free will, going in depth into the philosphical history of the concept and his personal reasons which come across as entirely genuine. He also speculates as to how he thinks the limited free will of particles could result in our free will. It's six lectures and a lot of hard work with highly respected physicists by a mathematician who's old, accomplished and distinguished.
Fair enough. I honestly find that a lot sadder than the idea that he knew what he was doing and was sexing it up a bit. Reminds me of Penrose going off the rails.
He notes in the first lecture that he thinks it is impossible to disprove determinism. A determined determinist can always resort to the argument: all of your senses are deceiving you and you are simply experiencing some predetermined script of qualia (he uses the analogy of watching a movie a second time).
I think the invulnerable argument for it is even simpler than that: whatever apparently non-determined behavior we observe may only appear that way because we don’t yet know the rules underlying it.
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.
Right: if you are a brain-in-a-vat observing some powerful play, what can you say about the world in which the vat is embedded? (or for that matter, how is it that you can even be made aware of the vat’s existence?)
We can perform some measurements [0] which show that spin exists. So, the 101 lemma used in the Kochen-Specker Theorem is related to existing laboratory experiments, and not just thought experiments. But indeed this doesn't say whether people have free will.
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.
