[lmm]

> 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.

> Have you watched the lectures ?

I attended the 2005 version IRL.

[Uhuhreally]

> 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

[lmm]

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.

[Uhuhreally]

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.

[lmm]

> 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.

[Uhuhreally]

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

[lmm]

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.

[Uhuhreally]

by "sleight of hand" of are implying Conway isn't being honest ? I think he was entirely sincere.

[lmm]

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.

[Uhuhreally]

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.

[lmm]

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.

[Uhuhreally]

maybe in that case you can help me see why Conway et al are wrong in this ? Because I'm only quoting here, and the paper is beyond me.