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.
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.