If I understand this correctly, this proof is used to exclude one of the two given explanations for the "Kochen-Specker Paradox"?
The article says the KS "paradox" implies that either
> 1. Each measurement of a particle is not independent but rather depended on
> context. In other words, the order in which you make measurements matters.
or
> 2. The particle does not decide what the value of its spin is in any direction
> until the experimenter actually makes a measurement!
As I understand it, the proof shows that the order in which you take the measurements can't matter, excluding explanation (1), because of the following thought experiment.
* Take two particles, entangled and then separated by some distance.
* More quickly than information can pass between the particles, measure one particle in three directions in some order, and measure the other particle just once in one direction which you choose right at that moment.
The second particle can't be affected by the order in which you measured the first particle's spins, but if I was able to choose a direction in which to measure the second particle's spin, then the second particle was able to choose a result to match the appropriate result from the first particle's measurements.
I think I followed this argument up until the last sentence above. What I (mis)understand to be happening here is "spooky action at a distance"; it doesn't at all appear to be a free choice on the particle's part.
In essence we established via the KS paradox that our two particles couldn't have "agreed" on their spins ahead of time, because there's no consistent way to assign all of their spins. But then we measured the two particles in the proscribed way and got a result that looks like the particles did agree on their spins beforehand.
I believe that this excludes explanation (1) from above, but I don't understand how explanation (2) is consistent with this. If it were the case that the particle was deciding its spin at measurement time (explanation (2)), wouldn't the two particles have to communicate faster than c (or whatever our speed limit is) in order to ensure that they made the same decision? We explicitly ruled out this possibility via the FIN axiom and our experimental setup.
The only way I can think of to make this work is to say that the universe doesn't "choose" which result I got until I meet up with my friend who measured the other particle. But this seems to be a far stronger claim than the article makes.
Talk about the particle "deciding" is coming from a Copenhagen interpretation viewpoint. I find the many-worlds view clearer:
When the two particles are set up, their wavefunctions are in sync (or rather, antisync) with each other. Particle A's wavefunction looks like an equal superposition of up and down (at least, when projected onto a single axis; the wavefunction for the full particle incorporating all the possible axes is more complicated); Particle B's wavefunction is the same but 180 degrees out of phase, so that A is up whenever B is down and vice versa.
When you make a measurement of particle A, you entangle yourself with it; that is, your own wavefunction becomes in phase with its. (Again, it's still an equal superposition between having measured up and having measured down). When your friend makes their measurement of particle B, they entangle themselves with it in the same way. So when you meet up with your friend, your wavefunctions are in (anti)phase; the universe as a whole is an equal superposition of the world where you measured up and your friend measured down, and the world where you measured down and your friend measured up.
(What does being in that superposition look like, subjectively? It looks like a 50% probability of the first world and a 50% probability of the second world. Which agrees with what we measure when performing the experiment)
> When your friend makes their measurement of particle B, they entangle
> themselves with it in the same way. So when you meet up with your friend,
> your wavefunctions are in (anti)phase; the universe as a whole is an equal
> superposition of the world where you measured up and your friend measured
> down, and the world where you measured down and your friend measured up.
If we take this perspective, are we still able to rule out possibility (1)? That is, our assumption was that what my friend did couldn't affect my experiment; we used this fact to rule out the possibility that the order of my friend's measurements affected my result. But if in some sense my experiment doesn't "occur" until I meet up with my friend, then this assumption seems not to be true any longer. Which is to say, we could explain this whole thing without requiring any "free will" / "true randomness" on the part of our particles.
From a many-worlds point of view there's not the same nondeterminism in the physics. There's nondeterminism in our subjective experience, but it's a surface phenomenon rather than something fundamental.
So I guess we've sidestepped the question the "theorem" is aimed at, because by adopting this viewpoint we're already assuming that humans don't have any kind of physical nondeterminism (or "free will", if you insist).
Personally I think the idea was stupid as stated; having a set of dice inside your head doesn't make you any more likely to have "free will" than if you didn't, and that's all that quantum nondeterminism really means. But I guess some philosophers really did claim that this was support for the notion of free will, so it's worth refuting that as directly as possible.
So I guess you're right: if anything, a many-worlds interpretation gives more support to the idea that quantum nondeterminism has something to do with free will, because it means the nondeterminism only comes in when we look at a human's subjective observations. So yes, I think we really do sidestep the claim this way.
The article says the KS "paradox" implies that either
> 1. Each measurement of a particle is not independent but rather depended on > context. In other words, the order in which you make measurements matters.
or
> 2. The particle does not decide what the value of its spin is in any direction > until the experimenter actually makes a measurement!
As I understand it, the proof shows that the order in which you take the measurements can't matter, excluding explanation (1), because of the following thought experiment.
* Take two particles, entangled and then separated by some distance.
* More quickly than information can pass between the particles, measure one particle in three directions in some order, and measure the other particle just once in one direction which you choose right at that moment.
The second particle can't be affected by the order in which you measured the first particle's spins, but if I was able to choose a direction in which to measure the second particle's spin, then the second particle was able to choose a result to match the appropriate result from the first particle's measurements.
I think I followed this argument up until the last sentence above. What I (mis)understand to be happening here is "spooky action at a distance"; it doesn't at all appear to be a free choice on the particle's part.
In essence we established via the KS paradox that our two particles couldn't have "agreed" on their spins ahead of time, because there's no consistent way to assign all of their spins. But then we measured the two particles in the proscribed way and got a result that looks like the particles did agree on their spins beforehand.
I believe that this excludes explanation (1) from above, but I don't understand how explanation (2) is consistent with this. If it were the case that the particle was deciding its spin at measurement time (explanation (2)), wouldn't the two particles have to communicate faster than c (or whatever our speed limit is) in order to ensure that they made the same decision? We explicitly ruled out this possibility via the FIN axiom and our experimental setup.
The only way I can think of to make this work is to say that the universe doesn't "choose" which result I got until I meet up with my friend who measured the other particle. But this seems to be a far stronger claim than the article makes.
What's the right way of thinking about this?