JesseM said:
What do you mean "not just in correlation with the result at 'A'?" You mean even before knowing what outcome was observed at A, you think you'd observe different results at B depending on the choice of measurement angles at A? This is definitely incorrect as it would imply the possibility of FTL communication.
colorSpace said:
I'll respond to the second paragraph first since it seems to me this needs to be clarified first. Your second question doesn't quite make sense to me, since in order to perform the experiment, one doesn't need to know the outcome of A, that is only necessary for the evaluation afterwards, when analyzing what happened in the experiment.
My second question didn't say anything about knowing the actual results at A, I was asking whether you thought the results at B would differ statistically depending on the choice of measurement angle at A. In other words, do you think the probability of getting a particular outcome at B will change depending on what angle is chosen at A? Again, this would imply the possibility of FTL communication. The entanglement only reveals itself in looking at the correlations between results at A and results at B, but when viewed in isolation, the probability of getting a given result at A does not in any way depend on what choice of measurement was made at B.
colorSpace said:
The answer to the first question is that the results of B do depend on the measurement angles at A, in their relation to the angles at B. That is, how A and B correlate depends on the relative angles at A and B. In other words, results at B correlate not just with the results at A, but with the combination of the results at A and the relative measurement angles at A and B.
Of course, I wasn't saying otherwise. But this is still just a matter of correlations that can only be seen once a classical signal has informed someone about both the choice of measurement and the result at both A and B.
colorSpace said:
This is, I think, the first time I hear about the concept of "pairing up", so I am not sure my response will be on the point. However my first response would be this:
If there is a third observer exactly in the middle "M", between A and B, and if A and B immediately send signals about the measurement result, then the universe (unless it has non-local intelligence) has no means of instantly pairing up the correct sub-universes, as it depends on the measurement angles how they will need to be paired up (especially in the GHZ case of more than two entangled particles). That is, there would need to be an intelligent process, yet no time for such a process. I hope this response reflects an adequate interpretation of this concept of "pairing up", of which I don't know more than you have written.
I think you're confusing yourself by all this talk of "sub-universes", all we really need to think about is which copy of a system over here is matched with which signal/causal effect from copies of a system over there.
Let's look at the simple case of two-particle entanglement. Suppose Bob and Alice are each receiving one member of an entangled pair, and each has three measurement settings A, B, and C, and the particles are entangled in such a way that they are always guaranteed to get opposite results if they pick the same measurement setting--if Bob picks setting A and gets result +1 then if Alice also picks setting A, she's guaranteed to get result -1. As I explained in post #5 of
this thread, in this situation local realism predicts that when they pick
different settings, they should get opposite results on at least 1/3 of all trials; but with the right choice of measurement angles it is possible to ensure that they actually get opposite results less frequently, say on only 1/4 of all trials, which is a violation of Bell's theorem.
But now look at this in a situation where we allow multiple copies of each experimenter. For concreteness, let's say we have A.I. experimenters doing a simulated version of this experiment on computers at different locations, and we want to reproduce this apparent violation of Bell's theorem in a purely classical way, just by running multiple copies of each A.I. experimenter on each computer. Now suppose on a given trial the Bob-A.I. picks a particular setting, say C, and the computer has to decide how to split Bob into copies who observe different results
before it gets a message from the other computer about what setting the Alice-A.I. chose. All it needs to do is split Bob into 8 copies with the following results:
1. Bob measures A, gets +1
2. Bob measures A, gets +1
3. Bob measures A, gets +1
4. Bob measures A, gets +1
5. Bob measures A, gets -1
6. Bob measures A, gets -1
7. Bob measures A, gets -1
8. Bob measures A, gets -1
Now sometime later, a group of signals from all the Alice-copies comes from the other computer, and the computer simulating Bob has to decide which Alice-copy-signal is received by each Bob-copy. Suppose it turns out that Alice had also chose setting A, and the computer simulating her had split her into 8 copies in the same way:
1. Alice measures A, gets +1
2. Alice measures A, gets +1
3. Alice measures A, gets +1
4. Alice measures A, gets +1
5. Alice measures A, gets -1
6. Alice measures A, gets -1
7. Alice measures A, gets -1
8. Alice measures A, gets -1
In this case the computer simulating Bob can match up signals like this:
Bob 1 gets signal from Alice 5 (Bob +1, Alice -1)
Bob 2 gets signal from Alice 6 (Bob +1, Alice -1)
Bob 3 gets signal from Alice 7 (Bob +1, Alice -1)
Bob 4 gets signal from Alice 8 (Bob +1, Alice -1)
Bob 5 gets signal from Alice 1 (Bob -1, Alice +1)
Bob 6 gets signal from Alice 2 (Bob -1, Alice +1)
Bob 7 gets signal from Alice 3 (Bob -1, Alice +1)
Bob 8 gets signal from Alice 4 (Bob -1, Alice +1)
This will guarantee that each Bob finds that Alice got the opposite result from his own.
On the other hand, suppose it turns out that Alice had chose setting C, and her computer had split her up like this:
1. Alice measures C, gets +1
2. Alice measures C, gets +1
3. Alice measures C, gets +1
4. Alice measures C, gets +1
5. Alice measures C, gets -1
6. Alice measures C, gets -1
7. Alice measures C, gets -1
8. Alice measures C, gets -1
In this case, the computer simulating Bob could match the signals like so:
Bob 1 gets signal from Alice 1 (Bob +1, Alice +1)
Bob 2 gets signal from Alice 2 (Bob +1, Alice +1)
Bob 3 gets signal from Alice 3 (Bob +1, Alice +1)
Bob 4 gets signal from Alice 5 (Bob +1, Alice -1)
Bob 5 gets signal from Alice 4 (Bob -1, Alice +1)
Bob 6 gets signal from Alice 6 (Bob -1, Alice -1)
Bob 7 gets signal from Alice 7 (Bob -1, Alice -1)
Bob 8 gets signal from Alice 8 (Bob -1, Alice -1)
In this case 6/8 of the Bob-copies find that Alice got the same result as their own, while only 2/8 = 1/4 find that Alice got the opposite result. If Bob and Alice don't realize they are living in computer simulations and have been split into multiple copies, they will think that their results violate Bell's theorem.
You could certainly have a third computer midway between the ones simulating Alice and Bob, simulating a third observer, "Marvin". Then if Alice and Bob each send their results to Marvin, and there are 8 copies of Marvin as well, you could match them up like so:
Marvin 1 gets signals from Bob 1 and Alice 1 (Bob +1, Alice +1)
Marvin 2 gets signals from Bob 2 and Alice 2 (Bob +1, Alice +1)
Marvin 3 gets signals from Bob 3 and Alice 3 (Bob +1, Alice +1)
Marvin 4 gets signals from Bob 4 and Alice 5 (Bob +1, Alice -1)
Marvin 5 gets signals from Bob 5 and Alice 4 (Bob -1, Alice +1)
Marvin 6 gets signals from Bob 6 and Alice 6 (Bob -1, Alice -1)
Marvin 7 gets signals from Bob 7 and Alice 7 (Bob -1, Alice -1)
Marvin 8 gets signals from Bob 8 and Alice 8 (Bob -1, Alice -1)
But there's no need for the computers simulating Alice and Bob to know which copy of Alice is paired up with which copy of Bob at the same instant--for example, Bob's computer doesn't have to decide this until a simulated message from Alice has had time to arrive there, or a simulated message from Marvin sent after he had received a message from Alice (if both messages were sent as quickly as possible they would reach Bob at the same moment). So, we can still simulate all the aspects of this situation that are predicted by QM perfectly well using classical computers that create multiple copies of each observer, with the actual signals between computers not able to travel any faster than the simulated messages between observers in the simulated universe.