If the answer really is that they have to wait for the end of the entire experiment, I think that settles it for me. Will think some more on it. (And again, as noted, I have not thought that hard on this. Even with my odd "would this work" you need some way to get entangled particles sent across stupid large distances. Which... already seems silly?)
Charlie doesn't see anything. He sends the electrons here and there. He's just produced the entangled electrons, he hasn't measured them. If he did he would destroy the entanglement and ruin the experiment (which is what secure quantum communication is about).
Unless he gets some reply (say a photon or electron sent by Bob), he doesn't know what either measure.
But if he does get a return particle then they're just communicating classically, so why not just pick up a phone?
Stated differently, the framing I saw was that the "spooky" action was somehow setting detector C to a specific setting would cause a different reading in detector B. And this was done in such a way that B could not know that C had changed. But, simply getting a new reading at B means that either A or C has changed, necessarily?
And again, going off old memory. Never my area of study, such that I assume I am misunderstanding. It is frustrating because most "pointing out my mistake" assumes I care about individual protons. I'm saying if we can agree to have A set to send with constant rate, then barring that getting broken, it seems you have a scheme whereby B and C can know what they are doing in aggregate.
That was the entire point of my initial post: there's no discernible difference in the actual individual measurement results regardless of detector settings.
The quantum correlations only show up if someone compares both measurements pair by pair. And to do so, regular communication must happen.
Many sources are very sloppy when it comes to phrasing this, so you're not alone in being confused. I too thought like you way back, thinking it could be used for communication.
I suppose all that is left in the intuition busting, is how the probabilities don't add up as expected?
Lets imagine electrons are objects in a program, then the "electron class" has a private field containing a seed value to a pseudo-random number generator (ie deterministic), and the two electrons are initialized with the same seed value.
Further imagine that performing a measurement of an electron amounts to taking the seed, generating a random number between 0 and 360 degrees (sample value), and then comparing that random number to the measurement angle. If the sample value and the measurement angle is closer than +/- 90 degrees we say the measurement result is up, otherwise down.
Alright, so, if we imagine that when Charlie prepared the electrons, he creates two "electron objects", and passes one to Alice and the other to Bob.
If Charlie prepares entangled electrons, he'll ensure both instances have the same seed value. If he wants to create regular non-entangled electrons, he'll make each have a random seed value.
For non-entangled electrons, Alice and Bob will not see any correlation if they later compare notes.
For entangled electrons, if Alice and Bob uses the same angle they must get the same result per definition[1]. And indeed one can find the correlation as a function of the difference in angle, and it's a linear function from perfect correlation if the angles are the same (zero difference) to zero correlation (perfect anti-correlation) when the angles are 180 degrees apart.
However on real, entangled electrons in the lab things are different. There you'll find that the correlation is higher than the linear function when the difference is smaller than 90 degrees, and less than the linear function when the difference is greater than 90 degrees[2].
Thus if we measure the entanglement at not just 0 and 90 degrees difference but also 45 degrees difference, we'll find that our lab measurements do not agree with our simulated measurements.
Hence we conclude that entangled electrons do not behave like small objects that were created with the same "hidden value", ie the seed value in my example.
That's the essence of Bell's theorem and the tests of it (at least according to my memory).
[1]: Note that measuring real entangled electrons Alice and Bob will get exactly the opposite result, they're perfectly anti-correlated, but this matters not for this explanation and not worrying about it will make the explanation easier.
[2]: IIRC it goes like cos(a/2)^2 or something along those lines, ie https://www.wolframalpha.com/input?i=plot+%7B1-abs%28x%2Fpi%...
I have not looked back at the book I read. I definitely remember it had examples that were not paired off. I'm assumingy memory is simply off.
Hidden variables, like my "electron objects", would give a linear relationship.
However what quantum mechanics predicts and what we measure in the lab is a non-linear relationship that for some angles yield stronger correlations. Hence the phrase "violating Bell's inequality".
After Bell people devised other inequalities for other experimental setups which also can be used to rule out local hidden variables. A popular example are the CHSH inequalities[1], which is easier to realize experimentally, and give a stronger disagreement with hidden variables.
I've never seen the particles not paired up, and I don't see how that would work.
The whole point is that according to quantum mechanics, the pair of entangled particles aren't two separate systems, but that they must be treated as having a single state.
But how could they?
Charlie prepares a pair of entangled electrons and sends one each to Alice and Bob. Alice performs a spin measurement along some angle and, entirely randomly, gets either up or down as a result.
Alice and Bob decide on their measurement settings and measure a bunch of electrons using the same angle for each measurement. They can even agree in advance so they both know which angle the other will use.
After the run, Alice will have a bunch of measurement results which are roughly 50% up and 50% down. Bob too will have a bunch of measurement results which are roughly 50% up and 50% down. Assuming ideal detectors and such, there will be no discernible pattern to the ups and downs for either.
Only if the afterwards come together and compare their results pair for pair will they see the quantum correlations between the value in each pair. For some angles, they're more likely to be anti-correlated, and for some angles there doesn't seem to be any correlation.
That is, if they both used the same angle, the they'll find that each time Alice measured up then Bob measured down, and every time Alice measured down then Bob measured up. And if they used a similar but not equal angle, then it's more likely that when Alice measured up then Bob measured down, and vice versa.
And since they by now know that this experiment has been done before and the predictions of quantum mechanics hold, they can even predict this result. However what good does it do for Alice? After all, regardless of measurement settings Bob will measure a uniform 50/50 distribution of ups and downs.