I don't really see how this answers my question. You just state that different observers will make the same predictions, but you don't explain how that can possibly be in the particular example I gave.

No, I didn't say that. It might be that the probability of getting spin up is much greater than the probability of getting spin down. My logic still applies.

Also, what I was trying to do, was to give an example where it seems that both particles might have spin up, so that they won't be "perfectly anti-correlated".

Yes, you are right----the correlation will be whatever is dictated by the initial state of the system. But the key point is that all observers will predict the same correlation, regardless of whether they describe the wave collapse as happening before or after your measurement.

(It seems to me that your original post does assume perfect anti-correlation, but the same argument applies whether you assume this or not.)

But if the wave function of B hasn't collapsed, then as I say, there is still some chance that a measurement of B will yield spin up. In other words, even though the wave function of A has collapsed, the wave function of B hasn't, so B is still in a superposition. Thus it seems like this is a counterexample of your claim that "all observers will predict the same correlation".

Yes, there is some chance that a measurement at B will yield spin up, in which case the measurement at A yields spin down. This in fact happens half the time. (I've gone back to assuming 50% probabilities and perfect anti-correlation; adjust these assumptions any way you like.) All observers agree on that. Again: What observable phenomenon do you think they might DISagree about?

I don't know about your last question, but it still seems to me that there is a problem here. For if I measure spin up for particle B, then I would say that the spin of A is down. But if someone else has already measured A and found that it is spin up, then there is a conflict here about what I think of A and what the other one thinks of A.

But the conflict you're describing never happens. The observed results always follow the probability distribution dictated by the initial state of the system. If the probability of UU is zero, it won't occur.

Will, right, and that is exactly what I don't understand. I don't understand why this never happens. I mean, what stops us from doing the expreiment I describe and violate the correlation?

What stops us is the same thing that stops gravity from being repulsive---the laws of physics.

But explain how. I mean, there's no invisible force or something stopping us from doing the experiment in practise and violate this. I would like you to take a look at Charles' answer, for I think he is into something there. What do you think about it?

Charles has a perfectly defensible viewpoint. You don't have to buy into that viewpoint to understand the physics. If your question is "why couldn't the laws of physics be different", that's not specifically a question about entanglement.

But that isn't my question though. All I am asking is what I am missing in my reasoning in the original question. I feel like you didn't really answer that, you just stated that this never actually works (namely that you can't have that both particles end up having spin up) without telling me where I have made a mistake in my reasoning. I mean, there has got to be an explanation here.

If I ask what stops heavy objects from floating on air, and you tell me that would violate the law if gravity, and if I persist in saying "yes, but what if I imagine a heavy object that DOES float on air? what would stop it?", how would you answer me? Your answer to that question is ky answer to yours.

To put this another way: physics is not required to explain the imaginary results of imaginary experiments. It's required only to explain things that actually happen. You've imagined an outcome. Physics says that can't happen. Your question, in essence, is: "Well then why can I imagine it?". Physics can't be expected to answer that question, just as your imagination can't be expected to be bound by the laws of physics.

Okay, Will, let me put this another way too. If somebody asks you about the twin paradox in special relativity, then I bet you wouldn't say, " this isn't a paradox, because we can observe that a twin can't be older and younger than the other twin at the same time." Instead, you would defend the theory and explain why there is no problem in it. Just like the twin paradox, my question is a doubt about the theory itself. So it is the theory that has to defend itself, not the universe.

And from what I know, this isn't an "imaginary" experiment. This seems like something you could do in practise, unlike making an object float in air. So now quantum theory has to defend itself and show why this isn't a flaw in the theory, because, like you said, we can't observe in reality two entangled particles having the same spin at the same time.

So now the theory has to explain this result.

@Felis When you have an entangled pair of particles A & B, you do not have two separate states. You have a single state containing a pair of particles. That's essentially the definition of quantum entanglement.

No theory has to "defend itself" against imaginary claims. If you claim that when Bob travels out and back, he might come back older than Alice, the only defense needed is "you just made that up". The theory predicts what it predicts, all REAL experimental results (as opposed to whatever alternative results you choose to imagine) support the theory, and that's that. Ditto here.

So let's see what the theory actually says: Suppose the initial state is UD+DU. A measurement is made on the first particle. With 50/50 probability the state is now UD and with 50/50 probability it's DU. In the first case, a measurement on the second particle gives D and in the second case it gives U. When results are compared afterward, they are perfectly anti-correlated.

Alternatively, make the first measurement on the second particle. The measurement either comes out U, collapsing the full state to DU, or it comes out D, collapsing the whole state to UD. These happen with 50/50 probability. Afterwrard, the results are seen to be perfectly anti-correlated. EXACTLY THE SAME as if the first particle had been measured first.

Your only question is: But what if the experimental results don't match the theory? The answer is: We don't have to worry about that, because they DO match the theory. Your followup question is: Well then, why can I IMAGINE results that don't match the theory? The only answr that's needed is: Probably because you have a good imagination. Nothing more needs to be said.