[alphydan]

What do you mean "When B resolves, press the button"? "When you measure A, something happens to B" ... that's the problem, we can't know what happend. Only after the fact, and after repeating the experiment and sharing the results between the two parties.

You're Alice, and you want to send Bob the message "1001010". Let's start with the first "1". You measure A and see "red", and thus alter the probabilities of B to "90/10" ... and you think to yourself: Awesome, I just sent a "90/10" probability to Bob, and that means "1". If I had gotten "blue", Bob would be receiving a "50/50" probability.

Now, you're Bob at Alpha Centauri, and a particle arrives. Then what? No matter if you get "red" or "blue", you'll never know if it happened as 50/50 (the inherent randomness of any quantum measurement), or because of the "90/10" probability. So when you have to write down was it a "1" or a "0" ... you can't know.

At that specific moment, in your lab, when particle B arrives .... the result doesn't tell you anything.

Once you meet again, or send an email (you can compare your stats and find out that, statistically A affected B ... but if you need email (classical communication) to find out, then it's definitely not faster than light)

There are more subtleties about the uncertainty principle, orthogonal basis, etc ... but you would need a more formal language to express it.

[hackuser]

I understand what you are saying but that's not what I meant to ask. The signal I'm proposing is not red/blue, it is superposition/resolved. Maybe this is more clear:

1) On Earth, Alice creates two entangled particles, both in superpositions, and gives one to Bob. She tells Bob: 'If your particle ever loses its superposition and resolves, whether to red or to blue, press the button!'

2) Bob goes to Alpha Centuri, Alice remains on Earth.

3) Alice wants Bob to press the button. She does something to resolve her particle.

4) Instantly, Bob's particle loses its superposition and also resolves. Bob gets the message and presses the button, in much less time than 4 years.

Why wouldn't that work? I suspect because you can't determine whether or not the particle is in a superposition, but my understanding is limited. Maybe the basis of my question is wrong.