Quantum entanglement and EPR

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Main Question or Discussion Point

We've just gone over the EPR paradox in class and I'm not really satisfied by the explanation of the professor and TA.
Firstly, with the example of the two spins, I still don't see why measuring one spin and then knowing the other one doesn't count as information travelling faster than light. We've been told it's only once you come together with whoever measured the other results and see the correlation that you have the information. Online, I've seen a few explanations saying the wavefunction collapses globally. I didn't understand why this would stop faster than light travel of the information, if anything it seems like it makes the problem worse. I think my confusion may come from what they define as information. We were never given a rigorous (or any) definition.
Secondly, a classmate asked the following question. Two observers start off together with synchronised clocks and decide a specific time to make their measurements. One will measure the momentum and the other will measure the position. They then go off respectively and make their measurements. When they get back together the one that measured the position will know the momentum by having the information about momentum of the other one (breaking the uncertainty principal). I spoke about this with the TA for a long time and the most satisfying explanation we got to was that we would never be able to say for sure that the particle started off with 0 momentum. Once we measure its momentum, we'd have to keep doing so to stop its time evolution (even if it's in some potential well). He also said it'd be impossible to measure the two things at exactly the same time and so the uncertainty principle is fine (but this seems like a practical problem due to our measuring equipment rather than the fundamental uncertainty due to nature).
 

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.Scott
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Regarding your "firstly": You are right that the fact that there is a non-local wave function "collapse" would seem to make things biased in favor of superphotic communication. But that's not a good way of thinking about it.

It's more like this: The speed limit on information transfer can be taken as a fundamental law. So any measurements made of a wave function collapse must follow that law. In fact, when the details are examined, there is no opportunity for such superphotic communication. As was probably explained to you, the observers at both detectors only see a random sequence of numbers. But when they look at the measurements from the other observer, they see a pattern. It is as if their choice of measurements combined with their measurement results played a major role in determining the results that the other observer made (and vice versa).

Regarding your "secondly": There is no issue about performing the measurements at the same time. Even if you miss by a few picoseconds, you can switch to a different inertial reference frame where the measurements would appear simultaneous.
As far as the main point is concerned, the devil is in the details. Here is exactly your question answered.
https://physics.stackexchange.com/q...ent-to-defy-heisenbergs-uncertainty-principle
 
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  • #3
DrChinese
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1. Firstly, with the example of the two spins, I still don't see why measuring one spin and then knowing the other one doesn't count as information travelling faster than light.

2. Two observers start off together with synchronised clocks and decide a specific time to make their measurements. One will measure the momentum and the other will measure the position. They then go off respectively and make their measurements. When they get back together the one that measured the position will know the momentum by having the information about momentum of the other one (breaking the uncertainty principal).
There are a number of ways to approach these questions, and .Scott's above is good. Here's some additional:

1. You can say - if you want to frame it in this manner - that measuring Alice's spin causes Bob's spin to change to fit. That would be faster than light transmission. And some scientists believe there is in fact non-local action at play here. A couple of key points:
a. You can just as easily say that Bob's measurement made Alice change to fit. That's the case regardless of the time ordering of the measurements. Strange but true, and as described by the quantum entangled state.
b. The idea that information is transmitted FTL is mitigated by the fact that the measurement outcome is purely random. So whatever you think is being transmitted, there is no way to predict it in advance. Makes signaling difficult, agree?

2. You can make the measurements as you describe. But if you think those tell you something about a single particle - say Alice - consider this. You measured Alice's position and Bob's momentum. But if you now measure Alice's momentum, you will find out there is no correlation between her momentum and Bob's. Makes it a bit difficult to prove your premise when you can't obtain any additional useful information about Alice by testing Bob.
 
  • #4
Strilanc
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I think my confusion may come from what they define as information. We were never given a rigorous (or any) definition.
Alice and Bob have an information-transferring mechanism if and only if they can use it to win the "communication game" more than chance. The "communication game" is as follows:

1. A referee who is with Alice flips a coin.
2. The referee tells Alice the coin flip result, heads or tails.
3. Elsewhere, Bob attempts to guess the coin flip result. He writes down heads or tails.
4. If Bob guessed correctly, that's a win.

If Bob is just guessing randomly, they will only win 50% of the time. If Alice can just tell Bob "Hey, it's head" or similar, they'll win closer to 100% of the time. When people say entanglement can't be used to transfer information, they mean it's not helpful for winning the above game. Despite that, entanglement is helpful for winning some other coordination games where the players are isolated, such as the CHSH game.
 

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