Quantum Entanglement: What I Know

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What I know of this only comes from popular presentations of the subject. So let's say there are two particles, A and B, known to have opposite values of a particular property such as spin. We don't know which particle has which spin until we measure the spin of one of the particles, say A. Then B "instantly" has the opposite spin. If A and B are very far apart, whatever signal that is causing B to have the opposite spin can reach it faster than the speed of light. It is explained that in this case no information has traveled faster than light so it doesn't violate SR, which I accept.

But the usual argument against signals traveling faster than light involves showing that there would exist a frame of reference in which the effect happened before the cause, thus violating causality. How does that relate to the example with A and B? There would exist a frame of reference in which B's spin was caused to have a specific value before A's spin was measured.

 

[Nugatory]

A and B, known to have opposite values of a particular property such as spin.

That's not right - they are not known to have opposite values. What we do know is that is that if we measure the spin of one of them, we know what we will get the opposite result if we measure the spin of the other one on the same axis. However, there are subtle statistical differences between "they have opposite spins" and "if we measure their spins on the same axis we will always get opposite results"; these differences can be tested experimentally; these experiments have been done; and they confirm that "they have opposite spins" is not correct. For more information, google for "Bell's theorem" and check out the web page maintained by our own @DrChinese.

But the usual argument against signals traveling faster than light involves showing that there would exist a frame of reference in which the effect happened before the cause, thus violating causality. How does that relate to the example with A and B? There would exist a frame of reference in which B's spin was caused to have a specific value before A's spin was measured.

We measure the spin of A on a given axis. Someone else measures the spin of B on the same axis. They then get together and compare notes (which may take a while if they were originally separated by many lightyears) and find that they have opposite results: one up, one down. Those are the experimental facts, and they are equally well explained by saying that A was measured first causing the B result, or B was measured first causing the A result. Thus, we're equally happy with a reference frame in which either of them happened first.

You will only get in trouble if you take the position that one of them had to cause the other in all frames... and although that position has a certain appeal to our classically trained common sense, it is no part of the mathematical formalism of quantum mechanics.

 

[DrChinese]

What I know of this only comes from popular presentations of the subject. So let's say there are two particles, A and B, known to have opposite values of a particular property such as spin. We don't know which particle has which spin until we measure the spin of one of the particles, say A. Then B "instantly" has the opposite spin. If A and B are very far apart, whatever signal that is causing B to have the opposite spin can reach it faster than the speed of light. It is explained that in this case no information has traveled faster than light so it doesn't violate SR, which I accept.

But the usual argument against signals traveling faster than light involves showing that there would exist a frame of reference in which the effect happened before the cause, thus violating causality. How does that relate to the example with A and B? There would exist a frame of reference in which B's spin was caused to have a specific value before A's spin was measured.

Whether or not causality is violated depends on your preferred interpretation of quantum mechanics. In some interpretations, causality is violated; while in others it is not. There is a separate subforum here to discuss those. There is no single generally accepted QM interpretation.

What is generally accepted is that the outcome of a measurement on an entangled pair is random (even though A and B are correlated). Further, whether A is measured first or B is measured first makes no observable difference to the combined results, which follow the predictions of theory. Therefore, reference frame does NOT matter anyway.

 

[bhobba]

Whether or not causality is violated depends on your preferred interpretation of quantum mechanics.

True, and I often forget that myself - I was going to say sometimes, but for me its often. I will often give the explanation similar to what Nugatory gave, and also something like it in answers to questions about non-locality. But if the electrons actually exist before measurement is interpretation dependent eg in the DBB interpretation they do - if they have opposite values or not is another matter - but in DBB they exist. Nugertory was careful however in limiting it to opposite values. I, not being as careful, may not express myself that well. Its one of the confusing aspects of QM - many issues are interpretation dependent and sometimes people forget to put the caveat that in this or that interpretation its not the case and/or to express themselves with the appropriate care.

Thanks
Bill

 

[Psnarf]

I'm a casual observer. From my feeble understanding, I have come to think that the Pauli Exclusion Principal applies the moment two particles become "entangled." Both particles, due to their close proximity as entanglement arises, cannot have the same quantum state. We cannot predict the quantum state of each particle upon creation, but they both cannot be the same. When one particle is measured, nothing happens to the other particle, it was already in the opposite quantum state. There is no spooky action at a distance.
My problem is, there is no way I can reconcile the two notions. Neither can be proven or dis-proven. The observed behavior is the same, whether it is spooky action at a distance, or pair creation of opposite quantum states. What are your thoughts? Am I as woefully off the mark as I must be?

 

[DrChinese]

1. I'm a casual observer. From my feeble understanding, I have come to think that the Pauli Exclusion Principal applies the moment two particles become "entangled." Both particles, due to their close proximity as entanglement arises, cannot have the same quantum state. We cannot predict the quantum state of each particle upon creation, but they both cannot be the same.

2. When one particle is measured, nothing happens to the other particle, it was already in the opposite quantum state. There is no spooky action at a distance.

My problem is, there is no way I can reconcile the two notions. Neither can be proven or dis-proven. The observed behavior is the same, whether it is spooky action at a distance, or pair creation of opposite quantum states. What are your thoughts? Am I as woefully off the mark as I must be?

1. Entanglement is in no way limited to electrons (or other spin 1/2 particles). The Pauli Exclusion Principle does not apply in any way. You can entangle lots of things, they don't even need to be the same particle type.

2. You must familiarize yourself with Bell's Theorem to understand why distant entangled particles cannot have a predetermined spin independent of how they are measured*. Your idea only works in a few special cases, such as when the particles are measured in exactly the same way. But in the general case: the statistics for predetermined spins don't match the quantum predictions.

*This is often referred to as "non-contextuality". On the other hand: The statistical predictions for quantum mechanics are contextual (the opposite of non-contextual). There are a number of so-called interpretations that attempt to explain this, but none are considered "proven".

 

[PeterDonis]

I have come to think that the Pauli Exclusion Principal applies the moment two particles become "entangled.

No, it doesn't. The Pauli Exclusion Principle applies to fermions whether they are entangled or not; and it does not apply to bosons whether they are entangled or not.

 

[Psnarf]

Thank you for your kind replies. I was expecting: "You must be new!" As Dr. Feynman once suggested regarding QED, you cannot ask why it is, you must accept that is the way it is. Back to the books I go.

 

[Psnarf]

Forget about Pauli. I know not exactly how or why entangled particles have opposite metrics. |ud> - |du> We know that in the quantum world an observer affects the state of affairs. We know entangled pairs have opposite characteristics. We cannot know if those measurable characteristics were created opposite at the moment they became entangled or if the observation of one somehow changes the other so that it "becomes" opposite. Therefore, we cannot assume one possibility over the other. Whether the pairs were created opposite, or the observation of one forces the other into an opposite state, the experimental results are the same. All I'm positing is that both explanations are possible. so spooky action at a distance is a possibility, not a proven fact. Popular explanations of entanglement assume the observation of one changes the state of the other, they never mention the possibility that the pairs were created that way and the observation of one does not change the other, it was already opposite at the time the particles arose.

 

[Nugatory]

We cannot know if those measurable characteristics were created opposite at the moment they became entangled or if the observation of one somehow changes the other so that it "becomes" opposite. Therefore, we cannot assume one possibility over the other. Whether the pairs were created opposite, or the observation of one forces the other into an opposite state, the experimental results are the same.

That is not correct. The predicted experimental results are different in some cases, these experiments have been done, and they confirm that the quantum mechanical prediction is correct and no theory in which the particles were created opposite can be correct. Google for "Bell's theorem" for more information.

Popular explanations of entanglement assume the observation of one changes the state of the other, they never mention the possibility that the pairs were created that way and the observation of one does not change the other, it was already opposite at the time the particles arose.

Some popular explanations do, some don't. The ones that don't are just leavng out the reason why we know that explanation cannot be correct.

 

[DrChinese]

1. We know that in the quantum world an observer affects the state of affairs.

2. We know entangled pairs have opposite characteristics.

1. Your statement is interpretation dependent. But probably most accept that the choice of measurement basis (what you call "observer") is relevant to the predicted statistics. (For example, spin measurements statistics depend on the difference between the 2 observers' angle settings.) In a classical world, this could occur in some situations, but not all.

2. Yes (at least in this particular scenario). However, it is not as you might imagine. The "opposite characteristic" is that if one is "U", then the other is "D". That is quite different from imagining they have some particular orientation (at a specific angle) which is opposite. The rule is a conservation rule. Total spin is a constant, in this case zero.

 

[bhobba]

Your statement is interpretation dependent.

Exactly - which is why this is unbelievably hard, and progress is at a snail's pace.

Personally I am edging towards a view of QM as just another mathematical model and try not to look behind the curtain so to speak. It's not really shut up and calculate - it's more like mental 'pictures' of what is behind the equations of physics does not seem that productive - eg what is an electric field - we know its effects and can measure it - but what really is it? Wigner had some theorems that it should exist because of Noether requiring things like momentum etc to be conserved - but that is not saying - what is it - it's just needed for our models to be consistent. I think Maxwell had a mechanical model in mind when developing his famous equations. To me they seemed to serve more a psychological purpose - the essence was in the math - not the picture he used. Could it be QM is similar - that 'pictures' are a chimera and the math is the 'truth'.

Thanks
Bill