# Quantum Entanglement

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## Main Question or Discussion Point

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.

## Answers and Replies

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Nugatory
Mentor
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
Gold Member
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
Mentor
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

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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
Gold Member

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".

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PeterDonis
Mentor
2019 Award
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.

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.