What happens if B measures the x-axis spin in an entangled pair?

[jeremyfiennes]

Watching an old (2012) youtube video (), the narrator says (time 10:38) that if A measures the y-axis spin of an entangled pair and communicates his finding to B, then B "cannot" measure his x-axis spin, because doing so would give him knowledge of the spins along both axes, which uncertainty doesn't "allow". But what happens if he does measure the x-axis spin?

 

[PeroK]

Watching an old (2012) youtube video (), the narrator says (time 10:38) that if A measures the y-axis spin of an entangled pair and communicates his finding to B, then B "cannot" measure his x-axis spin, because doing so would give him knowledge of the spins along both axes, which uncertainty doesn't "allow". But what happens if he does measure the x-axis spin?

Well, obviously, there is nothing to stop him measuring the x-axis spin. Whoever made the video has got his ideas all a bit mixed up.

Each lab can measure whatever they choose to measure, and the measurements on the entangled pair will always correlate.

 

[jeremyfiennes]

Agreed. But if A measures in the x-diretion and communicates his result to B; and B then measures the y-direction; then B knows both.

 

[Nugatory]

Agreed. But if A measures in the x-diretion and communicates his result to B; and B then measures the y-direction; then B knows both.

You'd think so, wouldn't you... That's how classical objects behave (I have a pair of socks; I send one of them to you and another to a mutual friend in London; you text me and the friend in London to say that your sock is brown; our London friend texts us saying that his sock is cotton; we can safely conclude that I started with a pair of brown cotton socks).

But quantum particles do not behave that way. If A measures in the x-direction and gets spin-up, the conclusion from the mathematical formalism of quantum mechanics is not that B's particle is spin-down in the x-direction, it is that if B had measured his particle on the x-axis he would have gotten spin-down - but he didn't, so the x-axis spin of his particle is undefined. It turns out that there is a subtle statistical difference between "the particle is spin-down on the x-axis" and "the particle will be spin-down on the x-axis if we measure it along the x-axis"; this difference is experimentally observable; the experiments have been done; and they unquestionably confirm the quantum-mechanical picture.

For more information you will want to google for "Bell's theorem"; a good starting point would be the web page maintained by our own @DrChinese

 

[PeroK]

Agreed. But if A measures in the x-diretion and communicates his result to B; and B then measures the y-direction; then B knows both.

No, because B's measurement of spin in the x-direction means he no longer knows what spin he would get in the y-direction if he measured it.

One of the problems with the video, from what I watched, was that the presenter talked about the spin as though the electron has a definite spin in all directions and we just don't know what it is.

Your confusion, in fact, is not about entanglement but about the basics of QM. Take the following experiment, for an unentangled electron:

1) Measure spin in the y-direction (let's say you get "up").

2) Keep measuring spin in the y-direction (you always get up).

At this stage you know that the spin is in an eigenstate that corresponds to y-spin-up and a measurement of spin in the y-direction will definitely give up. To some extent this allows you to say that the electron has up spin in the y-direction, although it is better to continue to talk about the electron being in the eigenstate, rather than saying what the electron is definitely doing while you're not measuring it.

3) Measure spin in the x-direction. You will get up or down with 50% probability.

Now your certainty about the result of spin in the y-direction has gone. The y-spin-up eigenstate has changed to an x-spin eigenstate.

4) Measure spin in the y-direction and you get up or down with 50% probability.

This is the basic theory of electron spin. The situation in the entangled situation is fundamentally no different in this respect. The only difference is that the original y-spin measurement was done on the other particle, which was then effectively a measurement of spin in the y-direction on the system of two particles and allowed B to know what measurement he would get in the y-direction without having to do a measurement himself.

 

[jeremyfiennes]

Thanks both. Sorry that I mixed up 'x' and 'y'. Let's say that Alice measures x (measures along the x-axis) and gets 'up'. And communicates her result to Bob. He, as you say, now knows that if he measured x he would get 'down'. So he doesn't bother, and decides instead to measure y. Does that however mean that if Alice repeated her x measurement, she would no longer necessarily get 'up'? And hence that if, after his y measurement, Bob does in fact measure x, he would no longer necessarily get 'down'?

 

[PeroK]

Thanks both. Sorry that I mixed up 'x' and 'y'. Let's say that Alice measures x (measures along the x-axis) and gets 'up'. And communicates her result to Bob. He, as you say, now knows that if he measured x he would get 'down'. So he doesn't bother, and decides instead to measure y. Does that however mean that if Alice repeated her x measurement, she would no longer necessarily get 'up'? And hence that if, after his y measurement, Bob does in fact measure x, he would no longer necessarily get 'down'?

No, because the correlation applies only to the first pair of measurements. The particles do not remain entangled after the first measurement.

 

[jeremyfiennes]

If the correlation only applies to the first pair of measurements, if Bob doesn't measure x the particles remain entangled. So if Bob then measures y and gets 'up', he knows that if Alice measures y she will get 'down'?

 

[PeroK]

If the correlation only applies to the first pair of measurements, if Bob doesn't measure x the particles remain entangled. So if Bob then measures y and gets 'up', he knows that if Alice measures y she will get 'down'?

Absolutely not. Alice's first measurement is correlated with Bob's first measurement. Subsequent measurements are not correlated.

 

[jeremyfiennes]

Ok. Thanks. So the author of the video in fact had precious little idea of what he was talking about.

 

[PeroK]

Ok. Thanks. So the author of the video in fact had precious little idea of what he was talking about.

The video goes hopelessly wrong at 10:30.

PS His explanation of the Pauli exclusion principle is fairly wild and wacky as well! In fact, there's something to this effect in the comments - by "Newsteller" and "AgentFriday", who point out the flaw.

PPS In replying to the comment from "realnagora", he reveals the problem when he talks about the "original" spin of the electron. Somehow, he's learned a lot of QM and got one or two basic principles a bit mixed up. There is no such thing as the "original" spin! Fascinating.

 

[stevendaryl]

The video goes hopelessly wrong at 10:30.

PS His explanation of the Pauli exclusion principle is fairly wild and wacky as well! In fact, there's something to this effect in the comments - by "Newsteller" and "AgentFriday", who point out the flaw.

PPS In replying to the comment from "realnagora", he reveals the problem when he talks about the "original" spin of the electron. Somehow, he's learned a lot of QM and got one or two basic principles a bit mixed up. There is no such thing as the "original" spin! Fascinating.

I haven't listened in detail, but it's a bizarre video, in the sense that most of it sounds very knowledgeable, while a few moments sound completely ignorant. I don't know how you can learn enough to make the sensible-sounding parts and still make those sorts of ignorant mistakes. It's vaguely possible that he's just bad at explaining, rather than ignorant...