Newbie Q on quantum entanglement

[ObbtiGime]

First post so I'll jump straight in at the deep end (for me).

Excuse me if this is a daft question but this is all new to me :)

In an experiment, two electrons are entangled then separated. Someone then measures the x spin of one of them and finds it to be +. The x spin of the second electron must be -. Is this correct so far?

The quantum explanation is a miraculous story about how the spin of the first particle can actually be anything until someone measures it (?). At the instant it is measured it then randomly decides what its spin is, and likewise the second electron immediately knows this and takes on the opposite spin. Is this correct so far?

How is this experimentally testable?

How is this different from the first electron having a certain spin right from the start (and the second electron having the opposite spin right from the start) but, obviously, the experimenter doesn't know what it is until he measures it?

 

[Demystifier]

How is this different from the first electron having a certain spin right from the start (and the second electron having the opposite spin right from the start) but, obviously, the experimenter doesn't know what it is until he measures it?

This would mean that measurement itself does not influence spin. But it is easy to show that it does: Take one electron and measure its spin in z-direction. Then measure its spin in x-direction, and then measure its spin in z-direction again. In 50% cases, the second measurement of z-spin will give the result opposite to that in the first measurement of z-spin. This shows that z-spin cannot be independent of measurement.

There are also more rigorous proofs (Bell inequalities, Hardy equalities, ...) but they are not so simple to understand.

 

[ObbtiGime]

This would mean that measurement itself does not influence spin. But it is easy to show that it does: Take one electron and measure its spin in z-direction. Then measure its spin in x-direction, and then measure its spin in z-direction again. In 50% cases, the second measurement of z-spin will give the result opposite to that in the first measurement of z-spin. This shows that z-spin cannot be independent of measurement.

Thanks, what would happen if you took that same electron, measured its z spin, then measured it again, then again. What would the results be?

There are also more rigorous proofs (Bell inequalities, Hardy equalities, ...) but they are not so simple to understand.

Are they proofs or theories?

 

[Demystifier]

Thanks, what would happen if you took that same electron, measured its z spin, then measured it again, then again. What would the results be?

Then you would always obtain the same result.

Are they proofs or theories?

Proofs.

See e.g. Sec. 5.5 of
http://xxx.lanl.gov/abs/quant-ph/0609163 [Found.Phys.37:1563-1611,2007]
for a simplified version of the Hardy proof.

 

[ObbtiGime]

Then you would always obtain the same result.

Thanks again. So measuring the z spin doesn't affect the z spin. But it randomly changes the x spin (and vice versa)?

Proofs.

See e.g. Sec. 5.5 of
http://xxx.lanl.gov/abs/quant-ph/0609163 [Found.Phys.37:1563-1611,2007]
for a simplified version of the Hardy proof.

Again thank you.

 

[Demystifier]

Thanks again. So measuring the z spin doesn't affect the z spin.

Right.

But it randomly changes the x spin (and vice versa)?

You may say so, but perhaps it would be more correct to say that it makes it uncertain. Even more correct is to say that quantum mechanics is CONTEXTUAL, i.e., that the values obtained by measurements depend on measurements themselves.

 

[ObbtiGime]

Right.

So measuring the z spin does not affect the z spin. So, the first time it is measured (back to the original experiment), how do we know that it wasn't already in that state? Where is the mystery? There is now no need for the second particle to instantaneously settle its state, because it was already in that state. What am I missing?

You may say so, but perhaps it would be more correct to say that it makes it uncertain.

Yes, my bad choice of words.

 

[jtbell]

So, the first time it is measured (back to the original experiment), how do we know that it wasn't already in that state? Where is the mystery?

Read up on Bell's Theorem.

 

[Demystifier]

So measuring the z spin does not affect the z spin. So, the first time it is measured (back to the original experiment), how do we know that it wasn't already in that state?

There are two ways to know it: a complicated but rigorous way (Bell, Hardy, ...), and a simple but not rigorous way.

The simple one is as follows:
Because we know it was in another state (we know that by performing different measurements).

 

[ObbtiGime]

Read up on Bell's Theorem.

Ok, done that. I fail to see how that (unproven) theory (which seems to have been more or less discounted by many) answers the question. Which bit am I not getting here?

There doesn't seem to be any mystery.

A pair of particles are entangled. We have no way of determining the spin until we measure it. When we measure it, we know what it is. We can then say with certainty what the spin of the other particle will be.

There seems to be this hugely complicated theory of QM to explain why we don't know what the spin is until we measure it. That's how it looks to an outsider.

 

[ObbtiGime]

Because we know it was in another state (we know that by performing different measurements).

Can you clarify on this please? If you can perform a different measurement that still allows you to know what the (say) z spin is, then you have, effectively, measured the z spin surely? Earlier we ascertained that measuring the z spin will not change the z spin (though it might change other spins). Now you're saying it might change it?

 

[Demystifier]

Can you clarify on this please? If you can perform a different measurement that still allows you to know what the (say) z spin is, then you have, effectively, measured the z spin surely? Earlier we ascertained that measuring the z spin will not change the z spin (though it might change other spins). Now you're saying it might change it?

No.

The measurement reveals that the system (of TWO particles) is in an eigenstate of a relatively complicated operator which does not commute with the z-spin operator. Therefore, the measurement of z-spin should influence z-spin. (I repeat that it is a simple, but not rigorous argument.)

 

[Demystifier]

I fail to see how that (unproven) theory (which seems to have been more or less discounted by many) answers the question.

Which source have you been reading? I suspect, not an appropriate one.

 

[ObbtiGime]

Which source have you been reading?

Whatever I can find on the net...

"Although no experiment had been conducted in which every loophole has been closed, most physicists accept that Bell's inequality has been violated."

(bold is mine)

From Kumar, M., Quantum, Icon Books, 2009, p. 350

 

[ObbtiGime]

No.
Therefore, the measurement of z-spin should influence z-spin. (I repeat that it is a simple, but not rigorous argument.)

So does measuring z spin affect z spin or does it not?

If it does, then measuring it twice will probably give 2 different results no?

If it does not affect it, then how do we know that it wasn't already in that state before measuring it the first time?

 

[jtbell]

"[...] most physicists accept that Bell's inequality has been violated."

(bold is mine)

From Kumar, M., Quantum, Icon Books, 2009, p. 350

Bell's theorem is that all local realistic theories (loosely speaking, "common-sense explanations" of QM) must satisfy Bell's inequality. Experiments show that nature violates Bell's inequality, therefore local realistic theories are untenable.

 

[Demystifier]

Whatever I can find on the net...

"Although no experiment had been conducted in which every loophole has been closed, most physicists accept that Bell's inequality has been violated."

(bold is mine)

From Kumar, M., Quantum, Icon Books, 2009, p. 350

For your information, violation of Bell's inequalities means that Bell was RIGHT! (I suspect that you haven't read carefully what these inequalities really say and imply.)

 

[ObbtiGime]

Experiments show that nature violates Bell's inequality, therefore local realistic theories are untenable.

Let's get this right, Bell had a theory, nature violates that theory, so nature is wrong and Bell's theory is right?

Have I got that right?

Edit: To clarify, nature doesn't agree with what Bell theorized should happen. Nature actually does something that diagrees with Bell's theorem, and yet it's nature that is mistaken? Bell was right all along?

 

[Demystifier]

So does measuring z spin affect z spin or does it not?

It depends on the state before the measurement. If it was a z-spin eigenstate, then it doesn't. Otherwise, it does. In our case, we know that it wasn't a z-spin eigenstate before the first measurement of z-spin.

 

[Demystifier]

Let's get this right, Bell had a theory, nature violates that theory, so nature is wrong and Bell's theory is right?

Have I got that right?

Edit: To clarify, nature doesn't agree with what Bell theorized should happen. Nature actually does something that diagrees with Bell's theorem, and yet it's nature that is mistaken? Bell was right all along?

No, you misunderstood all that. Try to read the source I suggested to you.

 

[jtbell]

Let's get this right, Bell had a theory, nature violates that theory, so nature is wrong and Bell's theory is right?

Bell's theorem does not deal with a specific theory about what lies behind QM. His theorem says that all theories that are based on assumptions of "locality" and "realism" must satisty Bell's inequality.

Many experiments have shown that nature violates Bell's inequality. Nature is always right, so local realistic theories must be wrong.