Getting to the Heart of Entanglement and Locality in Plain English

[Ben vdP]

This is disputed. What is true is that if you consider only measurements along the same axis or at right angles to each other then a local (hidden variable) theory can reproduce the QM predictions. Bell illustrated this in section 3 of his original 1964 paper.



Yeah, I spoiled the ending to this in post #22.

Bell was concerned with determinism. But not everything has to be deterministic. To explain correlations with measurements at an angle then there is still Pauli.

If I'm not mistaken then the probability distribution of measuring at an angle θ is :

$$ cos ^ 2 ( \frac { θ } {2} ) $$

When you take then the difference of angle settings of the two detectors, then the result is:

$$ cos ^ 2 ( \frac { α-β } {2} ) $$


The problem goes back an entire century when trying to describe an electron including spin.

Attempts to use a classical model that uses spin orientation and turn it into a qm model failed.
An electron is not a rigid body and has no internal structure, you cannot explain spin from it. Any spin can only originate from it's (EM) field.

G.E.Uhlenbeck and S.Goudsmit came up with the idea that an electron behaves like having a constant spin impulsmoment and magnetic moment in the chosen rotation z-axis.
( Nature 117 (1926) 264)

I may have lost some details in this. But W.Pauli found it "ein ganz witziger Einfall" or funny idea and continued with it. (Zeitschr. fur Physik 43 (1927) 601 of Handbuch der Physik, Band V, Teil 1.)

But I'm not informed much more about the history of it.

It looks tempting though that a hidden variable could be more specific on the spin then $S_z$ and eigenvalue $s_z$ in combination with the quantum nature of measurements. But that might get off topic.

 

[Ben vdP]

I need more coffee, I forgot to mention following example:

There is no actual spin orientation available for measurement only as mentioned above in the z-direction.
If there exists such a variable then conservation laws dictates they are opposite. That could explain some measurements around angles, or is there anything better.

 

[Matterwave]

Bell was concerned with determinism. But not everything has to be deterministic.

In the 1964 paper Bell used outcome determinism because that was a consequence of locality and perfect anti-correlation. He later relaxed the outcome determinism in future papers.

Unfortunately I don't really get what point(s) you're trying to make with the rest of your post.

 

[Ben vdP]

OK, I am not familiar with the later papers.

When rotating both angles of the two detectors in the same way then the result stays the same.
A hidden parameter needs to explain this, that the two photons of a pair will measure in similar ways,
regardless of the probability distribution of a single photon when measuring at angles in the context.
To me this points to some kind of orientation dependency of a hidden variable or I'm considering that. Conservation laws should be the explanation for it.

The second requirement is that known physical behaviour needs to be reproduced including the probability distribution at angles for a single photon measured at angles. From that it moves into Bell inequalities

I don't have definite answers, maybe we'll have to wait a few decades more.

 

[PeterDonis]

To me this points to some kind of orientation dependency of a hidden variable

As long as it's not a local hidden variable. For example, a model which assigns each photon a definite "spin direction", which is set up for the two photons in such a way that they will always give opposite results when measured in the same spin direction, would be a local hidden variable model ("local" because each photon "carries along" its own variable). And such a model will not work--it won't be able to produce correlations that violate the Bell inequalities when the photons are measured in different spin directions.

 

[Ben vdP]

Indeed that is the difficulty. But it seems we have moved more into Bell's theorem then just entanglement.

 

[pines-demon]

Indeed that is the difficulty. But it seems we have moved more into Bell's theorem then just entanglement.

Bell's theorem is the way to go. However we don't need the full Bell theorem to get that there is something non-classical going on in entanglement.

The best way to make one-self an interpretation of quantum mechanics is to imagine a classical world (including relativity but no quantum mechanics) and try to make a Mermin device. The answer of course is that it is not possible, it is only possible in the real world because we have entanglement. The hunch of what classical laws need to be broken for it to work allows to compose different interpretations of quantum mechanics.

 

[Ben vdP]

Thanks for the link.

 

[PeterDonis]

it seems we have moved more into Bell's theorem then just entanglement.

That's because any account of entanglement that does not account for violations of the Bell inequalities can't be right. You can't separate the two.

 

[Ben vdP]

I had a quick look at this issue.


Suppose an electron has a spin orientation that can be any direction.
The other electron has exactly the opposite direction.

One electron is being measured in the z-direction and the result is positive if
the z-component is positive. So all positive results span up the upper half of a ball.
The other electron will then measure negative due to conservation laws.

If however the detector is rotated say by 45 degrees, then the half ball will have rotated also
by 45 degrees and some directions are now positive along this rotated axes and some negative.

The service area is now 75% against 25% with the above angle. This is the classical result.
The quantum result is 85.36%.

It is an equivalent result as seen in Bell's theorem, but with entanglement eliminated.
The measure or criterium of what counts positive or negative might be too simple. The model might be too simple.
But it looks feasible to eliminate an entanglement this way and what remains is then a pure measurement problem.

This requires looking further into EM and its vector potential and spin and the Pauli matrices and anything else.
Considering also that one is not measuring a property of the electron but trying to measure a component of the property or derivative.

Unfortunately I have no more time to look further into this subject, but maybe someone gets more ideas from it.

 

[PeroK]

I had a quick look at this issue.


Suppose an electron has a spin orientation that can be any direction.
The other electron has exactly the opposite direction.

A classical object can have a spin orientation, but an electron, being a quantum object, does not have a spin orientation. Instead, it has a spin state, which is an abstract vector in a 2D complex Hilbert Space.

 

[pines-demon]

I had a quick look at this issue.


Suppose an electron has a spin orientation that can be any direction.
The other electron has exactly the opposite direction.

One electron is being measured in the z-direction and the result is positive if
the z-component is positive. So all positive results span up the upper half of a ball.
The other electron will then measure negative due to conservation laws.

If however the detector is rotated say by 45 degrees, then the half ball will have rotated also
by 45 degrees and some directions are now positive along this rotated axes and some negative.

The service area is now 75% against 25% with the above angle. This is the classical result.
The quantum result is 85.36%.

It is an equivalent result as seen in Bell's theorem, but with entanglement eliminated.
The measure or criterium of what counts positive or negative might be too simple. The model might be too simple.
But it looks feasible to eliminate an entanglement this way and what remains is then a pure measurement problem.

This requires looking further into EM and its vector potential and spin and the Pauli matrices and anything else.
Considering also that one is not measuring a property of the electron but trying to measure a component of the property or derivative.

Unfortunately I have no more time to look further into this subject, but maybe someone gets more ideas from it.

This is wrong. There are many ways to classically model why a single spin gives weird results. To get why entanglement is weird beyond hope, try the Mermin device in post #37.

 

[zonde]

A classical object can have a spin orientation, but an electron, being a quantum object, does not have a spin orientation. Instead, it has a spin state, which is an abstract vector in a 2D complex Hilbert Space.

Electron has an abstract vector in a 2D complex Hilbert Space? What is an electron in your book of things then?

 

[PeroK]

Electron has an abstract vector in a 2D complex Hilbert Space? What is an electron in your book of things then?

In this respect it's a spin 1/2 elementary charged particle. Described by QM.

 

[PeterDonis]

It is an equivalent result as seen in Bell's theorem, but with entanglement eliminated.

No, it's you making up your own local hidden variable model and discovering that, gee, its predictions have to satisfy the Bell inequalities, just like every other local hidden variable model, so your model, like every other local hidden variable, cannot explain what goes on in actual quantum experiments.

it looks feasible to eliminate an entanglement this way

I don't even know what this means, but it doesn't matter anyway, because, as above, your model, like every other local hidden variable model, cannot explain what goes on in actual quantum experiments.

Unfortunately I have no more time to look further into this subject

That's just as well, because you have now been banned from further posting in this thread, since you are not adding anything to the discussion.